Mind

doi: 10.1093/mind/fzy001pmid: N/A

Abstract The sample space of the chance distribution at a given time is a class of possible worlds. Thanks to this connection between chance and modality, one’s views about modal space can have significant consequences in the theory of chance and can be evaluated in part by how plausible these implications are. I apply this methodology to evaluate certain forms of modal contingentism, the thesis that some facts about what is possible are contingent. Any modal contingentist view that meets certain conditions that I specify generates difficulties in the philosophy of chance, including a problem usually associated with Humeanism that is known as ‘the problem of undermining futures’. I consider two well-known versions of modal contingentism that face this difficulty. The first version, proposed by Hugh Chandler and Nathan Salmon, rests on an argument for the claim that many individuals have their modal features contingently. The second version is motivated by the thesis that the existence of a possible world depends on the existence of the contingent individuals inhabiting it, and that many worlds are therefore contingent existents. 1. Modality and chance Metaphysical modality and chance are connected in a straightforward way: there can be a non-zero chance at t that P only if it is metaphysically possible that P. More generally, we can think of the chance distribution at t as a probability measure on the class of metaphysically possible worlds that are like actuality through t and never violate the actual laws. I will call these worlds the ‘possibilities that are open at t’ or the ‘opent possibilities’. Moreover (where ‘cht(P)’ stands for ‘the chance that P at t’): Modality-Chance Principle (MC): Necessarily, cht(P)=x if and only if the chance measure at t of the class of opent possibilities at which P holds equals x.1 Thanks to the connection between modality and chance articulated by this principle, some theses about modal space have significant implications concerning chance and can be evaluated partly by how plausible these implications are. In Kment (2012) I used this methodology to evaluate anti-haecceitism, arguing that the view fails to afford a sufficiently rich sample space for physical chance. In this paper, my target will be certain forms of modal contingentism, the view that some facts about what is possible are contingent. Modal contingentists hold that there are counterexamples to at least one of the characteristic axiom schemata of the modal logics S4 and S5 (‘□’ and ‘◊’ express the metaphysical modalities): 4 ◊◊P → ◊P2; 5 ◊P → □◊P. I will argue that any form of modal contingentism that meets certain conditions yields a cluster of interrelated problematic consequences about chance, including, most importantly, the problem of undermining futures. This problem is usually discussed as a difficulty for Humean frequentist accounts of chance. (See Lewis 1994, Thau 1994, Hall 1994.) Frequentists believe that the chances at t are determined by the frequencies of different patterns of events throughout history. However, these frequencies are determined in part by the outcomes of post-t chance processes. It may therefore be chancy at t what the chances at t are. For example, it could be that cht(P)=½ but that there is also a positive chance at t that cht(P)≠½. Following David Lewis, we can describe such cases by saying that the present chances ‘undermine themselves’. It is implausible that undermining should be possible and it is well known that commitment to the possibility of undermining generates other serious difficulties. The problem of undermining does not affect frequentism alone. It arises for anyone who holds that there are facts that meet two conditions: they are partly determined by the outcomes of post-t chance processes and it is therefore chancy at t whether they obtain,3 and they partly determine the chances at t. Modal contingentists have to face the problem of undermining if they believe that certain modal facts meet these two conditions, which they have to do if they think that the following is true in some scenarios. Whether P is (metaphysically) possible depends on the outcomes of post-t chance processes and it is consequently chancy at t whether P is possible. Whether P has a positive chance at t depends on whether P is possible: cht(P)>0 in those opent possibilities where P is possible but cht(P)=0 in those where P is impossible. (1) and (2) entail that there is a positive chance at t that (P is possible and cht(P)>0), but there is also a positive chance at t that (P is impossible and cht(P)=0). So, it is chancy at t what the chances at t are—the chances at t undermine themselves. At least two prominent forms of modal contingentism (when combined with very plausible background assumptions) generate undermining cases in this way. The first, which I will call modal-profile contingentism (MPC), is Hugh Chandler and Nathan Salmon’s well-known view that the modal profiles of many individuals are contingent. The second is what I will call modal existence contingentism (MEC), which is motivated by the thesis that many possible worlds are contingent existents. On reflection, it is not too surprising that modal contingentism can lead to cases of undermining. The concept of chance can be used to define modal operators, such as the operators ‘’ and ‘’ considered in §3.2, where ‘P’ says that cht(P)>0 and ‘P’ that cht(P)=1. We can formulate principles analogous to 4 and 5 for these operators. Given the aforementioned connection between modality and chance, if there are counterexamples to 4 and 5, then they might also be counterexamples to and . In particular, as discussed in §3.2, if there are counterexamples to 4 and 5 that meet conditions (1) and (2), then they violate and . Moreover, if there are counterexample to and , then they are cases of undermining. I will discuss MPC in detail in §§2–4 to illustrate the way in which modal contingentism can give rise to undermining cases. As we will see, proponents of MPC have to deny not only and , but also some other, equally compelling principles. These further principles are structurally similar to and but they are either diachronic (they concern the relationship between chance distributions at different times) or they involve modal operators that are defined in terms of the notion of an open possibility rather than in terms of chance. MPC-ists can avoid these problems only by endorsing revisionary views that seem ad hoc or by endorsing implausible views on other matters (§§3.5–4). §5 will briefly consider some alternatives to MPC that avoid the problems considered in this paper. Once the problem for modal contingentism has come into clear focus through the discussion of MPC, it will not be difficult to see that it arises for MEC as well. My discussion of MEC (§6) will therefore be very brief. 2. The case for contingent modal profiles Suppose your living room is graced with a table by the name of ‘Woody’, made from three equally large and non-overlapping parts, A, B, and C. It seems plausible that Woody could not have been made from completely different parts. To fix ideas, assume that: (3) Necessarily, if Woody exists, he is made from at least 2∕3 of ABC. However, Woody could surely have been made from slightly different parts. If a few atoms had been removed from ABC before a table was made from these pieces, the table would still have been Woody. Again, to fix ideas, assume that: (4) Possibly, Woody is made from parts that include no more than 2∕3 of ABC. Presumably, (3) and (4) are instances of some true general principles along the following lines. Necessity: Necessarily, where x is any table and the ys are x’s parts, it is necessary that if x exists, x is made from at least 2∕3 of the ys. Tolerance: Necessarily, where x is any table, the ys are x’s parts, and the zs include 2∕3 of the ys (and nothing else), x could have been made from the zs and some suitable other parts that are not among the ys.4 By Tolerance, the following is true for some X and Y that do not overlap with A, B or C, or with each other. (5) ◊Woody is made from XBC (6) □(Woody is made from XBC → ◊Woody is made from XYC) Given standard assumptions of modal logic, it follows from (5) and (6) that: (7) ◊◊Woody is made from XYC However, by Necessity: (8) ¬◊Woody is made from XYC (7) and (8) together constitute a counterexample to 4 (◊◊P → ◊P). Schema 5 (◊P→□◊P) is violated as well. Given that Woody is made from ABC, we can infer the following claims by Tolerance. (9) ◊Woody is made from ABY (10) ◊Woody is made from XBC From Necessity we can infer that: (11) □(Woody is made from XBC → ¬◊Woody is made from ABY) Given standard assumptions of modal logic, (10) and (11) entail that ◊¬◊Woody is made from ABY,5 and hence (if ‘◊’ and ‘□’ are duals) that: (12) ¬□◊Woody is made from ABY (9) and (12) together constitute a counterexample to 5. Let us use ‘modal-profile contingentism’ (‘MPC’) for the view that (some principles like) Necessity and Tolerance are true and that 4 and 5 are invalid for the reasons described. (See Chandler 1976 and Salmon 1979, 1982, pp. 238–40, for arguments along these lines.) As we will see, MPC-ists can give different explanations for the failure of these schemata. One possibility is to account for this datum by saying that it is contingent what possible worlds there are. For example, the reason why both (7) and (8) are true is this: at some possible world w there is a possible world w* where Woody is made from XYC, but there does not actually exist a possible world where Woody is made from XYC. (Those who take this line need not deny that the XYC-world w* that exists at w also exists at the actual world. Instead, they can say that at the actual world, w* exists but is an impossible world. In other words, they can say that it is not the existence but the modal status of XYC-worlds like w* that is contingent.) Alternatively, an MPC-ist can adopt counterpart theory and explain failures of 4 and 5 by appealing to the non-transitivity of the counterpart relation. (See §4.) That approach is consistent with the thesis that the same possible worlds exist at every possible world. Examples like the one considered provide good prima facie motivation for MPC, and it is not immediately clear what to say against the view. It is true that 4 and 5 are valid in the modal logic S5, which is sometimes called the ‘standard modal logic’ for metaphysical modality, and some authors seem to assume that it constitutes a substantial cost of a theory if it forces us to reject S5 (Linsky and Zalta 1994, 1996, Williamson 1998, 2013). But I think that this is far from obviously true. Offhand, it is hard to know what to think about 4 and 5, and it is difficult for me to imagine that anyone has strong views about these principles that are not motivated by theoretical considerations, the result of philosophical upbringing, or merely suggested by the imagery evoked by talk of possible worlds. There may be theoretical reasons for adopting S4 or S5 for metaphysical modality (Williamson 2013), but in my judgement there are at least equally weighty reasons against this choice (Adams 1981, Kment 2014, Ch. 4). However, I will argue that MPC’s implications about chance make the view considerably less attractive overall. §3 will present the argument as it applies to the non-counterpart-theoretic version of MPC, while §4 will expound the slightly different argument that applies to the counterpart-theoretic variant. If we reject MPC for the reasons I will discuss, we face the question of how to accommodate the data that motivate MPC. §5 will briefly discuss some options. 3. Non-counterpart-theoretic MPC 3.1 Sufficient conditions for being Woody Proponents of MPC accept Tolerance and therefore believe that if Woody is actually made from ABC, then some tables at other possible worlds that are made from BCD are identical with Woody. But they are not committed to saying that every such table is Woody. In other words, for all MPC says, being made from BCD may not be a sufficient condition for an otherworldly table to be Woody, and may not even be part of any non-trivial sufficient condition.6 It makes a difference to the arguments given below whether we assume that being made from BCD is part of a non-trivial sufficient condition, and (if we do) what we take that condition to be. Where x is any physical individual and t is any time, let us say that a condition C is a pre-t condition if and only if satisfying C consists in nothing more than having certain purely qualitative features and being related in certain ways to specific individuals that exist before t. In other words, C is a pre-t condition if and only if meeting C does not require being related in a certain way to specific individuals that come into existence at t or after t. Let a non-initial time be a time that is not the earliest moment in history, and let us say that a condition C is sufficient for being x just in case any entity at any possible world that satisfies C is identical with x. If the following principle is true, then, necessarily, for any non-initial time t and any table T made from parts that existed before t, there is some pre-t condition C that T satisfies and which is sufficient for being T. Sufficiency: Necessarily, if (i) the histories of two possible worlds w and w' are indiscernible (in qualitative and non-qualitative respects) before some non-initial time t and qualitatively indiscernible from t onwards and (ii) at some time t* after t, a table is made from the same parts at w and at w’ and (iii) these parts existed before t, then the table made at the one world is identical with the table made at the other. §§3.2–3.4 will present the arguments on the assumption that Sufficiency is true, while §3.5 will discuss what happens if we give up Sufficiency. Let t be the time at which Woody was made. Anyone denying Sufficiency must say that there could have been two possible worlds w1 and w2 such that (i) the histories of w1 and w2 are indistinguishable in all respects before the non-initial time t and qualitatively indistinguishable from t onwards, (ii) at some time t* after t, a table is made from the same parts at w1 and at w2, (iii) these parts existed before t, and (iv) the table made from them is Woody at one of the worlds but not at the other. Note that this is a very strong claim—much stronger than the thesis (which some haecceitists may accept) that there could have been two qualitatively indistinguishable possible worlds one of which features Woody while the other does not. The tables at w1 and w2 are not just qualitatively alike. They are made in the same way and at the same moment from numerically identical particles that are arranged in exactly the same way. Yet, the one table is Woody while the other is not. To me it sounds implausible that there could have been such a pair of possible worlds. Sufficiency therefore seems compelling to me. 3.2 MPC and undermining Let us say that the chances at t undermine themselves just in case they violate the following principle. Undermining Is Impossible (UII): For any possible world w and time t, cht,w(Chancet,w)=1, where Chancet,w is the conjunction of those claims about the chances at t that hold at w, and cht,w(Chancet,w) is the chance of Chancet,w at t at w.7 (UII) says that it cannot be chancy at t what the chances at t are. That seems very compelling. Even frequentists who accept the possibility of undermining cases tend to concede their implausibility. For example, David Lewis calls undermining cases ‘peculiar’ (1986a, postscript C). Moreover, he notes that their possibility contradicts a very intuitive principle that he takes to be central to our conception of chance: the original version of the ‘Principal Principle’, which relates a rational agent’s credences about the chance of an event to her credence that the event will occur.8 One way to bring out the implausibility of the idea that undermining is possible is to note its inconsistency with the following very compelling principle, which is a slightly strengthened variant of what Bigelow, Collins and Pargetter (1993) call the ‘Basic Chance Principle’: Basic Chance Principle* (BCP*): For every possible world w, time t, and claim P, if cht,w(P) > 0, then P is true at some possible world that is like w up to t and where the chances at t are the same as at w.9 The Modality-Chance Principle (MC) entails that (BCP*) is true of t and w if (UII) is true of the chances at t at w.10 The converse holds as well, provided that cht,w(Chancet,w) is defined.11 Hence, on the assumption that cht,w(Chancet,w) is defined, the instances of (UII) and (BCP*) that relate to t and w are equivalent. (UII) entails the following two principles considered in the introduction (where ‘P’ says that cht(P)>0 and ‘P’ that cht(P)=1). By (UII), any truth about the chances at t has a chance of 1 at t. In particular, if cht(P)>0, then cht(cht(P)>0)=1. So, holds. Similarly, (UII) entails that the class of worlds where the chances at t are different from what they actually are has a chance measure of 0 at t. Hence, if the class of worlds where cht(P)>0 has a positive chance measure, then actually cht(P)>0. Therefore, holds as well. MPC yields cases that violate and and therefore (UII) (as well as (BCP*)). Let us first consider an MPC-generated counterexample to . I will focus for now on a version of MPC that endorses Sufficiency. Example 1: At t, you resolve to toss a fair coin to decide whether to make a table from ABC, BCD, or CDE. If the coin lands heads, you will make the table from ABC. If it comes up tails, you will toss it again. If the second toss lands heads, you will make a table from BCD, if it comes up tails, you will instead make a table from CDE. In fact, the first toss comes up heads and you make a table from ABC. You call the table ‘Woody’. By Sufficiency, there must be some pre-t condition X (in the sense defined in §3.1) that Woody satisfies and which is a sufficient condition for any table at any possible world to be Woody. Let us assume that you have seen to it ahead of time that, if the first toss comes up heads and you make a table from ABC, then that table will meet condition X. Then, at all opent possibilities where a table is made from ABC (as at the actual world), that table is Woody. In a similar way, you have set things up so that at any opent possibility where a table is made from BCD, that table is Woody. Finally, let us suppose you have also made sure that the following is true at any opent possibility where Woody is made from BCD: at any opent possibility where a table is made from CDE, that table is Woody. (Of course, by Necessity, it is not true at the actual world that a table that is made from CDE at another opent possibility is Woody.) I will use ‘ABCW’ both as a name for, and as an abbreviated statement of, the claim that Woody is made from ABC (a harmless ambiguity). ‘BCDW’ and ‘CDEW’ will be understood analogously. Moreover, ‘ABC’ will both name and abbreviate the claim that some table is made from ABC (and analogously for ‘BCD’ and ‘CDE’). Figure 1 depicts the situation at the actual world. The black path represents the course that events are in fact taking. Unrealized opent possibilities are greyed out. Figure 1: View largeDownload slide The opent possibilities at the actual world and their chances in Example 1 Figure 1: View largeDownload slide The opent possibilities at the actual world and their chances in Example 1 Since MPC-ists hold that the table is not Woody at opent possibilities where it is made from CDE, they have to accept the following: (13) cht(CDEW) = 0. Moreover, the following also holds at the actual world: (14) cht({w1}) > 0.Figure 2 represents the situation at w1. At w1, there is an opent possibility w2 with a non-zero chance of actualization at t where Woody is made from CDE. By the Modality-Chance Principle (MC) stated in the introduction, that entails the following: (15) At w1, cht(CDEW) > 0. Given (14), (15) and (MC), the following must hold at the actual world: (16) cht(cht(CDEW)>0)>0. (13) and (16) together form a counterexample to : (16) says that CDEW, while (13) tells us that ¬CDEW. By the same token, (13) and (16) also constitute a case of undermining: cht(CDEW)=0, yet there is a non-zero chance at t that cht(CDEW)≠0. This example of undermining follows the pattern described in the introduction: CDEW’s chance at t depends on whether CDEW is possible—cht(CDEW)>0 at those opent possibilities where ◊CDEW, but cht(CDEW)=0 at those where ¬◊CDEW. Moreover, at t it is still chancy whether CDEW is possible, since CDEW’s modal status depends on the outcome of the first toss, which will not be determined until the coin hits the ground. It is therefore chancy at t whether CDEW has a positive chance at t. Figure 2: View largeDownload slide The opent possibilities at w1 and their chances in Example 1 Figure 2: View largeDownload slide The opent possibilities at w1 and their chances in Example 1 A variant of Example 1 shows that MPC conflicts with as well. Suppose that actually, the first toss comes up tails and the second heads and Woody is made from BCD. Then: (17) cht(ABCW)>0. Moreover, the class of opent CDEW-possibilities has a positive chance measure at t, and at these opent possibilities, cht(ABCW)=0. It follows by (MC) that cht(cht(ABCW)=0)>0, and therefore: (18) cht(cht(ABCW)>0)≠1. (17) and (18) constitute a counterexample to .12 3.3 Expected future chances , , and (UII) are synchronic principles: they are about the chances at a single time t. But MPC also conflicts with a very compelling diachronic principle about chance, that is, a principle that deals with the relationship between chances at different times. Let us start with an illustration of this principle. Sitting in front of two buttons, you are about to throw a fair six-sided die. If it lands 6, you will push the left button, an action that has an 80% chance of causing an explosion. If any other number comes up, you will push the right button, giving the explosion a 20% chance of occurring. What is the current chance of an explosion? Obviously, it is 1∕6×80% + 5∕6×20% = 30%. The current chance equals the average of the different possible future chances, weighted by the present chances of these future chances. More generally and formally: let t and u be times and let us write ‘t<u’ for ‘t is earlier than u’. Let Chu,w(P) be the function that assigns to every opent possibility w the chance that P has at time u at w if this chance is defined (and which is undefined for w otherwise). If the expected value of Chu,w(P) relative to the probability function cht is defined, then let us call it ‘Echt(Chu,w(P))’. Our example illustrates the following principle: Expected Chance Principle (ECP): cht(P)=Echt(Chu,w(P)) whenever t<u, provided Echt(Chu,w(P)) is defined. As the bomb example illustrates, (ECP) is useful for calculating or estimating the present chance that a certain event will occur in the future, in particular when its occurrence is known to depend on the outcomes of a small number of successive future random processes. The diachronic principle (ECP) does not follow from the synchronic principle (UII) alone. However, given the following plausible diachronic principle, it can be shown that if (UII) is true of t—if the chances at t do not undermine themselves—then (ECP) is true of t as well:13 (19) Necessarily, if t < u, then the chance distribution at u comes from the chance distribution at t by conditionalizing on the complete truth about post-t history up to u.14 Examples of undermining can violate (ECP), however. To see that this is true of MPC-generated undermining cases, it is best to note first that these cases can violate the following diachronic variant of (stated below in symbols and in words). Given standard assumptions about probability (including countable additivity), (ECP) can be shown to entail that holds for any claim P and times t and u for which Echt(Chu,w(P)) is defined.15,16 When Echt(Chu,w(P)) is undefined, (ECP) does not apply—it simply falls silent—and so (ECP) does not entail that holds in such cases. Nevertheless, it seems very plausible that is true in such cases as well, for is simply very compelling: if there is some (positive) chance now that there will be some chance tomorrow that we will win next week, then there is some chance now that we will win. MPC-ists have to deny that is true of Example 1. At w1, BCDW is true and CDEW is therefore metaphysically possible. Moreover: (20) At w1, chu(CDEW)=½. Given that cht({w1})>0, we can use (20) and the Modality-Chance Principle (MC) to infer that cht(chu(CDEW)>0)>0. And yet, since CDEW is actually impossible, actually cht(CDEW)=0. That violates . By the same token, (ECP) is violated as well: Echt(Chu,w(CDEW))=¼≠0=cht(CDEW).17 Hence, MPC-ists have to deny both and (ECP).18 3.4 The logic of open possibility Let us say that it is an opent possibility that P—or P, for short—if and only if it is the case that P at some world in the sample space of the chance distribution at t, that is, if and only if the claim that P is compossible with the history through t and the laws. Moreover, let us say that it is settled at t that P—or P, for short—if and only if it is not an opent possibility at t that not P. ‘’ is weaker than ‘’. The truth of ‘P’ requires merely that the class of opent possibilities where P be non-empty. The truth of ‘P’ requires in addition that this class have a positive chance measure at t. The first condition is satisfied without the second in examples like the following. You are throwing a dart with a point-sized (infinitely small) tip at a dartboard. For any point p on the dartboard, the past and the laws leave open that you will hit p, so that You will hit p. Moreover, the chance density is constant over all locations on the dartboard (that is, measurable regions of the same size have the same chance of being hit). Hence, for any point p on the board, cht(You will hit p)=0, so that ¬ (You will hit p). We can formulate both a synchronic and a diachronic S4 principle for ‘’. Both principles seem very compelling. If it is an open possibility now that it is an open possibility now that we will win the game next weekend, then it is an open possibility now that we will win (that is, then it cannot already be settled now that we will not win). Similarly, if it is an open possibility now that it will be an open possibility tomorrow, then it is an open possibility now. The synchronic version of the S5 principle for the new operators seems plausible as well: If it is an open possibility now that we will win, then it is settled now that that is now an open possibility.19 , , and are logically independent of the principles previously discussed. This should be unsurprising, since the one group of principles differs somewhat from the other in subject matter. The three principles about open possibility essentially tell us that the sample space of the actual chance distribution at t is related in a certain way to the sample spaces of the chance distributions (at t or at later times) at other opent possibilities. (For example, and together tell us that if one of the latter sample spaces includes a P-world, then so does the former.) But the three principles say nothing about how chances are distributed over these sample spaces at the actual world or at the other opent possibilities. The opposite is true of the principles discussed in §§3.2–3.3. They are about the chance distributions (at t and at later times) at the actual world and at other opent possibilities. But they have only minimal implications about the way in which the sample spaces of these chance distributions are related to each other. In particular, they do not entail , , or .20 Example 1 can be used to show that MPC violates , , and . I will focus on , but similar arguments could be used to show that and are violated as well. At the actual world, it is compossible with history through t and the laws that w1 will be actualized. Similarly, at w1 it is compossible with history through u and the laws that CDEW. So, at the actual world, CDEW. And yet, actually ¬CDEW, since actually ¬◊CDEW. That violates . 3.5 Possible responses by non-counterpart-theoretic MPC-ists I will consider two MPC-ist strategies for addressing the problems outlined in §§3.2–3.4. The first strategy is to say that under indeterminism the modal facts can vary over time. The principle Necessity of §2 should be restricted: it states constraints on what is possible for a table that apply at a given time only if it is already settled at that time which parts the table will be made from. In Example 1, CDEW is metaphysically possible at time t (before the coin has landed on the first toss). Once the coin has landed heads, so that it is settled that Woody will be made from ABC, Necessity kicks in and CDEW becomes metaphysically impossible. (BCDW remains metaphysically possible, even if it is no longer an open possibility that BCDW.) The sample space of the chance distribution cht is a class of worlds that are metaphysically possible at t (but some of which might become impossible after t). This view allows MPC-ists to say that at the opent possibilities where a table is made from CDE, the table is Woody, so that the following holds at the actual world: (21) cht(CDEW) = ¼. Since (21) also holds at the other opent possibilities, it follows that actually, cht(cht(CDEW)=¼)=1. Consequently, the chance at t is zero that the chance of CDEW at t is different from what it actually is. The chances at t do not undermine themselves. By the same manoeuvre, MPC-ists also prevent violations of (ECP)—Echt(Chu,w(CDEW))=¼=cht(CDEW), just as (ECP) predicts—and consequently of . Their view becomes consistent with , , and as well, as I will show for the case of . For any possible world w, let Ht,w be the complete truth about the history up to t as it is at w and let Lw be the conjunction of w’s laws of nature. The MPC-ist can say: it is true at a possible world w that P if and only if the conjunction of the claim that P with Ht,w and Lw is metaphysically possible at time t. (It does not matter whether the conjunction is possible at later times.) By this definition, it is actually true that CDEW. This avoids the counterexample to described in the previous section. A thorough evaluation of this dynamic conception of modal space is beyond the scope of this paper. Suffice it to say that relativizing metaphysical necessity and possibility to a time amounts to a significant shift in the way we think about modality. Without an independent motivation for this change, it seems ad hoc to propose such a major conceptual revision to save MPC from problematic consequences. A second strategy for solving the problems for MPC is to give up the thesis I called ‘Sufficiency’ in §3.1. Let t* be the time at which the opent possibilities in Example 1 diverge from each other. Denying Sufficiency allows MPC-ists to say that in Example 1, there is no combination of (i) (qualitative and non-qualitative) truths about history before t* and (ii) other qualitative truths, such that (i) and (ii) metaphysically necessitate that if a table is made from BCD, then that table will be Woody. MPC-ists who hold that all laws are qualitative truths can infer that the history before t* and the laws together do not necessitate that any table made from BCD will be Woody. In other words, contrary to what I assumed in my discussion in §§3.2–3.4, the opent possibilities include not only worlds where Woody is made from BCD, but also worlds where a table other than Woody is made from BCD. The assumption that cht(A table will be made from BCD)=¼ consequently does not force MPC-ists to say that cht(BCDW)>0. They can say instead that there is a ¼ chance at t that a table other than Woody will be made from BCD, and that the class of opent possibilities where Woody is made from BCD (while non-empty) has a chance measure of zero at t. (By analogous reasoning, they can say that at opent possibilities where BCDW holds, cht(CDEW) = 0.) That would vitiate the arguments from MPC to the claim that Example 1 is a case of undermining and to the conclusion that it violates (ECP) and . One would of course like to be given some independent reason for thinking that cht(BCDW) must equal zero in the example. But even if such a reason can be given, it should be clear that the MPC-ist response just sketched does not allow MPC-ists to avoid violations of , , or . I will consider for the sake of illustration. (The cases of and are analogous.) Irrespective of their attitude towards Sufficiency, their commitment to Tolerance requires MPC-ists to say that in Example 1, some BCDW-world is compossible with the history up to t and the laws, and that at this BCDW-world, CDEW is compossible with history up to u and the laws. Consequently, it is actually an opent possibility that it will be an openu possibility that CDEW. And yet, it is not actually an opent possibility that CDEW. That violates . In any case, the strategy of avoiding the difficulties for MPC by denying Sufficiency comes at a significant cost—as noted in §3.1, denying Sufficiency amounts to a strong and (I think) implausible commitment. 4. Counterpart-theoretic MPC Counterpart theorists analyse de re modal claims by appealing to a counterpart relation between individuals at different possible worlds. (See, for example, Lewis 1968, 1986b, Ch. 4, Fara 2009.) The simplest version of counterpart theory tells us this:21 ◊Fa at w if and only if some possible world w* contains a counterpart a* of a such that Fa*. Counterpart theorists can explain facts about the modal profiles of individuals by appealing to features of the counterpart relation. For example, they can explain the fact that Socrates could not have been a fried egg by saying that two objects need to meet certain minimum standards of mutual similarity to count as counterparts, and that a fried egg and a human being do not meet those standards. De re modal claims involving polyadic relations are somewhat more complex. The simplest counterpart-theoretic account entails the following (‘R’ is a placeholder for an n-place predicate, and ‘a’, ‘b’, …, ‘n’ refer to individuals existing at w): (22) ◊Rab…n at w if and only if some possible world w* contains counterparts a*, b*, …, n* of a, b, …, n, respectively, such that Ra*b*…n*. (And of course, ◊Rab…n if and only if at the actual world, ◊Rab…n.) However, this account does not quite work as it stands (Hazen 1979). Counterpart theorists typically want to allow for a possible world w2BO that contains two counterparts, j1 and j2, of Barack Obama Jr. and two counterparts, s1 and s2, of his father, Barack Obama Sr., with j1 being s1’s son and j2 being s2’s. Since j1 is the son of someone other than s2, it is true that at w2BO there are counterparts x and y of Obama Jr. and Obama Sr., respectively, such that x is the son of someone other than y. Therefore, the following is true according to (22): (23) Possibly, Obama Jr. is the son of someone other than Obama Sr. That seems wrong. Counterpart theorists can avoid this result if they assign truth-conditions to sentences of the form ◊Rab…n by appealing to counterparts, not of a,b,…,n taken individually, but of the ordered n-tuple <a,b,…,n> (Hazen 1979, Lewis 1986b, pp. 232–3). For one n-tuple to be a counterpart of another, it is not enough that each member of the first n-tuple stands in the right similarity relation to the corresponding member of the second. It is required in addition that the members of the one n-tuple be related to each other in ways sufficiently similar to the ways in which the members of the other n-tuple are related. There are different versions of this account (and the choice between them is not entirely trivial). For definiteness, I will work with a variant that appeals to what I will call ‘counterpart functions’, though my arguments equally apply (mutatis mutandis) to other versions. A counterpart function is a partial function fw*,w from the objects at one possible world w* to the objects at another possible world w that meets certain constraints that the counterpart theorist needs to specify. Importantly, it needs to meet the following condition (among others): whenever fw*,w maps certain objects at w* to certain objects at w, the way in which the former objects are related to one another is sufficiently similar (in the right respects) to the way in which the latter objects are related to one another. For example, since Obama Jr. is the son of Obama Sr., a counterpart function fw2BO,@ can map x to Obama Jr. and y to Obama Sr. only if x is the child of y. I will call this the ‘relational constraint’ on counterpart functions. Counterparthood can be defined in terms of counterpart functions: y at w* is a counterpart of x at w if and only if some counterpart function fw*,w maps y to x. An n-tuple <y1,y2,…,yn> of objects at w* is a counterpart of an n-tuple <x1,x2,…,xn> of objects at w if and only if some counterpart function fw*,w maps y1 to x1, y2 to x2, …, and yn to xn. (Note that there can be different counterpart functions from one world w* to another world w. Consequently, different objects (n-tuples of objects) at w* can be counterparts of a single object (n-tuple of objects) at w.) Finally: (24) ◊Rab…n at w if and only if some possible world w* contains individuals a*,b*,…,n* such that <a*,b*,…,n*> is a counterpart of <a,b,…,n> and Ra*b*…n*. The relational constraint on counterpart functions ensures that in our earlier example of w2BO, the counterparts of <Obama Jr.,Obama Sr.> can include neither <j1,s2> nor <j2,s1>, though they may include <j1,s1> and <j2,s2>. Counterpart theorists who endorse (24) can therefore avoid commitment to (23). Iterated modal claims can be explained along similar lines: (25) ◊◊Rab…n at w if and only if some possible world w* contains individuals a*,b*,…,n* such that <a*,b*,…,n*> is a counterpart of <a,b,…,n> and ◊Ra*b*…n* at w*. (24) and (25) do not amount to a general counterpart-theoretic account of de re modal claims, since they only yield truth-conditions for sentences formed by prefixing one or more possibility operators to an atomic sentence. However, that will suffice for the points I want to make. The Modality-Chance Principle can also be reformulated to obtain a counterpart-theoretic account of de re chance ascriptions. Again, I will not try to give a general account of this kind, but will restrict my attention to the special cases that matter to this discussion (the worlds that are opent possibilities at a world w will be called ‘opent,w possibilities’): (26) (i) cht(Rab…n) = p at w if and only if cht,w assigns p to the class of all opent,w possibilities w* such that, for some individuals a*, b*, …, n* at w*, <a*, b*, …, n*> is a counterpart of <a, b, …, n> and Ra*b*…n*.   (ii) cht(chu(Rab…n)=p)=q at w if and only if cht,w assigns q to the class of all opent,w possibilities w* such that, for some individuals a*,b*,…,n* at w*, <a*,b*,…,n*> is a counterpart of <a,b,…,n> and chu(Ra*b*…n*) = p at w*. Counterpart-theoretic MPC-ists can explain why (3) and (4) hold by endorsing principles along the following lines: NecessityCP: Where x is any table at any possible world w and the ys are x’s parts, if a counterpart function fw*,w maps an object x* at some possible world w* to x, then fw*,w maps parts of x* to at least 2∕3 of the ys; ToleranceCP: Where x is any table at any possible world w, the ys are x’s parts, and the zs include 2∕3 of the ys (and nothing else), there is a counterpart function fw*,w that maps an object x* at some possible world w* to x while mapping x*’s parts to the zs and to some suitable other objects that are not among the ys. Counterpart theorists who endorse these principles can explain what is going on in the counterexamples to 4 and 5 discussed in §2. Some possible world v1 contains five blocks of wood A1–E1 and a table Woody1 made from B1C1D1, such that some counterpart function maps A1 to A, B1 to B, …, and Woody1 to Woody. (In Figure 3, a solid arrow from one individual to another indicates that this function maps the first individual to the second.) There is also a possible world v2 that contains five blocks of wood A2–E2 and a table Woody2 made from C2D2E2, such that some counterpart function maps A2 to A1, B2 to B1, …, and Woody2 to Woody1. (This mapping is represented by the dashed arrows.) By (24), it is true at v1 that ◊Woody1 is made from C1D1E1, from which it follows by (25) that the following actually holds. (27) ◊◊Woody is made from CDE While <Woody2,A2,B2,C2,D2,E2> is a counterpart of <Woody1,A1,B1,C1,D1,E1> and <A1,B1,C1,D1,E1,Woody1> is a counterpart of <A,B,C,D,E,Woody>, NecessityCP ensures that <A2,B2,C2,D2,E2,Woody2> is not a counterpart of <A,B,C,D,E,Woody>. (Counterparthood is not transitive.) Moreover, since actually ABCW, NecessityCP guarantees that no counterpart function maps any table T in any possible world that is made from three parts to Woody while mapping T’s parts to C, D, and E. Combined with (24), this guarantees that: (28) ¬◊Woody is made from CDE (27) and (28) constitute a counterexample to 4. Counterexamples to 5 can be explained in a similar way. Figure 3: View largeDownload slide Counterpart-theoretic MPC-ist explanation of counterexamples to 4 Figure 3: View largeDownload slide Counterpart-theoretic MPC-ist explanation of counterexamples to 4 I will argue that counterpart theory does not put MPC-ists in a position to avoid the problems discussed in §§3.2–3.4. But first, I have to distinguish between two versions of counterpart theory that require somewhat different treatments. The two views differ on the question ‘Do the qualitative features of two worlds determine which objects at the one world are counterparts of which objects at the other?’ A qualitative counterpart theorist will answer ‘yes’, while a non-qualitative counterpart theorist will say ‘no’. While most counterpart theorists have followed David Lewis in endorsing the first view, the second position has also been held (Fara 2009). I will discuss qualitative counterpart theory first, before turning to the non-qualitative version. Qualitative counterpart theorists endorsing NecessityCP and ToleranceCP have to say that schema (29) has true instances and are therefore committed to the possibility of undermining. (29) cht(P) = x & cht(¬cht(P)=x)>0. To see this, note first that qualitative counterpart theory entails the following: where x is any individual or any n-tuple of individuals that inhabit the same world, there is some (possibly partly extrinsic) qualitative condition—call it ‘Condx’—that is necessary and sufficient for any object at any possible world to be a counterpart of x. Now consider Example 1 again, and suppose that things have been set up so that there are exactly three opent possibilities. Firstly, the world @, at which A–E exist and Woody is made from ABC. Secondly, the world v1, at which the blocks of wood A1–E1 exist and a table, Woody1, is made from B1C1D1, such that <Woody1,A1,B1,C1,D1,E1> meets the qualitative condition Cond<Woody,A,B,C,D,E>. Thirdly, the world v2, at which blocks A2–E2 exist and a table, Woody2, is made from C2D2E2, such that <Woody2,A2,B2,C2,D2,E2> meets the qualitative condition Cond<Woody1,A1,B1,C1,D1,E1>. The following is true: (30) (i) <Woody1,A1,B1,C1,D1,E1> is a counterpart of <Woody,A,B,C,D,E>;   (ii) <Woody2,A2,B2,C2,D2,E2> is a counterpart of <Woody1,A1,B1,C1,D1,E1>. The class of opent possibilities (and the chance distribution over them) is the same at all three opent possibilities. By NecessityCP, <Woody2,A2,B2,C2,D2,E2> is not a counterpart of <Woody,A,B,C,D,E>. Given that cht,v1({v2}) = ¼, we can infer the following by (26)(i) and (30)(ii): (31) At v1, cht(Woody1 is made from C1D1E1) = ¼. Moreover, given that actually cht({v1}) > 0, we can use (26)(ii) and (30)(i) to infer from (31) that the following actually holds: (32) cht(cht(Woody is made from CDE)=¼)>0. However, by NecessityCP and (24), ¬◊Woody is made from CDE. Hence: (33) cht(Woody is made from CDE) = 0. (32) and (33) together are inconsistent with and they constitute a case of undermining, since they entail an instance of schema (29). (A counterexample to could be constructed as well.) The commitment to the possibility of undermining has many of the same problematic consequences for MPC-ists who endorse qualitative counterpart theory as for non-counterpart-theoretic MPC-ists. Given that chu,v1({v2})=½, we can infer the following by (26)(i) and (30)(ii): (34) At v1, chu(Woody1 is made from C1D1E1)=½. Moreover, given that actually cht({v1})>0, we can use (26)(ii) and (30)(i) to infer from (34) that actually: (35) cht(chu(Woody is made from CDE)=½)>0. (35) and (33) together are inconsistent both with , and therefore with the Expected Chance Principle. , , or are violated as well. By counterpart-theoretic lights: Rab…n at w if and only if some possible world w* that is like w up to t and conforms to w’s laws contains individuals a*,b*,…,n*, such that <a*,b*,…,n*> is a counterpart of <a,b,…,n> and Ra*b*…n*; Rab…n at w if and only if some possible world w* that is like w up to t and conforms to w’s laws contains individuals a*,b*,…,n*, such that <a*,b*,…,n*> is a counterpart of <a,b,…,n> and Ra*b*…n* at w*. It is easy to see that in our example, CDEW but ¬CDEW. (The argument is essentially analogous to the one that shows that the example violates 4.) That is a counterexample to . and are violated as well, as can be shown by analogous arguments. Non-qualitative counterpart theorists can deny that there is a qualitative sufficient condition for an otherworldly object to be a counterpart of Woody or of <Woody,A,B,C,D,E>. To the charge that their view generates undermining cases, they can then give a reply analogous to that of non-counterpart-theoretic MPC-ists who reject Sufficiency. (See §3.5.) They can say: ‘For any world w that meets the following condition: (36) w contains an object T made from certain objects bcd, such that <T,b,c,d> is a counterpart of <Woody,B,C,D>, there is another world w* that is qualitatively indistinguishable from w but does not meet condition (36). (The objects that play the same qualitative roles in w* as T and b–d in w do not form an n-tuple that is a counterpart of <Woody,B,C,D>.) Let S be the class that contains the opent possibilities that meet condition (36) as well as every world that is qualitatively like some opent possibility that meets condition (36). I claim that, if the history up to t and the laws are jointly compossible with some worlds that meet condition (36), then they are also compossible with some worlds in S that fail to meet this condition. So, if the opent possibilities include any worlds satisfying (36), they also include S-worlds not meeting that condition. Moreover, I hold that, if the class of opent possibilities in S has a non-zero chance at t (say, 25%), then there is only one way in which this chance can be divided up between those opent possibilities in S that meet condition (36) and those that do not: the latter receive the entire 25% while the former receive a chance of zero. Therefore, cht(BCDW)=0. Moreover, the opent possibilities meeting condition (36) are the only ones containing entities T,c,d,e such that <T,c,d,e> is a counterpart of <Woody,C,D,E> and ◊(T is made from cde). Therefore, actually cht(◊CDEW)=0 and consequently cht(cht(CDEW)>0)=0. So, the chance at t is zero that CDEW’s chance at t is different from what it actually is. That shows that on my account, Example 1 is not a case of undermining (and it does not violate (BCP*), , or ). Similarly, it answers the objection that my account violates (ECP) (and ).’ To make this response more compelling, the MPC-ist would need to provide some independent justification for the assumptions underlying it, in particular the claim that the class of opent possibilities that meet condition (36) has a chance measure of zero at t. Most importantly, however, just like MPC-ists who deny Sufficiency, those who give the reply just considered cannot avoid violations of , , or . The argument given in §3.5 readily generalizes, as the reader can easily verify. Counterpart-theoretic MPC-ists can adopt a dynamic view of de re modality by relativizing counterpart functions and the counterpart relation to a time (that is, by making counterparthood a triadic relation between two objects and a time). They can then say that NecessityCP applies only to counterpart functions that are relativized to times at which it is already settled which parts the table will be made from. That will allow them to hold that, relative to time t of the first coin toss, Woody2 in world v2 is a counterpart of Woody and <Woody2,C2,D2,E2> is a counterpart of <Woody,C,D,E>. But <Woody2,C2,D2,E2> is not a counterpart of <Woody,C,D,E> relative to times after the coin has landed and it has been settled that Woody will be made from ABC. Consequently, ◊tCDEW but ¬◊uCDEW. Counterpart-theoretic MPC-ists who endorse this dynamic view can avoid the problems discussed in this paper in the manner described in §3.5. But unless they can provide independent motivation for making de re modal facts time-relative, it will seem like an ad hoc manoeuvre.22 5. Alternatives to MPC While by no means providing knock-down arguments against MPC, §§3 and 4 highlighted problems for the view that give us reasons to look for an alternative. What are the options? One possibility is to reject (3) along with Necessity. Another is to deny (4) and Tolerance. Both of these options are costly, as (3) and (4) are very plausible. A third option, which avoids these costs, is to endorse (37). (37) (3) and (4) are true. Moreover, contrary to MPC, they are necessary, for everything necessarily has the modal profile it does. I will first consider what this response would look like for proponents of non-counterpart-theoretic MPC before turning to the counterpart-theoretic version. It is actually true that Woody could have been made from ABX but not from CDE, and non-counterpart-theoretic MPC-ists who endorse (37) have to say that these modal claims are true even at possible worlds where Woody is made from BCD. Thus, Woody conforms to Necessity and Tolerance in actuality but not at possible worlds where BCDW holds. Necessity and Tolerance do not hold for all tables in all possible worlds or even for the tables in all nearby worlds. The obvious objection to this view is that it makes the metaphysical order of the universe seem implausibly fragile. The realm of de re modal facts is actually governed by certain general principles about which kinds of objects have which of their features necessarily. The principles include the universal claims that are in the scope of the necessity operators in Necessity and Tolerance (the claims you obtain by removing the necessity operators at the beginning)—call them ‘Necessity–’ and ‘Tolerance–’. But on the view described in the preceding paragraph, Necessity– and Tolerance– would have been false if some actual tables had been made from slightly different parts. Does that not mean that the modal facts would then have been less orderly than they actually are (that tables made from the same parts as in actuality would have conformed to Necessity– and Tolerance– while others would not have)? It seems that some scratches in a few blocks of wood would have been enough to upset the metaphysical order. Worse, once we accept that actuality is surrounded in modal space by metaphysically disordered worlds, we have to wonder how we can be so sure that the actual world is an orderly one. All of this sounds rather strange. To answer this objection, proponents of (37) need to give an account of the principles governing de re modality that does not include Necessity– or Tolerance–, but only principles that are more counterfactually robust. One option is to adopt what we may call ‘maximal multi-thingism’, the view that at all metaphysically possible worlds, the facts of de re modality are governed by the following principle (see Leslie 2011, Kment 2014, pp. 194–7):23 (38) For any material object x and any set S of x’s properties that meets certain minimal conditions, there is an object x* that is co-located with x and made from the same parts as x, such that the properties that x* has necessarily include all and only those in S. On this account, there is no difference between the principles governing de re modality in actuality and at BCDW-worlds. Just as Necessity– and Tolerance– fail for Woody at BCDW-worlds, they fail for many tables co-located with Woody at the actual world. For example, Tolerance– fails for those tables co-located with Woody that could not have been made from parts other than ABC. And just as Woody conforms to Necessity– and Tolerance– in actuality, many tables that are co-located with Woody at a BCDW-world conform to these two principles. Moreover, both in actuality and at BCDW-worlds, the facts of de re modality are governed by the same general principle: (38). There is nothing fragile about the metaphysical order. Counterpart theorists who wish to endorse (37) can easily do so. They will endorse the usual counterpart-theoretic strategy of explaining the fact that ◊BCDW by saying that the counterparts of <Woody,B,C,D> include some quadruple whose first member is made from its other members (such as the quadruple <Woody1,B1,C1,D1> of entities in world v1 depicted in Figure 3). Similarly, they will explain the fact that ¬◊CDEW by denying that the counterparts of <Woody,C,D,E> include any quadruple whose first member is made from the others. But they will reject MPC by saying that (3) and (4), and all other truths about the modal profiles of individuals, are necessary truths. One possible way they can do this is to say that counterparthood is an equivalence relation. On this view, a counterpart of x has the same counterparts as x itself (so that there are no cases where it could have been possible for x to meet a certain condition but it is not actually possible). Hence, no counterpart of <Woody,C,D,E>, not even the quadruple <Woody1,C1,D1,E1> of entities in v1, has a counterpart whose first member is made from the others. So, ToleranceCP, while true of Woody, cannot be true of Woody1. Does that mean that the metaphysical order governing de re modality is very fragile, in the sense that the criteria for counterparthood that apply to individuals at nearby worlds differ significantly from those applying to actual individuals? Non-qualitative counterpart theorists can avoid this conclusion by endorsing a counterpart-theoretic version of maximal multi-thingism. On that view, every physical object is co-located with many others that have the same qualitative non-modal properties but differ in the range of their counterparts. Hence, just as Woody at the actual world conforms to ToleranceCP, so do many tables that are co-located with Woody1 at v1. And just as Woody1 fails to conform to ToleranceCP, so do many tables co-located with Woody at the actual world. At both worlds, the same multi-thingist principles govern the range of a thing’s counterparts. Qualitative counterpart theorists are in a less good position to adopt this account. On their view, the range of an object’s counterparts (and hence its modal properties) is determined by its non-modal qualitative properties. For there to be co-located objects that differ in their counterparts, there would have to be relevant differences between the non-modal qualitative properties of these objects, and it is not clear what these differences could be. This is not the place to review the complex debate about the virtues and vices of (maximal) multi-thingism (Varzi 2012, Wasserman 2013), or to discuss how plausible it ultimately is to combine the view with non-qualitative counterpart theory. What is important for present purposes is to observe that multi-thingism provides one alternative to MPC that merits further exploration. 6. Modal-existence contingentism Some philosophers hold that, necessarily, every possible world existentially depends on the individuals inhabiting it, that is, it could not have existed without all of them existing.24 Since most of these philosophers also believe that some individuals exist contingently,25 they conclude that possible worlds where such individuals exist are contingent existents as well (see Fine 1977, Adams 1981, Stalnaker 2011, Kment 2014, §4.5; cp. McMichael 1983). For example, a possible world w where Woody exists fails to exist at possible worlds where Woody does not exist. Moreover, some who draw this conclusion believe that (39) is necessarily equivalent to (40). (39) Possibly, Woody exists. (40) There is a possible world where Woody exists. Since they think that (40) is false at possible worlds where Woody does not exist, they conclude that the same is true of (39). So, while (39) is actually true, it could have been false. Call the form of modal contingentism that is motivated in this way modal existence contingentism (MEC) (Adams 1981, Kment 2014, Ch. 4, in particular §4.7).26 MEC generates undermining cases. Suppose at t you decide to toss a fair coin. There are two opent possibilities: w1, where the coin lands heads and you make a table (called ‘Woody’) from ABC, and w2, where it lands tails and you burn ABC. cht({w1})=cht({w2})=½. Woody does not exist at w2. By MEC-ist lights, it follows that at w2, ¬◊Woody exists. By the Modality-Chance Principle (MC), ‘cht(Woody exists)>0’ necessitates ‘◊Woody exists’. Hence: (41) At w2, ¬(cht(Woody exists)>0). Given (MC), (41) and the fact that cht({w2})=½ entail that cht(cht (Woody exists)>0)≠1. And yet, cht(Woody exists)=cht({w1})>0. That violates () and therefore (UII). This example of undermining follows the pattern described in the introduction. The chance at t of Woody’s existence depends on whether ◊Woody exists: it is positive at the opent possibility (w1) where ◊Woody exists but equals zero at the opent possibility (w2) where ¬◊Woody exists. Moreover, it is chancy at t whether ◊Woody exists, since it depends on whether Woody will in fact exist. So, the chances at t depend on modal facts that are themselves chancy at t. That is a recipe for undermining cases. It remains a topic for future work to study the extent to which MEC generates the various other problems associated with undermining cases that were discussed in §§3–4, and what replies to the problem(s) are available to MEC-ists. 7. Summary and conclusion A theory about modal space should be consistent with a plausible account of physical chance. This constraint creates difficulties for philosophers who reject 4 or 5 and who hold that the chances at a given time can depend on modal facts that are partly determined by later chance processes. These philosophers, who include proponents of MPC and MEC, also have to deny various compelling S4- and S5-principles about chance and open possibility. I mentioned in §2 that I have very few untutored opinions about the formal properties of the metaphysical modalities and therefore find it hard to know offhand what to think of 4 or 5. By contrast, the S4- and S5-principles about chance and open possibility discussed in this paper are immediately compelling, and some of them follow from very plausible principles of greater generality such as (UII) and (ECP). This is not particularly surprising: unlike the notion of metaphysical possibility, the concepts of chance and open possibility arguably figure frequently in non-philosophical thinking. Moreover, it points to one important reason why it can be helpful in deciding controversies about modality to consider the implications of the competing views for the theory of chance: it allows us to draw on views we have about chance and the range of open possibilities that are often much firmer than those about metaphysical modality.27 Footnotes 1 While (MC) is very widely accepted, Nolan (2016) has recently argued for a view on which the principle needs to be restricted. However, these restrictions do not affect the arguments of this paper. 2 If ‘□’ and ‘◊’ are duals, then this principle is equivalent to: □P→□□P. 3 By saying that it is chancy at t whether P holds, I mean that both cht(P)>0 and cht(┌¬P┐)>0. 4 I borrowed the name ‘Tolerance’ from Forbes (1985). 5 Throughout this paper I will assume that the boxes and diamonds (with or without superscripts and subscripts), and all the other symbols to be introduced below, belong both to the object language and to the metalanguage in which I conduct the discussion. 6 We can obtain a sufficient condition for being Woody by conjoining being-made-from-BCD with, say, being-Woody. Sufficient conditions like that are irrelevant to my discussion. The qualification ‘non-trivial’ is meant to rule them out. 7 More precisely, where P is a singular term for some claim or a variable ranging over claims, ┌cht,w(P)┐ will abbreviate ┌P’s chance at t at w┐. For any sentence or open formula S, ┌cht,w(S)┐ will abbreviate ┌the chance of the claim that S at t at w┐. Where C is a singular term for a class of possible worlds or a variable ranging over such classes, ┌cht,w(C)┐ will abbreviate ┌C’s chance measure at t at w┐. 8 In a later paper (Lewis 1994, see also Hall 1994), Lewis offers a revised version of the Principal Principle that is consistent with the possibility of undermining but maintains that the original version is more intuitive. For more on the Principal Principle, see footnote 12. 9 The original version of the principle runs as follows: Suppose x > 0 and Chtw(A) = x. Then A is true in at least one of those worlds w’ that matches w up to time t and for which Cht(A) = x. (Bigelow, Collins, and Pargetter 1993, p. 459) Undermining cases generated by frequentism violate this weaker principle, those resulting from MPC only violate the strengthened version. 10 To see this, suppose that (MC) holds and assume that (UII) is true of t and w, that is: (42) cht,w(Chancet,w)=1. Let Ht,w be the conjunction of all claims about the history up to t that hold at w. Since the past is not chancy: (43) cht,w(Ht,w) = 1. (42) and (43) entail that: (44) cht,w(P) = cht,w(P & Chancet,w & Ht,w) for any claim P for which cht,w(P) is defined. Let P be any claim such that cht,w(P)>0. By (44), cht,w(P & Chancet,w & Ht,w) > 0. Given (MC), that entails that there is some (metaphysically) possible world where P & Chancet,w & Ht,w holds, that is, some possible P-world that is like w up to t and where the chances at t are the way they are at w. This shows that (BCP*) is true of w and t. 11 The easiest way of showing this is to argue for the contrapositive: if (i) cht,w(Chancet,w) is defined and (ii) (UII) fails for t and w, then (BCP*) fails for t and w. Suppose that (i) and (ii) hold. By (ii), not cht,w(Chancet,w)=1. Given (i), it follows that cht,w(Chancet,w)<1. So, cht,w(¬Chancet,w)>0. And yet, by the definition of ‘Chancet,w’, there is no possible ¬Chancet,w-world that is like w up to t and where the chances at t are the same as at w. That violates (BCP*). 12 The original version of the Principal Principle (PPO) proposed in Lewis (1986a) tells us that one’s credence Cr(P|cht(P)=x) ought to equal x, provided one has no ‘inadmissible’ evidence relative to P and t, that is, one’s evidence bears on P only by bearing on what P’s chance is at t. Here is an example that shows that MPC-ists who accept Sufficiency have to reject PPO. You explain to me that you will use a random device with three equiprobable possible outcomes to determine whether to make a table from ABC, BCD, or CDE. Leaving your workshop at t, I am certain that: (48) cht(ABC)=cht(BCD)=cht(CDE)=⅓. Returning later, I am introduced to the finished table (Woody) but not told from which parts it was made. It seems permissible to divide my credence over the three possibilities: (49) Cr(ABCW)=Cr(BCDW)=Cr(CDEW)=⅓. I am certain that (MC) and (50) are true (MPC-ists who accept Sufficiency cannot deny that it can be rational to accept (50)). (50) For any X,Y,Z among A–E, if Woody was made from X,Y,Z, then the opent possibilities where the table you make is Woody are just those where the table is made from parts that include at least two of X,Y,Z. (50) entails that if CDEW, then there are no opent possibilities where ABCW, so that (by (MC)) cht(ABCW)=0. Hence, Cr(cht(ABCW)=0|CDEW)=1 and therefore: (51) Cr(cht(ABCW)=⅓|CDEW)=0. Moreover, (50) entails that if either ABCW or BCDW, then the opent ABCW-possibilities are just those where ABC holds so that (by (48) and (MC)) cht(ABCW)=⅓. So, (52) Cr(cht(ABCW)=⅓|BCDW)=1 Cr(cht(ABCW)=⅓|ABCW)=1 (49), (51), and (52) entail that Cr(ABCW|cht(ABCW)=⅓)=½. But since I have no inadmissible evidence relative to ABCW and t, PPO entails that Cr(ABCW|cht(ABCW)=⅓) ought to equal ⅓. It would require more work to show that cases like this create a serious problem for MPC-ists endorsing Sufficiency. MPC-generated counterexamples to PPO concern de re credences about specific individuals, and there may be independent reasons for thinking that PPO yields false predictions when applied to some singular beliefs (cf. Hawthorne and Lasonen-Aarnio 2009, p. 97). If so, then PPO needs to be revised in response to these counterexamples in any case, and for all that has been shown, the revised principle might be consistent with the combination of MPC and Sufficiency. It is also worth mentioning that the (admittedly less compelling) undermining-resistant ‘New Principal Principle’ proposed in Lewis (1994) and Hall (1994) can be accepted by MPC-ists who endorse Sufficiency. 13 Proof. (1) Preliminaries. (a) Terminology. Let cht,w and chu,w be the chance functions at w at t and at u, respectively, let cht be the chance function that in fact prevails at t, and let Chancet be the conjunction of all claims about the chances at t that are in fact true. (b) Law of total probability (LTP). Consider some claim A and some partition X of the sample space Ω of probability function p. For every w ∈ Ω, let Xw be the cell of X containing w, and let P(A|Xw) be the function that, for every w ∈ Ω, assigns to w the number p(A|Xw) if p(A|Xw) is defined (and which is undefined for w otherwise). If the expected value of P(A|Xw) relative to p is defined, then let us call it ‘Ep(P(A|Xw))’. The so-called “Law of Total Probability” (LTP) tells us that p(A)=Ep(P(A|Xw)), provided Ep(P(A|Xw)) is defined. (When X has only countably many members, X1,X2,…, we obtain a familiar special case of (LTP): p(A)=Σi[p(A|Xi)×p(Xi)] if the terms are defined.) When P(A|Xw) is undefined for some w ∈ Ω, then Ep(P(A|Xw)) is undefined and (LTP) as stated does not apply. But we can generalize (LTP) to cover those cases where p({w ∈ Ω:P(A|Xw) is undefined})=0. Call a function f:Ω→[0,1] an extension of P(A|Xw) if and only if p({w ∈ Ω:f(w)=P(A|Xw)(w)})=1 and Ep(f) is defined. Any two extensions f and f* of P(A|Xw) are almost surely equal (that is, p({w ∈ Ω:f(w)=f*(w)})=1) and therefore have the same expectation relative to p. If P(A|Xw) has an extension f and Ep(f)=x, then let us call x the quasi-expectation of P(A|Xw) relative to p or ‘Ep*(P(A|Xw))’. (LTP) generalizes to what I will call‘(LTP*)’: p(A)=Ep*(P(A|Xw)) if Ep*(P(A|Xw)) is defined. (2) Proof of demonstrandum. Suppose that (UII) and (19) are true. Moreover, assume the following. (53) t<u (54) Echt(Chu,w(P)) is defined. Consider the partition of the sample space OPt of cht into equivalence classes of worlds that have the same post-t history up to u, that is, whose histories are indistinguishable during the half-open temporal interval (t,u]. For any w ∈ Opt, let H(t,u],w be the cell of the partition containing w. Let Cht(P|H(t,u],w) be the function that, for every w ∈ Opt, assigns cht(P|H(t,u],w) to w if cht(P|H(t,u],w) is defined and that is undefined for w otherwise. We can infer (55) from (LTP*), (56) from (UII), and (57) from (19) and (53). (55) cht(P)=Echt*(Cht(P|H(t,u],w)) if Echt*(Cht(P|H(t,u],w)) is defined. (56) cht(Chancet) = 1 (57) chu,w(P)=cht,w(P|H(t,u],w) for all w ∈ OPt. Now, Chancet is true at a possible world w if and only if the chances at t are the same at w as in actuality, that is, if and only if cht,w(P)=cht(P) and cht,w(P|Q)=cht(P|Q) for all claims P and Q. Consequently: (58) cht,w(P|H(t,u],w)=cht(P|H(t,u],w) for any Chancet-world w in OPt. By (57) and (58), chu,w(P)=cht(P|H(t,u],w) for any Chancet-world w in OPt. Hence, Chu,w(P) and Cht(P|H(t,u],w) assign the same values to all Chancet-worlds in OPt. Given (56) and (54), it follows that Chu,w(P) is an extension of Cht(P|H(t,u],w), so that (59) Echt(Chu,w(P))=Echt*(Cht(P|H(t,u],w)) (55) and (59) entail that cht(P)=Echt(Chu,w(P)). Discharging assumptions (53) and (54), we get: (ECP) cht(P)=Echt(Chu,w(P)) whenever t<u, provided Echt(Chu,w(P)) is defined. 14 The complete truth about the post-t history up to u could have a chance of zero at t (in particular if there are infinitely many ways this stretch of history could have unfolded consistently with the history up to t and the laws). (19) therefore assumes that it is possible to conditionalize on zero-probability claims, which in turn is inconsistent with defining conditional probabilities as ratios. To me that seems unproblematic, as I think that there are strong independent reasons for thinking that it is possible to conditionalize on zero-probability claims and that the ratio definition of conditional probabilities should therefore be rejected. (See Hájek 2011, §4 for an exposition of some of the problems for the ratio definition.) We can instead avail ourselves of one of the theories that view the notion of conditional probability as primitive, such as the theory proposed by Rényi (1970). 15 This can be shown using Markov’s Inequality: Ep(X)≥a×p(X≥a), where X is a non-negative random variable whose expectation relative to the probability function p is Ep(X). Assume that (ECP) is true. Moreover, suppose the following: (60) Echt(Chu,w(P)) is defined; (61) t<u; (62) cht(chu(P)>0)>0. Let Z+ be the set of positive integers, and for any i ∈ Z+, let I(i) be the half-open interval (1∕i+1,1∕i]. The following claims are clearly true. (63) I(i) ∩ I(j)=ø if i≠j. (64) Now assume the following for reductio: (65) cht(chu(P)∈I(i)) = 0 for all i ∈ Z+. Given the assumption that probabilities are countably additive, it follows from (63)–(65) that cht(chu(P)∈(0,1])=0 and hence that cht(chu(P)>0)=0, which contradicts (62). So, (65) is false. Hence, for some k ∈ Z+, cht(chu(P) ∈ I(k))>0. It follows that cht(chu(P)>1∕k+1)>0, which in turn entails (66) below. (67) can be inferred from Markov’s Inequality. (ECP), (60), and (61) entail (68). (66) 1∕k+1 cht(Chu,w(P)>1∕k+1)>0 (67) Echt(Chu,w(P)) ≥ 1∕k+1cht(Chu,w(P)≥1∕k+1) ≥ 1∕k+1cht(Chu,w(P)>1∕k+1) (68) cht(P)=Echt(Chu,w(P)) (66) and (67) entail that Echt(Chu,w(P))>0, which together with (68) entails that cht(P)>0. Discharging assumptions (61) and (62), we get: if t<u and cht(chu(P)>0)>0, then cht(P)>0. In other words, is true for P, t and u. Discharging (60), we can conclude: if Echt(Chu,w(P)) is defined, then is true for P, t and u. 16 The diachronic variant of runs as follows: whenever t<u. In other words: if chu(P)>0, then cht(chu(P)>0)=1 whenever t<u. That principle is not entailed by (ECP), and it is clearly false: it could be that the present chance that P is positive, but that there was some positive chance yesterday that the chance that P would sink to zero (and then stay at zero) before the present. 17 Echt(Chu,w(CDEW)) = cht,@({@})chu,@(CDEW) + cht,@({w1})chu,w1(CDEW) + cht,@({w3})chu,w3(CDEW) = ½×0 + ¼×½ + ¼×½ = ¼. 18 The proof that (ECP) entails that holds whenever Echt(Chu,w(P)) is defined (footnote 15) requires the principle of countable additivity. While this is a standard assumption and one of Kolmogorov’s axioms, some philosophers have denied the principle (De Finetti 1972, also see Howson 2008). Such philosophers might reject . (Those who take De Finetti lotteries to be possible can construct a counterexample. Suppose we decide to draw a positive integer by a De Finetti lottery just after t (but before u) and then to arrange things so that chu(P) = 1/i, where i is the integer we drew. Then cht(chu(P) > 0) = 1 > 0. Yet, cht(chu(P) < p) = 1 for all p > 0, from which it seems to follow that cht(P) = 0.) But even those who deny countable additivity have no reason to deny the weaker principle stated below. For, countable additivity is not needed to show that (ECP) entails that holds whenever Echt(Chu,w(P)) is defined. (The proof is similar to the one given in footnote 15.) If t<u and cht(chu(P)≥p)>0 for some p>0, then cht(P)>0. is very compelling. Moreover, the example that was used to show that MPC violates also shows that MPC violates . Denying countable additivity therefore does not help MPC-ists. 19 The diachronic S5 principle for ‘’ is clearly unacceptable. It runs thus: whenever t<u. Contrary to this principle, it might be that it is an open possibility now that P, but that it was not settled yesterday that it would still be an open possibility now that P. 20 This non-entailment claim is a corollary of one of the findings of §3.5, namely, that some views are consistent with the principles discussed in §§3.2–3.3, but not with , , or . 21 There are somewhat different versions of counterpart theory on the market. (See Fara and Williamson 2005 and Russell 2013 for partial overviews.) However, with the exception of the distinction between qualitative and non-qualitative counterpart theory described below, the differences do not matter to the points I want to make. 22 I argued in Kment (2012) that qualitative counterpart theory yields implausible consequences about chance. These difficulties are independent of, and additional to, those for counterpart-theoretic MPC-ists outlined in this section. 23 I borrowed the term ‘multi-thingism’ from Karen Bennett (2004), who writes that she picked it up from Stephen Yablo. 24 See Plantinga (1983) for the opposite view. 25 See Linsky and Zalta (1994, 1996) and Williamson (1998, 2013) for arguments against contingent existence. 26 Not everyone who believes that some possible worlds exist contingently accepts the necessary equivalence of (39) and (40) and endorses modal contingentism in my sense. See Stalnaker (2011). 27 For helpful comments, I am indebted to Cian Dorr, Adam Elga, Alan Hájek, Karen Lewis, David Manley, Alex Meehan, Carla Merino-Rajme, Kristin Primus, Jonathan Schaffer, Jack Spencer, the participants of a graduate seminar at Princeton, the audiences at talks I gave at Oxford University, the Chambers Modality Conference at the University of Nebraska, and the conference on haecceitism at the University of Neuchâtel, and the anonymous referees of this paper. References Adams Robert 1981 , ‘Actualism and Thisness’, in Synthese 49 . Bandyopadhyay Prasanta S. , Forster Malcolm R. (eds.) 2011 , Handbook of the Philosophy of Science, vol. 7: Philosophy of Statistics ( Oxford : Elsevier ). Bennett Karen 2004 , ‘Spatio-temporal Coincidence and the Grounding Problem’ , in Philosophical Studies 118 . Bigelow John , Collins John , Pargetter Robert 1993 , ‘The Big Bad Bug: What are the Humean’s Chances?’ , in British Journal for the Philosophy of Science 44 . Chandler Hugh 1976 , ‘Plantinga and the Contingently Possible’ , in Analysis 36 . De Finetti Bruno 1972 , Probability, Induction and Statistics ( London : Wiley ). Fara Delia 2009 , ‘Dear Haecceitism’ , in Erkenntnis 70 . Fara Michael , Williamson Timothy 2005 , ‘Counterparts and Actuality’, Mind 114 . Fine Kit 1977 , ‘Postscript: Prior on the Construction of Possible Worlds and Instants’, in Prior A. N. , Fine K. , Worlds, Times, and Selves ( Amherst : University of Massachusetts Press ). Forbes Graeme 1985 , The Metaphysics of Modality ( Oxford : Oxford University Press ). Hájek Alan 2011 , ‘Conditional Probability’, in Bandyopadhyay P. S. , Forster M. R. (eds.), Handbook of the Philosophy of Science, vol. 7: Philosophy of Statistics ( Oxford : Elsevier ). Hall Ned 1994 , ‘Correcting the Guide to Objective Chance’ , in Mind 103 . Hazen Allen 1979 , ‘Counterpart-Theoretic Semantics for Modal Logic’ , in Journal of Philosophy 76 . Howson Colin 2008 , ‘De Finetti, Countable Additivity, Consistency and Coherence’ , in British Journal for the Philosophy of Science 59 . Kment Boris 2012 , ‘Haecceitism, Chance, and Counterfactuals’ , in Philosophical Review 121 . Kment Boris 2014 , Modality and Explanatory Reasoning ( Oxford : Oxford University Press ). Leslie Sarah-Jane 2011 , ‘Essence, Plenitude, and Paradox’ , in Philosophical Perspectives 25 . Lewis David 1968 , ‘Counterpart Theory and Quantified Modal Logic’ , in Journal of Philosophy 65 . Lewis David 1986a , ‘A Subjectivist’s Guide to Objective Chance’, in his Philosophical Papers , vol. 2 ( Oxford : Oxford University Press ). Lewis David 1986b , On the Plurality of Worlds ( Oxford : Blackwell ). Lewis David 1994 , ‘Humean Supervenience Debugged’, in Mind 103 . Linsky Bernard , Zalta Edward 1994 , ‘In Defense of the Simplest Quantified Modal Logic’, in Tomberlin J. , Philosophical Perspectives 8: Logic and Language ( Atascadero : Ridgeview Press ). Linsky Bernard , Zalta Edward 1996 , ‘In Defense of the Contingently Concrete’, in Philosophical Studies 84 . McMichael Alan 1983 , ‘A Problem for Actualism about Possible Worlds’ , in Philosophical Review 92 . Nolan Daniel 2016 , ‘Chance and Necessity’, in Philosophical Perspectives 30 . Plantinga Alvin 1983 , ‘On existentialism’ , Philosophical Studies 44 . Rényi Alfréd 1970 , Foundations of Probability ( San Francisco : Holden-Day ). Russell Jeffrey 2013 , ‘Actuality for Counterpart Theorists’, in Mind 122 . Skow Brad 2008 , ‘Haecceitism, Anti-Haecceitism and Possible Worlds’, in Philosophical Quarterly 58 . Stalnaker Robert 2011 , Mere Possibilities: Metaphysical Foundations of Modal Semantics ( Princeton, NJ : Princeton University Press ). Thau Michael 1994 , ‘Undermining and Admissibility’ , in Mind 103 . Varzi Achille 2012 , ‘Mereology’, in Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/archives/win2012/entries/mereology/>. Wasserman Ryan 2013 , ‘Material Constitution’, in Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/archives/sum2013/entries/material-constitution/>. Williamson Timothy 1998 , ‘Bare Possibilia’, in Erkenntnis 48 . Williamson Timothy 2013 , Modal Logic as Metaphysics , ( Oxford : Oxford University Press ). © Kment 2018 This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

doi: 10.1093/mind/fzw035pmid: N/A

Abstract If it works, I can use Putnam’s vat argument to show that I have not always been a brain-in-a-vat (BIV). It is widely thought that the vat argument is of no use against closure scepticism – that is, scepticism motivated by arguments that appeal to a closure principle. This is because, even if I can use the vat argument to show that I have not always been a BIV, I cannot use it to show that I was not recently envatted, and it is thought that the claim that I am not justified in thinking that I was not recently envatted is all that the closure sceptic requires. In this paper I first argue that scenarios in which I have been recently envatted are inadequate for the sceptic’s purposes, and so the standard argument that the vat argument is of no use against closure scepticism fails. I then argue that it is not possible to revise the standard argument to meet my objection. I conclude that, if it works, I can use the vat argument as a defence against closure scepticism. If it works, I can use Putnam’s (1981, pp. 1-22) vat argument to show that I have not always been a brain-in-a-vat (BIV). Irrespective of whether the argument is adequate for Putnam’s purposes, it is widely thought that the vat argument is of no use against scepticism of the sort most commonly considered in contemporary epistemology, namely closure scepticism, so called because it is motivated by arguments that appeal to a closure principle.1 The vat argument is thought to be of no use against closure scepticism because even if I can use it to show that I have not always been a BIV I cannot use it to show that I was not recently envatted, and it is thought that the claim that I am not justified in thinking that I was not recently envatted is all that the closure sceptic requires.2 As a result, the vat argument is not much discussed by contemporary epistemologists. In this paper I will first show that, surprisingly, scenarios in which I have recently been envatted are inadequate for the closure sceptic’s purposes. This is because a sceptical argument that is based on such a scenario leaves the justification of some of my empirical beliefs intact, and so it is possible for me to appeal to these beliefs to show that I have not recently been envatted. The sceptic thus faces a dilemma: either she makes use of a scenario in which I have recently been envatted, and so enables me to appeal to my empirical beliefs to show that I have not recently been envatted; or she makes use of a scenario in which I have always been a BIV, and so enables me to use the vat argument to show that I have not always been a BIV. I will then argue that a more general version of this dilemma holds: either the sceptic makes use of what I will call a non-radical sceptical scenario, and so enables me to appeal to my empirical beliefs to show that I am not in that scenario; or she makes use of what I will call a radical sceptical scenario, in which case I can use the vat argument to show that I am not in that scenario. I conclude that if it works, the vat argument is of use against closure scepticism. I hope that this conditional conclusion will promote discussion of whether the vat argument does work in contemporary epistemology. 1. Closure scepticism I am now going to describe the general form of the argument for closure scepticism. My aim here is to be as generous as possible to the sceptic so as to offer the prospect of defeating her on her own terms; hence, I shall grant her much that she perhaps should not be granted. Let us suppose that the sceptic frames her argument in terms of justification rather than knowledge.3 She proposes the following necessary condition for justified belief: (J) For any belief b that I hold, b is justified only if my evidence indicates to me that b is more probable than not-b. The evidence that I may have for an empirical belief consists of sensory experiences, and of other justified beliefs. The notion that the justification of a belief depends, at least in part, upon whether my evidence indicates to me that the belief is more likely than its negation is not universally accepted. However, thinking about justification in this way gives the sceptical argument that I am about to discuss a great deal of its initial plausibility. In fact, one reason that is often given for preferring some other notion of justification is that doing so makes it harder to motivate scepticism.4 It is worth considering whether the sceptic can be defeated even whilst assuming an account of justification that seems to be particularly conducive to her argument, even if one does not subscribe to that account. One might accept the notion that the justification of one of my beliefs depends, at least in part, upon whether my evidence indicates to me that the belief is more likely than its negation, whilst questioning whether the necessary condition that I propose above is appropriate in this context. If my aim is to be concessive to the sceptic why not work with something stronger? Suppose, for example, that we accept the following strengthened version of (J) as a necessary condition for justified belief: (SJ) For any belief b that I hold, b is justified only if my evidence indicates to me that b is to some very high degree more probable than not-b. Won’t it be easier for the sceptic to show that my beliefs do not meet (SJ) than for her to show that they do not meet (J)? After all, my beliefs might meet (J) without meeting (SJ).5 It is a limitation of this paper that the discussion is framed in terms of a concept of justification according to which (J) is a necessary condition, and so any progress that the paper makes against a sceptic who works with such a concept of justification will not immediately be progress against a sceptic who works with a conception of justification according to which (SJ) is a necessary condition.6 However, I do not think that this limitation is severe. One reason for working with (J) rather than (SJ) is that the latter invites the question: to what degree must my evidence indicate to me that b is more probable than not-b in order for b to be justified? It may seem that there is no non-arbitrary answer to this question, which may in turn lead one to doubt that (SJ) is a condition on justification. However, my main reason for working with (J) rather than something like (SJ) is that I do not wish to deprive the sceptical conclusion of its teeth. Suppose a sceptic showed that my beliefs do not meet (SJ). This might be a surprising and disappointing conclusion, but for all that had been said, I might still claim that, nevertheless, many of my beliefs meet (J). If this is correct, then many of my beliefs possess a positive epistemic property, namely, the property of being supported by evidence that indicates to me that they are more likely to be true than their negations. For this reason, one might think that it would still be reasonable for me to continue to believe by and large what I do. But if the sceptic shows that my beliefs lack (J) this is a disaster: for all that my evidence indicates to me about the probabilities of my beliefs being true, I might just as well believe their negations. In that case it would be completely unreasonable for me to continue to believe as I do. That is a disastrous conclusion, and the fact that it is disastrous is what provides a lot of the motivation to resist the sceptical argument. For this reason, I will assume in this paper that (J), but not (SJ), is a necessary condition for justification.7 I now want to make a distinction between two sorts of sceptic. One sort of sceptic denies that I am entitled to think that most of my empirical beliefs are justified until I prove to her, relying only on non-empirical premises, that most of my empirical beliefs are justified. It is not immediately clear why I should respond to such a sceptic. Why should I have to prove an obvious claim before I am entitled to it? The sort of sceptic that I want to consider in this paper does not make such an unreasonable demand, regarding my empirical beliefs as ‘innocent until proven guilty’. She is happy to admit that I am entitled to think that most of my empirical beliefs are justified until someone gives me a good argument to think otherwise. If I cannot say what is wrong with this argument, I lose my entitlement to think that I have a lot of justified beliefs.8 The sceptic’s attempt to give me a good argument that my empirical beliefs are not justified proceeds as follows. Let SS stand for a sceptical scenario, and let p be an arbitrary empirical proposition that I justifiably believe to be logically incompatible with that scenario. We can then give the following argument schema: (C1) If I do not have a justified belief that SS is false, then I do not have a justified belief that p, but (C2) I do not have a justified belief that SS is false; so (C3) I do not have a justified belief that p. Call any argument that is an instance of this schema a closure argument. Any sceptical conclusion resulting from a closure argument is an instance of closure scepticism. In order to support (C1) the sceptic appeals to a closure principle such as the following: Closure principle: For any subject S, and propositions p, q: if S has a justified belief that p, and S has a justified belief that q is logically incompatible with p, then S has a justified belief that not-q. This principle may stand in need of refinement if it is to avoid counterexamples. However, we will concede to the sceptic that none of these refinements will prevent her from using the principle to support (C1).9 SS is, by definition, a scenario that I justifiably believe to be logically incompatible with p, and so (C1) is implied by the closure principle. The sceptic’s appeal to the closure principle highlights the fact that the conclusion of the closure argument is only that the beliefs that I justifiably believe to be incompatible with SS are not justified. This will be important later. In order to support (C2) the sceptic makes SS a scenario in which my sensory evidence would be exactly the same as it currently is.10 Thus, the sceptic claims, my sensory evidence does not indicate to me that it is more probable that SS than that not-SS, and so I am not justified in believing not-SS on the basis of my sensory evidence alone. We might immediately object that it does not follow from the fact that my sensory evidence would be the same in each of two incompatible scenarios that my sensory evidence does not indicate to me that I am in one scenario rather than the other. Consider the following scenario: Laptop: when I turned around to stare out of the window just now my laptop spontaneously disappeared. I turn back to look at the spot previously occupied by my laptop. However, by some trick of the late evening light reflecting off the glass table at which I am sitting, I have the sensory experiences that I would have had if my laptop were still in front of me. By stipulation, in Laptop my sensory evidence would be exactly the same as it currently is (at least so long as I do not try to touch the laptop). However, it is natural to think that I have a justified belief that Laptop is false. This thought is correct, and as it will play an important role later on it is worth making explicit why it is correct. Recall that my evidence for a belief can consist of my sensory evidence, and of other justified beliefs. My sensory evidence alone may not indicate to me that Laptop is false; however, the conjunction of my sensory evidence and evidence consisting of certain justified empirical beliefs that I have does indicate to me that Laptop is false. For example, I have a justified belief that it is vastly improbable that the light should reflect off the table so as to create the illusion of a laptop. This belief, together with my sensory evidence, does indicate to me that Laptop is false. Thus I have a justified belief that Laptop is false. The sceptic is aware that it does not follow from the fact that my sensory evidence is logically compatible with a scenario that my evidence doesn’t indicate to me that that scenario does not obtain. She responds by ensuring that SS is a scenario that is logically incompatible with any empirical belief that I might appeal to in an attempt to justify my belief that SS is false. The conclusion of the relevant closure argument will then imply that these empirical beliefs are not justified. Only justified beliefs can be part of my evidence; thus I cannot assume that I can appeal to these beliefs without assuming that the conclusion of the sceptic’s argument is false, and thereby begging the question against the sceptic. So I cannot claim that my sensory evidence in conjunction with my empirical beliefs indicates that SS is false. If the sceptic is also careful to choose a sceptical scenario that I cannot rule out by appealing to my non-empirical beliefs then it seems that my belief that SS is false is not justified. The following scenario seems to fulfil the above conditions on an effective sceptical scenario: Lifelong Envatment: I always have been and always will be a BIV. A computer stimulates my brain in such a way that I have all the experiences that I would have had if I had lived the life I take myself to be living. However, nothing except my brain and its vat exists, and so almost all my empirical beliefs are false. Lifelong Envatment is an example of a radical sceptical scenario; that is, it is a scenario that falsifies nearly all my empirical beliefs. Substituting Lifelong Envatment into the closure argument schema we get the following argument: (LE1) If I do not have a justified belief that Lifelong Envatment is false, then I do not have a justified belief that p, but (LE2) I do not have a justified belief that Lifelong Envatment is false; so (LE3) I do not have a justified belief that p. Call this the Lifelong Envatment argument When most of my empirical beliefs are substituted for p the closure principle implies (LE1). I would have the same sensory experiences in Lifelong Envatment as I would have if I were living the life I take myself to be living, so my sensory evidence alone does not indicate that Lifelong Envatment is false. Nor can I appeal to any of my empirical beliefs in order to justify my belief that Lifelong Envatment is false, because the conclusion of the Lifelong Envatment argument implies that all the empirical beliefs that I could otherwise appeal to here are not justified. I cannot, for example, appeal to my belief that the technology to envat people does not exist, unless that belief is justified. This is one of the beliefs that the Lifelong Envatment argument says is not justified, and so to appeal to it and thereby assume that it is justified would be to beg the question against the sceptic. Finally, it does not seem that I can appeal to my non-empirical beliefs in order to justify my belief that Lifelong Envatment is false. So it seems that (LE2) is true, and the sceptical conclusion follows. There are varieties of scepticism other than closure scepticism; for example, scepticism motivated by the idea that justification is iterative,11 and scepticism motivated by worries about the impossibility of justification that is not ultimately viciously circular, or that does not entail an infinite regress.12 However, in this paper I am concerned only with the consequences of the vat argument for closure scepticism. 2. The vat argument I am now going to sketch what I think is the best version of Putnam’s vat argument. I believe that the argument works, but I will not attempt to give a full defence of it here.13 My purpose is to discuss the consequences for closure scepticism if the argument works. However, I will make some remarks about features of the vat argument that will be important later. Here is the version of the vat argument that targets the Lifelong Envatment argument: (V1) If Lifelong Envatment is true, then I cannot entertain Lifelong Envatment, but (V2) I can entertain Lifelong Envatment; so (V3) Lifelong Envatment is false. (To entertain here means to represent, whether in thought, linguistically, or otherwise.) (V1) is supported by an appeal to what I will call the causal constraint on concept possession (or causal constraint for short). The causal constraint says that there are some things such that, in order for a subject to have the concept of that thing, the subject must have been in a particular kind of causal contact with it. Plausibly, the causal constraint is a consequence of any semantic externalist view that aims to endorse the judgements that we naturally make about what is being referred to in certain cases. Putnam’s ‘Twin Earth’ scenario is an example of one such case. Putnam imagines a planet, Twin Earth, which is identical to earth at the macro level. However, at the micro level, wherever there is H2O on Earth, there is XYZ on Twin Earth. We are asked to consider the question, what concept does my doppelganger on Twin Earth express with the word ‘water’? Most people are inclined to say that he expresses the concept of twater, which has in its extension all and only XYZ, rather than the concept of water, which has in its extension all and only H2O. A natural explanation for why this judgement is correct is that my doppelganger has had the right sort of causal contact with twater to acquire the concept of it, whilst he has not had the right kind of causal contact with water.14 The idea is that, without getting into the details of exactly what kind of causal contact is required, it is clear that someone in Lifelong Envatment would not have been in the sort of causal contact with brains necessary to have the concept of a brain. If Lifelong Envatment is true then I have never seen, heard, felt, smelt, or touched a brain. Of course, the causal constraint does not imply that I have to have come into direct causal contact with a thing in order to have the concept of it. Often people acquire the concept of a thing that they have never encountered by talking to someone who has the concept of that thing. However, if Lifelong Envatment is true, I cannot ever have met anyone who has the concept of a brain, because the universe contains nothing except me in my vat. For the same reasons, if Lifelong Envatment is true then I do not possess any of the concepts that would be required to refer to brains via a definite description. However, I need the concept of a brain in order to entertain Lifelong Envatment, so if Lifelong Envatment is true I cannot entertain Lifelong Envatment.15 Ordinarily (V2) would not need any defence. However, the sceptic may object that the argument made for (V1) suggests that I am not justified in thinking that I have the concept of a brain unless I am already justified in thinking that Lifelong Envatment is false, and so I am not justified in thinking that I can entertain Lifelong Envatment unless I am already justified in thinking that Lifelong Envatment is false. If this is true then the vat argument is epistemically circular: I must have justification for its conclusion before I can have justification for one of its premises, and so I cannot use the argument to justify my belief that its conclusion is true.16 However, if I am entertaining the Lifelong Envatment argument, then I can entertain the Lifelong Envatment scenario. Thus, it follows from the fact that I am entertaining the Lifelong Envatment argument that I have the concept of a brain.17 At this point it may be tempting to think that there is a sceptical worry about a scenario that I cannot entertain. This is an interesting possibility, but I am not going to pursue it here.18 I will assume that if there is a sceptical worry that I am in a scenario it is a worry that I can be confronted with directly in a way that involves my entertainment of that scenario. 3. Recent envatment and embodiment Let us suppose that the vat argument works as a reply to the Lifelong Envatment argument for scepticism. What progress have we made against the sceptic? One might think: none at all, because the sceptic can simply use a different closure argument to secure her conclusion. Consider the following sceptical scenario: Recent Envatment: One year ago I was sedated, and my brain was removed from my body and placed in a vat. From then on, a computer stimulated my brain in such a way that I had the experiences that I would have had if I had been living the life that I took myself to be living. Just after I was envatted everything in the universe except my brain in its vat was destroyed, so many of my empirical beliefs are false. In contrast to Lifelong Envatment, Recent Envatment is an example of a sceptical scenario that is non-radical; that is, there are large chunks of my empirical beliefs that Recent Envatment does not falsify. For example, Recent Envatment does not falsify my empirical beliefs about how things were up to one year ago. Substituting Recent Envatment for SS we get the following closure argument: (RE1) If I am not justified in believing that Recent Envatment is false, then I do not have a justified belief that p, but (RE2) I do not have a justified belief that Recent Envatment is false; so (RE3) I do not have a justified belief that p. Call this the Recent Envatment argument Whatever the exact nature of the causal constraint, it is not going to prevent me from having the concept of a brain if I have spent most of my life interacting with brains and other people who have interacted with brains in the way I ordinarily take myself to. Thus, I cannot reject (RE2) by using a version of the vat argument to justify my belief that Recent Envatment is false. Smith (1984, p. 117), Glymour (1982, pp. 173-5), Farrell (1986, p. 150), Tymoczko (1989, pp. 294-5), Wright (1992, pp. 86-90), Christensen (1993, pp. 314-5), Forbes (1995, p. 207), and Brueckner (1999, p. 237) have taken this to mean that the vat argument cannot save us from closure scepticism. According to Wright (1992, p. 86), for example, so far as closure scepticism is concerned, the conclusion of the vat argument ‘should merely be that some traditional sceptical arguments employ inept examples’. In a similar vein, Christensen (1993, p. 314) writes that the Recent Envatment argument seems to show that the vat argument ‘amounts to little more than a philosophical curiosity, without great significance for epistemology’.19 Although most authors are content to draw this conclusion about the vat argument immediately after reflection on the Recent Envatment argument, more needs to be said in order to make it plausible that the vat argument has no consequences for closure scepticism. When the schema of the closure argument was described in §1 it was stipulated that any proposition can be substituted for p in the argument, so long as I justifiably believe that proposition to be logically incompatible with SS. This stipulation is necessary if the first premise of the closure argument, which says that if I do not have a justified belief that SS is false then I do not have a justified belief that p, is to follow from the closure principle. Recent Envatment is a non-radical sceptical scenario: it is logically compatible with many of the empirical beliefs that I hold. These empirical beliefs cannot be substituted for p in the Recent Envatment argument, on pain of preventing the sceptic from supporting (RE1) by appealing to the closure principle. Thus, whilst the conclusion of the Lifelong Envatment argument seems to imply that I have no justified empirical beliefs (or at least, hardly any) the conclusion of the Recent Envatment argument is compatible with the claim that many of my empirical beliefs are justified. For example, it is compatible with the claim that the beliefs I have about how things have been up to one year ago are justified. Since I can appeal to the beliefs I have about how things have been in the past in order to obtain inductive justification for my more general beliefs about, for example, the laws of physics, it appears to be compatible with the claim that these more general beliefs are justified as well. If I can use the vat argument to defend myself from a sceptic who uses the Lifelong Envatment argument to show that I do not have any (or hardly any) justified empirical beliefs, then the vat argument does have significant consequences for closure scepticism. This is so even if I cannot use the vat argument to prevent the sceptic from using the Recent Envatment argument to show that many of my empirical beliefs are not justified. The conclusion of the Recent Envatment argument that my beliefs about how things have been this year and about how things are going to be in the future are not justified is a form of scepticism, but it is not nearly as strong a form of scepticism as the conclusion that I have no (or hardly any) justified empirical beliefs at all. However, it seems that the vat argument cannot save us from the strong form of scepticism after all. The sceptic claims to be able to mount another closure argument that, as it were, mops up the justification for my empirical beliefs that the Recent Envatment argument is unable to wash away. As usual, the sceptic starts by describing a sceptical scenario: Embodiment: For most of my life I have been a BIV, stimulated by a computer in such a way that I have had the experiences that I would have had if I had been living the life that I took myself to be living. In fact, however, nothing but my brain in its vat existed. Luckily for me things changed dramatically this time last year. My brain was placed in a normal human body, and the world came to be by and large the way that I believe it to be. This scenario can be substituted for SS, resulting in the following closure argument: (E1) If I do not have a justified belief that Embodiment is false, then I do not have a justified belief that p, but (E2) I do not have a justified belief that Embodiment is false; so (E3) I do not have a justified belief that p. Call this the Embodiment argument If I have spent a year interacting with brains in the way that I ordinarily take myself to, no plausible version of the causal constraint will prevent me from having the concept of a brain. Thus, the vat argument cannot be used to block the Embodiment argument. However, Embodiment is logically incompatible with precisely those beliefs that Recent Envatment is compatible with (that is, the beliefs I have about how things were before the time of my envatment in Recent Envatment). Therefore, the conclusion of the Embodiment argument is that the beliefs that the Recent Envatment argument did not touch are, in fact, not justified. Thus, the conjunction of the conclusions of the Recent Envatment argument and the Embodiment argument is equivalent to the conclusion of the Lifelong Envatment Argument.20 It seems that, notwithstanding the vat argument, the sceptic can get the strong sceptical conclusion of the original Lifelong Envatment argument by employing both the Recent Envatment argument and the Embodiment argument. If this is true, then the widely held view that the vat argument cannot be used as a defence against closure scepticism is correct. At best, the vat argument only forces the sceptic to be careful about the scenarios she makes use of, and forces her to employ two closure arguments rather than one. 4. The inadequacy of Recent Envatment and Embodiment I am now going to show that the sceptic’s response to the vat argument, as described in the last section, does not work. The Recent Envatment argument and the Embodiment argument are vulnerable to an objection to which the Lifelong Envatment argument is not vulnerable. The second premise of the Lifelong Envatment argument, (LE2), says that I do not have a justified belief that Lifelong Envatment is false. In §1 we saw that the Lifelong Envatment argument threatens all the empirical beliefs that I could otherwise have appealed to in order to justify my belief that Lifelong Envatment is false. The idea that I cannot appeal to these beliefs in order to justify my belief that Lifelong Envatment is false on pain of begging the question against the sceptic was a crucial part of the sceptic’s defence of the claim that I do not have a justified belief that Lifelong Envatment is false. Now consider the second premise of the Recent Envatment argument, (RE2), which says that I do not have a justified belief that Recent Envatment is false. Unlike the conclusion of the Lifelong Envatment argument, the conclusion of the Recent Envatment argument is compatible with the claim that many of the empirical beliefs I have about how things were up until one year ago are justified. Thus, it would not be question begging for me to appeal to any of these beliefs in an attempt to justify my belief that Recent Envatment is false. In fact, I can justify my belief that Recent Envatment is false by appealing to some of these beliefs, despite the fact that Recent Envatment is compatible with my sensory evidence. For example, I believe that one year ago no one was even close to having the technology required to envat someone, and I believe that no one had any sort of motivation to envat me. I can appeal to these beliefs, and to similar beliefs that I have, in order to justify my belief that Recent Envatment is false. If I do so, the second premise of the Recent Envatment argument, which says that I do not have a justified belief that Recent Envatment is false, is no longer true. The basic idea here is that my belief that Recent Envatment is false and my belief that Laptop is false are justified for the same reason. In both cases my sensory evidence alone does not indicate to me that the scenario in question is false, but my sensory evidence in conjunction with other justified beliefs that I have does. The sceptic might try to prevent me from appealing to these beliefs by altering Recent Envatment so that my envatment is not quite so recent. This will result in one of two things. Either the sceptic will not move the time of my envatment back far enough, in which case I will still be able to appeal to some of my empirical beliefs in order to justify my belief that I have not been envatted, or the sceptic will move the time of my envatment back far enough that there is no possibility that I can justify my belief that I am not envatted by appealing to my empirical beliefs. However, by moving the time of my envatment back this far, the sceptic will deprive me of the kind of causal contact with brains required to have the concept of a brain. If this is the case, I will be able to use the vat argument to justify my belief that I am not in the altered version of Recent Envatment. But couldn’t the sceptic specify that my envatment took place at a time when I have formed no beliefs that I can appeal to in order to justify my belief that I have not been envatted, and yet I have acquired the concept of a brain? No. It is a biographical fact about me that by the time that I had acquired the concept of a brain (not to mention the other concepts required in order to entertain any of the sceptic’s envatment scenarios) I had already been around for some time. I now have many beliefs about how things were before I acquired the concept of a brain that I can appeal to in order to justify my beliefs that I was not subsequently envatted. For example, I believe that there was no indication that the technology to envat people existed at that time. I expect that what I am saying here will apply to the reader as well. Let us turn our attention to the second premise of the Embodiment Argument, which says that I do not have a justified belief that Embodiment is false. Unlike the Lifelong Envatment argument, the Embodiment argument is compatible with the claim that many of the empirical beliefs I have about how things have been this year, and about how things are now, are justified. Thus it would not be question begging for me to appeal to any of these beliefs in an attempt to justify my belief that Embodiment is false. Again, I can justify my belief that Embodiment is false by appealing to these beliefs, despite the fact that Embodiment is compatible with my sensory evidence. I believe that nothing this year indicates that anyone has ever had the technology to envat someone at birth and then de-envat them later in life without their noticing; there is no old envatting machinery lying around, for example. I can appeal to these beliefs in order to justify my belief that Embodiment is false. If I do so, the second premise of the Embodiment argument will be false. The sceptic may re-describe Embodiment so that the time of my embodiment is moved forward in the hope that this will prevent me from appealing to my empirical beliefs in order to justify my belief that Embodiment is false. Again, one of two things may happen: either the time of my embodiment will not have been moved forward far enough, and I will still be able to appeal to my empirical beliefs in order to justify my belief that Embodiment is false, or the time of my embodiment will have been moved forward enough to prevent me from appealing to my empirical beliefs, but I will not have been in contact with brains for long enough to acquire the concept of a brain. As a result, I will be able to use the vat argument to justify my belief that I am not in the re-described version of Embodiment. One natural response that the sceptic might make at this point is that I am right that neither the Recent Envatment argument nor the Embodiment argument is sound on its own, but that both arguments are sound when they are run at the same time. There are two ways in which these arguments might be run ‘at the same time’. However, neither way will serve to save the arguments. First, suppose that the sceptic runs the Recent Envatment argument and I object by saying that I can appeal to some of my beliefs about how things were before last year in order to justify my belief that Recent Envatment is false. The sceptic replies that she has another argument to show that the beliefs to which I appeal are not justified either; namely, the Embodiment argument. Because they are not justified, I cannot appeal to these beliefs in order to justify my belief that Recent Envatment is false. I counter by saying that I can make the same objection to the Embodiment argument that I made to the Recent Envatment argument; there are empirical beliefs to which I can appeal to justify my belief that Embodiment is false. The sceptic is simply attempting to save one unsound argument by running another unsound argument. At this point someone might object that when the sceptic presents a closure argument based on a non-radical sceptical scenario that only threatens some of my empirical beliefs, she need not in the meantime concede that the rest of my empirical beliefs are justified. If she does not, my reliance on the rest of my empirical beliefs to rule out the non-radical sceptical scenario is illegitimate.21 However, this objection can only be made if we forget the type of sceptic we are dealing with. In §1 I drew a distinction between two sorts of sceptic. The first kind claims that I am not entitled to think that I have justified empirical beliefs until I have argued from non-empirical premises that I do. The second concedes that I am entitled to think that many of my empirical beliefs are justified until I am given a good reason to think otherwise, and then attempts to give me that reason. In this paper I am concerned only with the second kind of sceptic. If such a sceptic attempts to attack only some of my empirical beliefs with one argument, she must concede that the rest of my empirical beliefs are still justified, for no one has yet presented me with a good reason to think that they are not. Let us turn to the second way in which the arguments can be run ‘at the same time’. The sceptic may reply that my counter missed her point. She did not mean that she could run both arguments, one after the other. What she meant was that I am not justified in believing that a scenario that combines the past envatment of Recent Envatment and the future envatment of Embodiment is false. This Combination Scenario can be substituted for SS, resulting in the following closure argument: (CS1) If I am not justified in believing that the Combination Scenario is false, then I am not justified in believing that p, but (CS2) I am not justified in believing that the Combination Scenario is false; so (CS3) I am not justified in believing that p. Call this the Combination Scenario argument. The conclusion of this argument implies that all the empirical beliefs that I could otherwise have appealed to in order to justify my belief that the Combination Scenario is false are not justified. Thus the Combination Scenario argument does not succumb to the objection that we have made to both the Recent Envatment argument and the Embodiment argument. However, the Combination Scenario argument is vulnerable to the vat argument. The only difference between the Combination Scenario and Lifelong Envatment is that, according to the former, I was taken out of my vat and placed in a body before being re-envatted last year. This strange process happened in the blink of an eye and afforded me no opportunity to acquire the concept of a brain, so there is no more reason to think that I would have the concept of a brain in the Combination Scenario than there is to think that I would have the concept of a brain in Lifelong Envatment. It follows that if the Combination Scenario is true, then I cannot entertain the Combination Scenario. Once this claim is in place, we can run the vat argument to show that the Combination Scenario is false. 5. Radical scenarios and non-radical scenarios At this point I take it that I have replied to the usual argument that the vat argument cannot be used as a defence against closure scepticism. That is, I have replied to the version of this argument that takes Recent Envatment and Embodiment (or slight variations thereof) as examples of non-radical scenarios. That this argument has turned out to be unsound should alone be enough to prompt interest in the vat argument as a defence against closure scepticism. In this section I will try to do more to show that the vat argument provides a defence against closure scepticism, if it works. I will do this by showing that there is good reason to think that no variation on the objection to the vat argument (as a response to closure scepticism) considered in the last section will succeed. §3 and §4 effectively present a dilemma for the sceptic: either she makes use of Lifelong Envatment, in which case I can use the vat argument to show that Lifelong Envatment is false; or she makes use of Recent Envatment and Embodiment, and so enables me to appeal to my empirical beliefs to show that these scenarios are false. This suggests that the sceptic may face a more general dilemma: either she uses a radical sceptical scenario (like Lifelong Envatment), in which case I can use the vat argument to show that I am not in that scenario; or, she uses a non-radical sceptical scenario (like Recent Envatment or Embodiment), in which case I can appeal to my empirical beliefs to show that I am not in that scenario. All sceptical scenarios that might otherwise have been of use in a closure argument for scepticism are either radical or non-radical, and so there is no sound closure argument for scepticism. If the sceptic really does face the general dilemma, the vat argument is a very strong defence against closure scepticism indeed, and I think that there is good reason to think that the sceptic does in fact face it. The second horn is supported by the fact that so long as a sceptical scenario is non-radical there will be large swathes of my empirical beliefs that remain untouched. There is no principled reason these beliefs, in conjunction with my sensory evidence, will not indicate that the scenario is false, and it is not at all obvious that there is a non-radical scenario where this is not so. Even if the sceptic succeeded in describing such a scenario and employing it in a closure argument she would not have reached the strong sceptical conclusion that none (or hardly any) of my empirical beliefs are justified; empirical beliefs I have that are compatible with the non-radical scenario would be outside the scope of the closure argument. If the sceptic cannot reach this strong conclusion we are still making progress against scepticism. In order to mop up the remaining justification the sceptic must come up with another non-radical scenario that I am not justified in believing to be false that is incompatible with the empirical beliefs that the first sceptical scenario was compatible with. This second scenario would then be used in a second closure argument that mops up the justification left over from the first closure argument. The prospects for this strategy are dim, to say the least. The sceptic would do better to attempt to grasp the first horn of the dilemma and argue that there is a radical sceptical scenario that the vat argument does not rule out. The sceptic may be encouraged here by the fact that the causal constraint on concept possession described in §2 is vague, so it is not obvious that it will rule out all radical sceptical scenarios. However, this point cuts both ways: as stated, it is not clear which scenarios the causal constraint will rule out, but it is not clear which scenarios it will rule in either. If the sceptic wants to show that there is a radical sceptical scenario that the causal constraint does not rule out she will have to sharpen up the constraint. This will not be easy, because the correct way of sharpening up the constraint depends upon the correct account of the conditions under which a subject has a particular concept. However, it is controversial what the correct account of concept possession is. If the sceptic must make claims about the correct account of concept possession before she can make her sceptical argument, the dialectical force of scepticism will be considerably weaker than that of the sceptical argument considered in §1, which relied only on a few simple and (prima facia, at least) plausible epistemic principles. My point here can be illustrated by considering an example of how the sceptic might attempt to grasp the first horn of the dilemma. Button describes the following scenario: The Vat Earth Scenario: Earth has a distant neighbour, Vat Earth. This is a planet whose only inhabitants are eternally envatted brains. There is no relevant causal link between Earth and Vat Earth, but it so happens that, for every brain on Earth, there is a brain on Vat Earth in exactly the same state, and vice versa.22 Because there is no relevant causal link between Vat Earth and Earth, there is no more reason to think that the Vat Earth brains will have the concepts necessary to describe their scenario than I would in Lifelong Envatment. However, Button asks us to alter the scenario, moving Vat Earth closer to Earth, and allowing Earthlings to visit Vat Earth. Earthlings look at the brains on Vat Earth. We are then to suppose that some Vat Earthlings and an equal number of visitors from Earth simultaneously think the following words: ‘if I were envatted and someone were looking at me right now thought the glass walls of my vat, I would want to be judged according to the language of [those outside the vat], in thinking “I am envatted”’.23 It may seem more plausible that, if I were a Vat Earthling, I could possess the concept of a brain and the concept of a vat in the altered scenario than in Lifelong Envatment. If I could, then perhaps the sceptic has found a radical scenario that is not vulnerable to the vat argument. But could I have these concepts in the altered scenario? Button (2013, p. 157) reports that he ‘boggle[s] at the attempt to start answering that question’, (emphasis in original). He ultimately wants to claim that there is no clear cut answer to this question. This idea is interesting, but for present purposes we only need the weaker claim that it is not obvious that the answer to the question is yes. If a sceptic wants to employ the Vat Earth Scenario in a closure argument she will have to provide an argument that I would indeed have the relevant concepts in the altered scenario. In order to provide such an argument she will have to make strong and controversial claims about concept possession. It is not clear that she will ever be able to produce convincing arguments for these claims. It is even less clear that these arguments could ever be convincing enough to make us take seriously the sceptical conclusion that they are meant, in conjunction with the rest of the sceptical argument, to imply. At any rate, the burden is now on the sceptic to provide such arguments before we start worrying that the sceptical conclusion is true. If I were a sceptic I would not want to be laden with such a burden. If the sceptic wishes to avoid entangling herself in a debate about concept possession one natural strategy is to describe a radical sceptical scenario in the abstract, thereby avoiding making use of concepts, such as the concept of a brain, that I would not have were I to be in that scenario. This is the sort of strategy that Wright (1992, p. 91) pursues when he argues that the vat argument cannot be used to rule out the ‘bare’ possibility that I am in a sceptical scenario.24 However, this strategy does not succeed. Let us imagine that the sceptic gives an abstract definition of a sceptical scenario by saying only that it is a scenario that meets the criteria for a sceptical scenario that can be substituted for SS resulting in a plausible closure argument, as these conditions were described in §1. That is, the scenario is described as follows: Abstract Scenario: My sensory evidence is the same as the sensory evidence that I currently have. However, all my empirical beliefs are false. To be clear: this is all the description of this scenario that we are given. Consider the concepts required in order to entertain Abstract Scenario: the concept of belief, of sensory evidence, of a scenario, etc. The sceptic claims that the causal constraint would not prevent me from having these abstract concepts if I were in Abstract Scenario. For one thing, the casual constraint is most plausible when it is applied to concepts of medium-sized dry goods, such as brains; it may not apply to abstract concepts, such as the concept of belief, at all. For another, even if the causal constraint does apply to abstract concepts there seems to be no reason to think that I could not have had the kind of causal contact with, for example, beliefs required to have the concept of a belief if Abstract Scenario is true. Thus we shall admit, at least for the sake of argument, that there is no vat argument that I would not be able to entertain Abstract Scenario if that scenario obtained. However, this retreat into abstraction will not save the sceptic. As Cross (2010) has argued, sceptical scenarios can be viewed as hypotheses that attempt to explain why I have the sensory evidence that I do. If the sceptical hypothesis is just as good an explanation as any non-sceptical hypothesis according to which my empirical beliefs are largely correct, then I am not justified in believing one of the non-sceptical hypotheses to be true. If however the sceptical hypothesis is not as good as one of the non-sceptical hypotheses, then I am justified in thinking it to be false. What makes for a good explanation is not entirely clear. However, it is clear that it is not a good explanation of why it is the case that p to say that p. This is not an explanation at all, it is simply a restatement of the fact that needs explaining. So, as Cross points out, whatever scenario the sceptic employs had better do more than simply restate that I have the sensory evidence that I do. Now consider the statement that I have the sensory evidence that I do because I am in Abstract Scenario. Abstract Scenario is described only as a scenario in which I have the sensory evidence that I currently have, and yet my empirical beliefs are false. The first conjunct simply re-states that I have the sensory evidence that I am trying to explain, and so it cannot be an explanation of that evidence. The second conjunct adds that one possible explanation of why I have this sensory evidence – the explanation that states that most of my empirical beliefs are true – is unavailable. Stating that one possible explanation of my sensory experiences is not true is hardly sufficient to make Abstract Scenario an explanation of those experiences. So Abstract Scenario is not equal as an explanation of my sensory experiences to the non-sceptical explanation that is provided by my empirical beliefs about the external world. Thus, my belief that Abstract Scenario is false is justified, and the sceptic cannot make use of Abstract Scenario in a closure argument. An analogy may help to illustrate the point. Imagine that a scientist carefully hypothesises about some data, and is then confronted by someone who does not reject the data, but claims that this hypothesis is wrong. Suppose that the scientist asks why the hypothesis is wrong. If no answer is forthcoming, then it does not seem that any argument has been provided that the scientist’s belief in her hypothesis is not justified. This is because no alternative hypothesis has been introduced that can compete with the scientist’s hypothesis as an explanation of the data. However, things are different if the answer consists of a detailed hypothesis that explains the data and is logically incompatible with the scientist’s own hypothesis. If this new hypothesis is at least as good an explanation of the data as the scientist’s hypothesis, then we may conclude that the scientist is not justified in believing the new hypothesis to be false. We may go on to conclude that the scientist’s belief in her own hypothesis is not justified. When the sceptic claims that my belief that Abstract Scenario is false is not justified, this is analogous to the scientist’s confrontation with someone who claims only that her hypothesis is wrong. In both cases, a good alternative explanation of the evidence has not been provided, and so the rival hypotheses can be dismissed. The sceptic may attempt to fill in the details of her story by talking, for example, about BIVs. By doing so she hopes to put herself on the same footing as someone who presents the scientist with a detailed and convincing alternative explanation of the data. However, once she retreats from abstraction the sceptic is back with the general dilemma described at the beginning of this section: either she talks about a radical sceptical scenario, in which case I can use the vat argument to rule it out; or she talks about a non-radical sceptical scenario, in which case I can appeal to my empirical beliefs to rule it out. 6. Conclusion I have argued that, if it works, the vat argument is of use as a defence against closure scepticism. First I showed that the usual argument that the vat argument cannot be used as a defence against closure scepticism fails. Because closure arguments that make use of Recent Envatment and Embodiment do not threaten the justification of all my empirical beliefs at once, I am able to appeal to my empirical beliefs to show that I am not in those scenarios. I then argued that no variation on the usual argument works either. The sceptic faces the general dilemma described at the beginning of the last section: either she uses a radical sceptical scenario, in which case I can use the vat argument to show that I am not in that scenario; or the sceptic uses a non-radical sceptical scenario, in which case I can appeal to my empirical beliefs to show that I am not in that scenario. The conclusion of this paper is conditional: if the vat argument works, it can be used as a defence against closure scepticism. I have not argued at any length that the vat argument is sound. Interestingly, very few people have claimed that it is not.25 Perhaps epistemologists have thought that it is not worth discussing whether or not the vat argument is sound because they think that the sceptic only needs to make use of non-radical sceptical scenarios. However, if I am right that the sceptic cannot make use of such scenarios then it would be well worth considering whether or not the vat argument works. If it does, it is a powerful weapon when directed against closure scepticism.26 Footnotes 1 Putnam intends the vat argument to undermine a position he calls metaphysical realism. There will be no discussion in this paper of whether Putnam succeeds in realising this aim. 2 This argument can be found in Smith (1984), Glymour (1982), Farrell (1986), Tymoczko (1989), Wright (1992), Christensen (1993), Forbes (1995), and Brueckner (1999). 3 I think that, at least on some conceptions of knowledge, much of what I have to say in this paper would be applicable to a sceptic who framed her argument in terms of knowledge. However, I do not have the space to argue this here. 4Sosa (1997) suggests that we should endorse a reliabilist account of justification in order to avoid scepticism. Pryor (2000) motivates a dogmatist account of justification in a similar way. 5 I am grateful to an anonymous Mind referee for raising this point. 6 In fact I think it is likely that, with some tweaks, the discussion in this paper could be framed in terms of a stronger concept of justification. 7 Similar reasons might be given for considering scepticism about justification, as we are in this paper, rather than scepticism about knowledge. One response to the sceptical claim that I have no knowledge is to accept it, but to continue to maintain that at least many of my beliefs meet (J), so it is reasonable for me to hold them. If this retreat can be made, one might think that scepticism about knowledge is not as worrying as it may at first have seemed. 8 See Byrne (2004, pp. 300-3) for discussion of the distinction between these two kinds of sceptic, and for a convincing argument that we need only be concerned with the second kind. Indeed, it is unclear what the first sort of sceptic would need a closure argument for, since she does not need a sceptical argument at all; she operates by demanding that I make an argument that my empirical beliefs are justified, and then attempts to pick holes in it. 9Brueckner (2010, pp. 280-305) argues convincingly that the prospects for a plausible version of the closure principle that does not support (C1) are dim. Someone who wanted to halt the sceptic here would probably have to give up on the closure principle altogether; see for example Dretske (1992) and Nozick (1981). But most people do not find this option attractive, and if the response to closure scepticism that I discuss in this paper is correct there is no need to take it. 10 Thus, one way to resist the closure argument is to deny that my evidence could be the same if I were in a sceptical scenario. See, for example, Williamson (2000, pp. 164-208). 11Wright (1991) discusses scepticism motivated by the idea that justification is iterative. 12 Foglin (1994) discusses scepticism motivated by both circularity and regress worries. 13 See Button (2013) and Wright (1992) for defences of the soundness of the vat argument. 14 This paragraph is a summary of an argument that appears in Putnam (1973, 1975). Putnam invokes this argument in support of the vat argument in his (1981, pp. 18-9). I believe that there are good reasons to think that most (perhaps all) plausible views of semantics designed to be compatible with the judgements we make about cases like the Twin Earth case will imply (V1), whether or not they are externalist. For example, the causal descriptivist views endorsed in Jackson (1998) and Lewis (1984) plausibly entail (V1). If this is correct, the dialectical appeal of the vat argument is significantly strengthened. However, this is not the place to develop this thought. 15 See Button (2013, pp. 118-23) for a particularly comprehensive defence of the first premise of the vat argument. 16Johnsen (2003) makes a similar objection. 17 Bruckner (2006) makes a similar reply to Johnsen (2003). 18Moore (1996, 2011) and Button (2013) argue that we should reject the idea that we should worry that we are in a sceptical scenario that we cannot entertain. Wright (1992, p. 93) can be read as suggesting that we should take the idea seriously. 19 It should be noted that both Wright and Christensen go on to consider the possibility that the vat argument has significance for issues other than closure scepticism. 20Brueckner (2010, pp. 174-7) suggests a similar strategy for mopping up the justification left over by the Recent Envatment argument. 21 My thanks to an anonymous Mind referee for raising this objection. 22 The description of this scenario is taken with some very minor stylistic alterations from Button (2013, p. 156). 23 I am here directly quoting a bit of speech that Button (2013, p. 157) puts into the mouth (as it were) of a Vat Earthling. 24 It should be noted that when Wright considers this strategy he is no longer considering a sceptical scenario of the sort that could be employed in a closure argument. Button (2013) also considers this strategy. 25 One exception is Johnsen (2003). I deal with Johnsen’s objection in §2. 26 I would like to thank Tim Button, Adrian Haddock, Bernhard Salow, Peter Sullivan, Crispin Wright, and two anonymous referees for Mind for comments and discussion. References Brueckner Anthony. 2010 . Essays on Scepticism . Oxford : Oxford University Press . Brueckner Anthony. 2006 . ‘Johnsen On Brains In Vats’ . Philosophical Studies ( 129 ): pp. 435 – 40 . Brueckner Anthony. 1999 . ‘Transcendental Arguments from Content Externalism’. In Stern R. (ed.), Transcendental Arguments: Problems and Prospects . Oxford : Clarendon Press . Button Tim. 2013 . The Limits of Realism . Oxford : Oxford University Press . Byrne Alex. 2004 . ‘How Hard are the Sceptical Paradoxes?’ Nous 38 ( 2 ): pp. 299 – 325 . Google Scholar CrossRef Search ADS Christensen David. 1993 . ‘Skeptical Problems, Semantical Solutions’ . Philosophy and Phenomenological Research 53 ( 2 ): 301 – 21 . Google Scholar CrossRef Search ADS Cross Troy. 2010 . ‘Sceptical Success’. In Oxford Studies in Epistemology , pp. 35 – 62 . Oxford : Oxford University Press . Dretske Fred. 1992 . ‘Epistemic Operators’ . Journal of Philosophy 67 : pp. 1007 – 23 . Google Scholar CrossRef Search ADS Farrell Frank. 1986 . ‘Putnam and the Vat-People’ . Philosophia 16 ( 2 ): pp. 147 – 60 . Google Scholar CrossRef Search ADS Fogelin Robert. 1994 . Pyrrhonian Reflections on Knowledge and Justification . Oxford : Oxford University Press . Forbes Graeme. 1995 . ‘Realism and Skepticism: Brains in a Vat Revisited’ . The Journal of Philosophy 92 ( 4 ): pp. 205 – 22 . Google Scholar CrossRef Search ADS Glymour Clark. 1982 . ‘Conceptual Scheming or Confessions of a Metaphysical Realist’ . Synthese 51 ( 2 ): pp. 169 – 80 . Google Scholar CrossRef Search ADS Jackson Frank. 1998 . ‘Reference and Description Revisited’ . Philosophical Perspectives 12 : pp. 201 – 18 . Johnsen Bredo. 2003 . ‘Of Brains in Vats, Whatever Brains in Vats May Be’ . Philosophical Studies 112 ( 3 ): pp. 225 – 49 . Google Scholar CrossRef Search ADS Lewis David. 1984 . ‘Putnam's Paradox’ . Australasian Journal of Philosophy 62 ( 3 ): pp. 221 – 36 . Google Scholar CrossRef Search ADS Moore Adrian. 1996 . ‘Solipsism and Subjectivity’ . European Journal of Philosophy 4 ( 2 ): pp. 220 – 33 . Google Scholar CrossRef Search ADS Moore Adrian. 2011 . ‘Vats, Sets and Tits’. In Sullivan P. , Smith J. (eds.), Transcendental Philosophy and Naturalism . Nozick Robert. 1981 . Philosophical Explanations . Cambridge Mass : Harvard University Press . Pryor James. 2000 . ‘The Sceptic and the Dogmatist’ . Nous 34 ( 4 ): pp. 517 – 49 . Google Scholar CrossRef Search ADS Putnam Hilary. 1973 . ‘Meaning and Reference’ . The Journal of Philosophy 70 ( 19 ): pp. 699 – 711 . Google Scholar CrossRef Search ADS Putnam Hilary. 1981 . Reason Truth and History . Cambridge : Cambridge University Press . Putnam Hilary. 1975 . The Meaning of ‘Meaning’. In Gunderson K. (ed.), Language, Mind, and Knowledge . Smith Peter. 1984 . ‘Could we be Brains in a Vat?’ Canadian Journal of Philosophy 14 ( 1 ): pp. 115 – 23 . Google Scholar CrossRef Search ADS Sosa Ernest. 1997 . ‘Reflective Knowledge in the Best Epistemic Circles’ . The Journal of Philosophy 94 ( 8 ): pp. 410 – 30 . Google Scholar CrossRef Search ADS Tymoczko Thomas. 1989 . ‘In Defense of Putnam's Brains’ . Philosophical Studies 57 ( 3 ): pp. 281 – 97 . Google Scholar CrossRef Search ADS Williamson Timothy. 2000 . Knowledge and its Limits . Oxford : Oxford University Press . Wright Crispin. 1992 . ‘On Putnam's Proof that We are not Brains-in-a-Vat’ . Proceedings of the Aristotlian Society 92 ( 1 ): pp. 67 – 94 . Google Scholar CrossRef Search ADS Wright Crispin. 1991 . ‘Scepticism and Dreaming: Imploding the Demon’ . Mind 100 : pp. 87 – 116 . Google Scholar CrossRef Search ADS © Thorpe 2017 This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

doi: 10.1093/mind/fzw029pmid: N/A

Abstract Suppose you’d like to believe that p (for example, that you are popular), whether or not it’s true. What can you do to help? A natural initial thought is that you could engage in Intentionally Biased Inquiry: you could look into whether p, but do so in a way that you expect to predominantly yield evidence in favour of p. This paper hopes to do two things. The first is to argue that this initial thought is mistaken: intentionally biased inquiry is impossible. The second is to show that reflections on intentionally biased inquiry strongly support a controversial ‘access’ principle which states that, for all p, if p is (not) part of our evidence, then that p is (not) part of our evidence is itself part of our evidence. Sometimes, the truth is bleak. When this happens, we might prefer not to know; we might even prefer to have false beliefs. For the same reason, however, when a bleak claim is false, discovering that would be extremely reassuring. So, when faced with a question which may have a bleak answer, we often feel ambivalent about inquiring. Whether we want to know the answer depends on what the answer is. Take an example. If my colleagues like me, I’d love to know. But if they don’t, I still want to believe that they do. The negative effects that knowing they don’t like me, or even just becoming less confident that they do, would have on my self-esteem and my ability to sustain reasonably productive relationships far outweigh any possible advantages such knowledge or doubts might generate. Given such preferences, what am I to do? A somewhat plausible initial thought is that I could inquire into whether my colleagues like me, but do so in a way that is more likely to yield evidence in one direction rather than the other. I could, for example, talk primarily to people whom I expect to have a high opinion of me if anyone does; and I could avoid reading the blogs and Facebook comments which I expect to be particularly harsh. Moreover, doing this does not seem to require that I deceive myself or exploit any straightforward kind of irrationality, for instance, some predictable failure to assess my evidence correctly. In this paper, I hope to do two things. The first is to argue that this initial thought is mistaken: intentionally biased inquiry is impossible. The second is to show that reflections on intentionally biased inquiry strongly support a controversial ‘access’ principle, which is a natural component of epistemological internalism:1 For all p, if p is (not) part of one’s evidence, one’s evidence entails that p is (not) part of one’s evidence.2 I will begin, in §1, by precisifying and tentatively defending the claim that intentionally biased inquiry is impossible. I will then, in §2, turn to consider influential alleged counterexamples to the access principle, showing that, if they were genuine, they would support strategies for biasing one’s inquiries that obviously do not work. Finally, in §3, I will explain the more abstract connection between the two topics, by formalizing both questions in a Bayesian framework and showing that the access principle and the impossibility of intentionally biased inquiry stand and fall together. This strengthens the objection against access deniers, by showing that the problems we discovered are unavoidable consequences of denying the access principle rather than irrelevant issues arising from the particular examples. And it strengthens the initial defence of the impossibility of intentionally biased inquiry, by showing that strategies which exploit alleged counterexamples to access, strategies we previously saw to be patently absurd, are in fact the most promising ones. 1. Intentionally biased inquiry We are interested in questions for which our desire to know the truth depends on what the truth turns out to be. If intentionally biased inquiry were possible, it would be natural to use it in these cases. We have already seen one example with this structure: I want to know about my popularity only if I’m popular; and so I prefer receiving evidence that my colleagues like me whether or not they actually do. And other examples aren’t hard to come by. I want to know whether I have such-and-such a fatal illness only if I don’t; if I do have it, I’d rather live out my final days in blissful ignorance. Again, then, I prefer evidence reassuring me that I am in good health regardless of whether I am. In cases like these, intentionally biased inquiry would be appealing: I would like to inquire into the matter in a way that I know will only, or at least predominantly, yield evidence in a particular direction. But can I? Some philosophers think I can. Parfit, for example, writes:3 [W]e might cause ourselves to have some beneficial belief by finding evidence or arguments that gave us strong enough epistemic reasons to have this belief. This method is risky, since we might find evidence or arguments that gave us strong reasons not to have this belief. But we might reduce this risk by trying to avoid becoming aware of such reasons. If we are trying to believe that God exists, for example, we might read books written by believers, and avoid books by atheists. (Parfit 2011, p. 421) I will argue that, despite this initial appearance, intentionally biased inquiry is not possible. But before I do that, I will need to make more explicit what exactly would count as ‘intentionally biased inquiry’. 1.1 What is intentionally biased inquiry? I will think of inquiry as a process of evidence collection, to be characterized by the kind of evidence it yields rather than the opinions it results in.4 This means that we can immediately set aside some otherwise plausible examples of intentionally biased inquiry. It is undeniable that I can exploit known biases in my perception or reasoning to set up an inquiry that is more likely to leave me with one belief rather than another. For example, I might know that, if I were to print off the case for p in a clean, bold font on high-quality paper, and the case against p in Comic Sans, I would be more likely to believe p after reading both. But this is only because I would also be more likely to believe p even when this wasn’t supported by the total evidence; this printing manoeuvre thus doesn’t count as biasing my inquiry, since it doesn’t bias the evidence I receive.5 Similarly, if I exploit arational changes in my ‘standards’ or ‘inductive policies’ for assessing evidence (if these are possible6), I might succeed in biasing my future beliefs, this time without exploiting irrationality. But, again, this would not qualify as intentionally biasing my inquiry, since it doesn’t involve biasing what evidence I receive. This already makes clear that characterizing inquiry in terms of evidence, rather than beliefs, is a significant decision; and its significance will only grow in §1.2, when I argue that strategies such as reading selectively also bias at most one’s verdicts, and not one’s evidence. But it is the right decision. For if we characterize inquiry in terms of the attitudes it generates, it is unclear what distinguishes biasing one’s inquiries from cruder methods of manipulating one’s beliefs, such as hypnosis or brainwashing. Admittedly, most of us don’t have ready access to these cruder strategies. But the appeal of biasing one’s inquiries seems to be due less to greater practicality and more to the thought that it is less unsavoury, being quite consistent with only forming beliefs in response to evidence—or, to use Parfit’s phrasing, with ‘always respond[ing] rationally to any epistemic reason or apparent reason’ (Parfit 2011, p. 421). When is an inquiry, a process of evidence collection, biased towards p? Perhaps the most obvious case is when the inquiry is a sure-win investigation: the total evidence gathered in the investigation is guaranteed to be evidence for p. Slightly more generally, an inquiry still seems biased when it is what Titelbaum (2010) calls a no-lose investigation: it is designed so that the total evidence gathered might be evidence for p, but is guaranteed not to be evidence against p. Even this, however, is insufficiently general—as is clear from Parfit’s discussion, it can be enough to reduce, rather than eliminate, the risk of evidence against p. In particular, when an inquiry is very likely to yield strong additional evidence for p (that is, evidence that would significantly raise p’s evidential support) and has only a small chance of yielding at most quite evidence against p (that is, evidence that would lower p’s evidential support at most by a little bit), it still looks like an investigation skewed in p’s favour. The natural way of making this idea precise uses the idea of the expected value of a function V; this is the weighted average of all the values V might take, each weighted by the probability that it will take that value. Since we are interested in the rise and fall of p’s evidential support, our choice of V should measure the extent to which the evidential support for p at the end of inquiry exceeds the evidential support for p at the start of inquiry (so V will take a negative value when the inquiry results in a decrease in the support for p). The obvious such V simply subtracts the initial evidential support from the later evidential support; the expected value can then be calculated by assigning probabilities to the various values (positive and negative) which this difference might take. We can then say that an inquiry is biased towards p if the expected value of the difference is positive, biased against p if it is negative, and unbiased if it is zero. No-lose investigations count as biased by this definition, since they might result in a positive difference (when they yield evidence for p), but are guaranteed not to result in a negative one (since they can’t yield evidence against p), so that the expected difference must be positive. By contrast, an investigation that is simply guaranteed to conclusively settle whether p looks as though it will be unbiased.7,8 We now know what it is for an inquiry to be biased. Can an agent ensure that her own inquiries are biased in this way? We already saw that one obvious kind of approach – the kind where the agent exploits known irrationalities in how she forms beliefs—won’t qualify on our account. There remain two other types of strategies I want to set aside. The first are cases in which the agent’s current actions themselves provide evidence about p, as when p is ‘I develop lung cancer at some point in my life’ and the agent can decide to smoke. The second are cases in which the agent expects to lose relevant information in the course of the investigation, as when our agent asks a friend to tell her a year from now that she is popular, knowing that she will forget having given these instructions. These ways of biasing one's inquiry may succeed, but they seem intuitively very different from the one Parfit identifies.9 When I exploit the evidential relevance of my own actions, there is nothing weird about my inquiry (as opposed to the topic I am investigating). And when I exploit information loss, my biasing only succeeds because, at some point or another, I lack important information about what is going on. I will thus set these strategies aside, and restrict ‘intentionally biased inquiry’ to cases in which an agent succeeds in biasing her investigations in intuitively ‘open-eyed’ ways. 1.2 Intentionally biased inquiry is impossible With this sharpening of the question in mind, we can revisit the issue of whether intentionally biased inquiry is possible. Parfit’s brief discussion makes it sound straightforward. Suppose I can choose between reading a creationist book and a biology textbook; then surely I can bias my inquiries against evolutionary theory by choosing the creationist one. On reflection, however, this thought starts to become less obvious. For it might well be that the facts I encounter in the creationist book are (even) less impressive than I expected; if this is the case, my epistemic position with respect to evolutionary theory isn’t compromised, and may even be strengthened. Similarly, reading the biology textbook might well give me evidence against evolutionary theory, if the facts appealed to there turn out to be less conclusive than I thought they would be. Thought about in this way, it starts to seem plausible that each book will only give me additional evidence in the ‘expected’ direction if the facts presented there are actually more compelling than anticipated; and, of course, it is hard to see how I could think that to be particularly likely. How can we reconcile these two lines of thought? It’s a familiar observation that whether a proposition E is evidence for or against another proposition H often depends on what background information is available. And relevant background information can, amongst other things, include facts about how the evidence has been selected. Suppose, for example, that you are sitting on a jury. The prosecution has just finished making its fairly compelling case for the defendant’s guilt. Nonetheless, the rational thing for you to do at this stage is to keep an open mind. After all, you knew all along that they were only going to bring up the incriminating facts that present the defendant in a particularly negative light. And the facts they did present were no more compelling than you would expect from such one-sided advocacy. The evidence you received would, against ordinary background information, favour the defendant’s guilt. However, given what you know about how the facts you were exposed to were selected, they do not favour his guilt against your background information. Everything thus depends on the rebutting evidence which the defence is about to introduce. You can be pretty confident that, against ordinary background information, what the defence will present will be evidence of innocence. But, if that evidence ends up being weaker than you are currently expecting, you will (rationally) come to the conclusion that the defendant is probably guilty. There is thus no guarantee that what will be presented will be evidence of innocence against your background information. The case of choosing which books to read is exactly analogous. I expect the creationist book to contain facts which, against ‘ordinary’ background information, tell against evolution; that is to say, I think it likely that someone with no background expectations would be rational to be less confident of evolutionary theory after reading the creationist book than after reading the biology textbook. However, this doesn’t mean that I expect the creationist book to contain facts which, against my background information, tell against evolution. This is because I have expectations, and, as we saw above, these expectations change the evidential impact of the information I would obtain by reading the book. In particular, if I am confident that a book will contain facts of a certain kind—facts which are quite hard to account for in evolutionary terms—then I must already be confident that there are facts of that kind; so my current view about evolution should already ‘factor in’ these anticipated facts. Finding out that the book doesn’t contain facts of that kind (they are all easier to account for than I expected) would then suggest that I was ‘factoring in’ difficulties that, as it turns out, aren’t genuine; in this way, the facts I learn favour evolution (relative to my background information), despite highlighting its problems. What matters to our success in biasing our inquiries is what the new evidence will support against our own background information. So these considerations show that, pace Parfit, it isn’t obvious that we can intentionally bias our inquiries; the claim only looks obvious if we mistake it for the truth that one can manipulate one’s inquiry to make its outcome favour p relative to ordinary background information.10 In addition, the considerations suggest an explanation for why intentionally biasing one’s inquiries might be impossible. The evidential impact of a proposition on p depends on our (rational) expectation that it is true, and that we would learn it, if p is true. But those expectations depend on what we know about the set-up. It is no surprise that the prosecution can find some facts that make the defendant look bad; we would expect them to be able to do this even if he is innocent. Similar things apply to the creationist literature. When we try to bias our inquiry into p by affecting what evidence we might find, we are automatically changing what we should expect, and are thereby changing what counts as evidence for or against p. In other words, knowing of the bias (as we must if the biasing is intentional and ‘open-eyed’) undermines its effects. This dynamic is quite familiar with a question far more important than the controversy over evolution: the question of what others think of us. We may try to nudge others into saying nice things; but we also know that, as the nudging becomes more obvious (or is targeted at a more receptive person), the nice words will become less meaningful and their absence more painful. It doesn’t take much reflection to conclude that if we weren’t so good at selectively forgetting how hard we tried, and how often we failed, the nudges would be pointless. Despite this suggestive explanation, however, we don’t yet have a general argument that intentionally biased inquiry must be impossible. But once we have disarmed the thought that it’s obviously possible, this claim does look rather attractive. We experience questions like those concerning our popularity as putting us into a bind: we do not know how to inquire into them in a way that will get us what we want, and so we inquire, if at all, only reluctantly. The impossibility of intentionally biased inquiry would be an excellent explanation of this bind. Even if, say, you had a very loyal friend who knows you and your beliefs extremely well, and who also knows how popular you are, you couldn’t use him. Asking him to tell you if you’re popular, and say nothing if you’re not, is obviously pointless. And more complicated schemes (such as having him expose you only to carefully selected books) look as though they too would work only if you somehow failed to properly think through the information you would receive. Your efforts to bias your inquiries would keep undermining themselves. This is not a knock-down argument. One might remain hopeful that, with enough ingenuity, we will think of better strategies—intentionally biased inquiry might not be impossible, just really difficult. In §2, I will elaborate some strategies which, according to certain ‘externalist’ accounts of evidence, should succeed. But it will, I think, be intuitively clear that they would fail. In §3, I will argue that, given a Bayesian theory of evidential support, these ‘externalist’ strategies are really the only ones that stand a chance. With these additional pieces in place, we will then have a kind of impossibility proof to bolster the less conclusive reflections just presented.11 2. The Access Principle I have been building a case that intentional and open-eyed biasing of one’s own inquiry isn’t possible. Epistemologists rarely discuss this issue;12 this is a significant oversight, since it turns out to be tightly connected to the debate between epistemological internalism and externalism.13 A natural component of internalism is the access principle: The Access Principle: For all p, if p is (not) part of one’s evidence, one’s evidence entails that p is (not) part of one’s evidence. For internalism says, very roughly, that we can always work out which of our beliefs are justified (that is, supported by our evidence) merely by reflecting on what we’ve already got. But if that is to be true, then what we’ve already got (namely, our evidence) had better tell us what our evidence is. In other words, the access principle had better be true.14 It will be helpful to separate the access principle into the positive and negative access principles: Positive Access: For all p, if p is part of one’s evidence, one’s evidence entails that p is part of one’s evidence. Negative Access: For all p, if p is not part of one’s evidence, one’s evidence entails that p is not part of one’s evidence. Each of these two principles is controversial. Williamson’s (2000, ch. 9) view that one’s evidence consists of all and only the propositions one knows, abbreviated as E = K, helps to bring this out, since each of the corresponding ‘introspection’ principles for knowledge faces well-known objections.15 However, it should be clear that simply rejecting E = K does not make the principles unproblematic. For the very same considerations that made the ‘introspection’ principles problematic for knowledge can also be used to argue directly against the access principle for evidence. In the next two subsections, I will consider two different externalist arguments of this kind that seem, on first sight, quite convincing: one is based on an alleged epistemic asymmetry between ‘good’ and ‘bad’ cases (§2.1), the other on our limited discriminatory capacities (§2.2). I will sketch how these considerations motivate concrete (though perhaps oversimplified) counterexamples to the access principle; I will then show that if these cases really were counterexamples to the access principle, someone could exploit them to intentionally bias her inquiry in ways that obviously don’t work. This refutes the (alleged) counterexamples, and thereby casts some doubt on the considerations which motivated them. It thus constitutes an indirect defence of the access principle. More importantly, however, it sets the scene for §3, where I draw out the more systematic connection between the access principle and the possibility of biasing one’s inquiry, which, I argue, supports both the access principle and our tentative conclusion that intentionally biased inquiry is impossible. 2.1 Good and bad cases The first kind of example specifically targets the negative access principle. We propose a ‘good case’ and a ‘bad case’ such that (i) in the good case, my evidence entails that I am definitely in the good case, but (ii) in the bad case, my evidence leaves open whether I am in the good case or the bad one. I will thus be in the bad case if and only if it isn’t part of my evidence that I am in the good case. It follows that negative access must fail in the bad case. For if negative access held in the bad case, that case would yield the evidence that it isn’t part of my evidence that I am in the good case. But this piece of evidence (combined with the description of the cases) entails that I am in the bad case, contradicting the stipulation that my evidence in the bad case leaves open that I might be in the good case. One powerful motivation for accepting such examples arises from reflection on sceptical scenarios. It is part of my evidence that I have hands; after all, I can see that I have them just by looking, and denying that seeing yields evidence quickly leads to scepticism. A (handless) brain in a vat with my exact experiences could not have the corresponding claim as part of its evidence, since the corresponding claim is false.16 Yet the brain in a vat is presumably in no position to tell that it lacks this evidence: if it were, it could conclude that it is in a very unusual situation, and the tragedy of the brain’s predicament is exactly that it is in no position to figure this out. If one takes this position regarding me and the brain in a vat, there is pressure to take a similar line in more ordinary cases. Although the particulars won’t matter, I will take the following as representative: I can get conclusive evidence that a red wall is red by looking at it in favourable circumstances; but if the wall is actually a white wall lit by a red light, my only evidence will be that it appears red. In particular, in the case where I am being fooled, my evidence does not allow me to work out that ‘the wall is red’ is not itself part of my evidence.17 To isolate the structural feature, it might help to consult this diagram of the situation: Here, the dots represent the possibilities that might (for all your initial evidence entails) obtain, while an arrow from w to represents that is left uneliminated by the evidence to be obtained if w is the case. Reflecting on intentionally biased inquiry reveals problems in this way of thinking about the case. Consider again my interest in whether people like me. I would like my evidence to support that they do, whether or not people actually do like me. Normally, we think that this puts me in a bind when it comes to inquiring into the matter, even if I have a reliable and cooperative source I could consult. But if the above verdicts about the wall are correct, this is an illusion. What I should do is the following. I should find a white wall, and ask my friend (who knows about my popularity) to paint it red if I am in fact popular, and shine a red light on it otherwise. Once my friend has finished setting things up, I will take a peek. If people like me, I will see a red wall, and will thus receive conclusive evidence that they do. And if I am unpopular, I will get no evidence at all, and, in particular, no evidence confirming my unpopularity. This means that the strategy described may give me evidence for popularity, and certainly won’t give me evidence against it; it is a no-lose investigation. Since I want to be more confident that I am popular, and increasing what evidence I have for my popularity seems a good way of achieving this goal,18 it seems clear that I should initiate the strategy.19 This conclusion is obviously absurd: the procedure just outlined is no way out of the bind we have been discussing. It must, therefore, have been a mistake to think that if only the circumstances were favourable, looking at the wall would tell me more about its colour than that it appears red. But if that was a mistake, then so was the thought that this case is a counterexample to negative access. Of course, it is a deep puzzle how to accept this without falling into scepticism. But that is not a puzzle I can resolve in this paper. Someone convinced by the counterexample to negative access might respond instead that the example’s structure changes when I initiate the strategy described above: while in an ‘ordinary’ case the fact that the wall is red can become part of my evidence when I look at it in favourable circumstances, that fact can never become part of my evidence when I look at the wall my friend prepared.20 If there were such a change, we could say both that the attempt at setting up a no-lose investigation fails and that an ordinary case of looking at a wall is, nonetheless, a counterexample to negative access. But postulating such a change is theoretically unsatisfying. We can fill in the example so that it is highly unlikely, given my background information, that I am unpopular (and hence that the lighting would be misleading); and we can also postulate that, in fact, the possibilities in which I am unpopular are extremely ‘remote’ and ‘much less normal’ than the actual ones. It is then unclear what is supposed to distinguish my situation when I look at the wall my friend prepared from my situation in an ordinary case of judging the colour of a wall without verifying the lighting.21 And even if we waive this worry, it still seems to me that this style of response addresses only the symptoms, not the disease. For, according to this line of response, an ordinary case of looking at a wall is still a no-lose investigation; not, admittedly, into whether the wall is red (since it might look some other colour), but into whether the wall is the colour that it looks. After all, if the wall’s colour is what it looks to be, we get conclusive evidence that it is; and if the wall’s colour is not what it looks to be, we get no evidence either way. Using this (alleged) fact to set up a no-lose investigation first into whether the wall is red (by ensuring that I know beforehand that it will look red) and then into whether I am popular (by correlating redness with my popularity) dramatizes just how weird a claim this is. But it is, I think, primarily a dramatization of something whose weirdness we can also appreciate directly. For these two reasons, a response that focuses on the unusual circumstances of the inquiry described doesn’t seem promising. To see how robust our problem is for alleged examples of the good case/bad case structure, it’s worth looking at how matters play out in the more intuitive cases recently proposed by Lasonen-Aarnio (2015).22 The basic idea behind her examples is that, as she puts it, it’s not unusual that ‘coming across a fake, one can mistake it for the real thing, but when one sees (feels, hears, tastes, smells) the real thing, one can tell that it is not a fake’ (Lasonen-Aarnio 2015, p. 160). Here’s one such case (not quite the one used by Lasonen-Aarnio, but similar in spirit): you’re meeting a friend from school that you haven’t seen in many years. As you sit in the agreed coffee shop, several people walk in who look familiar enough for you to think they might well be that friend. None establish eye contact though, so you stay seated. Eventually your friend walks in and, despite the significant changes she’s undergone, you recognize her immediately. At least at first sight, this suggests a similar structure to the case of the red wall: seeing your friend (the good case) yields conclusive evidence that it’s her, while seeing the stranger (the bad case) gives you no evidence either way. Because the case has the same structure as that of the red wall, it can be exploited in exactly the same way. I ask my helper to present me with my friend from school if I’m popular, and with a somewhat similar looking stranger if I’m not. (The person will then leave before I have a chance to talk to her.) If the above account were correct, this should ensure that I have set up a no-lose investigation. But, intuitively, it is clear that I haven’t: unless seeing the person triggers a powerful feeling of recognition, and if I’m not popular it won’t, I will have received evidence that I’m not popular after all. Yet Lasonen-Aarnio’s thought about cases like that of the coffee shop also seems right. What is going on here? In the cases where the intuition she draws on is clearest, I don’t know beforehand that I will definitely recognize the real thing. For example, I don’t know beforehand that seeing my friend will trigger a powerful sense of recognition; for all I know at the outset, she will only look vaguely familiar. I also know little about whether a stranger will strike me as entirely unknown or as vaguely familiar, though I do know that a stranger would not trigger a powerful sense of recognition. There are thus (at least) four possibilities for what might happen when someone enters the coffee shop: it could be my friend, and I have a powerful sense of recognition; it could be my friend, and she looks vaguely familiar; it could be a stranger who looks vaguely familiar; it could be a stranger who strikes me as entirely unknown. When I see my friend and have a powerful sense of recognition, I can rule out all but the first of these, and thus get conclusive evidence that it is my friend. When I see a familiar looking stranger, I can rule out all but the middle two, and thus don’t get much evidence about whether the person is my friend or a stranger. But all of this is consistent with my always knowing exactly what evidence I have; in particular, when I see a familiar looking stranger, I know that my evidence doesn’t entail that I’m faced with my friend. To get a counterexample to negative access, we would need to argue that the situation remains unchanged if I know beforehand that I will definitely recognize my friend when I see her. For with that background knowledge in place, negative access would allow me to reason from ‘My evidence doesn’t entail that this is her’ to ‘It isn’t her’, and it was supposed to be counter-intuitive that I can reach this conclusion. But if we imagine my having the background knowledge in question, that reasoning actually seems attractive: if I know that I would recognize my friend if I saw her, it’s perfectly legitimate to reason from ‘That person only vaguely looks like her’ to ‘That’s not her’.23 This is well brought out by the attempt to use the case to set up a no-lose investigation. To do this, I have to think that I would definitely recognize my friend when I see her, since otherwise seeing someone who only looks vaguely familiar is evidence that I am unpopular (since I’m guaranteed to see someone like that if I’m unpopular, and less likely to see such a person if I’m popular). But once we make this assumption explicit, the intuition the example relied on disappears—or, at least, has no additional force over and above the anti-sceptical intuition some of us have even in cases like that of the red wall. 2.2 Limited discriminatory capacities Our second class of examples targets the positive access principle as well as the negative one. Williamson (2000) has used considerations stemming from limited discriminatory capacities and margins for error to argue for the existence of such cases; I will focus here on an example proposed in Williamson (2011), which has received sympathetic discussion even by philosophers not otherwise committed to Williamsonian epistemology.24 The basic case is as follows. Imagine that you are faced with an unmarked clock, with a single hand that can point in any one of 60 slightly different directions. Your ability to discriminate where it is pointing is good, but not unlimited. If you are to be reliable in your judgements, you need to leave yourself a margin of error. For example, if the hand is in fact pointing at 53 minutes, you can reliably judge that it is pointing somewhere between 52 and 54 (inclusive), but are unreliable about claims stronger than that. The same is true of every other position the hand could be in.25 It is somewhat natural to identify your evidence with the strongest claim about the hand’s position which you can reliably get right.26 But this means that the total evidence propositions we obtain in the various scenarios partially overlap. If the hand is in fact pointing at 53, my evidence will be that it is within [52, 54]; and if it is pointing at 52, my evidence will be that it is within [51, 53]. Each scenario yields evidence which is compatible with the other, and yet they yield different evidence. Again, it might help to present this in a diagram: It isn’t hard to see why this case involves a violation of the positive access principle. Given the above description, there is a 1–1 correspondence between positions of the hand and what evidence I have.27 So, if I know the set-up, the truth about what evidence I have entails the truth about where exactly the hand is pointing. But my evidence isn’t good enough to single out the hand’s position: after all, I can’t reliably do so (even if I do know the set-up), and this isn’t a failure of rationality. So positive access must fail. To see why this description of the case is problematic, however, let us return to the topic of my popularity. My friend knows whether I’m popular; and I would like to have additional evidence that I am, regardless of whether it is true. So I construct an unmarked clock of the kind Williamson describes, and I ask my friend to set the hand in the following way: if people like me, he will set it to 53; if they don’t, he will flip a coin to decide whether to set it to 52 or to 54. Having given the instructions, I know that the clock will be set somewhere between 52 and 54, so the situation is represented by this simpler diagram: Next, I take a look. If people actually like me, the hand will be set to 53, and so my evidence will only tell me that it is somewhere between 52 and 54, which I knew already. So if people like me, I get no new evidence. But if people do not like me, it will be set either to 52 or to 54. Suppose it is set to 52; then my evidence will allow me to rule out that it’s set to 54, since 54 is far enough away from the actual setting. But I knew that there was a fifty-fifty chance that it would be set to 54 if people didn’t like me. So seeing that it isn’t set to 54 gives me some evidence that I am popular. Moreover, my evidence cannot discriminate between the hand being set to 52 and its being set to 53, so that I get no evidence against my being popular. So, if the hand is set to 52, I will get evidence that I am popular; by similar reasoning, I will also get such evidence if the hand is set to 54. So if people don’t like me, I will get evidence that I am popular. Again, I have successfully set up a no-lose investigation into my popularity.28 This method may be slightly less satisfying than the one involving the wall. Both are no-lose investigations: I might get evidence that I am popular, and run no risk of getting evidence that I am not. But in the clock case, I will get evidence for my popularity only if it is misleading; if I actually am popular, I will get no evidence at all. Fortunately, I don’t care too much. Perhaps added evidence that I am popular is better when it’s pointing me towards the truth; but given the desirability of self-confidence, I welcome it even when it is misleading. This evaluation, however, is absurd. I cannot boost my evidence for my popularity in the way just described. The unmarked clock is no more a way out of my bind than the wall was. That much is obvious; what is surprising is that this is inconsistent with the Williamsonian judgements about the clock. The culprit, I think, was to identify my evidence with the strongest claim I am reliable about, given the actual setting, which was the move that gave rise to the failures of the positive (and negative) access principle we were exploiting. But what else could my evidence be in the scenario described above? One possibility, following Stalnaker (2009), might be to say that we need to distinguish scenarios, not simply by the position of the hand, but also by my ‘best guess’ about its position.29 Plausibly, my best guess won’t always match the actual position (that’s just what it is, we might say, for my discriminatory capacities to be limited), so that different hand positions will sometimes yield the same best guess and the same hand position will sometimes yield different best guesses. In fact, it is now natural to understand talk of ‘margins for error’ as talk about the maximum distance between my best guess and the actual hand (under ordinary conditions). Reflections on limited discriminatory capacities give no obvious reason to think that I can’t always tell what my best guess is—after all, these guesses are forced to take discrete values, and might be able to feature in ‘transparent’ inferences in a way in which details of my perceptual representations arguably do not. So if my evidence is determined by my best guess, rather than by the actual position of the hand, our previous reason for taking the case to violate the access principle disappears.30 Moreover, for exactly the same reason, the strategy for setting up a no-lose investigation will no longer succeed. For when the clock is set to 52, there is a good chance that my best guess will be that it is set to 51. But, since I know that my margin for error is less than 2 (I designed the clock to make sure it would be), and I also know that conditions are ordinary (if I didn’t know this, I could never draw any conclusions about the actual position of the hand, and hence about my popularity), this is compelling evidence that the clock isn’t set to 53. Since I also know that my friend would have set the clock to 53 if I were popular, it is compelling evidence that I am unpopular. Far from being a no-lose investigation then, the inquiry described might well end up establishing my unpopularity.31 2.3 Beliefs, rationality, and evidence I have argued that certain cases which supposedly illustrate failures of the access principle shouldn’t be thought to do so, since they would otherwise vindicate strategies for intentionally biasing one’s inquiries that obviously could not succeed. In discussing these cases, I have moved freely between a desire to be more confident that I am popular and a desire for evidence of my popularity, on the assumption that (since I’m fairly rational) these go together. Counterexamples to access, however, might be thought to put pressure on this assumption. Arguably, when one is in an access-violating scenario, one isn’t rationally required to become more confident in p even when one receives evidence for p.32 Alternatively, even if one is rationally required to become more confident in response to evidence, one’s doing so might still be entirely unreasonable, manifesting a disposition not generally conducive to conforming one’s confidence to the evidence.33 Either of these claims might allow us to explain why agents like us are unlikely to raise our confidence in response to the evidence we receive in these cases. The externalist could then accommodate the observation that the clock and wall strategies for boosting one’s evidence are an absurd way of pursuing one’s goals, yet maintain that this is not because they don’t yield evidence, but rather because that evidence won’t yield the desired beliefs in agents like us. Whatever the appeal of such a strategy in response to other objections to externalism, it will not solve the problem presented here. For I can use the kinds of examples we have been discussing to build not just no-lose investigations but also sure-win investigations: ones that are guaranteed to give me evidence that I am popular no matter what. And if I have set up a sure-win investigation, I will know at the end of the investigation that I just received additional evidence of popularity. Moreover, this knowledge need not itself be unreasonable, since it can be the result of perfectly ordinary belief-forming dispositions. This makes it hard to see how failing to raise my credence could be reasonable or rationally permissible in such a situation. Yet the strategies for biasing one’s inquiries seem equally absurd in these only slightly more complicated cases. The simplest sure-win investigation combines the strategies discussed in the clock and wall cases: I ask my friend to arrange both a wall and a clock in line with the instructions described above, and then look at one and then later at the other. This is a sure-win investigation. For either I am popular or I am not. If I am, looking at the wall will yield evidence that I am popular, and looking at the clock will yield nothing. If I am not popular, looking at the wall will yield nothing, but looking at the clock will yield evidence that I am popular. Either way, the total effect will be additional evidence that I am popular. So, since I know the set-up, I will know at the end of inquiry that I just received additional evidence of popularity. Since my knowledge about the set-up can be entirely reasonable, the same will be true about my knowledge at the end of inquiry that I just received additional evidence of popularity. But if I know that my evidence supports my popularity at least to a specific degree x, and that knowledge is not itself unreasonable, then I would surely be both irrational and unreasonable not to have at least the corresponding level of confidence in the claim that I am popular. If that is true, however, I would be irrational and unreasonable not to become more confident of my popularity after looking at both the clock and the wall.34 The combined case just described is effective against anyone who is sympathetic to both the wall and clock cases. But the epistemological motivations for these two cases are quite different, and one might be inclined to accept one without accepting the other. So it is worth noting that we only need one kind of case to set up a sure-win investigation. Let us look first at the cases motivated by our limited discriminatory capacities. The original instructions in the clock case were designed to generate no evidence either way when I’m popular and evidence that I’m popular when I’m not. But they are easily adapted to provide evidence that I’m popular when I’m popular and no evidence either way when I’m not. The new instructions to my friend will simply be to set the hand to 52 or 53 if I am popular (to be decided by a coin flip), and to 51 or 54 if I am not. If I am popular, the evidence I’ll get will then allow me to rule out exactly one of the possibilities in which I’m not, and will hence generate evidence of my popularity. And if I’m not popular, the evidence will let me rule out one possibility of either kind, and will thus leave the initial probabilities unchanged. I will thus get evidence for popularity if I’m popular, and no evidence at all if I’m not. Alternating this strategy with the original one, I can ensure that I’ll receive evidence of my popularity no matter what; I can thus know, at the end of the process, that I’ve just received evidence that I am popular (though I won’t know what exactly that evidence was). Let us next look at the cases motivated by the thought that the good case yields strictly more evidence than the bad one; this time I will construct a case which, just by itself, allows for a sure-win investigation. If you liked the wall case, you should also like the following case: when I hear a bird call nearby, I receive conclusive evidence that there is a bird nearby; this is true even though I cannot distinguish bird calls from the noises produced by sophisticated bird flutes. And, plausibly, my abilities to tell red walls by sight and nearby birds by their sound are quite independent: one of them malfunctioning should not prevent the other from yielding the evidence it usually does. If that is right, I can give my friend the following instructions. If I am popular, he is to present me with a red wall and a genuine bird call; if I am unpopular, he is to toss a coin to decide which of these to replace with the corresponding illusion. There are thus three possibilities consistent with my knowledge of the set-up; and the evidential relations amongst them are as represented in this diagram:35 What will happen to my evidence about my popularity? If I am popular, I will get conclusive evidence that I’m in Red/Bird, and thus that I am popular. If I am not popular, there are two possibilities. One is that I am in White/Bird; in that case, my evidence will rule out Red/Flute and nothing else. The other is that I am in Red/Flute; my evidence will then rule out White/Bird and nothing else. So if I’m unpopular, my evidence will eliminate exactly one possibility in which I am unpopular and nothing else, meaning I get evidence that I am popular. So I will get evidence that I am popular whether I am popular or not. Afterwards, I will thus not only have more evidence of popularity but also know that I do. Explaining the absurdity of the strategies described in §§2.1–2.2 by forcing a gap between evidence and rational (or reasonable) belief has some initial appeal. It is not entirely unnatural to think that, in some sense, one shouldn’t become more confident of one’s popularity even if one just received evidence for it when one doesn’t (and isn’t in a position to) know that one received such evidence. But we have just seen that the motivations driving the initial cases can be used to generate cases in which one not only receives evidence for one’s popularity but knows that one does. Yet the strategies described in these cases seem equally absurd. The attempted alternative explanation of the absurdity thus fails. 3. The systematic connection In the paper so far, I have done two things. I have given prima facie reasons to be sceptical about the possibility of intentionally biased inquiry. And I have shown that we can cast doubt on otherwise compelling (if somewhat oversimplified) counterexamples to the access principle by showing that, if genuine, they would enable us to intentionally bias our inquiries in highly counter-intuitive ways. What I haven’t done so far is establish a systematic connection between access and intentionally biased inquiry. This gives rise to questions that challenge the force of the arguments. Can every counterexample to the access principle be exploited to bias one’s inquiries? If not, the problems with the particular cases discussed might stem from idiosyncratic features of, or simplifying assumptions about, those cases, and so need not be taken to support the access principle more generally. Could there be ways of biasing one’s inquiries that do not exploit failures of the access principle? If not, the fact that the intentionally biased inquiry made possible by access failures is so counter-intuitive does little to reinforce our tentative early conclusion that intentionally biased inquiry is impossible. In this section, I will show that there is a systematic connection between our topics. In §3.1, I explain how to formalize the notion of intentionally biased inquiry within a Bayesian theory of evidential support. This will allow me, in §3.2, to show (i) that the impossibility of intentionally biased inquiry in fact follows from the access principle (together with any assumptions implicit in the Bayesian theory), and (ii) that if the access principle has any counterexamples, people should be able to exploit these to bias their own investigations. We thus get affirmative answers to both of the questions raised above, strengthening both the case for the access principle and the case against the possibility of intentionally biased inquiry. Along the way, we will see some interesting connections between the possibility of biased inquiry and ‘reflection principles’ widely discussed in formal epistemology. 3.1 Formalizing biased inquiry Recall the discussion of §1.1. We were wondering whether you could embark on a course of action (for instance, set up your inquiry in a certain way) that would (from your perspective) make your investigations favour a claim p over its negation, even though which action you choose does not itself provide evidence regarding p. The action was not supposed to achieve this goal in a way that exploits irrational biases or information loss; it was instead meant to have its effect by influencing what evidence would become available to you. And ‘favouring’ was supposed to be understood in terms of expected value: p would be favoured over its negation if the expected difference between future and present evidential support for p, given that you decide to inquire in this way, was positive. To formalize the claim that one cannot do this, we need to introduce some technical notions. Let be the total, and thus pairwise incompatible, courses of action you might take (for all that your evidence entails); and let be the corresponding propositions stating which (if any36) of those actions you perform. Moreover, let Pr(p) represent p’s current evidential probability. Then the expected value of some function V on the hypothesis that I perform action ak will be the weighted average of the values which V might take, weighted by , the probability that V will take that value if I perform ak. The function whose expected value we’re interested in measures the difference between the initial and future evidential support for a proposition p. Each of these is plausibly determined by two factors: which propositions are part of the agent’s evidence at the relevant time, and what those propositions support.37 It seems possible to imagine uncertainty about either of those factors: I can be unsure both about the colour of the thirty emeralds I will examine and about the extent to which the observation that all of them are green would support the hypothesis that the next emerald to be mined is green. But, for our purposes, it makes sense to idealize away from the second kind of uncertainty. For uncertainty about the evidential support relation is orthogonal to both the access principle and our reasons for analysing biased inquiry in terms of expected probabilities, namely, that we don’t typically know beforehand what particular evidence some investigation will yield. And if we idealize away from uncertainty about the evidential support relation, we can take the values of the initial and future evidential support, and thus the value of the difference between them, to be fully determined by what our initial and future evidence is. To make use of these conceptual points, we need further terminology. Let be the propositions which might, for all your initial evidence entails, be your total initial evidence; and let be the propositions which might, for all your initial evidence entails, be your total evidence at the relevant future time, the time at the end of the investigation. Furthermore, for each , let E = Ei be the proposition that your total evidence at the initial time is Ei; and for each , let be the proposition that your total evidence at the future time is .38 Finally, let P be (what you know to be) the evidential support relation, so that is the difference between the future and the initial evidential support if your total initial evidence is Ei and your total later evidence is . Then we can write the claim that, conditional on any Ak, the expected difference is 0 as39 Such large equations are difficult to survey, so it will be helpful to have an alternative notation. I will use ‘’ as an abbreviation for the expected value of V, as calculated by Q; and I will use ‘’ as a label for the probability function obtained by setting for every Y. (IBI) can then be rewritten as In what follows, I will always give both ways of writing each equation. Assuming that the E=Ei and E+=E+j are independent, we can rearrange and simplify (IBI) to yield From this equation, we can make our way towards something more recognizable. For note that the actions in question, being total courses of actions for the relevant time span, are mutually incompatible; moreover, since the list is a complete list of the actions you might take, your evidence entails that you either perform one of them or fail to act at all. This means that the set of propositions forms a partition of the set of possibilities compatible with your evidence (that is, every such possibility is one in which exactly one of these propositions is true). But it is a straightforward theorem of the probability calculus, known as the law of total probability, that the probability of H is equal to the weighted average of the conditional probability of H on the members of a (finite) partition of the underlying space of possibilities. In symbols, . But then we can use (IBI) to get a principle from which the action propositions have dropped out altogether, namely,40 And this claim, stating that the expected future probability is equal to the expected current probability, is the obvious consequence of two instances of van Fraassen’s (1984) reflection principle, one synchronic and one future-directed:41,42 In fact, I want to go slightly further, and say that (EQEXP) is the result of ‘subtracting’ a commitment to (S-REF) from a commitment to (F-REF), the natural way of holding on to ‘what we really wanted out of’ (F-REF) without presupposing (S-REF). To explain what I mean by this, I should emphasize a non-standard feature of (F-REF) and (S-REF). Unlike other formulations of reflection principles, mine ask that an agent’s probabilities match expected evidential support, not expected credences. This is a good thing, because it means that we sidestep objections to reflection arising from the fact that future credences might be formed a- or ir-rationally.43 And, crucially, it means that (S-REF) is a version of Christensen’s (2010) rational reflection principle, stating that the probability of a proposition matches the expected current evidential support. But it’s well known that it’s hard to reconcile rational reflection with denials of the access principle, and rational reflection is widely rejected for this reason.44 Moreover, violations of (S-REF) will quickly make for violations of (F-REF), for example, if the agent knows that she will get no evidence in the relevant time span. So anyone, such as me, who is interested in the specifically diachronic aspects of (F-REF) needs to find a way of articulating the specifically diachronic thought underlying (F-REF) in a way that insulates it from more immediate worries about (S-REF). I submit that (EQEXP) is the natural candidate for such a principle: in the presence of (S-REF), it’s equivalent to (F-REF); but, unlike (F-REF), it is not subject to ‘cheap’ counterexamples constructed by considering a case in which (S-REF) fails and adding to the story that the agent knows she will receive no new evidence.45 This is not to say that (EQEXP) is or should be neutral on whether the access principle is true. Williamson (2000, ch. 10) and Weisberg (2007) highlight a serious tension between (F-REF) and denials of the access principle;46 and, as we will see in the next section, the particular tension they discuss doesn’t go away when we move from (F-REF) to (EQEXP). The point of replacing (F-REF) with (EQEXP) thus isn’t to preserve neutrality, but to gain dialectical effectiveness. By focusing on (EQEXP), we make clear that the problem of intentionally biased inquiry is an additional problem for access deniers, over and above any problems they might face because of their rejection of rational reflection. In particular, it shows that this problem cannot be dismissed as arising from an intuitively attractive, but ultimately mistaken, endorsement of ‘level bridging’; after all, the two sides of (EQEXP) are both at the same epistemic ‘level’. 3.2 Reflection and access What exactly is the connection between (EQEXP), (F-REF), and (S-REF) on the one hand, and the access principle on the other? It is relatively easy to see that (S-REF) will be true whenever the current evidence satisfies the access principle, and that (F-REF) will be true whenever the current evidence entails that the total future evidence will satisfy the access principle.47 The point about (S-REF) is rather trivial. For suppose the agent has evidence Ej. Since Ej obeys the access principle, Ej entails E = Ej.48 So whenever . (S-REF) thus holds trivially. The argument for (F-REF) is only slightly more complex. Even without the access principle, the plausible claim that only truths can be evidence already means that each entails the corresponding . As we just saw, the access principle for the future evidence allows us to establish the converse, that each entails the corresponding . The access principle thus guarantees that, for any H, and any you might receive, . Moreover, since E+ subsumes your initial evidence E, . It is also clear that is a partition of the possibilities left open by the current evidence, so that is simply an instance of the law of total probability. Substituting for , this yields (F-REF).49 If the access principle holds in general, then, we would expect both (S-REF) and (F-REF) to be true. (EQEXP) follows trivially from their combination; and a directly analogous argument shows that (IBI) also holds. This settles one of the two questions motivating our more formal investigations: rather than being a weird case to focus on, counterexamples to the access principle are in fact the only possible cases of intentionally biased inquiry. Or, more cautiously, they are the only such cases compatible with the idealizing assumptions we have made explicit (finitely many evidence propositions, no possibility of information loss, no uncertainty about the evidential support relations) and those which are implicit in the formalism we have been employing (logical omniscience, no discovery of new possibilities, evidential support measured by exact values). Since these assumptions seem like adequate idealizations for modelling a large number of relatively ‘ordinary’ investigations, even this more cautious conclusion is still a significant result.50 To settle our second question, and generalize the argument from the impossibility of intentionally biased inquiry to the access principle, we need something like the converse entailment: that (EQEXP) fails unless the access principle is true. Unfortunately, the connection is not quite so straightforward. For (EQEXP) holds trivially of an agent who is certain not to receive any evidence, regardless of whether she satisfies the access principle.51 There is, however, a less straightforward connection that is strong enough for our purposes. Suppose that there are possibilities in which the access principle fails. That is, suppose there is some possibility w such that the total evidence we have in w does not allow us to rule out that we are instead in possibility , in which we have different evidence. Then either the evidence in allows us to rule out that we are in w or there is a third possibility which the evidence in one, but not the other, of w and allows us to rule out. In other words, the ‘doesn’t rule out’ relation between the possibilities will either fail to be symmetric or fail to be transitive.52 So, without loss of generality, we can assume that the ‘ruling out’ relation between the possibilities will exhibit one of the following structures: These structures should look familiar: they are, respectively, the structure of the wall case and that of the clock case (once we add to the clock case the background information that ensures that only three settings are possible). But then it seems possible to imagine an agent whose initial evidence establishes that, and only that, he is in one of w, and , and who knows he is about to receive whatever evidence is associated with those possibilities. Then the evidential probabilities of our agent will violate (EQEXP). For the expected initial probabilities will match the initial probabilities (since in all of the possibilities, the agent’s initial evidence establishes that, and only that, he is in one of w, or , so that there is no uncertainty about the initial evidence). And the expected future probability of w is higher than its initial probability in both cases, regardless of which (non-zero) initial probabilities are assigned to each world. That’s precisely why, in discussing the wall and clock cases, we thought it desirable to somehow associate w with the possibilities in which I am popular. This argument gives us a general recipe for converting counterexamples to the access principle into examples of cases where agents can bias their inquiries. In fact, it should now be clear that our discussion of the particular examples in §2 was simply an application of this general recipe. But the full force of our argument for the access principle requires both the general recipe and its application to specific cases. If we have only the general recipe, it may not be obvious why we should resolve the tension between the denial of the access principle and the claim that intentionally biased inquiry is impossible in favour of the latter. And if we consider only the particular cases, it is natural to worry, as we did earlier, that the oddities we observe arise simply from idiosyncratic features of the particular example. But we have now seen both (i) that it really is the (supposed) violation of the access principle which makes it possible to use a case to intentionally bias one’s inquiries and (ii) that it really is absurd, even in the cases which are the best candidates for such access violations, to think that intentionally biased inquiry is possible. This makes it hard to see a credible alternative to accepting the access principle. 4. Conclusion We have covered a lot of territory. We began with the question of whether we can intentionally bias our own inquiries so as to favour one hypothesis over another. Our discussion suggested that the intuitive answer is no, at least once we have the relevant kind of biased inquiry clearly in view. This answer is particularly clear when we imagine trying to use such biased inquiry, for example, to reassure ourselves of our own popularity. We then observed that certain popular counterexamples to the access principle would, if genuine, enable agents to bias their inquiries after all. But the relevant reasoning in those cases was clearly absurd; we should thus conclude, not that such biasing is possible, but rather that we were wrong about the examples. Finally, we saw that the connection between the access principle and the possibility of intentionally biased inquiry is in fact both tight and perfectly general: formalizing the thought that we can’t bias our inquiries, in a way closely related to the reflection principle, allows us to see that intentionally biased inquiry is possible if and only if the access principle is false. This connection, I suggested, both reinforces our argument that intentionally biased inquiry is in fact impossible and provides a powerful new reason to believe in access. It is worth emphasizing that accepting the access principle is a radical conclusion. (So radical, perhaps, that some will be inclined to modus tollens my argument, and conclude that intentionally biased inquiry is possible after all. That would still be an interesting discovery.) We have already encountered several reasons to reject the access principle when motivating the alleged counterexamples above. But let me add, in closing, what I think might be the best reason for denying access. This reason, nicely formulated by Weatherson (2011, p. 451), adapts the obvious argument against ‘negative introspection’ for knowledge into a direct argument against the negative access principle. The argument has two premisses: (i) rational agents can be wrong about any (non-epistemological) subject matter, and (ii) only truths can be evidence. Now let p be a proposition of the kind that could be evidence. Then, by (i), a rational agent might believe p even though it is false, and thus fail to realize that, by (ii), p isn’t part of her evidence. But if negative access were true, her evidence would entail that her evidence doesn’t contain p, and so our agent’s failure to realize that it doesn’t would seem to be a failure of rationality (at least if she considers the question). Neither of the premisses is undeniable,53 but both are intuitively appealing.54 In addition to defending the view that intentionally biased inquiry is impossible and offering a novel argument in favour of the access principle, I hope to have offered a new perspective on reflection-like principles such as (F-REF) and (EQEXP). This shift might be clearest if we contrast our discussion of reflection with Williamson’s. For Williamson, in addition to being perhaps the most prominent critic of the access principle, also discusses the reflection principle at some length, and my own discussion owes a lot to his. Despite this debt, we obviously disagree about whether reflection is true. I think this is, at least in part, because we think of the principle quite differently. Williamson presents reflection as something that it would be nice to have, if only we could have it.55 The defender of reflection, as Williamson sees him, is an overly enthusiastic optimist, who wants to reach ahead and make use of information he hasn’t yet received. This allows Williamson to cast himself in the role of the cautious and sensible, if somewhat sombre, realist: But we cannot take advantage of the new knowledge in advance. We must cross that bridge when we come to it, and accept the consequences of our unfortunate epistemic situation with what composure we can find. Life is hard. (Williamson 2000, p. 237) The connection I’ve drawn between intentionally biased inquiry and reflection paints a less rosy picture of the principle: it imposes a frustrating limitation on our pursuit of desirable beliefs. The denier of access is the true optimist, promising us wonderful tools for shaping the outcomes of our inquiries, tools that we would love to employ. But we do not have these tools. We should save our composure for facing up to this, far more unfortunate, realization.56 Footnotes 1 Titelbaum (2010) offers related, but less general, considerations. I should note that, in presenting the argument in this way, I am being a little disingenuous. I suspect that we can do justice to our observations about intentionally biased inquiry even if we reject the access principle, provided we maintain that rational agents always have to be sure that it is true of them in the present and future. But it is far from obvious that this gap is interesting: if a principle sometimes fails, why couldn’t people suspect that it will fail for them? In other work, I try to show that this question can be answered, and that other important arguments for the access principle can also be avoided in this way; but, since my views on this are idiosyncratic, I will set them aside here. The point of this footnote is thus simply to note that, while this paper is written as an argument for the access principle, readers sceptical of this conclusion can instead read it as an advertisement for the kind of view just hinted at. 2 Here, and throughout, I assume that evidence consists of propositions. 3 A similar thought is implicit in Kripke’s (2011) discussion of his dogmatism paradox. Kripke’s paradox is an argument for (amongst other things) deciding to further favour a known claim over its negation by selectively avoiding counter-evidence. He explains that what he has in mind is a resolution to avoid ‘reading the wrong books (for they contain nothing but sophistry and illusion), associating with the wrong people, and so on’ (Kripke 2011, p. 49). This assumes that the actions described could be a way of intentionally favouring the known claim over its negation. 4 One might worry that this precludes armchair inquiry, which (arguably) doesn’t generate new evidence, but instead tries to determine what our old evidence supported all along. But this is not altogether unwelcome, since some of my arguments (especially the formal arguments of §3) do not straightforwardly apply to cases of armchair inquiry. I’m thus happy to leave open whether an intentionally biased armchair inquiry is possible; though the informal considerations of §1.2 suggest that it is at least much harder than one might have thought. 5 This is compatible with different accounts of the relevant biases. On the most straightforward account, they lead to belief without supplying any additional evidence. Even if they do supply evidence, however (for instance, by affecting what ‘feels plausible’, which may be a form of evidence), the import of this evidence is plausibly nullified if I know that it arises only because of the biased mechanism—cf. Kelly (2008), who offers a sophisticated account of how various biases can offer evidence, but agrees (p. 629) that once we know about these biases, the import of this evidence is undermined. But I need to know about my biases if I am planning to exploit them. So, either way, my total evidence at the end of the investigation is not particularly likely to support p any more than it does at the outset, even if I am likely to form the belief. 6 See Kelly (2013) and Schoenfield (2014) for discussion. 7 We can prove this, on the assumption that the evidential support of a proposition is measured by its probability on the evidence. For let x be p’s initial probability, and hence the degree to which the initial evidence supports p. Then the investigation has an x chance of boosting that support from x to 1, and a chance of reducing that probability from x to 0, resulting in an expected difference of . So the investigation is unbiased. 8 A few comments on this definition: Strictly speaking, the definition doesn’t say what it is for an inquiry to be biased, but rather, what it is for a body of information to classify an inquiry as biased; we need a body of information to determine the probability of the possible changes in evidential support (or, in the less general versions, to determine what is ‘guaranteed’ to happen and what ‘might’ happen). Since I will be interested in inquiries that are biased from the investigator’s point of view, I will suppress this qualification, and say that A’s inquiry is biased if it is biased relative to A’s (initial) evidence. The definition assumes that we can talk about the probability, given the agent’s initial evidence, of V taking various values. I don’t know how to characterize the intuitive idea that unlikely but large increases can be ‘balanced out’ by small but likely decreases without that assumption; but if there is a way to do it, the definition could be amended to use such an alternative characterization instead. It’s also worth emphasizing that even if we can talk about the probability of a proposition on the agent’s evidence, it doesn’t follow that this is what measures the evidential support of that proposition; if we prefer a non-probabilistic theory of evidential support, we are free to use that theory in determining V’s values instead. To that extent, the definition does not presuppose full-blown Bayesianism; and the considerations I offer against the possibility of intentionally biased inquiry in §1.2 are similarly ones that any theory should recognize. The definition allows that an inquiry can be biased towards or against p even if the inquiry is not an inquiry into whether p (or, more generally, into a question to which p is an answer). This is desirable: many investigations are unbiased about their ‘official’ topic, but biased about a related issue, on which the evidence gathered also seems to bear. It also means that our definition is not restricted to inquiries with yes/no answers, or even to inquiries with an antecedently understood range of possible answers. (Thanks to the associate editor for pushing me to clarify this.) There are investigations motivated by a desire for a certain kind of outcome that are unbiased by this definition. Suppose I care very unevenly about evidence of my own popularity: the only thing I want is to have evidential support of degree at least 0.9 that I am popular. Support of degree 0.3 is no worse than support of degree 0.7, and support of degree 0.99 is no better than support of degree 0.91. Then I could, as Kelly (2002, p. 170) points out, decide to keep inquiring until the first moment the evidential support exceeds 0.9, and stop immediately after. That decision increases the chances that my preferences will be satisfied; but this investigation may come out as unbiased. A different kind of unbiased, yet ‘motivated’, inquiry exploits the fact that we can desire evidential support for a specific opinion under a non-transparent mode of presentation. For example, I might not know where my friends stand on the issue of whether p, and care only about standing on the same side as them. As long as I think that their opinion is likely to be true, I could then simply inquire into whether p, and thereby increase my chances of obtaining evidence for the answer I want to believe. (Thanks to the associate editor for this example.) 9 In fact, Parfit (2011, p. 421) explicitly sets aside the cases where one’s own actions are evidentially relevant to the question. 10 Of course, it is also plausible that people generally don’t give adequate weight to information about how the evidence they have was selected when they form their beliefs; see, for example, Kahneman (2011), who refers to this phenomenon as ‘what you see is all there is’. The kinds of strategies Parfit describes might thus be quite effective in helping us form the desired beliefs; but they will achieve this only by exploiting our failure to conform our beliefs to our total evidence. 11 This might be a good point at which to mention a very different kind of case that initially seems to raise doubts for my position (Thanks to Caspar Hare, Vann McGee, Jack Spencer and Roger White for discussion). We can investigate using ‘stopping rules’ that intuitively seem biased. Suppose, for example, that I want to know whether a coin is fair or biased towards heads, knowing already that it isn’t biased towards tails. I could decide to keep tossing the coin until it has landed heads more often than it has landed tails. Since I know that the coin isn’t biased towards tails, I can be sure that this will happen at some point, so that such an investigation is bound to yield a result. (If I didn’t know that the coin isn’t biased towards tails, I could not be sure of this.) But couldn’t I know in advance that this result will favour heads bias? Interestingly, I cannot. The reason is that more heads than tails needn’t favour heads bias over fairness. Given normal background beliefs, a sequence containing 49 tails and 50 heads supports fairness over heads bias; and no matter what background beliefs I have, there will always be some length such that sequences of length larger than that will support fairness over heads bias. Admittedly, these sequences are less likely to occur than the ones favouring heads bias; but this is balanced out by the fact that the ones favouring heads bias generally favour it only very weakly. 12 Which is not to say that the considerations I have been raising are entirely original. They clearly connect to Popper’s (1961) famous claim that falsifiability is a precondition for testability (and hence, we might add, for confirmation). For some recent related discussion, see also White (2006, pp. 543–9), Sober (2009) and Titelbaum (2010). 13 The issue also bears on whether we should postulate epistemic norms for how agents should structure their inquiries, or whether all apparent need for such norms is covered by the requirement that we conform our beliefs to the evidence. See Hedden (2015, ch. 10) for discussion. 14 Different theses go under the label ‘internalism’, and not all of them will be committed to the access principle; Wedgwood (2002), for example, emphatically denies it. But since I will be defending the principle, I will not pursue these subtleties. 15 Hintikka (1962) rejected the ‘negative introspection’ principle because it seems clear that, when we mistakenly believe something, we fail to know it without knowing that we so fail. Williamson’s (2000) more recent arguments against ‘positive introspection’ (also known as the KK principle) have also proven influential. 16 Here and elsewhere I assume that only truths can be evidence. Williamson (2000, ch. 10) influentially defends this claim; Goldman (2009) seems to deny it; see Littlejohn (2013) for a discussion of the more recent literature. 17 There are other cases we might go to for examples of this kind. One might maintain that when one sees (as opposed to hallucinates) that p, it becomes part of one’s evidence that p, yet also maintain that in the hallucination case one doesn’t have evidence that one isn’t seeing. Similarly, one might hold that when a person A testifies (knowingly) that p, it becomes part of one’s evidence that p even though had A been lying, one would not have been able to tell. 18 One might challenge this step, since the cases in question are cases in which I might not be able to tell what my evidence is, and it isn’t clear that in such cases increased evidence really does lead to increased confidence. In §2.3, I explain why a response along such lines doesn’t allow us to avoid all versions of the problem. 19 Titelbaum (2010) makes the same observation about cases like that of the wall. He presents this as a diagnosis of why the ‘bootstrapping’ reasoning apparently supported by the wall case (as observed by Vogel 2000 and Cohen 2002) is so bad. Since, as I will argue in §2.2 and §3, we can set up similarly biased investigations whenever we have a violation of the access principle, and not all these cases seem to exploit ‘bootstrapping’, I am less sure about the connection between these two problems. 20 The thought might be that my knowledge that I asked my friend to set up misleading lighting if I am unpopular gives me reason to think that circumstances are unfavourable; and externalists have recognized that reasons to think that the circumstances are unfavourable can prevent us from receiving evidence, even when the circumstances are actually good, since at least Goldman (1979, p. 20). 21 Could the difference simply be that in this case, but not in an ‘ordinary’ one, the error possibility is salient to me? (Thanks to the associate editor for raising this question.) It seems implausible that, as the response considered in the main text would require, the salience of the error possibility should affect what evidence I receive (as opposed to, say, which beliefs I form based on that evidence). But it may be that, as an epistemic contextualist might hold, the salience of the error possibility can affect what I mean by ‘evidence’, and hence what ‘evidence’ I believe myself to have. This seems like a promising start for developing a way out along the lines suggested in footnote 1. 22 Thanks to Jack Spencer for discussion. 23 My dentist recently told me that if I needed further treatment, I’d know that I did. This was useful information: it allowed me to reason from ‘I feel (only) mild pain’ to ‘I don’t need further treatment’, which I would not have been able to do otherwise. 24 See, for example, Christensen (2010), Elga (2013) and Horowitz (2014). The discussion could easily be adapted to other alleged counterexamples to ‘positive introspection’ for knowledge, such as the case of Mr Magoo in Williamson (2000, ch. 5). 25 This last claim is, of course, unlikely to be true of actual humans. It is also unrealistic to suppose that our evidence allows us only to rule out some positions; presumably it also supports the remaining possibilities to a degree which is proportional to their proximity to the true value. Finally, the description is misleading in so far as it is vague what margins are sufficient for my guesses to count as ‘reliable’. But these idealizations won’t matter. 26 See also Williamson (2011), Christensen (2010) and Elga (2013) for slightly different routes to the same conclusion. (If there are worries about the clock being part of the external world, we can instead change the case to be about where the hand is pointing according to your visual experience. Plausibly, the point about limited discriminatory abilities applies here too.) 27 There is also a 1–1 correspondence between positions of the hand and what evidence I lack; so a similar argument establishes that the case violates the negative access principle. 28 To design the right clock, I need to know something about my margin of error. But I don’t need to know its exact value; I only need to know of some d that I’m not reliable at discriminating positions that are d millimetres away from each other, but am reliable at discriminating positions that are 2d millimetres away from each other. A little bit of research and experimentation should enable me to discover such a d. 29 For a different access-friendly account, see Smithies (2012). 30 Of course, I might not make a guess; if this happens, my evidence is presumably determined by what my best guess would have been, and one might worry that I’m not always in a position to know what that is. But it is important to keep track of temporal indexes here. I clearly don’t know now what my best guess would have been if I had made one back when I looked at the clock; but that only shows that I can’t tell now what my evidence was then, and even the access principle doesn’t require that I be able to do so. Was I in a position to know at the time what my best guess would have been then? Maybe I was. After all, I could have found out merely by taking a guess and registering its value. 31 For further elaboration of the ‘best guess’ model, see Cohen and Comesaña (2013); for criticism, see Hawthorne and Magidor (2010), Goodman (2013, p. 34) and Williamson (2013, pp. 80–3). Since I can’t discuss how to respond to such criticisms here, gesturing towards this alternative construal of the case remains a promissory note. 32 This claim is somewhat analogous to Hawthorne and Stanley’s (2008, pp. 580–5) view that one should only act on one’s evidential probabilities if one knows what they are. It is also suggested, albeit somewhat loosely, by Williamson’s (2009, pp. 360–1) view that there are different senses or precisifications of ‘justified confidence’, one which requires merely that the confidence matches one’s evidence, and others which require in addition that one knows this (and perhaps knows that one does, etc.). For this view implies that if the agent doesn’t know of the evidence boost, the increased confidence would not be justified in at least one sense of ‘justified’; it is thus plausible that increased confidence isn’t rationally required, in at least one sense of ‘rationally required’. 33 See Lasonen-Aarnio (2010); see also Hawthorne and Srinivasan (2013) and Williamson (forthcoming), who connect this to the idea that raising one’s confidence may be blameworthy. 34 This style of argument also applies to responses, perhaps inspired by Gallow (2014), Bronfman (2014) and Schoenfield (forthcoming), which maintain that agents should update by a rule other than conditionalization in situations where the access principle isn’t antecedently known to hold. For an alternative update rule can prevent agents from manipulating their confidence in the combined case only by sometimes forbidding agents from raising their confidence in a claim even though they are certain that their total evidence now supports it more than it did previously; and that still strikes me as an unfortunate consequence. (Thanks to J. Dmitri Gallow for discussion.) 35 This case has the same structure as Williamson’s (2000, ch. 10) ‘simple creature’ example, but the epistemological story is different. 36 This qualification, that you might not perform any action at all, means that one proposition in the list (the one stating that you don’t perform an action) will not correspond to anything on our list of actions. I will assume that one can’t expect failing to act to bias one’s inquiries for the same reason that one can’t expect particular actions to. 37 Or, perhaps, what they support relative to the agent’s ‘standards’ or ‘inductive policies’, if one is sceptical about an objective evidential support relation. Recall that, since changes in these standards or policies seem to be based on something other than the evidence one receives, ways of biasing one’s future opinions which exploit such changes don’t qualify as ‘intentionally biased inquiry’; we thus lose no generality by ignoring such relativity in the support relation. 38 Recall that, if the access principle fails, Ei and E = Ei can be very different. If you are in the bad case, your evidence is entirely uninformative about the colour of the wall. But the proposition that you have this uninformative evidence is itself highly informative: it entails that you are in the bad case, and hence that the wall is white. 39 If we hadn’t idealized away from uncertainty about P, we would have had to take a different approach. We would have used Pr+ to stand for the agent’s future evidential support; and we would have taken to be a finite set containing all the values the future evidential support might take and to be a finite set containing all the values the initial evidential support might take. (IBI) would then have been written as The other equations in the text can be rewritten in similar ways, and the same connections hold between the rewritten principles as between the ones I discuss. The rewritten principles, however, strike me as less illuminating: they fail to capture the idea that in determining whether an inquiry is biased, we wonder about how likely we are to learn various things and what impact those things would have on the proposition in question. Moreover, the connection between the rewritten principles and the access principle is a bit less straightforward. 40 Proof: 41 I am here stating the reflection principle as a claim about expected values; that claim is usually treated as an important and immediate consequence of the principle rather than as the principle itself—see, for example, van Fraassen (1995, p. 19) and Weisberg (2007, p. 180)—though Williamson (2000, pp. 230–7) also focuses on the claim about expected values when discussing reflection. In our terminology, the ‘standard’ version of the (future-directed) principle would be , where E+ is a non-rigid designator for the agent’s future evidence. Given that we are abstracting away from uncertainty about the evidential support relation, this ‘standard’ principle entails, but is not entailed by, (F-REF). 42 Kadane, Schervish and Seidenfeld (1996) take a principle similar to (F-REF) to capture the thought that agents cannot ‘reason to a foregone conclusion’. I explain below why (EQEXP) is the better choice if we want to avoid begging the question against access deniers. 43 See Briggs (2009) for an excellent survey of those objections. Another well-known worry about reflection, also discussed by Briggs, arises from cases where an agent might lose evidence; since we’ve noted from the very beginning that (IBI) is only plausible in cases where we can be sure this won’t happen, these worries are likewise not relevant for our purposes. 44 See, for example, Christensen (2010), Williamson (2011), Elga (2013) and Lasonen-Aarnio (2015). 45 Thanks to Jeremy Goodman and Harvey Lederman for extremely helpful discussion on this point. The claim that (EQEXP) articulates the key insight behind (F-REF) can be further bolstered by showing that it, rather than (F-REF), is the principle which other arguments for (F-REF) really support, once we give up on (S-REF). I plan to do this in future work. 46 See also Hawthorne (2004, pp. 75–7) and Weatherson (2011) for briefer discussion. 47 We also need that the current evidence entails that all evidence is true and that there will be no information loss; I will suppress these assumptions henceforth. 48 Why? Consider any . Then either there is some p which is part of Ei but not Ej or there is some p which is part of Ej but not Ei (or both). If the former, Ei rules out E = Ej via positive access; if the latter, Ei rules out E = Ej via negative access. Since this is true for every , the only remaining possibility compatible with the initial evidence, and thus with Ei, is E = Ei. 49 Note that, in guaranteeing the equivalence of and , the access principle ensures that our future evidence forms a partition of the (current) epistemic possibilities. That the future evidence forms such a partition is a standard assumption in attempts to derive reflection principles: see, for example, van Fraassen (1995, p. 17) and Briggs (2009, p. 69). Weisberg (2007, pp. 183–4) discusses the partitionality assumption in such proofs in detail, and concludes that it can only be motivated by something like the access principle. 50 Kadane, Schervish and Seidenfeld (1996) show that principles like (EQEXP) may fail if we move to formal models which relax some of these assumptions; they leave open whether this is a problem for the principle or for the models, and I will too. 51 Elsewhere, I show that there is a good sense in which cases where the agent learns nothing are the only cases in which (EQEXP) holds despite failures of the access principle. However, the proof requires additional formalism, and so I will not appeal to the result here. 52 Another way to see this is that the access principle, together with the claim that only truths can be evidence, implies that ‘one’s evidence entails that’ obeys an S5 logic. And it’s a well-known theorem of modal logic that a modal operator obeys an S5 logic if and only if the corresponding accessibility relation is reflexive, symmetric and transitive. 53 Smithies (2012) would deny (i) by maintaining that ideally rational agents would never be wrong about their phenomenal states; Goldman (2009) seems to deny (ii). 54 This is why I hold out hope for a way out along the lines hinted at in footnote 1. 55 See also Hawthorne and Srinivasan (2013) for a similar picture of the access principle. 56 Ideas from this paper have been presented at the 2012 ARCHE/CSMN graduate conference, the MIT Dissertation Workshop, the 2014 MITing of the Minds, the 2014 Formal Epistemology Workshop, and the 2014 Joint Session of the Aristotelian Society and the Mind Association. Thanks to the audiences and my commentators Stew Cohen, Declan Smithies and Jeff Dunn on these occasions. In addition, the paper has been improved greatly as a result of comments from Andrew Bacon, Dan Barras, Alex Byrne, Nilanjan Das, Kevin Dorst, Jane Friedman, J. Dmitri Gallow, Jeremy Goodman, Dan Greco, John Hawthorne, Brian Hedden, Sophie Horowitz, Abby Jacques, Brendan de Kenessey, Harvey Lederman, Jack Marley-Payne, Damien Rochford, Ginger Schultheis, Kieran Setiya, Jack Spencer, Bob Stalnaker, Josh Thorpe, Jonathan Vogel, Ian Wells, Steve Yablo, four anonymous referees, an associate editor for Mind, and, especially, Roger White. References Briggs Rachael 2009 : ‘Distorted Reflection’ . Philosophical Review , 118 , pp. 59 – 38 . Google Scholar CrossRef Search ADS Bronfman Aaron 2014 : ‘Conditionalization and Not Knowing that One Knows’ . Erkenntnis , 79 , pp. 871 – 92 . Google Scholar CrossRef Search ADS Christensen David 2010 : ‘Rational Reflection’ . Philosophical Perspectives , 24 , pp. 121 – 40 . 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In Steup Matthias , Turri John , Sosa Ernest (eds.), Contemporary Debates in Epistemology , 2nd edition . Malden, MA : Wiley Blackwell . Kripke Saul 2011 : ‘Two Paradoxes of Knowledge’. In his Philosophical Troubles . Oxford : Oxford University Press . Lasonen-Aarnio Maria 2010 : ‘Unreasonable Knowledge’ . Philosophical Perspectives , 24 , pp. 1 – 21 . Google Scholar CrossRef Search ADS Lasonen-Aarnio Maria 2015 : ‘New Rational Reflection and Internalism about Rationality’. In Gendler Tamar Szabo , Hawthorne John (eds.), Oxford Studies in Epistemology , Vol. 5 . Oxford : Oxford University Press . Littlejohn Clayton 2013 : ‘No Evidence is False’ . Acta Analytica , 28 , pp. 145 – 59 . Google Scholar CrossRef Search ADS Parfit Derek 2011 : On What Matters , Volume Vol. 1 . Oxford : Oxford University Press . Popper Karl 1961 : The Logic of Scientific Discovery . New York : Science Editions . Schoenfield Miriam 2014 : ‘Permission to Believe: Why Permissivism is True and What It Tells Us about Irrelevant Influences on Belief’ . Noûs , 48 , pp. 193 – 218 . Google Scholar CrossRef Search ADS Schoenfield Miriam forthcoming: ‘Conditionalization Does Not (in General) Maximize Expected Accuracy’ . To appear in Mind . Smithies Declan 2012 : ‘Mentalism and Epistemic Transparency’ . Australasian Journal of Philosophy , 90 , pp. 723 – 41 . Google Scholar CrossRef Search ADS Sober Elliott 2009 : ‘Absence of Evidence and Evidence of Absence: Evidential Transitivity in Connection with Fossils, Fishing, Fine-Tuning, and Firing Squads’ . Philosophical Studies , 143 , pp. 63 – 90 . Google Scholar CrossRef Search ADS Stalnaker Robert 2009 : ‘On Hawthorne and Magidor on Assertion, Context, and Epistemic Accessibility’ . Mind , 118 , pp. 399 – 409 . Google Scholar CrossRef Search ADS Titelbaum Michael 2010 : ‘Tell Me You Love Me: Bootstrapping, Externalism, and No-Lose Epistemology’ . 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Oxford : Oxford University Press . © Salow 2017 This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

doi: 10.1093/mind/fzw069pmid: N/A

Abstract I argue—contra moderate grounding pluralists such as Kit Fine and more extreme grounding pluralists such as Jessica Wilson—that there is fundamentally only one grounding/in-virtue-of relation. I also argue that this single relation is indispensable for normative theorizing—that we can’t make sense of, for example, the debate over consequentialism without it. It follows from what I argue that there is no metaethically-pure normative ethics (in contrast to Ronald Dworkin’s claim that there is no normatively-pure metaethics). 1. Introduction Is the good prior to the right? This question—one of the most central in all of ethics—is not a question about supervenience, or counterfactual dependence, or conceptual priority. Rather, it is a question about that distinctive variety of non-causal dependence which metaphysicians now call ‘grounding’. In what follows, I offer a defence of the claims I have just made. Thus I will be arguing that the metaphysicians’ notion of grounding is the very same one being employed in ethics. One prominent threat to this thesis comes from within that group of metaphysicians who have of late been touting the philosophical significance of grounding. Kit Fine, to whom we owe the expression ‘ground’, and whose work has played a crucial role in the resurgence of interest in the notion, holds that there are three varieties of grounding: metaphysical, natural, and normative. So for Fine, the sort of grounding at issue in metaphysical debates is distinct from the sort of grounding at issue in ethical debates. In what follows, I argue that Fine is mistaken in thinking that grounding is disunified in this way. Fine is what we might call a ‘moderate grounding pluralist’: he holds that there exist a small number of fundamentally distinct types of grounding. Grounding pluralism, when pushed to the extreme, becomes a source of scepticism about the importance and interest of grounding. One representative ‘extreme grounding pluralist’, as we might call them, is Jessica Wilson, who argues that although there are a large number of specific dependency relations such as the part–whole relation and the determinate–determinable relation, these specific relations do not form a unified kind and nothing is gained by theorizing in terms of a general grounding relation. In what follows, I defend the theoretical usefulness of unqualified ‘grounding’-talk against the challenge posed by extreme grounding pluralists such as Wilson. Therefore I have three primary goals in this essay. The first is to argue that a metaphysical grounding relation is indispensable for normative theorizing. (For the most part I focus on the case of ethics, but I intend my thesis to extend to other normative disciplines, such as epistemology, political philosophy, and the philosophy of law.) The second is to argue against Fine’s form of moderate grounding pluralism. And the third is to argue against the sort of extreme grounding pluralism that gives rise to scepticism about the very topic of grounding. These three goals are interrelated in various ways. As already mentioned, achieving my first goal requires achieving the second, since Fine’s pluralism represents a notable challenge to my claim that metaphysical grounding is indispensable for normative inquiry. Moreover, success with my first goal helps with the third, since it is precisely in normative contexts that the claims of extreme grounding pluralists such as Wilson are at their weakest. And my second and third goals are likewise interrelated, since my arguments against Fine also have traction against Wilson. It is because of these interrelations that I take on all three tasks in the same essay. Furthermore, pursuing all three goals will allow us to establish a surprising conclusion, at the essay’s end, about the relationship between normative ethics and metaethics. First, though, I should provide some background about the nature of grounding and its history. 2. Grounding: the very idea What is grounding? The name might sound imposing, but the notion of grounding is no more and no less obscure than the word ‘because’. The following sentences are equivalent ways of making the same claim about grounding: An act is pious because it is loved by the gods; An act is pious in virtue of its being loved by the gods; The fact that an act is loved by the gods grounds the fact that it is pious; An act’s being loved by the gods makes it the case that the act is pious. I will be assuming throughout that these four locutions are different ways of getting at the same idea.1 As a result of Kit Fine’s—no pun intended—ground-breaking work on the notion (2001, 2010, 2012a, 2012b), it has become customary to use ‘grounds’ and its cognates as the primary term for the sort of dependency at issue in sentences of this sort. I will do so as well, but not without some reservations. Personally I prefer expressions such as ‘in virtue of’ and ‘because’ over the now-ubiquitous ‘grounds’, for two reasons. First, ‘grounds’-talk lends itself to the surprisingly common misconception that ‘grounds’ is a technical term referring to a wholly new relation that was invented by Fine in 2001. But nothing could be further from the truth, and the intended equivalence of ‘grounds’-talk to ‘in virtue of’- and ‘because’-talk helps us see that. Although the use of the word ‘grounds’ in roughly Fine’s sense is a relatively recent phenomenon, ‘in virtue of’- and (non-causal) ‘because’-talk have been with us from the very beginning, as my Platonic example shows. My second reason for preferring the locutions ‘in virtue of’ and ‘because’ is that, to my ears at least, ‘grounds’-talk is not yet a dead metaphor—it calls to mind both the base of a building and electrical connections to the earth. As such, the expression ‘grounds’ tempts us into assuming that everything which is grounded can eventually be traced back to a set of ungrounded grounders that serve as the foundation for the whole metaphysical edifice. Perhaps such a form of metaphysical foundationalism is correct; however, I don’t think that view is inevitable, and it would be unfortunate if lingering metaphors attached to our philosophical terminology were unduly to sway our thinking here. Less of a danger arises when we theorize using the terms ‘in virtue of’ and ‘because’, since any metaphorical content they might have once had is long since dead. (It takes real work to remind ourselves that ‘virtue’ is part of ‘in virtue of’ and that ‘cause’ is part of ‘because’.) However, despite these misgivings, I will be making free use of ‘grounds’-talk in this essay, partially because that term has now become standard, and partially because ‘grounds’-talk allows us to easily state dependency claims in both directions.2 I urge my readers to ignore any metaphorical content that might be attached to such phraseology, and I urge them to remember that all ‘grounds’-talk can be translated into language using ordinary terms such as ‘because’. Recently, grounding has become a hot topic in metaphysics, due not only to Fine’s work, but also to important and influential papers by Jonathan Schaffer (2009) and Gideon Rosen (2010). An explosion of research has resulted, as metaphysicians have turned their attention to a variety of question about the nature of grounding and its relation to other ideas in the vicinity. Is grounding a relation or an operator? If it is a relation, what are its relata? Can pluralities serve as grounds, and can pluralities be grounded? Do full grounds always necessitate that which they ground? What is the logic of grounding? What are the semantics of ‘grounds’? What is the relation, if any, between grounding and essence, between grounding and fundamentality, between grounding and reduction? What, if anything, grounds grounding facts? These questions will not be the central focus of this essay. Nevertheless, it is difficult to discuss grounding without weighing in on at least some of them. So I will simply assume without argument that grounding is a relation rather than an operator. I will also assume that the relata of the grounding relation are facts, and that the grounding relation is singular on the side of what-is-grounded and plural on the side of what-does-the-grounding, so that in some cases one fact is grounded in several facts taken together. Nothing I go on to argue will turn on these assumptions, and making them will streamline our discussion.3 During the tumult of research on grounding over the past decade, a sort of narrative has emerged.4 According to this narrative, although analytic philosophers during the twentieth century occasionally made use of ‘in virtue of’- or ‘dependence’-talk in their unguarded moments, most of these philosophers either officially disavowed such language or tried to cash it out in terms of more familiar ideas such as entailment or supervenience. But then Fine, Rosen, Schaffer, and others came along in the first decade of the twenty-first century and taught us that entailment, supervenience, and the like are too coarse-grained to capture what we want from ‘in virtue of’- and ‘dependence’-talk. Moreover—so the narrative goes—Fine, Rosen, and Schaffer also showed how a notion of grounding is indispensable for asking certain questions in metaphysics we would otherwise not be able to ask, and they demonstrated how we can theorize about the nature of grounding and its interrelation to other notions in a rigorous manner. Eventually—the narrative concludes—we came to learn that not only is grounding a useful item to have in our analytical toolkit, but it itself can be the subject of serious philosophical inquiry. Now I count myself a fan of grounding, so I welcome the attention that metaphysicians are now lavishing on the notion. And I certainly agree that the work of Fine, Rosen, and Schaffer has been instrumental in rehabilitating the legitimacy of appeals to the in-virtue-of relation in our theorizing, whether metaphysical or otherwise. I also agree with the growing consensus that supervenience is too blunt a tool to capture the notion of grounding. But there are other aspects of the creation myth I have just told which I consider just that: mythical. I focus here on three of those aspects. First, the actual history of the relationship between grounding and supervenience is more complicated than the standard narrative would have it. R. M. Hare’s The Language of Morals (1952) is usually credited with being the first appearance in print of the distinctively philosophical use of the term ‘supervene’.5 However, when we turn to Hare’s text, we find something rather surprising. Here are the first two passages in which Hare explains what he means by ‘supervenient’: Let me illustrate one of the most characteristic features of value-words … It is a feature sometimes described by saying that ‘good’ and other such words are the names of ‘supervenient’ or ‘consequential’ properties. Suppose that a picture is hanging upon the wall and we are discussing whether it is a good picture … Suppose that there is another picture next to P in the gallery (I will call it Q) … Now there is one thing that we cannot say; we cannot say ‘P is exactly like Q in all respects save this one, that P is a good picture and Q not’. If we were to say this, we should invite the comment, ‘But how can one be good and the other not, if they are exactly alike? There must be some further difference between them to make one good and the other not’ … Sometimes we cannot specify just what it is that makes one good and the other not; but there always must be something. (Hare 1952, pp. 80–1, bold emphasis added) Since, as we have already remarked, ‘good’ is a ‘supervenient’ or ‘consequential’ epithet, one may always legitimately be asked when one has called something a good something, ‘What is good about it?’ Now to answer this question is to give the properties in virtue of which we call it good. Thus, if I have said, ‘That is a good motor-car’ and someone asks ‘Why? What is good about it?’ and I reply ‘Its high speed combined with its stability on the road’, I indicate that I call it good in virtue of its having these properties or virtues. Now to do this is eo ipso to say something about other motor-cars which have these properties. If any motor-car whatever had these properties, I should have, if I were not to be inconsistent, to agree that it was, pro tanto, a good motor-car. (Hare 1952, p. 131, bold emphasis added) In both of these passages we find the idea that supervenient properties necessarily covary with certain other properties: no difference in the first set of properties without a difference in the second set of properties. However, that familiar way of understanding supervenience is combined with another idea, namely, that the supervenient properties hold in virtue of certain other properties.6 Indeed, in these two passages it is difficult to tell which of these two ideas—(a) that supervenient properties necessarily covary with other properties, and (b) that supervenient properties are always grounded in other properties—is primary, or whether Hare in fact intends both ideas to be definitive of supervenient properties (so that supervenient properties are always grounded in certain other properties with which they necessarily covary). Overall, the textual evidence suggests that Hare was not clear in his mind whether he meant supervenient properties to be defined as properties that necessarily covary with other properties, or as properties that hold in virtue of other properties, or both.7 Hare’s use of the term ‘supervenience’ did not catch on until Donald Davidson put it to use in these sentences from his 1970 article ‘Mental Events’: Although [anomalous monism] denies there are psychophysical laws, it is consistent with the view that mental characteristics are in some sense dependent, or supervenient, on physical characteristics. Such supervenience might be taken to mean that there cannot be two events alike in all physical respects but differing in some mental respect, or that an object cannot alter in some mental respect without altering in some physical respect. (Davidson 1970, p. 88, emphasis added) This passage led to two trends. First, it became standard to define supervenience as a relation of necessary covariation. Second, often it was thought that this covariation relation just is the grounding/dependence relation. (Note Davidson’s use of the ‘or’ of identity in the first italicized portion of the quotation.) Now, as I said, an important theme in recent work on grounding has been to insist that this second trend is a mistake—to insist that the supervenience relation (which I will understand, from this point on, purely as a relation of necessary covariation) and the grounding relation are distinct from one another, and more generally to insist that grounding cannot be defined in terms of supervenience. We can extract from the recent grounding literature two main forms of argument for these claims. The first—call it the argument from formal structure—is not terribly convincing.8 It goes as follows: ‘We know the grounding relation is not the supervenience relation because they have different formal properties. Grounding is irreflexive and asymmetric, whereas supervenience is reflexive and non-asymmetric’. This argument is too quick. At most it is a way of blocking the proposal that grounding is supervenience. However, the argument is powerless against the proposal that grounding is one-way supervenience (where X one-way supervenes on Y if and only if X supervenes on Y but not vice versa), since one-way supervenience is both asymmetric and irreflexive. The second form of argument in the recent grounding literature—call it the argument from fineness of grain—is more compelling. The central idea is this: the grounding relation can draw distinctions between necessarily co-obtaining facts and between necessarily coextensive properties, but the supervenience relation cannot. This disparity leads to a variety of counterexamples to the proposal that grounding is supervenience (as well as to the proposal that grounding is one-way supervenience). Some of these counterexamples involve two necessarily co-obtaining facts, F1 and F2, which are plausibly held to bear a grounding relation in one direction but not the other; this is problematic, because if F1 supervenes on F2, then F2 also supervenes on F1. For example, as Fine has famously emphasized, the fact that the set {Socrates} exists is presumably grounded in the fact that the individual Socrates exists, and not vice versa. However, the fact that {Socrates} exists and the fact that Socrates exists supervene on one another: no difference with respect to either fact without a difference with respect to the other. A second sort of counterexample involves a fact, F, and two necessarily co-obtaining sets of facts, Γ1 and Γ2, such that it is plausible that F obtains in virtue of Γ1 but not plausible that F obtains in virtue of Γ2; this is problematic, because if F supervenes on Γ1, then F also supervenes on Γ2. For example, as Mark Greenberg (2004, p. 159) and Rosen (2010, pp. 113–4) have emphasized, the debate over legal positivism can be interpreted as a debate over whether the legal facts are wholly grounded in the social facts, or whether they are grounded in the social facts plus the moral facts. But if the basic moral facts are necessary, then a given legal fact will supervene on the social facts if and only if that legal fact supervenes on the social facts plus the basic moral facts. So although we can understand this debate in terms of grounding, we cannot understand it in terms of supervenience. According to the standard narrative, these two forms of argument are innovations due to Fine, Rosen, Schaffer, and the other early contributors to the twenty-first century grounding literature. But—and here we reach the second way in which I think that narrative is inaccurate—a number of authors had already offered these exact arguments against identifying supervenience and grounding in the 1980s and 1990s, as well as a host of other arguments not as often cited. For instance, Jonathan Dancy’s ‘On Moral Properties’ (published in Mind in 1981) is mostly known these days as the first appearance of the view he eventually dubbed ‘moral particularism’, but that article is primarily devoted to arguing that supervenience and grounding are distinct relations. Another example is Michael DePaul’s ‘Supervenience and Moral Dependence’ (1987), which features versions of both the argument from fineness of grain and the argument from formal structure. And similar objections to identifying grounding/dependence with supervenience were offered around the same time by a variety of other authors (Lombard 1986, §8.3; Grimes 1988; Kim 1990, §4; Kim 1993, §3; McLaughlin 1995, §1; Savellos and Yalçin 1995a, §6; Garrett 1997). Thus, on my retelling of the standard narrative, there was only a short period during which supervenience-as-necessary-covariation and grounding were kept cleanly separated from each other and the former preferred over the latter. Not only was ‘supervenient property’ originally introduced in its distinctively philosophical sense in a way that made it ambiguous between ‘property that necessarily covaries with some other set of properties’ and ‘property that is always possessed in virtue of some other property or properties’ before philosophers’ practices shifted in the 1970s and the first of these meanings became primary (this was my first point of disagreement with the standard narrative), but moreover all the standard arguments against taking supervenience to be a form of dependence were well known to those working on these issues by the early 1990s (this was my second point of disagreement with the standard narrative). Still, this way of telling the entwined history of grounding and supervenience might seem to share one feature with the standard narrative: it might seem to situate the recent wave of enthusiasm for grounding as a return, albeit a return to the mid-twentieth century, instead of a return to antiquity. But talk of ‘a return’ suggests that grounding had temporarily disappeared from the scene. Perhaps it had in metaphysics. However—and this constitutes my third point of disagreement with the standard narrative—there is one branch of philosophy where the grounding/in-virtue-of/non-causal-‘because’ relation most certainly never disappeared, namely, moral philosophy. 3. Appeals to grounding in normative inquiry I now want to argue that there are a number of central debates in moral philosophy—and in normative inquiry more generally—which it is both natural and proper to formulate in terms of a metaphysical grounding relation. Let us start with so-called ‘first-order’ or ‘normative’ ethics, and with the debate that has dominated that field for the past century or so: the dispute between consequentialists and their opponents. The old way of formulating this debate was to ask ‘Is the right prior to the good, or the good prior to the right?’ More recently, that snappy formulation has given way to a more nuanced one, now that it is generally recognized that even non-consequentialists can hold the good to be prior to the right, as long as they endorse a distinctively non-consequentialist account of the nature of value and how we should respond to it. So now the central question has become ‘Is it the case that (a) the good is prior to the right, and (b) all good is to-be-promoted?’ with non-consequentialists being free to deny (a), (b), or both.9 Note, though, that even this more complicated way of characterizing the debate appeals to a notion of priority. But what exactly is the variety of priority at issue here? When a consequentialist philosopher asserts ‘The good is prior to the right’, and when some (but not all) of her opponents deny this, what exactly is being asserted and denied? There are a number of proposals we can set aside rather quickly. The consequentialism debate, at least as it exists today, is clearly not a debate over semantic or conceptual priority. Although G. E. Moore insisted in Principia Ethica (1903) that maximizing act-consequentialism is an analytic truth, few philosophers since then have thought we can determine the truth of consequentialism merely by considering the meanings of our moral terms, and even Moore himself changed his mind by the time he wrote Ethics (1912). The idea that maximizing act-consequentialism might be a conceptual truth is equally implausible.10 Can we really believe that non-consequentialists—and, for that matter, consequentialists of a non-maximizing or non-act persuasion—are conceptually confused when they insist that maximizing act-consequentialism is false? Surely consequentialists disagree with their opponents—and with each other—over substantive matters, not over linguistic or conceptual matters. It is also clear that ‘prior’ in ‘Is the good prior to the right?’ does not refer to a form of epistemic priority. Normative ethics is not moral epistemology, and consequentialists are free to accept an account of the order in which we come to know moral truths on which it sometimes is the case that our knowledge of the good is parasitic on our knowledge of the right. Nor does ‘prior’ in this debate refer to a form of causal dependence. It is widely believed that evaluative properties (such as being good) and deontic properties (such as being right) do not have causal powers. And even if such properties do have causal powers, it would be odd if making sense of the consequentialism debate required us to take such a controversial stand on that particular issue. A more plausible suggestion is that the sort of priority at issue in debates over consequentialism can be understood in terms of supervenience. However, a variant of DePaul’s (1987, pp. 433–4) version of the argument from fineness of grain shows that this suggestion cannot be correct. Consider the relation between the properties being right and being optimific (where, by definition, an action is optimific if and only if it produces at least as much overall good as any alternative). If maximizing act-consequentialism is the correct moral theory, then: (Op) Necessarily, an action is right if and only if it is optimific. It follows that being right supervenes on being optimific, and vice versa. But maximizing act-consequentialists will presumably want to say that the fact that an action is optimific is prior to the fact that it is right, but not vice versa. So the notion of priority in this dispute cannot be a matter of supervenience. Similar reasoning shows that the consequentialism debate is not about counterfactual dependence or about logical entailment. We cannot construe the maximizing act-consequentialist’s claim that being optimific is prior to being right, but not vice versa, as the claim that if an action were optimific, then it would be right, but not vice versa. According to standard accounts of the truth-conditions for subjunctive/counterfactual conditionals, (Op) entails both <If an action were optimific, it would be right> and <If an action were right, it would be optimific>.11 Of course non-standard accounts are available, but, as with the casual-dependence proposal, it would be surprising if making sense of the debate between consequentialists and their opponents required us to adopt non-standard truth conditions for subjunctive conditionals. Similarly, we cannot construe the maximizing act-consequentialist’s priority thesis as the claim that <Action A is optimific> entails <A is right>, but not vice versa. On some accounts of logical entailment, if < p> necessitates <q>, then <p> entails <q>. It follows from such accounts that if (Op) is true, then <A is optimific> both entails and is entailed by <A is right>. Other accounts of logical entailment deny that necessitation is sufficient for entailment, perhaps on the grounds that <There’s water in that cup> does not entail <There’s H2O in that cup>, and <Carol is Henry’s mother> does not entail <Carol is female>.12 But on almost all accounts of this latter sort, it will—given (Op)—neither be the case that <A is optimific> entails <A is right> nor that <A is right> entails <A is optimific>. So either way, we fail to have an entailment in one direction but not the other. Perhaps, then, we should interpret the sort of priority claim being made by consequentialists as amounting to a claim about identity; perhaps, for example, we should understand the maximizing act-consequentialist’s distinctive priority thesis as consisting in the claim that the property being right is identical to the property being optimific, and hence the fact [Action A is right] is identical to the fact [A is optimific].13 But this proposal is not a way of interpreting the maximizing act-consequentialist’s claim that the latter of these two facts is prior to the former; rather, it involves denying that priority claim, since no fact can be prior to itself. As such, this proposal does violence to our usual way of understanding consequentialism. (Consequentialism, as we usually understand it, does not answer the question ‘Is the right prior to the good, or the good prior to the right?’ with the retort ‘Neither: they’re identical’.) Moreover, even if this suggestion were a charitable way of construing the relationship being put forward by maximizing act-consequentialists between [A is right] and [A is optimific], it would not allow us to sidestep the issue of how to understand the priority relation being invoked in debates over consequentialism. Presumably maximizing act-consequentialists hold that there are various facts about the goodness of specific actual and possible outcomes that are prior to the general evaluative fact [A is optimific]. So even if [A is right] is identical to [A is optimific], we can still ask about the nature of the priority relation that holds between that general evaluative fact and the more specific evaluative facts about the goodness of each outcome. And at this point we cannot invoke the identity relation once again, since one fact cannot be identical to a plurality of facts. Where does this leave us? What we are looking for is not a semantic, conceptual, or epistemic notion of priority, but rather a metaphysical notion, in the thin sense of concerning how things are, not our knowledge of those things or our words or concepts for them. Causal dependence, supervenience, counterfactual dependence, identity, and (arguably) logical entailment all count as metaphysical relations, in this thin sense, but they are the wrong tools for the job. A far better proposal—and a much more natural suggestion, I might add—is that the type of priority at issue here is grounding. On this proposal, consequentialists insist that facts about rightness obtain in virtue of certain facts about goodness, that the latter facts are what make it the case that the former facts obtain, that it is because of the relevant facts about goodness that the corresponding facts about rightness hold. These claims just roll off the tongue, and for good reason. Grounding is what we are after. I do not intend my proposal here to be controversial; in fact, I think this is the default way of understanding the notion of priority at stake when we ask ‘Is the good prior to the right?’ It has been standard for a while now to insist that consequentialism provides an account of an action’s right-making characteristics.14 All I am suggesting is that we take this ‘making’-talk at face value and see it as picking out the grounding/in-virtue-of relation. Similarly, if a maximizing act-consequentialist were to formulate her central thesis as: (Op*) Necessarily, an action is right if and only if, and because, it is optimific instead of (Op)  Necessarily, an action is right if and only if it is optimific I don’t think anyone would look askance at her for including the ‘and because’-qualifier. Indeed, when consequentialists drop that qualifier and write (Op) rather than (Op*), I think it is customary to take the ‘and because’-qualifier as understood. I have just been emphasizing the way in which consequentialism should be interpreted as a view that makes certain distinctive claims about the grounds of rightness (and, in turn, about the grounds of goodness). The same is true of consequentialism’s traditional opponents: their positive positions are also best interpreted as consisting in various claims about the grounds of rightness, goodness, and whatever other normative notions are under their purvey. For example, one alternative to consequentialism is W. D. Ross’ theory of prima facie duties. According to Ross, (i) there are a small number of distinctive sorts of properties (such as being a breaking of a promise or contributing toward the improvement of one’s own character) in virtue of which an act is either prima facie right or prima facie wrong, (ii) the degree of prima facie rightness or prima facie wrongness grounded in those properties depends on all the facts of the case at hand in an uncodifiable manner, and (iii) an act is either right (sans phrase) or wrong (sans phrase) in virtue of the overall balance of prima facie rightness and prima facie wrongness possessed by that act in comparison to its alternatives. My summary here of Ross’ view has made free use of the phrases ‘in virtue of’ and ‘grounded’, but this is no anachronistic re-reading on my part. Ross first presents his theory in a chapter titled ‘What Makes Right Acts Right?’ (Ross 1930, ch. 2, emphasis added), and his discussion is shot through with many of the traditional ways of picking out the grounding relation, including the expressions ‘makes’ (pp. 16, 24, 33), ‘because’ (pp. 18, 44, 46, 47), ‘in [or: by] virtue of’ (pp. 19, 28, 29, 30, 32, 33, 43), ‘depends’ (pp. 33, 43, 47), ‘ground’ (pp. 37, 46, 47), and ‘due to’ (p. 46). It would be a gross misreading of Ross to take him to be formulating his theory using a notion other than grounding. I believe something similar is true of most other non-consequentialist moral theories. When such theories are in the business of seeking exceptionless principles, they should be understood not merely as proposing biconditionals of the form (Bi)  Necessarily, an action is right if and only if _____ but rather as offering accounts of the grounds of moral notions, like so: (Bi*) Necessarily, an action is right if and only if, and because, _____. Similarly, when non-consequentialist moral philosophers focus on particular verdicts about particular scenarios, they should be understood not merely as seeking to establish a bald claim of the form (Ver)  Action A is right in circumstances C but rather as seeking to understand why that verdict holds, so that we have (Ver*) Action A is right in circumstances C because _____. Again, I don’t think I am saying anything controversial here. It is almost a truism that we want our moral theories not merely to be extensionally adequate, but moreover to be properly explanatory. Thus I see first-order moral philosophy as fundamentally in the business of proposing (and assessing, and establishing) various grounding claims. Moreover, I think the same is true of most other first-order investigations of normative notions. For example, consider the widely popular ‘reasons first’ approach to normativity, according to which reasons are the fundamental particles of the normative realm, and all other normative facts, properties, and relations can be analysed or accounted for in terms of the reason relation. Two theses are being put forward here: first, that reasons are not analysable or accountable in other terms (as a catchphrase: ‘Reasons are first’) and, second, that every other normative notion can be analysed or accounted for in terms of reasons (as a slightly-less-catchy phrase: ‘Reasons are not tied for first’). When interpreting either of these theses, I think we do best to understand the relevant notion of analysis or accounting-for in terms of the grounding relation, for reasons very similar to the ones we considered in the case of consequentialism. Consider the second thesis first. When reasons-firsters say that all evaluative and deontic facts can be analysed or accounted for in terms of facts about reasons, they are not—or, at least, not only—making a semantic or conceptual claim, or a claim about epistemic or causal dependence, or a claim about supervenience, counterfactual dependence, or logical entailment. Rather, they are claiming that all evaluative and deontic facts are grounded in facts about reasons, that it is in virtue of the facts about reasons that these other normative facts obtain. What makes it the case that I ought to perform such-and-such action in such-and-such circumstances? A reasons-firster will say: the various reasons for and against that action and its alternatives. What makes it the case that I ought to believe such-and-such proposition in such-and-such situation? A reasons-firster will reply: the various reasons for and against my holding a belief in that proposition. In other words, the reasons-firsters’ second thesis, as captured in the slogan ‘Reasons are not tied for first’, is most naturally expressed in terms of grounding. Similarly, I think we also do best to interpret the reason-firsters’ first thesis, as captured in the slogan ‘Reasons are first’, in terms of the grounding relation. The sense in which it is being proposed that nothing comes before reasons is an explanatory sense: their central claim is that it is not because of any facts about other normative categories that facts about reasons obtain. This way of characterizing the reasons-first program allows us to easily explain an otherwise puzzling aspect of that program. There is in fact a divide among reasons-firsters: although some of them think that (at least some) facts about reasons are ungrounded, other self-professed reason-firsters think that certain natural facts always serve to explain why a given consideration counts as a reason in a given context. But if natural facts can come before facts about reasons, in what sense are reasons first? The answer is that, when it comes to the reason-firsters’ first thesis, we need to distinguish between a stronger and weaker way of reading that thesis, corresponding to a stronger and weaker way of reading the slogan ‘Reasons are first’, as follows: ‘Reasons are first, full stop’: All basic facts-about-reasons are ungrounded.15 ‘Reasons are normatively first’: All basic facts-about-reasons are not grounded (even partly) in any normative facts (although they may well be grounded in certain non-normative facts). Reasons-firsters who are non-naturalists (Parfit 2011, Scanlon 2014) tend to embrace the first way of interpreting the slogan ‘Reasons are first’, whereas those who are naturalists (Schroeder 2014, Street 2006) tend to embrace the second. It must be conceded that here I am going against how reason-firsters sometimes characterize their own program. I have been suggesting that we do best to understand that program in terms of the grounding/in-virtue-of/non-casual-‘because’ relation. Although reasons-firsters occasionally frame their program using the idiom of grounding and talk of explanation, much more frequently reasons-firsters characterize their view in terms of reduction. For example, Parfit rarely formulates his non-naturalist view about the nature of reasons in terms of grounding, but he repeatedly says that, on his view, facts about reasons are irreducibly normative truths.16 Similarly, here is Scanlon describing the reasons-first view he dubs ‘reasons fundamentalism’: Truths about reasons are fundamental in the sense that truths about reasons are not reducible to or identifiable with non-normative truths, such as truths about the natural world of physical objects, causes and effects, nor can they be explained in terms of notions of rationality or rational agency that are not themselves claims about reasons. Reasons might be fundamental in the further sense of being the only fundamental elements of the normative domain, other normative notions such as good and ought being analyzable in terms of reasons. (Scanlon 2014, p. 2, bold emphasis added) A number of potentially distinct notions are mentioned here, including reduction, identity, explanation, and analysis. But most often when Scanlon goes on to discuss the commitments of reasons fundamentalism, he appeals to the idea that truths about reasons are irreducible (or irreducibly normative). Now the exact relation between reduction and grounding is controversial. On some views, reduction and grounding are one and the same,17 and if that is so, then my characterization of the reasons-first program in terms of grounding is equivalent to the characterization its practitioners provide in terms of reduction. However, on other views, reduction is distinct from grounding, and if that is so, then it is more in the spirit of the reasons-first program to formulate it in terms of grounding rather than in terms of reduction. The argument for this claim is simple. First, as Rosen (2010, §10) has argued, it is extremely plausible that reduction entails grounding, in the following sense: (Re)  Necessarily, if fact F reduces to set of facts Γ, then F is entirely grounded in Γ.18 So the only way in which reduction can pull apart from grounding is in a case in which we have grounding without reduction. But in such cases, I think reasons-firsters are more likely to take the presence of grounding, rather than a lack of reduction, to be the issue which is more relevant to their position. For example, if a philosopher were to claim (†)  [Agent A has a reason to ϕ in circumstances C] obtains entirely in virtue of, but is not reducible to, [A ought to ψ in circumstances D] I think reasons-firsters would view this claim as being in tension with their first thesis. Isn’t (†), on its own, enough to block the claim that reasons are first, in the relevant sense? Similarly, if a different philosopher were to claim (††)  [Agent A ought to ϕ in circumstances C] obtains entirely in virtue of, but is not reducible to, [A has a reason to ϕ in C, has no reasons against ϕ-ing in C, and has no reasons for or against any alternative to ϕ-ing in C] I think reasons-firsters are likely to see this claim as offering partial confirmation of their second thesis. Isn’t (††), on its own, enough to support the claim that reasons come before oughts, in the relevant sense? In short: if we mark a distinction between reduction and grounding, it is better to formulate the reasons-first program in terms of grounding, and if we don’t mark such a distinction, it is harmless to phrase things in terms of grounding. I have just argued that the very grounding relation being touted by metaphysicians plays a central role in one important debate in moral philosophy—namely, the debate over consequentialism—and also plays a central role in an equally important debate concerning normativity in general—namely, the debate over whether reasons are first. I believe the same is true of most other areas of normative inquiry: each features a number of key debates that turn on the truth of certain grounding claims. Moreover, in many of these cases, framing the relevant debate in terms of grounding is not some innovation we have only recently come to appreciate; rather, most of these debates have been formulated using language such as ‘in virtue of’, ‘because’, ‘makes the case’, and ‘depends’ from their inception. 4. The threat of grounding pluralism I have been claiming that appeals to a metaphysical notion of grounding are a crucial component of normative theorizing. If I am right, then philosophers investigating normative matters should welcome the recent upsurge of interest among metaphysicians in the grounding relation. Moreover, they should view grounding not as some new-fangled invention that can help them with their theory building (or theory destroying), but rather as a tool they have been using all along, albeit not always with full self-consciousness. In making these claims, I have spoken indiscriminately of ‘the’ grounding relation and acted as if the sort of dependence relation being studied by metaphysicians is the same as that being employed in normative contexts. It turns out, though, that these assumptions of mine are controversial. In particular, Kit Fine—probably the philosopher whose work has had the single largest influence on the burgeoning field of grounding studies—disagrees with these assumptions. According to Fine, there are three distinct grounding relations: metaphysical grounding, normative grounding, and natural grounding.19Fine (2012a, p. 37) provides the following examples of each type of grounding: [The ball is red and round] is metaphysically grounded in [The ball is red] and [The ball is round]. [His action was wrong] is normatively grounded in [His action was performed with the sole intention of causing harm]. [The particle is accelerating] is naturally grounded in [The particle is being acted upon by a positive net force]. Moreover, Fine (2012a, p. 39) denies that ‘each of these explanatory relations [can] be defined in terms of a single generic relation’. But if this is so, then it is not true that the relation being studied by metaphysicians is the same as the one whose importance in normative debates I have been urging. It is also not true that we can argue against the idea that metaphysical grounding is something new by appealing to its ubiquity in normative disciplines over the past few decades. Thus Fine’s brand of grounding pluralism constitutes an objection to my earlier claims. In what follows, I shall argue that Fine is wrong to hold that grounding is disunified in the way he proposes. In other words, I shall argue for grounding monism, the view, roughly, that there is only one grounding relation. But first, I would like to be a bit clearer about what these two positions—grounding monism and grounding pluralism—come to. So far I have characterized grounding monism and pluralism in terms of the number of grounding relations they countenance: either one (grounding monism) or more than one (grounding pluralism). However, some qualifications are needed here, or else it will turn out that grounding monism is patently false. For instance, it is widely agreed that we need to distinguish between partial grounding and full grounding. Not only do we want to say that [The ball is red and round] is fully grounded (whether metaphysically or in a single, unified sense) in [The ball is red] and [The ball is round], taken together, but we also want to say that [The ball is red and round] is partially grounded in [The ball is red] by itself. Does this mean that there are at least two grounding relations, and that grounding monism is a non-starter? No. All it means is that we need to be more careful when formulating our respective forms of monism and pluralism. Here we can take a hint from Fine. Recall that he denied that there is a generic grounding relation in terms of which metaphysical, normative, and natural grounding can be defined. Thus the crucial issue is not the mere number of distinct grounding relations that we can list, but rather the number of grounding relations in terms of which all other grounding relations can be defined. Let us say that grounding relation R1 is fundamentally distinct from grounding relation R2 if and only if (a) R1 and R2 are distinct relations, (b) R1 cannot be defined in terms of R2, (c) R2 cannot be defined in terms of R1, and (d) there is no other grounding relation in terms of which both R1 and R2 can be defined. And let us say that grounding relation R is fundamentally unique if and only if all other grounding relations can be defined in terms of it. We may then formulate grounding monism and pluralism as follows: grounding monism: There is a fundamentally unique grounding relation. grounding pluralism: There are at least two fundamentally distinct grounding relations. These formulations avoid the worry that distinguishing between partial and full grounding renders grounding monism obviously false. It is standard to hold that partial grounding can be defined in terms of full grounding, like so (Rosen 2010, p. 115): (Par)  Fact [p] is partially grounded in set of facts Δ = df for some set of facts Γ, [p] is fully grounded in Γ, and Δ is a subset of Γ. Since partial grounding can be defined in terms of full grounding, the two grounding relations are not fundamentally distinct, and thus countenancing both does not jeopardize any commitment one might have to grounding monism.20 This way of characterizing grounding monism and pluralism invites the following question: what sense of ‘define’ do I have in mind? My answer: whatever sense in which partial grounding can be defined in terms of full grounding, that is the sense we should use when formulating grounding monism and pluralism. In what follows I simply treat ‘definition’ as a black box into which one can insert one’s favourite definition of definition, as it were. 5. Against moderate grounding pluralism Fine is a grounding pluralist, but his form of grounding pluralism is relatively moderate: he only countenances three fundamentally distinct varieties of grounding, and he does not see his pluralism as licensing scepticism about the significance of grounding as a tool for philosophical theorizing or as a topic for philosophical research. Eventually we shall encounter a more extreme form of grounding pluralism, according to which there is no generic grounding relation underlying all others, but rather only a large number of already familiar dependence relations such as the set-membership relation and the determinate–determinable relation, with the result being that we should be sceptical of the idea that there is an exciting new topic here. I intend to argue against both sorts of pluralism, but it will help to start by explaining my argument as it applies to moderate pluralists such as Fine.21 The basic idea behind my argument is simple. It is standard to assume that there are various logical principles governing the grounding relation, such as a principle of transitivity or the principle that a disjunction is always grounded in at least one of its disjuncts. Some of these principles, when formulated in a pure way so that the same grounding relation appears throughout the principle, hold for each of the grounding relations posited by the pluralist. But what about mixed versions of those principles, in which we formulate them using several different grounding relations in the same principle? If the mixed versions of the logical principles are just as plausible as the pure ones, this gives us excellent reason to think that there is in fact a unity here, not several distinct relations that cannot be defined in terms of each other. Otherwise why would these various distinct relations be logically related to one another in this way? More specifically, here is how my argumentative strategy works, when applied to Fine’s brand of pluralism. Each iteration of the argument involves three steps: Find a logical principle which relates several grounding claims to one another and which holds when it is applied exclusively to metaphysical grounding, or exclusively to natural grounding, or exclusively to normative grounding; Argue that the logical principle also holds in mixed cases; Infer that the best explanation of (i) and (ii) is that there is a single generic grounding relation underlying these more specific grounding relations. There are any number of logical principles for which, I believe, this strategy can be pursued. However, I shall restrict myself to showing how the argument works when applied to two of the most widely accepted logical principles governing grounding, namely, a principle of transitivity and a principle of asymmetry. I focus on these two principles because they are so widely accepted, and because they demonstrate importantly different ways in which my argumentative strategy can work. In what follows I only demonstrate how this strategy can be used to unify Fine’s notions of metaphysical and normative grounding, since that is the case that most concerns me. It is easy enough to use similar arguments to unite natural grounding with the others as well. 5.1 The Argument from Transitive Links Let us begin, then, with the argument as applied to transitivity. I call this way of implementing my strategy ‘the Argument from Transitive Links’. Let us grant to Fine, for the sake of argument, that there is both a metaphysical and a normative grounding relation. It is extremely plausible that each of these relations is transitive, so that the following principles hold: (Tranmet)  If [p] is partially metaphysically grounded in [q], and [q] is partially metaphysically grounded in [r], then [p] is partially metaphysically grounded in [r]. (Trannor)  If [p] is partially normatively grounded in [q], and [q] is partially normatively grounded in [r], then [p] is partially normatively grounded in [r]. For example, if [The ball is red and round, or the ball is orange and oval] is fully (hence partially) metaphysically grounded in [The ball is red and round], and if [The ball is red and round] is partially metaphysically grounded in [The ball is red], then surely [The ball is red and round, or the ball is orange and oval] is partially metaphysically grounded in [The ball is red]. Similarly, if [Action A is right] is fully (hence partially) normatively grounded in [A is optimific], and if [A is optimific] is fully (hence partially) normatively grounded in [A maximizes happiness], then surely [A is right] is normatively grounded (both partially and fully) in [A maximizes happiness]. It is also extremely plausible that the following mixed versions of these principles hold: (Tranmet/nor)  If [p] is metaphysically grounded in [q], and [q] is normatively grounded in [r], then [p] is grounded (in some non-rigged-up sense) in [r]. (Trannor/met)  If [p] is normatively grounded in [q], and [q] is metaphysically grounded in [r], then [p] is grounded (in some non-rigged-up sense) in [r]. (Here I drop the ‘partially’-qualifiers to reduce clutter; from this point on those qualifiers should be taken as understood, unless I specify otherwise.) It is necessary to include the phrase ‘in some non-rigged-up sense’ in these principles because we can always cook up a variety of grounding that would make (Tranmet/nor) and (Trannor/met) true if that phrase were dropped—by, for instance, defining a (supposed) grounding relation that consists in the transitive closure of the disjunction of metaphysical and normative grounding. But this is a cheap way of ensuring adherence to mixed transitivity principles. By a similar trick, we can make any two relations obey a mixed transitivity principle. I think we have a strong intuition that (Tranmet/nor) and (Trannor/met) are true without our needing to resort to such manoeuvres. Examples which support these two mixed principles are plentiful. Suppose the moral fact W = [She acted wrongly in telling him] obtains normatively in virtue of the natural fact S = [She could have done something else instead of telling him that would have brought about more overall happiness]. And suppose the disjunctive fact O = [Either she acted wrongly in telling him, or she acted in a way she believed to be wrong] obtains metaphysically in virtue of W. Then it is very natural to hold that O also obtains in virtue of S, in some non-rigged-up sense of ‘in virtue of’. This offers partial confirmation of (Tranmet/nor). Similarly, suppose that W still normatively obtains in virtue of S, and suppose that, in addition, S obtains metaphysically in virtue of L = [She could have lied instead of telling him, her lying would have brought about 100 overall units of happiness, and her telling him brought about 20 overall units of happiness]. Then it is very natural to hold that W also obtains in virtue of L, in some non-rigged-up sense of ‘in virtue of’. This offers partial confirmation of (Trannor/met). However, if metaphysical and normative grounding were fundamentally distinct grounding relations, as Fine holds, then it would be very puzzling why (Tranmet/nor) and (Trannor/met) are true. Why on earth are metaphysical and normative grounding logically related to each other in this way, given Fine’s conception of their relation (or lack thereof)? Why on earth is it possible to link these two relations together via applications of transitivity and derive additional grounding claims, if the two grounding relations have, at a fundamental level, nothing to do with each other? Two analogies will help. Sometimes when we say that one city is larger than another, we mean that the first city is larger in area than the second, and sometimes we mean that the first city is larger in population than the second. Let us use ‘largerarea’ to refer the first of these relations and ‘largerpop’ to refer to the second. Both of these relations are transitive, but they don’t obey mixed transitivity principles analogous to (Tranmet/nor) and (Trannor/met). Dallas is largerarea than New York City, and New York City is largerpop than Los Angeles, but it doesn’t follow that Dallas is larger, in some sense, than Los Angeles. Why does mixed transitivity fail in this case? Because these two relations are fundamentally distinct: definitionally, they have nothing to do with one another. Now contrast that case with another. Being a matrilineal descendant of and being a patrilineal descendant of are two transitive relations for which analogues of (Tranmet/nor) and (Trannor/met) do hold. Why? Because each of them can be defined in terms of being a child of and either being female or being male in such a way that the relevant mixed transitivity principles follow. The case of largerarea vs. largerpop is a typical example of what happens when we consider mixed transitivity principles for two fundamentally distinct transitive relations of a given sort. Similarly, the case of matrilineal descendance vs. patrilineal descendance is a typical example of what happens when we consider mixed transitivity principles for two fundamentally related transitive relations of a given sort. If metaphysical and normative grounding really were fundamentally distinct grounding relations, as Fine suggests, then we would expect mixed transitivity principles involving metaphysical and normative grounding to be as implausible as the analogous mixed transitivity principles involving the two larger-than relations. But what we find is the opposite: the mixed transitivity principles for metaphysical and normative grounding are as plausible as they are in the case of the two descendance relations. All of which gives us excellent—though, of course, defeasible—evidence that metaphysical and normative grounding are fundamentally linked to one another in some way.22 It might appear that in offering this argument, I have relied on an assumption that at least some authors in the grounding literature dispute, namely, that grounding is transitive. Presumably those who deny the transitivity of grounding will deny (Tranmet), (Trannor), (Tranmet/nor), and (Trannor/met) as well. Does the force of my argument thereby dissipate? It does not. For what matters to the argument are the overall patterns evinced by the metaphysical and normative grounding relations and the way those two patterns interact so as to entail the presence of additional grounding relations. This pattern of interaction can still occur even if transitivity does not hold in general, for usually those who deny transitivity still admit that for the most part grounding is transitive. For instance, Schaffer (2012) has argued that the following is a counterexample to the transitivity of grounding. Imagine a metal ball that, aside from one minor dent, is a perfect sphere. Let ‘B’ refer to the ball and ‘S’ to the ball’s maximally determinate shape. According to Schaffer, [B has the particular dent it does] partially grounds [B has shape S], and [B has shape S] partially grounds [B is more-or-less spherical], even though [B has the particular dent it does] does not partially ground [B is more-or-less spherical]. Now, as it turns out, I don’t think Schaffer’s example here is convincing.23 But even if we concede to Schaffer his counterexample, the Argument from Transitive Links for grounding monism is not thereby imperilled. For although Schaffer’s example might perhaps show that transitivity does not hold in every possible situation, it does nothing to undermine the many individual cases in which it is plausible that instances of (Tranmet/nor) and (Trannor/met) hold. And that is all we need to run the Argument from Transitive Links. In particular, Schaffer’s example does not weaken our conviction that if [She could have done something else instead of telling him that would have brought about more overall happiness] normatively grounds [She acted wrongly in telling him], which in turn metaphysically grounds [Either she acted wrongly in telling him, or she acted in a way she believed to be wrong], then there must be some non-rigged sense in which the first of these facts grounds the third. Moreover, it would be utterly mysterious why this would be so if normative and metaphysical grounding were fundamentally distinct grounding relations. In short, all we need to run the Argument from Transitive Links are the particular instances in which our mixed transitivity principles are true, not those principles in their full generality. This is enough to give us excellent reason to believe that there must be some sort of fundamental link between metaphysical and normative grounding. But if such a connection between metaphysical and normative grounding exists, what does it look like? One possibility—call it the identity proposal—is that there is just a single generic grounding relation, and the so-called ‘metaphysical’ and ‘normative’ grounding relations are identical to this relation. Another possibility—call it the suppression proposal—is that so-called ‘metaphysical’ grounding is just the generic grounding relation, and normative grounding can be defined in terms of that relation as follows: (Nor)   [p] is (fully) normatively grounded in Δ = df there exists a non-empty set, Γ, of fundamental normative truths such that [p] is (fully) generically grounded in Δ ∪ Γ. In short: normative grounding is metaphysical grounding in which the appeal to fundamental normative truths has been suppressed. Now personally I prefer the first of these proposals, for the following reason. As already mentioned, I think a typical fundamental normative truth is of the form (Op*) Necessarily, an action is right if and only if, and (fully) because, it is optimific rather than of the form (Op)  Necessarily, an action is right if and only if it is optimific.24 However, if we want to say that [Action A is right] is fully normatively grounded in [A is optimific] due to the fact that [A is right] is fully generically grounded in (Op*) and [A is optimific], taken together, we face a dilemma. What variety of grounding does the ‘because’ in (Op*) pick out? If it picks out grounding in the generic sense, then (Op*) is not needed in order to fully generically ground [A is right]; [A is optimific] on its own is enough. But if the ‘because’ in (Op*)—and in the other fundamental normative truths—picks out normative grounding, then our definition of normative grounding becomes objectionably circular, since the normative grounding relation has been defined in terms of something that itself involves a normative grounding relation. Regardless, though, of whether we prefer the first way I have mentioned of linking metaphysical and normative grounding, or the second way, or some other way all together, I think the plausibility of (numerous instances of) our mixed transitivity principles gives us good reason to think that some linkage is needed. Additional evidence is provided by consideration of mixed versions of an asymmetry constraint on grounding. 5.2 The Argument from Asymmetric Dovetailing Grounding seems to be an asymmetric relation of dependence. So if we distinguish between metaphysical and normative grounding, as Fine does, then presumably each of these relations will be governed by a pure asymmetry principle, like so: (Asymmet)  If [p] is metaphysically grounded in [q], then [q] is not metaphysically grounded in [p]. (Asymnor)  If [p] is normatively grounded in [q], then [q] is not normatively grounded in [p]. However, as with transitivity, mixed versions of these principles are just as plausible as the pure versions. In particular, we are very strongly inclined to hold that (Asymmet/nor)  If [p] is metaphysically grounded in [q], then [q] is not normatively grounded in [p].25 But if metaphysical and normative grounding really were fundamentally distinct grounding relations, it would be utterly mysterious why these two relations would ‘get out of each other’s way’ in this manner. Our two analogies from before help here as well. The relations being largerareathan and being largerpopthan are both asymmetric. However, it is undeniable that here a mixed asymmetry principle is false: Dallas is largerarea than New York City, but New York City is largerpop than Dallas. Thus in a typical case in which we have two fundamentally distinct relations of the same broad type, the asymmetry of each relation fails to manifest in a true mixed asymmetry principle. The opposite happens, however, in the other case we considered. If we assume that time travel is impossible (or, at the very least, that time travellers can’t be their own ancestors), then being a matrilineal descendant of and being a patrilineal descendant of are both asymmetric relations. However, in this case a mixed asymmetry principle is extremely plausible. Why? Because if a is a matrilineal descendant of b while b is a patrilineal descendant of a, it follows—given the way in which matrilineal descendance, patrilineal descendance, and descendance sans phrase can all be defined in terms of the relation being a child of together with other material—that a is her own descendant, which contradicts our assumption that it is not possible to be one’s own ancestor. In short, it is because the matrilineal-descendance and patrilineal-descendance relations are not fundamentally distinct kinship relations that a mixed asymmetry principle is true. Mixed asymmetry is strong evidence that two relations of a given type can be definitionally linked. As before, the argument I am offering here has force even for those who deny that grounding is always asymmetric. One such denier is Elizabeth Barnes (MS), who provides examples of a number of contemporary metaphysical systems which, she argues, are plausibly interpreted as featuring pairs of entities that metaphysically depend on each other.26 However, for all these systems, even though asymmetry fails in general, it holds within certain domains. More specifically, although, in each system, there are certain privileged entities that can mutually ground each other, the grounding relations between privileged and non-privileged entities, as well as among the non-privileged entities themselves, are always asymmetric. But then we can run my argument by restricting its scope to the non-privileged entities for which asymmetry holds in general. When it comes to those entities, a pure version of asymmetry holds for both metaphysical and normative grounding, and presumably a mixed version of asymmetry holds as well. But why would this be so, if metaphysical and normative grounding were unrelated to each other? Why would metaphysical and normative grounding ‘get out of each other’s way’ within this restricted region, if Fine-style grounding pluralism were true? Even if grounding is not universally asymmetric, my argument still has sway. I call this application of my argumentative strategy ‘the Argument from Asymmetric Dovetailing’ because the overall picture we get is one in which the pattern of metaphysical grounding relations between facts neatly dovetails with the pattern of normative grounding relations between facts: overlaying the two patterns on one another does not result in any cases in which [p] grounds [q] in one of these two senses and [q] grounds [p] in the other. In the case of the Argument from Transitive Links, we saw a somewhat different phenomenon: instead of the metaphysical and normative grounding relations meshing with one another in an all-too-convenient manner, we saw that a given instance of a metaphysical grounding relation and a given instance of a normative grounding relation can entail the existence of an additional instance of a grounding relation of some sort. So (to anthropomorphize a bit) in the case of transitivity, it is as if the two ostensibly unrelated grounding relations interact with one another to produce yet more grounding relations, whereas in the case of asymmetry, it is as if the two ostensibly unrelated grounding relations manage to steer clear of each other as they go about their business. What miraculous behaviour! Rather than holding that a pre-established harmony, twice over, has led metaphysical and normative grounding to function in this way, I think we do better to reject Fine’s pluralism about these two relations. It is worth pausing here to clarify the nature of my argument. I am offering an abductive argument from the existence of mixed asymmetry and transitivity principles to the unity of metaphysical and normative grounding. I am not claiming that if two relations are governed by mixed asymmetry and transitivity principles, then this deductively entails that the two relations are fundamentally connected (either by being the same relation, or by being definitionally linked to one another in some way). There are cases in which either a mixed asymmetry principle or a mixed transitivity principle holds between two relations, but the best explanation of why this is so appeals to something other than a fundamental connection between the two relations. Consider, for instance, the relations being the son of and being the nose of.27 These two asymmetric relations obey the following mixed asymmetry principle: (Asymnose/son)  If x is the nose of y, then y is not the son of x. However, in this particular case we can explain why mixed asymmetry holds merely by appealing to facts about the relata of our two relations: the left-hand side of the is-a-nose-of relation must be a body part, whereas the right-hand side of the is-a-son-of relation cannot be a body part, so if x bears the first of these relations to y, it follows that y does not bear the second to x. But no such explanation can be offered in the case of (Asymmet/nor). Perhaps it is true that only normative facts can stand in the is-normatively-grounded-in relation to some other fact or facts. However, since it is undoubtedly the case that normative facts can stand in metaphysical grounding relations to other normative facts,28 we cannot derive (Asymmet/nor) from this restriction on the relata of the normative grounding relation, in the way in which we can derive (Asymnose/son) from restrictions on the relata of its constituent relations. And, I claim, no other explanation of (Asymmet/nor) is in the offing, short of positing a fundamental link between metaphysical and normative grounding. Finally, although I have presented the Arguments from Transitive Links and from Asymmetric Dovetailing as if they constitute separate arguments that serve as independent sources of abductive evidence for grounding monism, these two arguments are at their strongest when they are combined into a single abductive argument that is stronger than the sum of its parts. Combining the arguments increases their strength because some explanations of mixed transitivity commit us to denying mixed asymmetry, and some explanations of mixed asymmetry commit us to denying mixed transitivity. So finding a plausible explanation of all three of the following (Tranmet/nor)  If [p] is metaphysically grounded in [q], and [q] is normatively grounded in [r], then [p] is grounded (in some non-rigged-up sense) in [r]; (Trannor/met)  If [p] is normatively grounded in [q], and [q] is metaphysically grounded in [r], then [p] is grounded (in some non-rigged-up sense) in [r]; (Asymmet/nor)  If [p] is metaphysically grounded in [q], then [q] is not normatively grounded in [p] is more difficult than finding an explanation of the first two on their own and a separate explanation of the third. In particular, most attempts to explain (Asymmet/nor) by appealing to restrictions on the relata of the metaphysical and normative grounding relations are incompatible with taking (Tranmet/nor) and (Trannor/met) to be non-vacuously true (that is, to be true, but not true because their antecedents are never satisfied). Presumably such attempts would involve arguing either that (i) the same type of fact cannot be both on the left-hand side of the is-metaphysically-grounded-in relation and the right-hand side of the is-normatively-grounded-in relation or that (ii) the same type of fact cannot be both on the right-hand side of the is-metaphysically-grounded-in relation and the left-hand side of the is-normatively-grounded-in relation. But notice that the non-vacuous truth of (Tranmet/nor) entails the falsity of (ii), and the non-vacuous truth of (Trannor/met) entails the falsity of (i). I see little hope of explaining the combination of (Tranmet/nor), (Trannor/met), and (Asymmet/nor) unless we posit a fundamental connection between metaphysical and normative grounding.29 6. Against extreme grounding pluralism I have just argued that the sort of grounding pluralism embraced by Fine is untenable: when we look at the logical behaviour of each of the types of grounding posited by Fine and, in particular, look at how those types of grounding interact (or fail to interact) with one another, the striking patterns in this behaviour and in these interactions give us excellent reason to conclude that there is a single generic notion of grounding underlying these putatively distinct grounding relations. I now want to consider how my argumentative strategy applies to a different kind of grounding pluralist. This sort of grounding pluralist uses her pluralism as a way of casting doubt on the importance and significance of the recent wave of research on grounding. She does this by insisting that ‘the’ grounding relation really bifurcates into a large number of distinct dependence relations, and moreover that these distinct relations are ones that have been familiar to analytic philosophers for decades, not some important innovation that has only recently been brought into respectability. I call such a grounding pluralist an extreme grounding pluralist, and I shall use Jessica Wilson as my representative example of such a pluralist, since her version of the view is the most detailed and fully developed currently on offer.30 According to Wilson (2014), we need to distinguish the specific grounding relations (with a small g) in whose terms metaphysicians have been theorizing for years from this new-fangled general Grounding relation (with a big g) being advocated by Fine, Rosen, Schaffer, and others. Wilson’s (2014, p. 539) canonical list of small-g grounding/dependence relations is as follows: type identity; token-but-not-type identity; functional realization; the classical mereological part–whole relation; the causal-composition relation; the set-membership relation; the proper-subset relation; the determinate–determinable relation. Wilson argues that (i) the big-g Grounding relation can’t do any theoretical work on its own, without supplementation by the small-g grounding relations, and (ii) once the small-g grounding relations are on the scene, there is no additional work for the big-g Grounding relation to do.31 Thus we can see Wilson as advocating a form of extreme grounding pluralism, one which licenses scepticism about the theoretical usefulness of unqualified ‘grounding’-talk. From Wilson’s perspective, when we consider the explosion of work on the big-g Grounding relation over the past few years, it is as if a group of scientists suddenly started publishing papers about the physical properties of jade without realizing there are two different minerals which go under that name. Worse, it is as if these scientists started doing all this when there already existed well-established results about the physical properties of jadeite and well-established results about the physical properties of nephrite.32 Before I assess Wilson’s position, I should mention a complicating factor. So far I have been assuming that grounding is a relation between facts. However, many of Wilson’s relations (a)–(h) do not take facts as relata on both sides of the relation; for example, facts do not have members (in the set-theoretic sense), and facts are not themselves determinates or determinables. (Only properties and relations are.) So to give Wilson a proper hearing, I will temporarily relax my assumption that facts are the relata of the grounding relation(s) and allow entities of arbitrary ontological category to stand in grounding relations with one another. My sketch, up to this point, of Wilson’s position has been incomplete in a crucial way. This aspect of Wilson’s view emerges when she replies to a certain objection due to Kit Fine to her position. Since a version of Fine’s objection applies to almost all varieties of extreme grounding pluralism, let us consider that objection, and Wilson’s clarification of her view in light of it. Fine’s objection is as follows (Wilson 2014, p. 558): for many of the specific relations in list (a)–(h), Fine points out, the mere holding of that specific relation is not enough to establish a relation of ground, and—when there is a relation of ground—also not enough to establish the direction of priority among the relata. For example, <X is a proper part of Y> is compatible with all the following: <X and Y do not bear a grounding relation to each other>, <X grounds Y>, and <Y grounds X>. So, Fine insists, in order for one of Wilson’s specific relations to serve as a grounding relation in a given direction, additional facts or assumptions are needed, and these further facts or assumptions crucially involve an appeal to Grounding. Wilson replies that relations (a)–(h) ‘are all capable of serving as “small-g” grounding relations, but … their serving in this capacity will typically depend on certain other facts or assumptions’, facts or assumptions which do not crucially involve an appeal to big-g Grounding (Wilson 2014, p. 569). For example, to handle cases in which one relatum is fundamental while the other is non-fundamental, Wilson endorses the following principle: (Wil)  If X bears one of the relations (a)–(h) to Y, and X is fundamental while Y is not, then that specific relation serves as a small-g grounding relation between X and Y, with Y being small-g grounded in X, and not vice versa.33 Wilson is here appealing to a primitive notion of fundamentality—big-f Fundamentality, as it were—which she argues is not just an appeal to big-g Grounding in disguise (Wilson 2014, pp. 560–1). In this reply to Fine, Wilson makes an important concession: she is now no longer claiming that relations (a) through (h) are in themselves small-g grounding relations. Rather, these eight relations sometimes ‘turn on’ and become small-g grounding relations when certain other conditions are present. (Worse still, some of these specific relations can ‘turn on’ in two different directions of priority.) Therefore, we should be suspicious of Wilson’s claim that her relations (a) through (h) deserve to be called ‘grounding relations’ at all. Rather, they appear to be relations that sometimes underwrite—either in the weak sense of ‘being present when’, or in the strong sense of ‘helping ground’—a grounding relation between their relata (or between facts intimately related to their relata).34 Not that it matters much how we label these specific relations; Wilson’s position cannot be rejected on mere terminological grounds. Let us turn, then, to the heart of the matter. Can we really conduct our theorizing in the way we want if we restrict ourselves to ‘turned on’ versions of relations (a)–(h) instead of a generic big-g Grounding relation? And do we really have good reason to suppose that the versions of relations (a)–(h) that have been ‘turned on’ as small-g grounding relations are not unified in any way? Here we can return to themes we encountered earlier in this essay. It is when we theorize about normative matters that Wilson’s claim that we can make do with relations (a)–(h) in lieu of a generic grounding relation is at its weakest. When consequentialists and their opponents ask ‘Is the good prior to the right?’ none of Wilson’s relations (a) through (h) adequately captures the notion of priority at issue. Taking them in reverse order: the idea that the good might bear the determinate–determinable relation to the right is an intriguing proposal, but it most certainly is not the sort of claim that consequentialists typically make when they insist that the good is prior to the right.35 We can immediately set aside the proposal that we can understand the notion of priority in this debate as the proper-subset relation or the set-membership relation. Since it should be possible for consequentialists and non-consequentialists to have their dispute even if they agree that evaluative and deontic properties do not have causal powers, we can also set aside the proposal that we understand the sort of priority at issue in terms of the causal-composition relation. Perhaps if we embrace a heavy-duty conception of facts according to which they can literally stand in the part–whole relation with one another, then we can make sense of the idea that, for consequentialists, a given fact about the goodness of some outcome is a proper part of a given fact about the rightness of some action. However, surely it is possible for consequentialists and their opponents to have their dispute without endorsing such a controversial view about the nature of facts. When it comes to functional realization, while it is true that there are some philosophers who call themselves ‘moral functionalists’ (Jackson and Pettit 1995, Jackson 1998), and while it is true that these philosophers are usually consequentialists, their commitment to moral functionalism is independent of their commitment to consequentialism. Moreover, it is possible to be a consequentialist without being a moral functionalist. Finally, I have already dealt, earlier in this essay, with the suggestion that we understand the consequentialism debate in terms of identity (whether token or type): not only does such a suggestion do violence to our usual way of understanding consequentialists as positing an asymmetric relation of priority between facts about overall goodness and facts about rightness, but such a suggestion leaves unexplained the relation between facts about the comparative overall goodness of all outcomes and facts about the pro tanto goodness of specific outcomes, since that relation cannot be identity.36 In short, none of Wilson’s relations (a)–(h) is a natural way of construing the priority relation at issue in the debate over consequentialism. The same is true, I believe, of my other examples of normative views that I argued are best understood in terms of a grounding/in-virtue-of/non-causal-‘because’ relation. When Ross insists that I have a prima facie duty to read your manuscript in virtue of my promise to do so, he is not making a claim about type identity, or set membership, or the determinate–determinable relation. When advocates of the reasons-first program insist that facts about what one ought to do can be analysed in terms of facts about reasons, they are not making a claim about causal composition, or functional realization, or the part–whole relation. If all we are left with are Wilson’s specific relations (a)–(h), it becomes difficult to make sense of much of normative inquiry. Of course, we could always try to supplement Wilson’s list with an additional specific dependence relation to handle the normative cases, but what would that relation be? Why not just add to that list the relation in whose terms philosophers in normative disciplines have been theorizing for over a century, the relation that arguably the expression ‘supervenience’ was meant to pick out before it became co-opted as a way of referring to relations of necessary covariation, namely, the relation we pick out with expressions such as ‘because’, ‘in virtue of’, ‘makes the case’, and ‘grounds’? There is no need to demean or belittle these expressions by using them with capital letters. When a consequentialist proposes (Op*) Necessarily, an action is right if and only if, and because, it is optimific we do not need to stop her and ask ‘Wait, do you mean big-b “Because”, or are you schematically referring to some small-b “because”-relation?’ Our consequentialist is using ‘because’ in a perfectly natural and sensible way. Of course, there are difficult questions about the logic, metaphysics, and epistemology of the notion being picked out by that expression, as well as difficult questions about the semantics and pragmatics of the expression itself, and these difficult questions deserve to be their own area of philosophical investigation. But the same is true of most of the other words in (Op*), including ‘necessarily’, ‘action’, and ‘if’. Thus Wilson’s form of grounding pluralism leaves out the very relations we most want when theorizing about normative categories such as rightness or reasons for action. Wilson’s extreme grounding pluralism is also susceptible to the form of argument I used against Fine’s more moderate grounding pluralism. First of all, we can run a version of the Argument from Transitive Links. The following principle is extremely plausible: (Transmall-g)  If X bears a ‘turned on’ version of one of (a)–(h) to Y (in the from-grounds-to-grounded direction), and Y bears a ‘turned on’ version of one of (a)–(h) to Z (in the from-grounds-to-grounded direction), then there is a non-rigged up notion of grounding such that X grounds Z. For example, if Socrates’ body parts small-g ground Socrates, because they stand in a ‘turned on’ version of the part–whole relation to him, and if Socrates small-g grounds {Socrates}, because he stands in a ‘turned on’ version of the membership relation to that set, then we are very strongly inclined to hold that Socrates’ body parts also ground the set {Socrates}, in some non-rigged-up sense. Similarly, if Socrates small-g grounds {Socrates}, and if {Socrates} small-g grounds {{Socrates}}, then we are very strongly inclined to hold that Socrates also grounds {{Socrates}}, in some non-rigged up sense. Finally, if certain physical states of Socrates’ brain small-g ground certain neural states of Socrates’ brain, because they stand in a ‘turned on’ version of the causal-composition relation to those latter states, and if those neural states of Socrates’ brain small-g ground Socrates’ desire to seek the truth, because they stand in a determinate–determinable relation to Socrates’ desire to seek the truth (in a Yablo-style way), then we are very strongly inclined to hold that the physical states of Socrates’ brain also ground Socrates’ desire to seek the truth, in some non-rigged-up sense. But in all these cases, none of Wilson’s relations (a)–(h) can serve as the needed non-rigged-up type of grounding relation. Socrates’ body parts are neither a part of nor a member of {Socrates}, Socrates is not a member of {{Socrates}}, and something which causally composes a determinate of some determinable is not itself a determinate of that determinable. Nor do any of Wilson’s other specific relations seem up to the task in each of these cases. This leaves us searching for more dependence relations than the eight relations which Wilson extracts from the recent philosophy-of-mind literature. And it leaves us wondering why, when Wilson’s eight relations are ‘turned on’ as small-g grounding relations, they can be linked together via applications of a mixed transitivity principle, despite Wilson’s claim that there is no generic Grounding relation underlying the ‘turned on’ versions of those eight relations.37 We can also run a version of the Argument from Asymmetric Dovetailing against Wilson’s brand of grounding pluralism. Wilson allows for the possibility that the asymmetry of grounding (whether big or small) might fail when we are considering fundamental entities: she thinks it is a live possibility that there might be fundamental entities X and Y such that X grounds Y and Y grounds X. But when it comes to cases in which at least one of X and Y is non-fundamental, Wilson adheres to the following (very plausible) asymmetry principle: (Asymsmall-g)  If X or Y is not fundamental, and if X bears a ‘turned on’ version of one of (a)–(h) to Y in the from-grounds-to-grounded direction, then Y does not bear a ‘turned on’ version of one of (a)–(h) to X in the from-grounds-to-grounded direction.38 But now we can ask: why on earth do the ‘turned on’ versions of Wilson’s small-g relations get out of each other’s way in the manner predicted by (Asymsmall-g), if those relations are fundamentally distinct from one other? Why do these supposedly disparate relations exhibit patterns of instantiation that so neatly dovetail with one another? If, as I have been proposing, what it means for there to be a ‘turned on’ version of one of Wilson’s specific relations between two entities, X and Y, is for it to be the case that, in addition to—and possibly in virtue of—that specific relation between X and Y, there is a (generic, unqualified) grounding relation between X and Y (or between two facts intimately related to X and Y, such as [X exists] and [Y exists]), then we have a ready explanation of why the ‘turned on’ versions of these relations mesh with each other in this way. But Wilson’s pluralism leaves this meshing utterly mysterious. Once again we are led to the conclusion that grounding is unified. 7. A surprising consequence I have argued that we have good reason to reject Fine’s brand of moderate grounding pluralism, according to which a metaphysical variety of grounding must be distinguished from normative and natural varieties of grounding. And I have also argued that we have good reason to reject Wilson’s brand of extreme grounding pluralism, according to which there is a large number of specific grounding relations such as the functional-realization relation and the set-membership relation, but no generic grounding relation underlying these specific relations. On my view, such a generic relation does exist, and it is precisely this relation which is being invoked when philosophers use locutions such as ‘in virtue of’, ‘makes the case’, and ‘grounds’ (as almost all of them do, at some point), and when they use ‘because’ in the way characteristic of grounding claims. Grounding is a unity, not a heap of disconnected relations. I have chosen Fine and Wilson as my foils because they develop the pluralist view in two importantly different ways. Fine’s is the sort of pluralism typically favoured by grounding’s proponents, Wilson’s the sort typically favoured by grounding’s critics. One important issue I do not address here is whether there are other forms of grounding pluralism that can escape my general form of argument. I suspect there are not, but it is difficult to say without seeing what these other pluralist positions come to. Another important issue I do not address here is the degree to which my arguments generalize. Do the Argument from Transitive Links, the Argument from Asymmetric Dovetailing, and other arguments of that general form show not just that various candidates for different types of grounding form a unity, but moreover that grounding and other notions usually thought distinct from it also form a unity? For example, it is standard to distinguish between at least three uses of the word ‘because’: the ‘because’ of causation (as in: ‘The table broke because he put too much weight on it’), the ‘because’ of rational basis (as in: ‘He put too much weight on the table because he wanted to see how many chairs he could stack on it at one time’), and the ‘because’ of grounding (as in: ‘It was wrong of him to stack that many chairs on the table because the table wasn’t his and he should have known that much weight would break it’).39 Do arguments similar to the ones I have provided here show that the relations picked out by these three uses of the word ‘because’ are not fundamentally distinct from one another? I will not take up that issue here, although I hope to do so on a future occasion.40 Instead, I want to end by noting a surprising consequence of the arguments I have offered in this essay. Put most provocatively, the consequence is this: it follows from the unity of grounding that normative ethics is a branch of metaethics. Put less provocatively but more accurately, the consequence is this: it follows from the unity of grounding that many of the central claims of normative ethics are at once claims in normative ethics and claims in metaethics. The argument for this consequence is straightforward, given what we have already established. As argued in §3 above, when in normative ethics we are concerned with general theories, we are not just searching for extensionally adequate biconditionals of the form (Bi)  Necessarily, an action is right if and only if _____ but rather searching for biconditionals that are explanatory, like so: (Bi*) Necessarily, an action is right if and only if, and because, _____. Similarly, when in normative ethics we are focusing on a particular verdict about a particular scenario, we usually are not merely interested in establishing a claim of the form (Ver)  Action A is right in circumstances C but rather interested in establishing an explanation of why that verdict holds, like so: (Ver*) Action A is right in circumstances C because _____. It follows from my arguments in §§5–6 against grounding pluralism that the ‘because’ in both (Bi*) and (Ver*) is picking out a generic relation of metaphysical grounding, not some special type of normative grounding (as Fine would have it) or a specific small-g grounding relation such as the determinate–determinable relation (as Wilson would have it). Thus a central portion of normative ethics is concerned with establishing certain metaphysical claims: when we are doing this sort of normative ethics, we are thereby doing moral metaphysics. But, by definition, metaethics includes within it the metaphysics, epistemology, semantics, and so on of morality.41 So when we are doing a central portion of normative ethics, we are thereby making a contribution to one branch of metaethics—the branch devoted to the metaphysics of morality. In short, one core part of normative ethics is also, at the same time, a subfield of metaethics. An obvious reply suggests itself. Perhaps we need to distinguish between two distinct ‘because’-relations that are employed in the study of moral notions: the first-order ‘because’ of normative ethics and the second-order ‘because’ of metaethics. But it is precisely here that my arguments for the unity of grounding can be applied. How do these putatively distinct ‘because’-relations interact? Can we string them together using applications of transitivity? I am inclined to say that we can. Do these two putatively different relations conform to a mixed asymmetry principle? I am inclined to say that they do. And so on. The pattern of interaction and avoidance between the ‘becausemetaethics’-relation and the ‘becausenormative-ethics’-relation is precisely the sort of pattern we would expect from two relations that are not fundamentally distinct from one another. Therefore, we cannot avoid the implication that normative ethics traffics in metaphysical claims by attempting to cordon off the ‘because’ of first-order investigations of morality from the ‘because’ of second-order investigations of morality. Instead, since some of our canonical examples of first-order moral theories are also, at the same time, second-order moral theories, we should be suspicious of the very distinction between ‘first-order’ and ‘second-order’ ways of investigating moral matters. It might seem that what I am proposing here is the reverse of a move made famous by Ronald Dworkin (1996, 2011). According to Dworkin, many claims that philosophers have put forward as second-order/metaethical claims external to normative ethics, such as the claim that morality is mind dependent, are in fact first-order claims within normative ethics. So it might seem that what I have just argued for is the opposite: many claims put forward as first-order claims within normative ethics are in fact metaethical claims, insofar as they concern the metaphysical dependence of moral matters. But this characterization of my position as simply a ‘reverse Dworkin’ is inaccurate in an important respect. Dworkin’s claim is that certain views often taken to be purely metaethical views are in fact not metaethical views at all, but instead are views in normative ethics. My own position is that certain views often taken to be purely normative ethical views are in fact views both in normative ethics and in metaethics, as those two fields are standardly conceived. Both Dworkin and I offer our arguments as a way of destabilizing the traditional metaethics-versus-normative-ethics divide. However, Dworkin wants to destabilize that divide in order to get us to stop asking certain questions traditionally taken to fall on the metaethical side of the divide. I, on the other hand, want us to continue to ask all the questions that have traditionally fallen on both sides of the divide. I want self-styled ‘metaethicists’ to go on asking all the questions they have been asking, and I want self-styled ‘normative ethicists’ to go on addressing all the issues they have been addressing. I simply want us to stop seeing these questions as sorting into two natural piles of non-overlapping issues, the ‘metaethical’ ones and the ‘normative ethical’ ones. There is just one field here: ethics. The term ‘metaethics’ first gained its currency during the era of linguistic philosophy. In those days, it was easy to say what distinguished metaethics from ethics proper: metaethics was the study of moral language, and ethics proper wasn’t even a part of philosophy. As linguistic approaches to philosophy receded, our conception of the field of metaethics changed: metaethics shifted from being devoted exclusively to the meanings of moral terms to also being concerned with the metaphysics, epistemology, and so on, of first-order moral claims. Hence the currently popular grab-bag conception of metaethics, whereby it just is the metaphysics, epistemology, philosophy of mind, philosophy of language, and so on, of moral matters. However, this common conception of how to draw the line between metaethics and normative ethics rests, I believe, on an overly naive view of normative ethics. Many of the so-called ‘first-order’ moral claims at issue in normative ethics are at the same time ‘second-order’ claims concerning the metaphysics of morality, insofar as they concern what makes right acts right, what makes good people good, and so on—that is, insofar as they concern claims about metaphysical grounding.42 Anyway, I think a destabilization of the divide between metaethics and normative ethics has been happening for a while now. In one way, my talk of ‘metaethics’ here is a little quaint. Over the past two decades, the field formerly known as ‘metaethics’ has become broadened to include within its scope—here I revert to the standard language—second-order questions directed at first-order normative claims of any type, not just second-order questions directed at first-order claims about narrowly moral or ethical notions such as what one is morally required to do or how it would be best to live. Metaethics has, in effect, been superseded by ‘metanormative studies’. The standard way of effecting this widening of scope is to discuss reasons in general, not just moral reasons for action, or to discuss rational requirements in general, not just moral requirements on action. But during this transition, something odd happened. Investigations of what, on the surface, appear to be purely first-order issues about reasons or rational requirements in general became perfectly acceptable at a conference or in an anthology ostensibly devoted to ‘metaethics’ (understood now to have been broadened to ‘metanormative studies’). This has led to a bizarre taxonomic situation whereby a paper on desire-based theories of well-being is forbidden at a metaethics conference, but a paper on desire-based theories of reasons for action is perfectly fine for such a conference, even though the positions discussed in each paper might be identical in structure, equivalent in terms of their explanatory ambitions, and subject to the same objections and counter-replies. As long as your seemingly first-order investigation is devoted to a sufficiently general normative category such as rational requirement or reason, you still count as doing metaethics, in the broad sense. In effect, I have provided an argument that legitimizes this taxonomic promiscuity within metanormative studies. Moreover, my argument suggests that such taxonomic promiscuity should also be embraced within metaethics, narrowly conceived. If grounding is unified, then a properly explanatory moral theory is both a position in normative ethics and a position in metaethics. It does not answer all questions in these two fields, but it answers some in each. And, when we broaden our historical focus, isn’t that the right way to view things? Consider Kant and Aristotle. Is Kant’s Groundwork of the Metaphysics of Morals a book in metaethics or normative ethics? The correct answer is: both. Is Aristotle’s Nicomachean Ethics devoted to ‘first-order’ or ‘second-order’ questions? Again, the answer is: both. And in each case, it is not as if these authors include separate discussions of each type of issue, or use their conclusions in one field as premises to help them establish claims in the other. Rather, in both cases their discussions of questions that we might sort as either ‘metaethical’ or ‘normative ethical’ are intertwined with one other. This is why, I believe, it is so difficult to say where contemporary neo-Kantian and contemporary neo-Aristotelian views fall in the traditional metaethics-versus-normative-ethics divide. Such views are positions in both fields at once. And, if my arguments here are correct, the same is true even of utilitarianism and Ross-style pluralism. The unity of grounding grounds the unity of ethics.43 Footnotes 1 Some authors take the following sentence to be synonymous with (1)–(4): (5) An act’s being pious is nothing over and above the fact that it is loved by the gods. ‰‰‰‰‰‰‰However, this is a mistake. Among other problems, the logic for nothing-over-and-above claims is not the same as the logic for grounding claims. For example, nothing-over-and-above claims obey the following principle: if F1 is nothing over and above G, and F2 is also nothing over and above G, then it is not the case that F1 is something over and above F2. But there is no analogous principle for grounding claims. 2 When using the expression ‘grounds’, we can write either ‘F grounds G’ or ‘G is grounded in F’, but with the expressions ‘in virtue of’ and ‘because’ it is more difficult to formulate things in the former, from-grounds-to-grounded direction. 3 On the difference between relational and operational views, see Correia and Schnieder (2012a), pp. 10–12. (They use the label ‘predicational’ for the former sort of view, but I think the term ‘relational’ is more apt since the fundamental distinction here is metaphysical, not semantic: it concerns the nature of grounding itself, not the nature of the terms we use to talk about grounding.) In the recent grounding literature, relationalists include Audi (2012a, 2012b), Chudnoff (2011), deRosset (2013), Evans (2012), Leuenberger (2014a, 2014b), Maguire (2015), Raven (2012, 2013), Rosen (2010, 2015), Schaffer (2009, 2012, 2016), Skiles (2015), Trogdon (2013), and Whitcomb (2012); operationalists include Correia (2010), Dasgupta (2014a, 2014b, 2016), Fine (2001, 2010, 2012a, 2012b), Litland (2013, 2015), and Schnieder (2011). Among relationalists, taking grounding’s relata to be facts is the mainstream view; the primary exception is Schaffer, who takes grounding’s relata to be entities of arbitrary ontological category. The view that grounding—whether construed as a relation or an operator—is singular on the side of what-is-grounded and plural on the side of what-does-the-grounding is also the mainstream view; the primary exception is Dasgupta, who takes it to be plural on both sides. 4 Not only does one occasionally encounter this narrative in print (see, for instance, Clark and Liggins 2012), but, in my experience, one very frequently encounters it in conversation. 5 I say ‘first appearance in print’ because Hare (1984, p. 1) claims the term was already being used that way in 1940s Oxford, and because the same idea appears without the label ‘supervenience’ in earlier works by Sidgwick (1907, pp. 209, 379), Moore (1922, p. 261), and Ross (1930, pp. 109, 120, 122–3), among others. 6 It was Jonas Olson who first pointed out this feature of Hare’s text to me. McLaughlin (1995, pp. 51–2, n. 8) makes a similar observation. 7 We find a similar commingling of claims about dependence with claims about necessary covariation in Sidgwick (1907, p. 209), Moore (1922, pp. 261–2), and Ross (1930, pp. 109 and 120–3). 8 Versions of this argument are offered by Schaffer (2009, p. 364), McLaughlin and Bennett (2011, §3.5), Raven (2012, p. 690; 2013, p. 194), Leuenberger (2014a, p. 228), and Koslicki (2015, p. 308). 9 See Berker (2013a, §2) for a defence of this way of understanding the central issue dividing consequentialists and their opponents. (And see pp. 382–3 of that article if you are wondering why I do not refer to consequentialists’ opponents as ‘deontologists’.) 10 Although some philosophers treat ‘analytic truth’ and ‘conceptual truth’ as synonyms, these terms have different meanings: ‘analytic truth’ refers to a truth that holds in virtue of the meaning of words, ‘conceptual truth’ to a truth that holds in virtue of the nature and composition of concepts. 11 Throughout, I use ‘<p>’ to denote the proposition that p. 12 See Beall and Restall (2013, §1). 13 Throughout, I use ‘[p]’ to denote the fact that p. 14 The locus classicus for this view is Bales (1971). 15 By ‘basic fact-about-reasons’ I mean a fact-about-reasons that is not itself grounded in any facts-about-reasons. The ‘basic’-qualifier is needed here because almost all reasons-firsters will want to allow that some facts-about-reasons obtain in virtue of other facts-about-reasons. For example, it might be in virtue of my having a reason to pursue some end that I have a reason to pursue the indispensable means to that end. 16 See Parfit (2011). Although Parfit does not formulate his version of non-naturalism in terms of grounding, the grounding relation does feature prominently in those two books, albeit not under that name. (Parfit prefers the label ‘non-causal making’; see vol. 1, p. 368, and vol. 2, p. 299.) 17 See, for instance, Ichikawa (2014, p. 185). 18 Here I assume that facts are the relata of the reduction relation, to fit with reasons-firsters’ talk of one fact or truth being reducible to another. 19 Actually, Fine wouldn’t put the matter this way, for two reasons. First, as already mentioned, Fine (2001, p. 16; 2012a, p. 43) believes that grounding is fundamentally an operator, not a relation. Second, Fine prefers to use the mass noun ‘ground’ instead of the mass noun ‘grounding’ to refer to the notion in question (as in ‘relation of ground’, not ‘grounding relation’). Neither of these issues is important for our purposes, so I will continue to ignore them in the main text. 20 What if partial grounding cannot be defined in terms of full grounding because sometimes a fact has a partial ground but no full grounds? Well, in that case, if full grounding also cannot be defined in terms of partial grounding, and if both cannot be defined in terms of a third type of grounding, then I think grounding pluralism would be true after all. So really it is not the mere distinction between partial and full grounding that should be compatible with grounding monism, but rather that distinction together with the standard way of defining one side of the distinction in terms of the other. 21 I lack the space to discuss Fine’s (2012a, pp. 39–40) positive argument for his brand of moderate grounding pluralism. That argument relies on two key assumptions: grounding necessitarianism (the view that a full set of grounds necessitate that which they ground) and modal pluralism (the view that there are several varieties of necessity, none of which can be defined in terms of the others). However, both of these assumptions are controversial. (On necessitarianism, see Chudnoff 2011, Leuenberger 2014a, and Skiles 2015; on modal pluralism, see Leech 2016.) Moreover, the argumentative strategy I pursue here against grounding pluralism can be adapted to argue against modal pluralism as well. 22 Moreover, the first of these analogies gives us extra reason to call into question the idea that we can account for (Tranmet/nor) and (Trannor/met) through the transitive-closure gambit. The transitive closure of the disjunction of the larger-in-area-than and larger-in-population-than relations is not itself a larger-than relation. (As an anonymous referee helpfully observed, not only does such a transitive closure intuitively not count as a larger-than relation, but moreover it fails to be either asymmetric or irreflexive.) So, if metaphysical and normative grounding really have as little to do with one another as the larger-in-area-than and larger-in-population-than relations do, then the transitive closure of the disjunction of the metaphysical and normative grounding relations should not itself count as a grounding relation. 23 See Litland (2013) and Raven (2013). 24 Or, at least, if the fundamental normative truths are exceptionless general principles, then that is their form. A similar result follows if the fundamental normative truths take the form of ceteris paribus laws or of particular normative verdicts, and also follows if there are no normative truths that qualify as fundamental, since in that case (Nor) is a non-starter. 25 In this case there is no need to consider two mixed principles, since by contraposition they are equivalent to one another. 26 Actually, Barnes only officially argues that her examples feature instances of mutual ontological dependence, not that they feature instances of mutual grounding (she takes these notions to be distinct), but most of her examples, if they do indeed involve the former, can also be interpreted as involving the latter. 27 I owe this example to John Mackay. 28 For instance, [He did something wrong last week] might be metaphysically grounded in [He hit his brother last Tuesday, and that was wrong]. 29 Combining my two arguments also helps address the following reply to the Argument from Asymmetric Dovetailing (inspired by a line of reasoning Karen Bennett attributes to Mark Heller in her 2011, pp. 99–100). Suppose the metaphysical and normative grounding relations both stand in the determinate–determinable relation to a generic grounding relation. Then, assuming that determinates cannot be defined in terms of their determinables, such a view could count as a form of grounding pluralism. But this view can also explain mixed asymmetry in the following way. Suppose, for reductio, that [p] metaphysically grounds [q], and [q] normatively grounds [p]. Then, because these relations are determinates of our generic grounding relation, it follows that [p] generically grounds [q], and [q] generically grounds [p]. However, this violates the asymmetry of the generic grounding relation. The main problem with this reply to my arguments is that, while such a proposal might help with the Argument from Asymmetric Dovetailing, it does not fare particularly well when we consider the Argument from Transitive Links. If [p] metaphysically grounds [q], and [q] normatively grounds [r], then—if metaphysical and normative grounding really were co-determinates of a generic grounding relation—it should follow that [p] stands in a type of grounding relation to [r] that is at the same ‘level of determination’ as metaphysical and normative grounding. However, there is no such relation in the offing. So either we must deny mixed transitivity, or we must give up on the determinate–determinable form of grounding pluralism. 30 Other extreme grounding pluralists include Koslicki (2015) and—subject to a proviso—Hofweber (2009). (The proviso is that since Hofweber refuses to refer to his familiar dependency relations as types of ‘grounding’, preferring instead to call them ‘ordinary notions of priority’ (2009, p. 268), it would probably be more accurate to label him an ‘extreme priority pluralist’. However, he is an extreme grounding pluralist in all but name.) 31 I lack the space to discuss Wilson’s positive arguments for (i) and (ii). For criticisms of those arguments, see Raven MS and Schaffer MS. In the main text, I focus on the plausibility of her overall position, regardless of how one might argue for it. 32 Koslicki (2015, pp. 318–9) makes a similar analogy. 33 Here I generalize from Wilson (2014, p. 559). Wilson omits my ‘while Y is not’-qualifier, but it is clear from context that she meant to include it. 34 Or at least that is true of some of them. I am suspicious of the idea that token identity, type identity, and the proper-subset relation ever underwrite a grounding relation between their relata, but I won’t take up that issue here. 35 Moreover, there are technical obstacles that must be overcome if we are to construe a consequentialist’s commitment to the good being prior to the right as a commitment to being good being a determinate of being right. To start with, a determinate property is attributed to the same object as its determinable, but the primary bearers of goodness in a consequentialist theory are often not the same as the primary bearers of rightness. And even if we circumvent this problem by taking actions to be derivatively good to the degree to which they promote good states of affairs, there is the additional problem that—except in rare cases, such as absolute-threshold forms of satisficing consequentialism—it is not just the goodness (in our derivative sense) of an action that, according to consequentialists, determines its rightness, but moreover the goodness of that action in comparison to the goodness of its alternatives. So the properties that a typical consequentialist must propose as being determinates of the determinable being right are properties such as being 10 utiles better than one alternative and 50 utiles better than every other alternative—a much less attractive idea than the simple thought that being good is a determinate of being right. 36 Nor is it plausible to take this last relation to be any of Wilson’s other small-g relations: the pro tanto goodness of an individual outcome does not stand in the determinate–determinable relation to the comparative overall goodness of all outcomes, nor is the former a subset, member, or part of the latter, nor does the former functionally realize or causally compose the latter. 37 As before, a version of this argument can be offered even if (Transmall-g) does not hold with full generality, since there are many specific cases—including the ones I have just mentioned—in which it is plausible that an instance of that schema holds. 38 My evidence that Wilson adheres to this principle is twofold. First, in cases in which either X or Y is fundamental and the other is not, (Asymsmall-g) directly follows from (Wil) (the principle Wilson uses to say what extra conditions are needed in such cases to ‘turn on’ one of her specific relations in a particular direction). Second, in cases in which neither X nor Y is fundamental, Wilson appears to work with (Asymsmall-g) as an unstated background assumption. For example, when considering whether her (non-fundamental) hand depends on her (non-fundamental) body or vice versa or neither, Wilson (2014, pp. 564–5) sets aside, without argument, the possibility that her hand might depend on her body due to one of the relations (a)–(h) while at the same time her body depends on her hand due to another of those relations (or due to the same relation being ‘turned on’ in the opposite direction). 39 Some authors refer to this second ‘because’ as ‘the “because” of action explanation’, but I prefer Matt Evans’ (2012, p. 17) term, ‘the “because” of rational basis’, since that same ‘because’ can be used in contexts in which rationally-assessable items other than actions—such as beliefs or emotions—are being explained. (That said, one downside of Evans’ terminology is that it suggests that such a ‘because’-claim can only be true when the item being explained is rational. But such ‘because’-claims are compatible with irrationality. So maybe a better term yet is ‘the “because” of rationalizing basis’?) 40 For an argument in favour of unifying the ‘because’ of causation and the ‘because’ of grounding that is in some ways similar to my Argument from Transitive Links, see Schaffer (2016, pp. 89–90). 41 This claim might hold because metaethics is nothing more than the metaphysics, epistemology, and so on, of morality, or it might hold because that disjunctive list of subfields follows from the correct definition of metaethics, whatever that may be. 42 My use of the term ‘metaphysical’ here will no doubt scare some people off. But it should be remembered that I use that word in a thin sense whereby it mainly serves as a contrast term for ‘epistemic’, ‘conceptual’, ‘semantic’, and the like. As I understand them, metaphysical claims are those that concern how things are, epistemic claims are those that concern our knowledge of things, conceptual claims are those that concern our concepts, and so on. Thus, the issue of whether the grounding relation is metaphysical, in my sense, does not yet settle whether that relation is ‘metaphysically robust’ or ‘metaphysically lightweight’. 43 I am grateful to Ralf Bader, Ruth Chang, Tyler Doggett, Tom Donaldson, Catherine Elgin, Jeremy David Fix, Adam Kern, Neil Mehta, Daniel Muñoz, Jake Nebel, David Plunkett, Michael Rabenberg, Alexander Skiles, Aleksy Tarasenko-Struc, and Kate Vredenburgh for written comments on earlier drafts of this essay; to Nicolas Alfonsi, Fatema Amijee, Ahson Azmat, Benjamin Bagley, Nathaniel Baron-Schmitt, Timothy Clarke, Michael Della Rocca, Louis deRosset, Hasan Dindjer, Luca Ferrero, Edmund Tweedy Flanigan, Johann Frick, Micha Glaeser, Daniel Greco, Ned Hall, Frank Jackson, Shelly Kagan, Leonard Katz, Thomas Kelly, Niko Kolodny, Gregory Kristof, Jon Litland, Errol Lord, John MacFarlane, John Mackay, Paolo Mancosu, Paul Marcucilli, Elizabeth Miller, Benjamin Morison, Ram Neta, Cory Nichols, Kate Nolfi, Hille Paakkunainen, Derek Parfit, Christopher Peacocke, Alejandro Pérez Carballo, Philip Pettit, Joseph Raz, Kevin Richardson, Gideon Rosen, Paolo Santorio, T. M. Scanlon, Daniel J. Singer, Shanna Slank, Zeynep Soysal, Jack Spencer, Amia Srinivasan, Sarah Stroud, Sigrún Svavarsdóttir, Alberto Tassoni, Achille Varzi, Jonathan Vogel, Jonathan Way, Quinn White, and Seth Yalcin for discussion of the issues addressed here; and to audiences at Columbia University, NYU Abu Dhabi, Princeton University, University of California–Berkeley, University of Vermont, University of Wisconsin–Madison, and Yale University, as well as the participants in my Spring 2015 graduate seminar at Harvard co-taught with Parfit, for their feedback on presentations of material from this essay. I am especially grateful to three anonymous referees and the editors at Mind, who outdid themselves with their amazingly helpful and perceptive comments and suggestions; to Gabriel Oak Rabin, who was my commentator at NYU Abu Dhabi; and to Doug Kremm, who helped with the historical research discussed in §2. 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doi: 10.1093/mind/fzx011pmid: N/A

Abstract A dogma of contemporary ethical theory maintains that the nature of normative support for affective attitudes is the very same as the nature of normative support for actions. The prevailing view is that normative reasons provide the support across the board. I argue that the nature of normative support for affective attitudes is importantly different from the nature of normative support for actions. Actions are indeed supported by reasons. Reasons are gradable and contributory. The support relations for affective attitudes are neither. So-called reasons of the right kind for affective attitudes are facts that make those very attitudes fitting. Unlike reasons, fit-making facts for affective attitudes do not conflict with each other or combine in the explanation of further normative facts. More fit-making facts just make a more complex set of reactions fitting. This result undermines various analyses and unity theses in the philosophy of normativity. 1.1 Introduction There are no reasons for affective attitudes. There are no reasons for admiration, delight, fear, envy, gratitude, disgruntlement, contempt, Schadenfreude, relief, pity, shame, or amusement. There is no reason to want to listen to the Köln concert, or to want to avoid a grisly death. No reason to hope for a brighter day. There is no reason for your incredulous reaction to this announcement, but it might be fitting all the same. I do not deny that there are normative standards that apply to these attitudes. Rather, I claim that these two relations of normative support—being favoured by a reason or various reasons, and being made fitting—are importantly different in various ways. Contrary to a common assumption, affective attitudes are not supported by reasons but by facts that make them fitting. That is the central thesis of this paper. I start out by clarifying the target notion of a normative reason, and distinguishing two classes of would-be reasons for affective attitudes: the right kind and the wrong kind. I restrict my argument to the so-called right kind of reasons for affective attitudes.1 The heart of my argument is this: so-called reasons of the right kind for affective attitudes have a different nature from reasons for action. Reasons for action are gradable—they have weights—and they are contributory—they are incomplete parts of a specific kind of explanation of overall normative facts, such as facts about what you ought to do. But so-called reasons of the right kind for affective attitudes are neither gradable nor contributory. They do not have weights and they do not explain ought facts. They are themselves, if you like, a kind of ought fact. So-called reasons of the right kind for affective attitudes are facts each of which makes a different attitude fitting. Here’s a case from my own life that got me thinking about these issues. My grandmother passed away recently. She was an amazing lady, the only woman driving a Jaguar in Glasgow in the 1950s. She had been suffering terribly with Alzheimer’s for the last several years of her life, with no hope of improvement. She believed she would rejoin her beloved first husband in the afterlife. But she was our family matriarch, and she had great chat right up until the end. She used her last words to make fun of my dad’s bald spot. What is the fitting response to a death such as this? Here’s one thought: the facts about her disease and her religious beliefs weigh against the facts about her being a matriarch and a good laugh. They cancel each other out. One should feel utterly unmoved. Clearly this is not right. Rather, in response to my grandmother’s passing, both sadness and a certain kind of relief were fitting. The facts that made the sadness fitting didn't make the relief unfitting, nor did the facts that made the relief fitting make the sadness unfitting. These facts don’t participate in any kind of ‘weighing explanation’. Each of them directly makes a specific response fitting. So, at least, I’ll argue. I hope that this discussion will be of as much interest to the theory of reasons as to the theory of the normativity of affective attitudes. The terminological question of what we should call a reason and what we shouldn’t doesn’t matter much, except that calling two different things by the same name invites confusion when the difference matters. The terminology I offer seems best, but it’s the distinct natures of the relations of normative support that is important. 1.2 What is at stake? I hope that, like me, you’ll find the business of trying to get clear about the nature of different normative properties and relations interesting for its own sake. In our ordinary normative practice, we use the term ‘reason’ profligately, and it seems reasonable to expect that this usage will occasionally conceal interesting differences. Indeed, it seems clear that even in the case of reasons for action, the uniformity in our reasons talk conceals differences between, for example, motivating reasons and normative reasons, and, more subtly, between considerations that metaphysically explain ought facts and considerations from which one ought to reason (Wedgwood 2015). We should be open to the possibility that our talk about ‘this or that reason for this or that attitude’, while perfectly felicitous, might be best understood as picking out some different support relation from our talk about reasons for actions. It is common nowadays for philosophers to assume various strong ‘unity of reasons’ theses: it’s not just that moral, prudential, and epistemic reasons are reasons in the very same sense, but that there are reasons for affective attitudes in this very same sense. Such theses have been used as premises in objections to the Value-based Theory of Reasons and Desire-based Theory of Reasons (Joseph Raz 2011, Jonathan Way 2013). Such unity theses are also implicit in defences of ‘Global Consequentialism’, which maintains that actions and affective attitudes are normatively assessed in exactly the same way, namely by evaluating their consequences (Derek Parfit 1984, Toby Ord 2009). But such unity theses are a working hypothesis, not a datum. They have not been subjected to scrutiny, especially not within the ‘reasons’ literature. To assess these theses on their merits we need to attend carefully to putative disunities, attempting to give as clear an account of them as possible. A number of prominent views aim to account for some class of normative facts in terms of facts about reasons for affective attitudes. Some views explain the fittingness of an affective attitude in terms of the balance of the right kind of reasons for and against the attitude. (See Schroeder 2010.) This view is a central target of the arguments to come. Other views explain value in terms of reasons for desires (Scanlon 1998) or some other privileged positive attitudes (Suikkanen 2009, Way 2013). These are variations of the so-called ‘buck-passing’ theory of value. Relatedly, some views define the aesthetic, or aesthetic value, in terms of the kinds of things we have reason to appreciate (Walton 1993). If my argument is successful, such views will need to be reconsidered. The search for an account of the distinction between reasons of the ‘right’ and ‘wrong’ kind presumes not just that right and wrong reasons are right and wrong reasons, but also that right and wrong reasons are right and wrong instances of the same category of thing. (This assumption is universal in the literature; for salient discussions see Schroeder op. cit., Howard forthcoming, and Suikkanen op. cit.) But if my argument succeeds, this is a mistake. So-called reasons of the wrong kind for attitudes may well be bona fide reasons, either for the attitude itself, or perhaps for bringing it about that one has some attitude. (I’m officially agnostic about this.) But so-called reasons of the right kind are not reasons, they are fit-making facts. 1.3 Terminology We have two relations: the reason relation, and the fit-making relation.2 A reason is a fact that stands in the reason relation to an option. A fit-making fact is a fact that stands in the fit-making relation to an attitude or something else. In each case we can distinguish the fact that is the reason or the fit-making fact from the fact that this fact is a reason or a fit-making fact. I will use the word ‘supporting’ when I want to remain non-committal about the kind of normative or even non-normative support, whether favoured by a reason, made fitting, partially grounded, or something else. I assume the things doing the supporting are facts.3 I restrict my conclusion to so-called reasons for affective attitudes.4 I talk mostly about emotions; I do occasionally discuss desires (in the sense of passions or wants rather than motives). I take no stand on whether my arguments can be generalized to conative attitudes (the action-oriented attitudes such as preference and intention) or epistemic attitudes.5 I will be focusing on occurrent mental states rather than dispositions or traits of character (on episodes of anger rather than being ornery) and rather than enduring states (such as loving Charlie or caring about poverty). I also restrict my focus to object-directed attitudes rather than moods or feelings (being angry about your low wages rather than just ‘having got out of bed on the wrong side’). The goal of this essay is to draw the advertised contrast as clearly as possible, so I will focus on paradigmatic cases. I leave for another occasion the task of characterizing more precisely which things stand on the ends of these two relations, the reason relation and the fit-making relation.6 2. Reasons and the right/wrong distinction 2.1 The relevant features of reasons Let’s start by characterising reasons, by which I will always mean normative reasons. I will work with a precise and restrictive characterisation. This suits my dialectical goal of making the contrast between the reason relation and the fit-making relation as clear as possible. I extend the argument to an alternative characterization in §4.2. For an illustration of reasons for action, we can start with Peter Singer’s famous example: If you are walking past a shallow pond and see a child drowning in it, you ought to wade in and pull the child out. This will mean getting your clothes muddy, but this is insignificant, while the death of the child would presumably be a very bad thing. (Singer 1971, p. 231) The fact that by wading into the pond you can save the life of a child is a reason to do so. The fact that by doing so you’ll get your clothes muddy is a reason not to wade into the pond. Each of these reasons has some gradable property that is usually called its weight. These weights can be compared with each other, by and large.7 In this example, the ‘saving the child’ reason has more weight than the ‘getting your clothes muddy’ reason. These weights can interact in different ways. Sometimes reasons compete with each other, as do the reason to save the child and the reason to protect your clothes. Sometimes reasons combine, as both the satirical punch and historical interest in Gogol’s novels combine to favour reading them. In most cases, there will be lots of reasons for and against any given option. The mere fact that some fact is a reason to do something, even a weighty reason, doesn’t yet make it the case that you overall ought (henceforth simply ‘ought’) to do that thing, or that you would be criticisable for not doing it. It is a mistake—albeit a common one—to say that individual reasons ever justify or require anything on their own. On their own, reasons are normatively impotent. The fact that this is a reason for that, even a weighty reason, is simply silent about what other reasons there might be. Even a weighty reason, if significantly outweighed, would fail to justify the action it favours. The fact that the child will drown, for instance, would fail to justify wading into the pond if the alternative were defusing a bomb on dry land, set to destroy Chicago.8 Together, however, the facts about the weights of all the reasons for and against any given option, together with the fact that these are all the reasons bearing on the given option, explain some fact about the net weight of reason supporting that option. These facts about the net weight of reason supporting each option (together with some fact about what options there are) in turn explain the fact that there is most reason in support of some option. Assuming that you ought to do what you have most reason to do, this fact explains the fact that you ought to take that option.9 This last fact, the fact that you ought to take this option, is an overall normative fact. It obtains in virtue of all the contributory normative facts together with a ‘normative totality fact’ to the effect that these are all the relevant normative facts.10 Let me explicitly draw your attention to the three most important properties that emerge from this characterization. Firstly, reasons are individually impotent, or equivalently, they are non-strict.11 Strict facts are directives; facts about what you overall ought to do are the paradigmatic strict facts. Secondly, reasons are essentially12contributory. Contributoriness is the property of playing a specific role in a ‘weighing explanation’ of an overall normative fact. Characteristically, reasons play this role either by combining or by competing with each other. Thirdly, reasons are essentially gradable. They stand in ‘weightier than’ relations to each other. (For simplicity, we can talk as though these weights come in degrees. I show in §4.2 that my central contrast relies on a weaker assumption than this.) I will argue that fit-making facts are not gradable and they are not contributory; fit-making facts are not impotent: they are strict facts, but they are local, rather than overall, strict facts. They are like reasons in being local facts but like the overall ought in being strict. It is important to distinguish reasons in the metaphysical sense just characterized from a broader functional role that considerations can play as representatives in reasons-giving conversational and deliberative contexts.13 It is well-known in the theory of explanation that the provision of salient considerations can play different pragmatic roles in virtue of variations in our shared background knowledge and specific interests in reasons-giving contexts. Quite generally, the considerations we actually offer as reasons are those that are saliently needed, in some specific conversational context, to pick out a larger explanatory structure. (Compare Grice (1975), Raz (1975), and Schroeder (2007).) It is permissible to say of considerations that they are reasons even if they are not reasons in my sense. For instance, it is permissible to say that the reason for you to ϕ was that ‘there was no reason not to ϕ’ or that ‘a reliable informant advised ϕ-ing’ or that ‘there was most reason to ϕ’ or that ‘Mildred didn’t mind’, and so on. But none of these are reasons in the sense of considerations that play the metaphysical role I have in mind. This is a crucial point, because it is often permissible to say that some consideration or other is the reason for you to have some attitude. It doesn’t follow that these considerations play the same metaphysical role as reasons as I understand them. 2.2 Distinguishing right from wrong I need to briefly distinguish the ‘right’ from the ‘wrong’ kind of supporting considerations in order to focus attention on the so-called reasons of the right kind for affective attitudes. This distinction is widely accepted but difficult to analyse. (See Rabinowicz & Rønnow-Rasmussen (2004) and especially D’Arms and Jacobson (2000).) First exclude incentive cases. The fact that the gunman will shoot unless you hope that the Socialist candidate wins the election seems to be a reason to hope that she wins, but the wrong kind of reason. Intuitively the right kind of reason to hope that the Socialist candidate wins is that she favours universal health care, or free child care, or hefty anti-discrimination provisions. Intuitively the gunman’s threat provides the wrong kind of reason to have this attitude in this context.14 We can draw a further distinction between reasons of the right kind and moral or prudential considerations. Sometimes a joke can be funny even though it wouldn’t be appropriate to laugh—a plane-crash joke at a funeral, for example. Often emotions can be fitting but unpleasant, or unwise: too much anxiety about whether you will fall off the rickety bridge and you just might. When Joseph Raz says ‘A murderous rage … appears never to be appropriate’ (2011, p. 49), this is true, if ‘appropriate’ is understood broadly, but false, if understood to mean that there is no such thing as the (so-called) right kind of reason to fly into a murderous rage. Consider the circumstances of The Bride in Tarantino’s Kill Bill after the massacre of her friends and unborn baby on her wedding day, for example. Following D’Arms and Jacobson (2000), let us classify considerations such as these—incentive cases, as well as moral and prudential considerations bearing on attitudes in these ways—as of the wrong kind. 3. Fit-making facts are not contributory I will now begin the argument. Reasons are non-strict, contributory, and gradable. In this section I will argue that fit-making facts are strict and not contributory. In the following section I will argue that fit-making facts are not gradable. It follows that fit-making facts are not reasons. In the final section I consider and reject an objection, namely, that some fit-making facts play a contributory role in explaining overall strict facts about attitudes to complex states of affairs. Here is the strategy for this section. Start with some very specific affective attitude, distinguished by kind, degree, and content, for instance, being very pleased at your friend’s promotion. Then try to find considerations that bear on the fittingness of this attitude that either compete, or combine, with each other—these being the two ways that reasons characteristically contribute to the explanation of an ought fact. I argue that in the case of affective attitudes we do not find either kind of interaction. The simplest way for considerations to compete is for one to make an attitude fitting and for another to make that very attitude unfitting.15 Suppose you didn’t get some promotion, but your good friend Andrew did. You know that you would have deserved the promotion, but it is really good that Andrew got it. The fact that you didn’t get the promotion makes it fitting to feel disappointed. The fact that your friend got the promotion makes it fitting to feel pleased. But the considerations supporting these attitudes do not compete. The fact that you didn’t get the promotion doesn’t make it unfitting to feel pleased, and the fact that your friend got it doesn’t make it unfitting to feel disappointed. It is fitting to feel pleased and disappointed in these different respects in this case. Suppose that Andrew didn’t really deserve the promotion (there were some shenanigans) but that it will enable him to avoid getting kicked out of his apartment. The fact that your friend will be able to stay in his apartment makes it fitting for you to be pleased about the promotion, but the fact that the promotion wasn’t really deserved seems not to make it fitting for you to be pleased about the promotion as such. This is all plausible, but notice that we have again distinguished two attitudes both of which are fitting and that are perfectly compatible with each other: being pleased that he can stay in his apartment and not being pleased as such about the promotion. Just as in the case of my grandmother’s death, one feels a certain amount of ambivalence, which is best explained by giving this more detailed interpretation of one’s response. There is still no competition here. Could it be fitting to be pleased that your friend Andrew can stay in his apartment and also fitting to be displeased that Andrew can stay in his apartment? We can make sense of this, but only by offering a particular interpretation of the attitudes in question. Suppose that moving would be inconvenient for Andrew but he has a chance of finding somewhere better. Another friend, Margaret, would move into the apartment; it would be a dream move for her. It is perfectly fitting to be sad for one friend’s misfortunes while pleased for another friend’s good fortune. The considerations supporting these attitudes each, one by one, make a different attitude fitting. But to say that two affective attitudes are both fitting is not to say that a single attitude is supported by one ‘right kind of reason’ and opposed by another ‘right kind of reason’. More fit-making facts just make a more complex set of reactions fitting. These considerations suggest two contrasts between reasons and the support for these affective attitudes. Firstly, the facts supporting these attitudes are strict. Unlike reasons, they are not normatively impotent in isolation. Each of these considerations—that Andrew can stay in his apartment, that Margaret can’t move in, that Andrew got a promotion—individually provides strict normative support for a distinct response. (These are local, rather than overall, strict facts.) Secondly, these fit-making facts are not contributory. They don’t compete with each other. In addition to competing with each other, reasons also combine with each other, lending their total weight to some option. Let’s see if we can find an analogue of this relationship in the case of support for affective attitudes. In the above example, suppose that the fact that Andrew can stay in his apartment means that his daughter, Rebecca, won’t need to change schools. Would that be ‘another reason’ to feel pleased that Andrew got his promotion? I don’t think so. As before, this further fact supports a distinct attitude alongside being pleased that he won’t have to move apartments, namely, being relieved that Rebecca won’t have to change schools. Similarly, if your impoverished friend James had bet money on Andrew getting the promotion, that would support the more specific attitude of being pleased for James that he won his bet. So far, these are cases in which considerations do constitute distinct sources of support, but for distinct attitudes (for example, being glad that James won his bet and relieved that Rebecca won’t have to change schools). There are also cases in which distinct considerations do provide some support for one affective attitude, but not normatively distinct sources of support. Here is such a case. You are a knight, about to face the terrible dragon. The dragon has sharp claws. She has the ability to swipe at you with the claws. She also has a look in her eye that suggests she might quite like to. Do these distinct facts about the dragon constitute distinct ‘reasons’ to fear the dragon? They are distinct considerations, to be sure. But intuitively they work together to constitute one source of normative support for fear at the prospect of being cut open by a swipe from the dragon. Plausibly, you have a different ‘reason’ to be concerned about the fact that the dragon might burn all your crops. Or as I would say: it is also fitting to be concerned about the destruction of your crops. This is a distinct affective attitude. Both are, in this unfortunate circumstance, fitting. What I deny is that there are distinct sources of normative support for any one attitude.16 By contrast, you might have lots of distinct reasons for and against some specific action, say, running away from the dragon. One final challenge. Suppose you don’t know how many claws the dragon has. Your scout is peering through a telescope, and reporting as follows: ‘Three! No, four! No, five! Oh God, six!’, and so on. It is natural to say that each pronouncement is a reason to be even more fearful of the dragon. Surely with each pronouncement it becomes fitting to be more fearful of the dragon than before. So isn’t each pronouncement a reason that makes a different attitude (or the same attitude to a different degree) fitting? No. The timing here is the important thing. The fact that your scout reports five sharp claws on the dragon at one time makes it fitting to be fearful to some degree at that time. The fact that your scout reports six sharp claws on the dragon at a later time makes it fitting at that later time to be fearful to some higher degree. These considerations are not parts of the same explanation, and a fortiori they do not compete or combine in the same explanation, as reasons do. 4. Gradability and normative explanations 4.1 Fit-making facts are not gradable Normative reasons are gradable. But fit-making facts are not gradable. Fit-making facts do not support the affective attitudes they make fitting more or less than other fit-making facts. Strictly speaking, it is a mistake to talk about some affective attitude’s being more fitting or less fitting. This is unobvious, I suggest, partly because of the important distinction between a gradable normative fact about an attitude and a normative fact about a gradable attitude. Suppose you learn that two individuals have died. One is a peaceful octogenarian, her most important projects behind her. The other is a talented, educated, motivated, and popular twenty-one-year-old. Generally speaking, it is worse for someone to die in their twenties than their eighties. So let’s just assume that the death of the youngster is more tragic than the death of the octogenarian. Now consider the following two claims: The fact that the death of the youngster is very tragic makes it fitting to feel more sad about her death. The fact that the death of the youngster is very tragic makes it more fitting to feel sad about her death. It is very plausible that claim (a) is true. It is plausible that the fact that the death of the youngster is more tragic makes it fitting to feel more sad about her death. The greater the tragedy, the greater the amount of sadness that is fitting. This seems to apply to many other affective attitudes that are fittingness-apt. The more shameful some event, the greater the shame that is fitting. The more stunning some victory, the greater the degree of pride that is fitting. The worse the thing you did, the more guilty it is fitting to feel—perhaps you should buy your friend dinner rather than merely a drink. The more claws the dragon has, the more afraid it is fitting to be. What about (b)? Does the fact that the death of the youngster is more tragic make it more fitting to feel sad about her death, or more unfitting to feel unmoved by her death? I don’t think so. Consider an analogy. Suppose you asked two children for the product of 7 and 5. One says 42. The other says 33. Which answer is more correct? I think there is an error in the question. Any answer other than 35 is incorrect. The two children’s answers are both incorrect. But there is more we can say. We can say that the first child probably gave the product of 7 and 6, so she was one multiple off, as it were. She probably used a better method. We can say the other was numerically closer to the correct answer. In different contexts we might implicitly invoke these alternative standards of assessment, to substantiate the claim that one is more or less incorrect. These are ways of generating some alternative standard by which to assess their degree of failure. This alternative standard is gradable; this is the property we are tracking with our ‘how incorrect’ talk. So it is with fittingness. An attitude is either fitting or unfitting; there are no degrees, no comparisons, and there is no maximization. We can talk about degrees of fittingness, to be sure. But when we are doing so we are subtly shifting to assessment by some other pertinent standard, usually a gradable notion.17 This is a debunking explanation for our practice. Consider a case in which someone ran a fractionally faster time in the 100 metre sprint than had been predicted. Distinguish the claim that it is more fitting to be impressed by the slightly faster time, from the claim that it is fitting to be more impressed by the slightly faster time. I’m inclined to think that the former is a slightly sloppy way of saying the latter. But if one wanted to insist upon comparing the two attitudes we could say: it is more fitting to be moderately impressed by this performance than to be mildly impressed. That claim may well be felicitous, even if it is not literally true. The felicity conditions are explained by the fact that it would be fitting to be impressed, together with the fact that being moderately impressed is closer (along the relevant dimension) to being impressed than is being mildly impressed. Sometimes what is fitting is a range of attitudes or strengths of an attitude. For example, the fact that rush-hour traffic in Los Angeles is light today makes it fitting to feel more than mildly pleased but less than ecstatic.18 The boundaries will be vague, to be sure. That will yield another property that seems to come in degrees, namely, clearly falling within the fitting range of attitudes. Then we can say that one attitude is more fitting if it more clearly falls within the fitting range. But it doesn’t follow from the fact that a property is vague that it is gradable. It might be vague whether it is impermissible to use a particular curse word in your lecture. It doesn’t follow that impermissibility itself comes in degrees. Consider an objection. Many fittingness adjectives are gradable, for example, ‘admirable’, ‘enviable’, ‘delectable’, ‘exhilarating’, ‘hilarious’, ‘estimable’, and ‘deplorable’. Does this suggest that fittingness itself is gradable? My reply is in two parts. Firstly, ‘more hilarious’ and ‘more exhilarating’ just mean ‘more hilarity is fitting’ and ‘more exhilaration is fitting’, just like ‘more fearsome’ and ‘less beautiful’ mean ‘fitting to be feared more’ and ‘fitting to appreciate less’. Secondly, I accept that ‘fitting’ is a gradable adjective. It is perfectly felicitous to talk about this or that being more or less fitting, a better or worse fit, completely fitting, and even completely unfitting. However, I deny that the property of fittingness is gradable. In giving a semantics for fittingness language, we need both the property of fittingness and some other gradable property; this other gradable property sets the relevant scale. It may help to think about the truth predicate here. We often indulge in talk about claims being more or less true, closer to the truth, or completely true. But many theorists want to insist that the property of being true is not gradable all the same. We can do so without revisionism by giving a semantics for these comparative and superlative forms in terms of truth and some other gradable property, for example, accuracy or truthlikeness. (Compare Oddie (2014).) Consider another objection.19 Suppose that you receive some evidence that a wonderful, or tragic, event has occurred. Perhaps it is evidence that your daughter has been in an accident, or perhaps evidence that she has been accepted to her top choice of university. However, the evidence is weak. More evidence keeps coming in slowly, piece by piece. Each piece of evidence raises the probability that the terrible thing, or the wonderful thing, has happened. Here is the objection: doesn’t this evidence increasingly make it more fitting to be delighted, or more fitting to be devastated? I don’t think so. At each moment, the available evidence makes some specific response fitting. It is uncontroversial that different attitudes are fitting towards, respectively, a tiny chance of something bad having happened, and towards certainty that the bad thing happened. Hope that the bad thing didn’t happen is fitting in the one case and not the other. Grief does not become more fitting as you get more evidence about a tragedy, though it becomes more understandable. Grief is always unfitting absent sufficient evidence that the bad thing happened. This is part of the tragedy of missing person cases, for instance. Quite generally, different affective attitudes are fitting given different evidence about some outcome. A similar point applies to our attitudes to nearby possible worlds. Different attitudes are fitting towards chopping your finger off and towards nearly chopping your finger off. But these attitudes are very different: in the one case the fitting attitude is intense anxiety, in the other it is relief. Different attitudes are fitting for past events (disappointment, anger, envy) and future events (hope, excitement, anxiety), and for different degrees of likelihood. (Right now you know that it is possible, but unlikely, that something will fall out of the sky and crush the building you are in.) Consider a final objection, based on the hypothesis that there are ‘modifiers’ for fittingness. Modifiers of reasons are considerations that intensify or attenuate the weight of those reasons (for example, discounting or prioritizing outcomes). Since modifiers operate on weights, examples of modifiers for fit-making facts would be problematic for my denial that fit-making facts have weights. The examples I have in mind are easy to come by. Take some case in which some tragedy would have been greater, some event more shameful, or some victory more stunning, but for some consideration p. It would be natural in such a context to say that p is a reason to feel less pride, shame, or sadness than we would otherwise have expected. In some cases, this wouldn’t be right: as above, this additional consideration doesn’t attenuate the degree of an attitude that would be fitting; rather, it makes a separate attitude fitting. Contrast the fact that someone ran a fractionally slower time in the 100 metre sprint with the fact that she gave an arrogant acceptance speech. The speech doesn’t make the victory less impressive; it makes the victor less admirable. But this leaves our question on the table. What about the fact that she ran a slightly poorer time? Is that fact a reason to admire her race less? Well, less than what? For sure, it would have been fitting to admire a slightly faster time a little more. But she didn’t get a faster time. It is fitting to admire this time this much. The putative modifier is really a consideration that distinguishes the state of affairs that one is responding to from some salient alternative situation. Some different attitude would have been fitting in this different situation, for example, slightly more admiration or pride. 4.2 Two theories of the weight of reasons To what extent does the contrast I have been drawing between reasons and fit-making facts depend upon optional assumptions about reasons? The argument from gradability just discussed relies on the idea that reasons have weights, but not necessarily on the stronger thesis that the weights of reasons come in degrees. At least, that argument does not presuppose that facts about the weights of reasons are explanatorily prior to the facts about which reasons are weightier than others. Contrast two accounts of weight (Lord & Maguire 2016). On a ‘weight-first’ theory of the kind implicit in the discussion so far, facts about the weights of reasons explain facts about which reasons are weightier than others. For instance, according to a simple value-based or desire-based theory of reasons, the weight of a reason is explained by the value of an outcome or the strength of a desire. For example, the fact that you’ll muddy your clothes in Singer’s pond case has some amount of disvalue; the fact a life will be saved has some amount of value. The relevant reasons have weights proportionate to these amounts of value. These weights in turn explain the fact that the clothes reason is significantly less weighty than the saved life reason. On another view, facts about which reasons are weightier than others are explanatorily prior to facts about the individual weights of reasons. For instance, W.D. Ross (1930)—widely held to have introduced contributory notions to contemporary ethical theory—plausibly held a view of this latter kind. One interpretation of Ross’s account of conditional or prima facie duties goes as follows. You have some small number of distinct duties—fidelity, reparation, gratitude, benevolence, and so on. You have a prima facie duty to perform any action falling under these descriptions. If there is one such action in a situation and no other action of one of these kinds (a normative totality fact), then, in virtue of those facts, your prima facie duty to perform that action becomes your duty sans phrase. If more than one of these kinds of actions are available in a situation, then which of these becomes your duty sans phrase is determined by some ranking of these duties.20 For instance, the duty of non-maleficence is more important than the duty of beneficence (op. cit. p. 21). The duties of fidelity, reparation, and gratitude in general trump the duty of beneficence (for example, op. cit. pp. 19, 30, 41-2; see also fn. 1 on p. 42). On this view as so characterized, prima facie duties have the following properties. They are contributory: they play a specific role in explaining distinct overall strict facts (facts about your duty sans phrase are overall facts since they essentially obtain partly in virtue of normative totality facts). Prima facie duties are not themselves strict facts.21 And they are gradable: they stand in weightier-than relations. Prima facie duties do not have weights ‘on their own’ on this view and they may not have weights that come in degrees. But the ranking explains which duties come out on top in cases in which many different prima facie duties compete in a single situation. These reasons are non-strict, they are contributory, and they are gradable. In short, all the hallmarks of the contrast between reasons and fittingness are also present in this alternative theory of reasons.22 5. Overall affective attitudes? In this section I consider the objection that some fit-making facts play a contributory role in explaining overall strict facts about overall attitudes to complex states of affairs. Let me give a quick road-map for this discussion. In §5.1 I introduce the objection and present a preliminary response. In §5.2 I develop this response by addressing a puzzle about disagreement over emotional responses. In §5.3 I consider the hypothesis that there are no overall attitudes at all, and hence no overall strict facts about overall attitudes. This hypothesis is interesting but too strong for my purposes. In §5.4 I consider a weaker hypothesis, that there are overall attitudes without fittingness conditions. I sketch an account that supports this hypothesis of which affective attitudes do, and which do not, have fittingness conditions. In §5.5 I point out two features that distinguish reasons and fit-making facts even if the central objection of this section is conceded. But we needn’t concede the objection. In §5.6 I offer an explanation for our temptation to think that there must be overall normative facts about attitudes. 5.1 The objection from overall affective attitudes What should we think about affective responses to complex states of affairs, or what we can call, for short, ‘overall affective attitudes’? It is common to ask questions, either of oneself or others, like the following. What do you really want? Are you upset overall? Is he or she enviable, desirable, or admirable overall? Here we seem to be asking for an account of an affective attitude towards something that takes into account all (or some pertinent subset) of its normatively significant features. We can ask whether you want your grandmother to pass away peacefully in her sleep, whether you like the summer in New York City, or whether you are pleased overall that Andrew got the promotion. In many such cases there appear to be considerations supporting both sides. Don’t these considerations stand to the fittingness of the overall affective attitude as reasons stand to the fact that you ‘overall ought’ to take some particular option? And wouldn’t this provide support for the claim that there are reasons for affective attitudes, namely, the very considerations that provide normative support for or against such overall attitudes?23 I don’t think so. Suppose someone asks whether you want your grandmother to pass away peacefully in her sleep. Here we are deliberately asking for an overall verdict about your emotional state. To answer this question, it may seem as though your more specific attitudes have a contributory character, as though you weigh your desire for her to stop suffering against your desire not to lose her, or perhaps the discomfort she would experience, or its disvalue, against your own loss without her. But if the conversation continued much longer, you would go into further detail. You would say that you really do not want her to pass away because you would miss her greatly, but …. This suggests that really your attitude (which we assume is fitting) is complex. Take another example. Someone asks you whether you like the summer in New York City. You explain that you dislike the heat and the humidity, but the wind blowing off the water helps, and it is easy to spend the heat of the day indoors. And the city comes alive in the heat: people are more boisterous and enthusiastic and the streets are full of bustling life. There are concerts in the park, although tickets are increasingly restricted to the wealthy…. In short, it is complicated. What is the answer to the original question? Yes. You do like the summer. But you also like grapefruit juice and violent Korean films. The question is not probative. Insofar as your attitudes towards the summer in New York are fitting, you are sensitive to these many evaluatively significant features of the experience. It is worth reemphasizing here that our ways of talking about our attitudes are often misleading. A stranger asks you how you feel about spending the summer in New York. You might not feel inclined to say more than ‘rather pleased’, even though your attitude is more complex. Often your interlocutor won’t have much patience for a longer answer anyway. On the other hand, it may be that your actual attitude is quite simple, but only because you failed to respond fittingly to the complexity of the situation. You may be simply delighted at the passing of the bill, even though it involved the rolling back of funding for important social services—because you never read the fine print. 5.2 An argument from disagreement It might be helpful to develop this thought a little further. Consider the following dialogue upon seeing a photograph in a newspaper of a supporter of a presidential candidate earnestly giving a Nazi salute. First person: ‘Ugh, that’s awful’. Second person: ‘No, this is great. The more photographs like this come out, the poorer the candidate’s chances’. Importantly, they seem to be disagreeing about something—this is signified by ‘No …’. This disagreement seems to be about what constitutes a fitting response. Presumably the second person agrees with some kind of ‘Ugh’, that is, that it is disturbing and disappointing to see an earnest Nazi salute at a presidential primary. But still, they seem to be disagreeing, and it is natural to assume that they are disagreeing about an overall fact about the fitting response to this picture, and that this overall fact is explained by some weighing of the expected instrumental value that this picture will have in galvanizing support against the white supremacist candidate, against the intrinsic awfulness of it. Let me start by saying that it is not clear that there are any competing attitudes here. It is fitting to be disgusted at the salute while also being pleased at the reduction in the candidate’s chances for the presidency. (Really, even this latter claim is itself too coarse. What is fitting is a set of attitudes towards the probabilities of this photograph becoming well-known, towards the candidate’s losing because people rejected his fascistic tendencies, and so on.) I don’t think the two speakers would disagree, in the end, about the relative significance of the intrinsic horror and the instrumental value. More likely, this disagreement concerns the conjecture that expressing just the attitude of disgust is evidence that the first speaker may have overlooked the upside. ‘No …’ indicates that the original ‘Ugh’ leaves something out of the full fitting response. Furthermore, ‘No …’ might be intended to signify that if one were to express just one response to the photo, it might as well be rueful satisfaction as disgust. This further thought might indeed be based on some comparison of the values at stake. The thought might be this: ‘Well, sure, this is disgusting, but the disvalue of the disgust is significantly less than the expected value of this sort of publicity’. (Assume this is true.) There may well be a disagreement here, but this is not a disagreement about which overall response to this complex state of affairs would be fitting. 5.3 Scepticism about overall affective attitudes? The hard-line position to take at this point is scepticism about whether we have any overall attitudes to such complex states of affairs, rather than just the more specific attitudes to the parts of the complex. It may be that talk about overall affective attitudes is an abstraction or an oversimplification, just as contour lines on a map are an abstraction or an oversimplification of the slope on a hill. Insofar as you are sensitive to the various specifics, you do not have any overall attitude towards staying in New York for the summer, or towards your grandmother dying peacefully tomorrow, or towards the promotion of one friend, or towards the loss of his apartment. You just have the many more specific attitudes. If there are no overall affective attitudes, there are no standards pertaining to them. Hence there could be no contributory considerations bearing on any standards for overall affective attitudes. But I don’t want my argument for a metaphysical thesis about two normative relations to lean on a speculative thesis in the philosophy of mind. I am inclined to think that affective attitudes are cheap. People seem to get upset and excited about all kinds of things, often rather coarsely grained things. It is surely possible to be rather pleased about the passing of the bill, generally excited about the camping trip, or impressed by the free jazz concert—even though the various significant features in these events make fitting a range of more specific responses. 5.4 The fitting-value link I suggest instead that not all affective attitudes have fittingness conditions. Plausibly, fitting responses are precisely as finely grained as the states of affairs to which they are responsive. The distinctions that fitting affective attitudes are responsive to are, by and large, evaluative distinctions of one kind or another. The question is whether there are fit-making facts for overall affective attitudes, that is, attitudes in response to complex or overall states of affairs, and if so, whether these fit-making facts are explained by the fit-making facts for attitudes towards parts of the overall states of affairs. Sometimes complex states of affairs do have distinctive evaluatively significance, for instance, when they instantiate organic value. Such cases pose no trouble for my argument. Organic values are values instantiated by some complex state of affairs as such, and not just a function of the values of the parts of the complex (cf. Moore (1903) and Hurka (1998)). The cello part for Pachelbel’s Canon in D is pretty uninspiring on its own, but the result when your friend joins on the violin is quite wonderful. This complex state of affairs might well directly make appreciation fitting. A distinctive value emerges at the level of this whole, and plausibly a distinctive kind of appreciation is fitting in response. This explanation is local in the relevant sense, since it responds directly to the organic value. Take another example: perhaps a particular kind of admiration is fitting when someone is both extraordinarily gifted and genuinely humble.24 Sometimes complex states of affairs are instrumentally evaluatively significant, as when the election of one candidate for U.S. President will have implications for foreign policy, judicial nominees, trade policy, and so on. But sometimes complex states of affairs are not evaluatively significant. Sometimes no response is made fitting by a particular complex, for instance, by the fact that the President started speaking at 3.47p.m. precisely, or that she doesn’t like green beans, or by the fact that you are wearing a red jumper today and you wore a blue jumper on this day five years ago. Except in extraordinary circumstances, that complex makes no response fitting at all—even if both jumpers are lovely. This suggests a more general theoretical hypothesis. Consider the fitting-value link: the individuation of fitting attitudes correlates with the individuation of evaluatively distinctive states of affairs. This biconditional thesis is fairly uncontroversial. It enjoys wide bipartisan support. Far from being inconsistent with ‘fitting attitudes’ accounts of value, the fitting-value link (or something similar) is entailed by such accounts (for example, Anderson (1993), Scanlon (1998), Schroeder (2010), Way (2013), Howard (forthcoming)).25 Given the fitting-value link, once we have an account of what individuates evaluatively significant states of affairs we will also have an account of what individuates fitting attitudes. I hypothesize that facts about overall value (as opposed to facts about organic value, symbolic value, and so on) are often not evaluatively significant in the relevant sense. For an example, think about totally unrelated evaluatively significant (or evaluatively insignificant) states of affairs: the complex consisting of both need not be evaluatively significant. 5.5 All fit-making facts are strict; some are not contributory The worst-case scenario here for my argument is not that bad. Suppose we were to grant that (1) there are overall affective attitudes, (2) that some such attitudes are fitting, and (3) that the fact that some such overall affective attitude is fitting admits of a ‘weighing explanation’ in which the local fit-making facts play the ‘reasons role’, providing support for or against the overall attitude in virtue of the fact that they are fit-making facts—not in virtue of their value, or other properties.26 It would follow that some fit-making facts are contributory. But even if I were to concede these three strong premises, at least the following two differences between fit-making facts and reasons would remain. Firstly, the various fit-making facts would still be strict.27 Even if there were some fitting overall attitude in a situation, this would not displace the fitting local attitudes (neither the ‘positive’ ones nor the ‘negative’ ones). All these more specific attitudes would remain fitting. For instance, even if it were fitting to be relieved overall that your grandmother passed, it would remain fitting to be sad that you won’t be able to talk with her. Even if it were fitting in the earlier example to be disappointed overall that you didn’t get the promotion, it would remain fitting to be pleased for Andrew. I do not maintain that reasons are essentially non-strict. (See fn. 11.) But fit-making facts are essentially strict. Secondly, the fit-making facts for overall affective attitudes would not be contributory; since reasons are essentially contributory it would follow that these ones are not reasons. To be a reason, in part, just is to play a certain kind of role in a ‘weighing explanation’ of a distinct strict normative fact, such as a fact about the overall ought. But the overall normative fact here, if there is one, is a fit-making fact. So even if fit-making facts are sometimes contributory, they are not essentially contributory, so they are not reasons. Given these two considerations, it is simpler to assume—against claim (3) above—that any fit-making facts for overall affective attitudes are direct responses to evaluatively significant states of affairs, just like all the rest of the fit-making facts we have considered. The nature of such a fitting overall response—being generally impressed, being relieved overall, and so on—would be qualitatively explained by the fact that it is a response to the overall value in question. There is no need for this explanation to advert to the more specific fit-making facts as such, and hence no real support for the hypothesis that even these fit-making facts are contributory. 5.6 The practical importance of overall judgements Let me end with a diagnosis for our inclination to assume that there is something important about overall affective attitudes to complex states of affairs. Sometimes we need to make an all-or-nothing judgement about some relatively coarse-grained question, such as whether a particular judge is admirable. Perhaps you are Chair of the Town Admiration Committee and the judge is one of the favourites for the Annual Prize. Then you do the best you can. But this is a question about reasons for action. The question is not whether it is fitting to admire the judge. The question is whether you ought to give her the prize. Lots of reasons will bear on this question: how people would react either way, whatever precedents there might be, what the Town Admiration Committee rule-book says, and so on. It is the same with wants, for example. Suppose you want to spend some time in the mountains, and you want to spend some time on the beach, and you’d also like to spend some time on your book. What do you want overall? Well, all those things. We can introduce a specific choice situation, and ask what you want to do most. For instance, we say that the mountains are awfully far away and you need a break from your book and what do you want to do this weekend overall? But this is clearly a practical matter. What we do here is precisely to move from considerations that are fitting, to reasons for and against different actions. Perhaps the main point is that there is no real need for facts about the fittingness of overall affective attitudes. Perhaps we can persist in asking questions about which overall attitude is fitting, and even give felicitous answers. But it would be a mistake to infer that these facts play a central role in the normativity of attitudes, in the way that facts about which options are supported by the overall weight of reason is central in the normativity of actions. Here is the punchline for this discussion of overall affective attitudes: when it comes to actions, the overall normative property is all important. It is what really matters. Indeed, this is one of the reasons why ‘reasons theory’ is so late on the scene: consequentialists and Kantians have been working away with overall properties this whole time. By contrast, in the case of attitudes, overall normative facts hardly matter at all. It is contentious whether there are any overall affective attitudes, and if so whether they have fittingness conditions, and if so which facts explain them. But whatever you think about this, we have a clear contrast. With action, the overall normative property is all important. With affective attitudes, it hardly matters at all. Conclusion Let me summarise the argument. My central thesis is that affective attitudes are not supported by normative reasons but by fit-making facts. Reasons paradigmatically support actions. They participate together in weighing explanations of which actions you ought to perform. They participate in such explanations in virtue of facts about their weights. This is true whether facts about the weights of reasons explain or are explained by facts about which reasons are weightier than others. On their own, reasons are impotent. They are team players, democrats, always and only working together to issue in strict normative facts. By contrast, fit-making facts are amenable anarchists, happy in each other’s company but each one working alone. Each fit-making fact for an affective attitude makes that attitude fitting. More fit-making facts just make a more complex set of attitudes fitting. Fit-making facts plausibly support responses that are as finely grained as the evaluatively significant features of the world that call for these responses. Complex states of affairs with a range of evaluatively significant features will (distributively) make fitting a complex set of finely grained responses. Organic values aside, the complex state of affairs as such may not make anything fitting, just as the complex consisting in your reading this paper and the last novel you read may not make any particular response fitting over and above the fitting responses to this paper and that novel.28 Footnotes 1 I am agnostic about whether there are reasons of the wrong kind for affective attitudes. 2 I assume that the being a reason for relation and the being a reason against relation are distinguished just by their valence. 3 I don’t deny that justified false beliefs about outcomes can provide normative support. But issues about evidence-sensitivity are largely orthogonal to the central points here (apart from briefly in §4.1). I stick with facts for simplicity. 4 For a seminal overview of the affective/conative/epistemic trichotomy of mind in empirical psychology, see Hilgard (1980). 5 Elsewhere, Jack Woods and I (ms.) defend a related account of normative support for epistemic states. 6 I don’t rule out the possibility that some actions are fitting (for example, expressive actions in symbolic contexts). 7 It will not be necessary to address questions about, for example, whether and how moral and prudential reasons can be compared. For important recent discussions see Harman (2016) and Schafer (2016). 8 It is implicit in Singer’s example that you don’t have any reasons that are weightier than your reason to save the child. For discussion of the relations between contributory reasons and ‘sufficient reasons’, ‘decisive reasons’, and ‘conclusive reasons’, see Lord & Maguire (2016). 9 The thesis that you ought to do what you have most reason to do is controversial but not for reasons relevant to our discussion. 10 Compare the discussion of ‘weighing explanations’ in Broome (2013), the reply in Kearns and Star (2015), and the reply to both in Maguire (2016a). We can distinguish normative facts that are necessarily explained in part by some normative totality fact, such as facts about what you ought to do, from normative facts that are not so explained, such as facts about reasons (and, for example, facts about particular values, such as the beauty of a smile, or the pleasure in a glass of whisky). The former types of normative facts are overall facts; the latter are local facts. Notice there are various totality facts in the explanation of ought facts—that these are all the options, and that these are all the reasons for any given option (and there will be one of those for each option). For a related distinction in epistemology, see Selim Berker (2013). 11 I use ‘impotent’ and ‘non-strict’ synonymously. I leave open the question whether it is essentially true that reasons are non-strict. For instance, it may be that obligations are contributory (that they play the relevant role in a weighing explanation of the overall ought) but also strict (a mark of this being that you are criticisable for failing to fulfil an obligation even if the balance of reasons tells against doing so). 12 By ‘x is essentially F’ I mean that it lies in the nature of xs to be F, as it lies in the nature of water to be H2O. This entails that it is necessarily true that all xs are F. For further discussion, see Rosen (2015). 13 On this distinction see Raz (1975, p. 22), Broome (2013, p. 49), Wedgwood (2015), Maguire (2016b), and especially Daniel Fogal (2016, p. 86), from whom I borrow the term ‘representatives’. This is an instance of a more general distinction between metaphysical or causal explanations and considerations that one can give as an answer to a ‘why’ question in a specific context. (See David Lewis (1986, p. 215).) 14 Some incentive cases are subtler. The fact that some affective attitude will be pleasant/unpleasant is usually the wrong kind of reason to have/not have the attitude. Even the fact that manifesting an attitude in a situation will help you to develop the disposition to manifest that attitude in similar situations—‘fake it ‘til you make it’ reasons—are reasons of the wrong kind. Only in unusual cases would this incentive affect whether some attitude is fitting. Suppose I tell you I will shoot you unless you are scared of me, or that I’ll give you a million dollars if you are excited about an offer I make you. Are these reasons of the right kind for these attitudes? To answer this, I suspect we need to distinguish different objects: the fact that someone is threatening you with being shot, and the fact that you will be shot unless you are scared of the person making the threat. The first is definitely the right kind of reason to be scared (if there are any). I’m not sure about the second. What is important is that these are fringe cases. This shows we are cottoning on to the relevant distinction. 15 There is a subtlety here. Distinguish the suggestion that F1 makes A1 fitting and F2 makes A1 unfitting from the suggestion that F1 makes A1 fitting and F2 makes A2 fitting (A2 might be some distinct attitude, or the negation of A1), where A1 and A2 are incompatible in some sense. As will become clear, I am doubtful about both. Here’s a nice example from The West Wing: President Bartlett, upon discovering that one of his senior staff has given state secrets to a journalist asks, rhetorically: ‘Is it possible to be astonished, and, at the same time, not surprised?’ 16 I provide further theoretical support for this argument in §5.4. 17 Julia Staffel (2015) attempts to work out just such an alternative standard for Bayesians. She writes: ‘The standard framework of subjective Bayesianism only allows us to distinguish between two kinds of credence functions—coherent ones that obey the probability axioms perfectly, and incoherent ones that don’t. An attractive response to this problem is to extend the framework of subjective Bayesianism in such a way that we can measure differences between incoherent credence functions. This lets us explain how the Bayesian ideals can be approximated by humans’. 18 For another nice example see the discussion of gratitude in Roberts (2004, p. 64). 19 For which, thanks to Daniel Star. 20 It doesn’t matter for current purposes how this ranking is determined, whether particularistically or generally, whether by ‘moral perception’ or some higher-order rule. Also, notice the implicit appeal to a normative totality fact in this explanation: this plays the role of determining that some prima facie duties are the only relevant ones. 21 For even if there are no other prima facie duties, the fact that ϕ-ing is your prima facie duty does not fully ground the fact that ϕ-ing is your duty sans phrase. You also need some fact about whether you have any other prima facie duties in that situation. You still need a normative totality fact: this prima facie duty is the only one in the situation. 22 Similar reasoning extends to the ‘higher-order reasons’ theory of Mark Schroeder (2007), and the ‘sufficiency-first’ theory of T.M. Scanlon (2014) (if we restrict our attention to his ‘pro tanto’ reasons). The same reasoning does not apply to the more neutral contrastive theory of reasons defended by Justin Snedegar (2014), according to which reasons are relative to sets of alternatives. This view about the existence of reasons leaves open these questions about the weight of reasons, apart from imposing the constraint that the weight of a reason is relative to the alternatives. Thanks to Justin Snedegar for discussion. 23 Compare Schroeder (2010) and the brief reply in Way & McHugh (2015, p. 35). 24 The fitting attitude to this complex would not displace the fitting attitudes to that person’s talent and to her humility. In such organic cases, we don’t have competition between considerations for fitting attitudes. There is no ‘weighing explanation’ here and no tension with my thesis. On the contrary, we have even more complexity. The fitting attitude towards the organic value is added alongside the fitting attitudes towards the various parts. All these fit-making facts are strict. 25 It bears emphasizing that the fitting-value link is silent about whether attitudes are fitting partly in virtue of being responses to valuable states of affairs, or whether these states of affairs are valuable in virtue of the fact that these attitudes are fitting. 26 There are lots of other properties around that could do this explanatory work: the intensities of the localized attitudes, the value-making properties (that is, the facts that are the fit-making facts), and the values themselves. In order to argue that these local fit-making facts are reasons, one needs additionally to argue that the facts about fittingness are doing explanatory work, rather than some of these other candidates. 27 At this point, the distinction between strictness and contributoriness is significant. 28 Special thanks to Chris Howard for terrific feedback and many helpful conversations about these issues, and two anonymous referees for many suggestions that greatly improved the paper. Thanks also to Geoff Brennan, Brookes Brown, Daniel Fogal, Eden Lin, Kathryn Lindeman, Meghan Maguire, Tristram McPherson, Carla Merino-Rajme, Geoff Sayre-McCord, Eric Sampson, Knut Skarsaune, Daniel Star, Jack Woods, and audiences at Boston University, Cambridge University, CSMN at the University of Oslo, The University of Nebraska at Lincoln, The University of North Carolina at Chapel Hill, The University of Reading, the St. Louis Annual Conference on Reasons and Rationality, and Uppsala University. 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doi: 10.1093/mind/fzx047pmid: N/A

Abstract It is notoriously difficult to find an intuitively satisfactory rule for evaluating populations based on the welfare of the people in them. Standard examples, like total utilitarianism, either entail the Repugnant Conclusion or in some other way contradict common intuitions about the relative value of populations. Several philosophers have presented formal arguments that seem to show that this happens of necessity: our core intuitions stand in contradiction. This paper assesses the state of play, focusing on the most powerful of these ‘impossibility theorems’, as developed by Gustaf Arrhenius. I highlight two ways in which these theorems fall short of their goal: some appeal to a supposedly egalitarian condition which, however, does not properly reflect egalitarian intuitions; the others rely on a background assumption about the structure of welfare which cannot be taken for granted. Nonetheless, the theorems remain important: they give insight into the difficulty, if not perhaps the impossibility, of constructing a satisfactory population axiology. We should aim for reflective equilibrium between intuitions and more theoretical considerations. I conclude by highlighting one possible ingredient in this equilibrium, which, I argue, leaves open a still wider range of acceptable theories: the possibility of vague or otherwise indeterminate value relations. It sometimes happens that one possible population is better than another with respect to the distribution of welfare.1 A population axiology, in a sense I will later make precise, is a theory of such comparisons. For example, suppose that two populations have the same size, and that in the first population everyone has a happy and fulfilling life, while in the second population every life is unhappy and devoid of meaning. Then any plausible population axiology will rule that the first population is better than the second. Note that, as in this example, I will often speak of ‘happy’ lives, and so on, just to mean those lives with a high level of welfare, without commitment to any particular theory of well-being. It turns out to be hard to find a population axiology that accords with certain strong and widely held intuitions. For example, consider a large population of happy and fulfilling lives, and a second, perhaps larger one, in which life is barely worth living. Many people strongly intuit that the first population must be better than the second. On the other hand, it appears that if the second population is sufficiently large, it will inevitably have more total welfare than the first. And so one obvious criterion for betterness seems to entail what Parfit (1984) calls the Repugnant Conclusion: the second population may be better than the first.2 Can we avoid the Repugnant Conclusion? By itself, of course. But concrete attempts to do so have turned out to violate other intuitions of comparable strength. This has led several authors to produce formal arguments that seem to rule out any completely satisfactory population axiology.3 These arguments reach their culmination in Gustaf Arrhenius’s Population Ethics, intended to be the major survey of the current state of the field.4 His six increasingly subtle ‘impossibility theorems’ claim to show that our core intuitions stand in contradiction. The implications of this claim are potentially profound. At a basic level, we are simply learning what kinds of bullets we must bite. But if we cannot adjudicate between the core intuitions, we may be pushed into a wider methodological and metaethical inquisition. In this paper I will review some of the basic ideas used in these impossibility theorems, and identify some problems with them. Because Arrhenius has approached the subject systematically and aimed for the best possible results, it is convenient to focus on his work: it means that the issues I raise are relevant to similar arguments found elsewhere in the literature, as I will make clear along the way. The theorems deploy two basic strategies, and I will divide up my analysis accordingly. The first basic strategy relies on the background assumption—typically suppressed—that one can get from a low welfare level to any higher welfare level by a finite number of appropriately ‘small’ increments. I will call this premiss ‘Small Steps’. In §2, I argue that Arrhenius’s defence of Small Steps is inadequate, and show that, without it, there are counterexamples to four of his six theorems. One such counterexample is a lexic version of total utilitarianism. Of course, this leaves open the question of whether it is ultimately plausible to deny Small Steps. But this question would be less urgent if the second basic strategy, used in the remaining two theorems, were a success. Instead of using Small Steps, this second strategy appeals to egalitarian intuitions. However, as I argue in §3, the key principle, the Inequality Aversion Condition, is poorly motivated, and, despite its name, is not necessary for an acceptable degree of inequality aversion. Indeed, while my example of total lexic utilitarianism does not satisfy the Inequality Aversion Condition, it nonetheless satisfies two more compelling egalitarian conditions from which the Inequality Aversion Condition is typically derived. Because of this, none of the six theorems tells strongly against total lexic utilitarianism, provided only that we deny Small Steps. Now, total lexic utilitarianism is one of a family of views that Arrhenius has called ‘Welfarist Superitarianism’ (Arrhenius, 2013, ch. 6). So another way to state the point is that Arrhenius’s arguments against Welfarist Superitarianism are ineffective, and a number of his claims about it are mistaken. In such a context, the denial of Small Steps is a tempting possibility. Indeed, most other assumptions of the impossibility theorems are much more intuitively compelling. On one side we have the headlining adequacy conditions, like the need to avoid the Repugnant Conclusion. These assumptions are meant to be justified by strong evaluative intuitions that many people, at least, would find it repugnant to set aside.5 Small Steps is not like that: its denial might be surprising, but not in itself repugnant. On the other side, we have a handful of formal assumptions, the most widely discussed of which is the transitivity of the relation better than. Although indeed some, like Rachels (2004) and Temkin (2012), have taken the impossibility theorems as evidence of intransitivity, many others of us share Broome’s sense that transitivity is simply ‘an analytic feature’ of comparatives (Broome, 2004, §4.1). Giving it up means giving up—or at least fundamentally revising—the traditional conception of value. Again, Small Steps is not like that: it is not central to the concept of value or to the concept of well-being. But one should not be too sanguine. For even if it is difficult to justify Small Steps within the abstract and minimalistic formal framework of the impossibility theorems, there are important arguments in its favour once we consider the dependence of well-being on continuous parameters such as the duration of some pleasure. One aim of this paper, then, is to highlight the role of such further considerations. Having sketched one type of argument for Small Steps in §4, I then suggest a final way in which its use is problematic. Even if Small Steps is true for every standard of smallness, arguments based on it are especially susceptible to worries about axiological vagueness. The upshot is that, granting Small Steps, there need not be determinate counterexamples to the most important adequacy conditions. Allowing for borderline counterexamples provides a conservative way to weaken those conditions— conservative because our intuitions may not easily distinguish between certain cases of determinate and borderline truth.6 1. The framework and key examples To set the stage, I will first describe the framework in which all of the impossibility theorems take place. The idea is to assume as little as possible beyond what is needed to state the main adequacy conditions. I have omitted some possible complications that are irrelevant to the issues I want to discuss, but otherwise this framework is meant to be common ground. I will start a bit informally, and then say officially what data constitute a population axiology. The first idea is that one life may be better than another. When, as here, I evaluate individual lives, as opposed to populations, the question is always how good the lives are for the people living them. If two lives are equally good in this sense, I say they have the same welfare level. So a welfare level can be understood as an equivalence class of lives, all equally good. I assume that the relation ‘at least as good as’, applied to lives or, derivatively, to welfare levels, is a preorder, that is, reflexive and transitive. (I do not require it to be complete, although it will be in my examples.) A population is a collection of lives, and a population axiology will also give a preorder on populations—a specification of when one possible population is at least as good as another. All the example axiologies I will consider will be ‘anonymous’: they hold that the value of a population depends only on how many lives instantiate each welfare level (so that, in particular, the identities of the people do not matter). Since my arguments will be based on what the impossibility theorems say about these examples, I may as well, in contrast to Arrhenius, assume that all population axiologies of interest are anonymous in this sense.7 Doing so will significantly simplify the formulation of various principles. With this in mind, let me define a distribution to be a finite, unordered list of welfare levels, perhaps containing repetitions. Each finite population determines a distribution.8 The assumption of anonymity means that we can make evaluative comparisons between distributions, in such a way that one population is at least as good as another just in case its distribution is at least as good. Again purely as a matter of simplification, I will assume that every logically possible distribution—every finite unordered list of welfare levels—lies in the domain of this preorder. Here is some useful terminology. If a is a welfare level, then a population or distribution ‘at level a’ is one in which only level a occurs (perhaps many times). And if A and B are distributions, then is the distribution obtained by concatenating the lists A and B. Finally, the size of a distribution is the number of people involved, that is, the length of the list. The impossibility theorems articulate various adequacy conditions for a population axiology, and state that these adequacy conditions are mutually incompatible. It is important to realize that these adequacy conditions are officially about the form of the population axiology; they don’t explicitly concern themselves with the interpretative question of which welfare levels correspond to which lives. However, to formulate the adequacy conditions in an understandable way, it helps if we can refer to a few broad features of this correspondence. For example, one of the main adequacy conditions is that the population axiology must avoid the Repugnant Conclusion. The Repugnant Conclusion in turn refers to a class of happy, fulfilling (henceforth ‘blissful’) lives and a class of lives barely worth living (henceforth ‘drab’). Officially: The Repugnant Conclusion: For any distribution at a blissful welfare level, there is a better one at a drab level. It is possible to eliminate this classification by quantifying over sufficiently high and sufficiently low welfare levels, as Arrhenius effectively does. But, for ease of presentation, I will take the classification as a part of the axiology. Officially, then, a population axiology consists of the following data: first, a set of welfare levels; second, a preorder on that set; third, a preorder on the corresponding set of distributions; fourth, a particular welfare level, singled out as ‘neutral’. We can then say that a welfare level is ‘positive’ or ‘worth living’ if it is higher than the neutral one.9 And fifth, among the positive welfare levels there is a class of ‘blissful’ ones, and a disjoint class of ‘drab’ ones. For my purposes, the only further assumptions are that there exists a blissful level, and that for any blissful level there is a lower drab level and another, even lower drab level. Some of Arrhenius’s more complicated arguments require three blissful and three drab levels, but those complications are irrelevant to what I shall say. To illustrate this framework, let me lay out two examples. First, according to total utilitarianism, welfare levels can be represented by numerical ‘utilities’, in such a way that higher numbers correspond to better welfare levels, and one distribution is at least as good as another just in case its total utility is at least as high. For convenience, I require that the utility of each welfare level is an integer, and that any integer can occur. I stipulate that utility 0 represents the neutral welfare level, that 1 and 2 represent drab levels, and that 100 represents a blissful one.10 Here is a second example, which I call total lexic utilitarianism (TLU). Let me begin with an informal picture. (As I emphasize below, this picture gives one possible interpretation of TLU, rather than being part of TLU per se. Its purpose is just to give a handle on the formalism coming up.) There are two things that make life good—call them ‘love’ and ‘money’. The neutral level of welfare corresponds to a life with no love and no money; a blissful life has at least a little love, while a drab life has none. Moreover, a little love is worth any amount of money.11 So one population, or one life, is at least as good as another if it contains either more love in total or the same amount of love and at least as much money. Formally, TLU has a similar structure to total utilitarianism: it claims that welfare levels can be represented by utilities, in such a way that higher utility means higher welfare, and distributions are ranked by total utility. The difference is that this time I require the utilities to be, not integers, but arbitrary pairs of integers (corresponding, in the picture above, to quantities of love and money respectively). For this to make sense, I have to explain how these pairs are ordered and how they can be added together. The ordering is lexicographic: (a1, a2) is at least as great as (b1, b2) just in case either or else a1 = b1 and . Addition is component-wise: . It thus makes sense to compare distributions based on their total utility. To round out the example, I will stipulate that (0, 0) represents the neutral welfare level, that (1, 0) represents a blissful level, and that the drab welfare levels are those represented by pairs of the form , with m > 0. To put it another way, a positive welfare level is drab just in case it is only finitely many levels above neutrality. To be clear, this paper is not a defence of total lexic utilitarianism. Rather, I introduce it because it is a very simple theory that illustrates a wide variety of important ideas. The reader will naturally wonder whether welfare could really have the structure accorded it by TLU. I think that is a very good question. In fact, the basic argument of SS2 and 3 is that the impossibility theorems are ineffective without a negative answer to this question, or, more precisely, without a proper argument for the ‘Small Steps’ condition I mentioned in the introduction. Before we get to that more detailed discussion, let me explain in general terms why the impossibility theorems get so little traction on TLU. The first point is that TLU does not entail the Repugnant Conclusion. According to my stipulations above, a drab life contains no love. Therefore a population of drab lives contains no love, and must be worse than any population of lives at the blissful level (1, 0). At this point one might object that (1, 0) could not reasonably correspond to a blissful life. After all, a life with a minimal amount of love is not much better than a life with none at all. We must recognize that a life at level (1, 0) is barely worth living, and then we will obtain a version of the Repugnant Conclusion. But this objection is based on a misunderstanding. My interpretation in terms of ‘love’ and ‘money’ was picturesque and convenient. I will continue to use these terms in informal discussion. But this interpretation is not part of the axiology. TLU as such does not theorize about the components of well-being at all, and in particular does not claim that utility (1, 0) involves low levels of some component.12 A related misapprehension might arise if one imagines pairs of integers as labelling points on a plane in the usual way. Then (1, 0) is geometrically adjacent to (0, 0), and one might presume that the welfare levels represented by these pairs must therefore be similar in value. However, nothing in the definition of TLU validates this presumption. The fact is that there are infinitely many welfare levels between those two; they are not adjacent in any evaluative sense. So there is no reason (1, 0) cannot represent a high level of welfare. The second point is that TLU shares many properties with ordinary total utilitarianism, inasmuch as it is a theory of ‘total utility’. The only way in which total utilitarianism runs foul of the impossibility theorems is that it leads to the Repugnant Conclusion. TLU avoids this problem, but it also remains similar enough to total utilitarianism that it satisfies almost all of the other adequacy conditions. There is one condition, the Inequality Aversion Condition, which ordinary total utilitarianism satisfies and TLU does not. But, as I argue in §3, this is a reason to reject the Inequality Aversion Condition, not a reason to reject TLU. 2. Against Small Steps Now let me begin my analysis of the impossibility theorems. One strategy used by these theorems relies on the following principle. Small Steps: Any blissful welfare level a can be reduced to any lower drab level z in a finite sequence of small steps.13 Of course, ‘small’ is context-dependent. It invokes an implicit standard for smallness—that is, for each welfare level a, a specification of which other welfare levels count as differing from a by a ‘small’ amount. The standard must be weak enough to make Small Steps true. But it must also be strict enough to make various adequacy conditions seem compelling. For example, here is a simplified version of Arrhenius’s first impossibility theorem.14 The simplified claim is that no population axiology can avoid the Repugnant Conclusion while satisfying The Quantity Condition: Suppose that a and b are positive welfare levels, that b is lower than a, and that the difference between a and b is small. Then for any distribution at level a, there is a larger, better distribution at level b. Informally, we should accept a small decrease in welfare levels in exchange for a sufficient increase in population size. It is easy to see how one might argue from the Quantity Condition to the Repugnant Conclusion. Starting from a distribution at a blissful level a, we should accept a small decrease in welfare levels in exchange for a sufficient increase in population size. But, according to Small Steps, a sequence of such small decreases can lead us from a to a drab level z. We should therefore accept a decrease in welfare levels from a to z in exchange for a sufficient increase in population size. That is the Repugnant Conclusion. So no population axiology can satisfy the Quantity Condition and Small Steps while avoiding the Repugnant Conclusion. The first, fourth, fifth and sixth of Arrhenius’s theorems follow this sort of strategy, proceeding through a sequence of small steps. (Recognizing that the Quantity Condition is open to criticism, the latter three theorems rely instead on the so-called Non-Elitism Condition, which I will discuss in §3.) Each theorem is implicitly of the following form: Given any population axiology, there can be no standard of smallness according to which (a) Small Steps is true; and (b) certain intuitively compelling adequacy conditions are all true, perhaps including the Quantity Condition or the negation of the Repugnant Conclusion. There are several types of objection one might make to such a theorem while conceding the force of the underlying intuitions. One possible objection is that an argument via Small Steps has the character of a sorites argument. Although I think this objection has merit, its force is not immediately clear; for a critical discussion, see Temkin (2012, ch. 9). I will make some related comments in §4. A second objection calls into question the way in which the adequacy conditions formalize the underlying intuitions. Let me say a little about this second objection, and then focus on the main line of thought: we can defuse the impossibility theorems by giving up Small Steps. To see why the formal adequacy conditions might not properly reflect the underlying intuitions, consider the case of the Quantity Condition. As far as I can tell, the intuition is that any sufficiently small decrease in the quality of lives can be compensated by a sufficiently large increase in the quantity of lives. But that is not what the Quantity Condition actually says. The intuition as just stated is better represented by the weaker Trade-Off Condition: Suppose we have a distribution at a positive welfare level a. There is some standard of smallness such that if the difference between a and a lower positive welfare level b is small, then there is a larger, better distribution at level b. The worry is that the Quantity Condition gains plausibility by conflation with the strictly weaker Trade-Off Condition. At any rate, it is not obvious to me that intuition supports the Quantity Condition over and above the Trade-Off Condition. The Trade-Off Condition is weaker, because what counts as a ‘small’ difference between a and b can depend on the size of the population at level a. The Quantity Condition, in contrast, requires there to be a single standard of smallness that works for all populations. Small Steps refers to that same universal standard. To see that this matters, consider Ng’s axiology, which he calls ‘Theory ’ (Ng 1989). He assumes that welfare levels are represented by real numbers, with 0 as the neutral level. We might take level 100 to be blissful, and those between 0 and 2 to be drab. Ng then gives a rule for aggregating these numbers, with populations ranked by their aggregate scores. The rule, in one concrete version, is that a population of n people with average welfare a has aggregate score It is easy to see that this axiology satisfies the Trade-Off Condition and avoids—as Ng argues—the Repugnant Conclusion. It also satisfies Small Steps, for any standard of smallness (see footnote 31 below). However, Arrhenius’s first impossibility theorem rules out Theory , because it does not satisfy the Quantity Condition for any standard of smallness. The failure of Theory to satisfy the Quantity Condition over and above the Trade-Off Condition does not, in itself, seem like a compelling ground for criticism.15 At a minimum, the Trade-Off Condition might be a relatively attractive fallback position. One can tell a similar story about the other adequacy conditions that refer to small differences. Now let me turn to my main objection. While I accept that on its face Small Steps is plausible, I do not think it is compelling enough to be considered a basic adequacy condition. Barring some deeper justification—which Arrhenius does not provide—the simplest response to the impossibility theorems is just to give up Small Steps. First, let me show that the use of Small Steps is no mere convenience: without it, the impossibility theorem fails. Consider the example of total lexic utilitarianism that I introduced in §1. I explained there that this axiology does not entail the Repugnant Conclusion. On the other hand, it does satisfy the Quantity Condition, for the following standard of smallness: the difference between a and b is small if and only if there are finitely many welfare levels between them.16 (To put it another way, a and b must have the same amount of ‘love’—as I suggested in §1, differences in love are in no way small. For example, by this standard, any drab life is only a small distance above the neutral level.) Thus the only objection that the first impossibility theorem raises against TLU is that it violates Small Steps. In fact, TLU satisfies all the adequacy conditions (excluding Small Steps) that are required by Arrhenius’s first, fourth, fifth and sixth impossibility theorems. Why then accept Small Steps? One might, with Arrhenius, be inclined towards Discreteness: For any welfare levels a and b, there are at most finitely many welfare levels worse than a and better than b.17 According to Discreteness, one can get from a to b through a finite sequence of consecutive welfare levels. Let us grant the plausible further assumption that the difference between consecutive levels counts as small by any relevant standard. We then obtain Small Steps. The question, though, is why we should believe Discreteness. Arrhenius has very little to say about this. On the other hand, he does not actually rely on Discreteness. He claims that even if Discreteness is not true, we can focus attention on some subset of all welfare levels in which Discreteness holds, and in which the difference between consecutive levels is small. But this claim is little more than a restatement of Small Steps. It gives no new argument.18 Are there some other, more convincing arguments in favour of Small Steps? No doubt; I will explain one kind of argument in §4. First I want to consider the question of whether the impossibility theorems that do not use Small Steps are effective. If they are, then questions about Small Steps are less urgent (although, I think, independently interesting). 3. Against the Inequality Aversion Condition Now let me consider the second basic strategy of the impossibility theorems. (The reader primarily interested in Small Steps can skip to §4.) It involves the following adequacy condition:19 The Inequality Aversion Condition: Suppose that a, z, b are welfare levels, with a higher than z and z higher than b. For any distribution A at level a, there are distributions Z at level z and B at level b such that Z has the same size as and Z is better than . Informally: the decrease of some people’s welfare levels from a to z can be compensated by the increase of sufficiently many others’ from b to z. Before discussing the merits of this condition, let me explain how it is used in the impossibility theorems. The simplest argument appeals to the following principle: The Mere Addition Principle: Suppose that A and B are distributions containing only positive welfare levels. Then is at least as good as A. The claim is that no population axiology can satisfy the Inequality Aversion Condition and the Mere Addition Principle while avoiding the Repugnant Conclusion. This is a simplified version of Arrhenius’s second impossibility theorem.20 Here is how the argument goes. Take a to be a blissful welfare level, z to be a drab level lower than a, and b to be a drab level even lower than z. (Recall that my official definition of ‘population axiology’ in §1 stipulated that such levels exist.) For any distribution A at level a, the Inequality Aversion Condition gives us distributions Z and B, with Z at least as good as . The Mere Addition Principle tells us that is better than A. So, by transitivity, Z is better than A. That is the Repugnant Conclusion. Arrhenius’s second and third theorems elaborate on this basic strategy, replacing the Mere Addition Principle with intuitively weaker ones. These two theorems take the Inequality Aversion Condition as a basic adequacy condition. The special interest of these theorems in this paper is that they do not rely on Small Steps. Total lexic utilitarianism, my counterexample to Small Steps, is ruled out by the Inequality Aversion Condition instead.21 Should we accept the Inequality Aversion Condition as a fundamental constraint on population axiology? In particular, does it offer a compelling objection to total lexic utilitarianism? I will suggest that the Inequality Aversion Condition is not particularly compelling in its own right. Then I will criticize two important arguments for the condition. Finally, I will give a general argument that it cannot be justified on egalitarian grounds alone.22 First, is the Inequality Aversion Condition compelling in its own right? To answer that question, consider how the condition is used in the argument just described. It is used to show that large penalties for some people (the people in A, reduced from blissful to drab lives) can be compensated with small benefits to sufficiently many others (the people in B, raised from one drab level to another). I think it is far from clear that we should favour such trade-offs. For example, can all-but-imperceptible benefits to sufficiently many people make up for the loss of all real joy in the world? Admittedly, it may be that some of the intuitions here are not axiologically driven; talk of ‘penalties’ may, for example, evoke questions about rights.23 Nonetheless, if, as it seems to me, the verdict on the Inequality Aversion Condition in relevant cases is intuitively negative or unclear, we should not accept it as a fundamental adequacy condition. But perhaps we can derive it from more compelling premisses. Arrhenius (cognizant of worries like the one I just raised) considers two such arguments. I will show that these two arguments fail to establish the Inequality Aversion Condition as an adequacy condition, at least if we are in doubt about Small Steps. First, Arrhenius’s favoured argument for the Inequality Aversion Condition (2000a, §6.3) begins from The Non-Elitism Condition: Suppose that a, z, b are welfare levels, with a better than z and z better than b, and that the difference between a and z is small. Then, for some number n, it is always a net improvement to reduce one person’s welfare from a to z while increasing that of n others from b to z.24 I agree that this condition sounds compelling. It should also be clear, at least in outline, how the argument from Non-Elitism to Inequality Aversion is supposed to go. The basic difference between the two conditions is that the Non-Elitism Condition only allows us to compensate for the loss of a small amount of one person’s welfare, while the Inequality Aversion Condition allows us to compensate for the loss of a large amount of many people’s welfare. But a sequence of small losses to one person at a time can amount to large losses for many people. Thus recursive application of Non-Elitism leads to the Inequality Aversion Condition.25 However, this argument relies on Small Steps: it assumes that a sequence of small decreases in welfare can amount to a large one. Indeed, total lexic utilitarianism does not satisfy the Inequality Aversion Condition, but it does satisfy the Non-Elitism Condition.26 To see this, recall that the difference between a and z is ‘small’ only if they have the same amount of love. Suppose, then, that a and z differ only by m units of money. Since the difference between z and b is at least one unit of money, a decrease in the welfare of one person from a to z can be compensated by an increase in the welfare of m + 1 people from b to z. Thus while the Non-Elitism Condition may ultimately support the Inequality Aversion Condition, it certainly does not help us avoid the use of Small Steps. Now let me turn to Arrhenius’s second argument for the Inequality Aversion Condition (Arrhenius 2000a, §6.1, following Ng 1989). It starts from The Non-Anti-Egalitarianism Principle: A perfectly equal distribution is better than an unequal distribution of the same size and with lower total (and thus lower average) welfare. Note that the Non-Anti-Egalitarianism Principle presupposes a notion of ‘total welfare’, and my definition of a population axiology does not involve such a notion.27 So, as Arrhenius notes, one way to resist arguments from Non-Anti-Egalitarianism is simply to deny that welfare has the right kind of structure for total welfare to make sense. I agree that one could do that, but it seems worth pointing out that the argument still has problems, even if one countenances talk of total welfare. After all, many people have agreed with Ng that the Non-Anti-Egalitarianism Principle is extremely compelling, and have followed him in using it to derive the Repugnant Conclusion via the Inequality Aversion Condition.28 The main problem is that it is not true that the Non-Anti-Egalitarianism Principle entails the Inequality Aversion Condition. We can see this by once again appealing to total lexic utilitarianism. This theory ranks populations by total utility, and we can apply the Non-Anti-Egalitarianism Principle on the supposition that total utility is the mathematical representation of total welfare. Then TLU satisfies the Non-Anti-Egalitarianism Principle. (After all, it considers the population with higher total welfare to be better, whether or not it is perfectly equal.) But, as we have already seen, TLU does not satisfy the Inequality Aversion Condition. Of course, proponents of the Non-Anti-Egalitarianism Principle invariably assume that welfare is to be represented by real numbers, and total welfare by their sum, instead of using pairs of numbers, as in TLU. On this assumption, Non-Anti-Egalitarianism does indeed entail the Inequality Aversion Condition.29 But the appeal to such a real-valued representation of welfare requires justification. There are two different ways of spelling out what the problem is, depending on how one thinks about total welfare. On the one hand, we might be able to find some common ground, such as the axioms of expected utility theory, that allows us to assign real numbers to welfare levels. We could then define ‘total welfare’ in terms of these numbers. But then it would be an open question why total welfare, defined in this particular way, is at all relevant to evaluating populations, let alone in the specific way claimed by Non-Anti-Egalitarianism. Greaves (2015) discusses this type of issue carefully in the context of prioritarianism. On the other hand, perhaps the thought is that we have some pre-existing notion of total welfare according to which the Non-Anti-Egalitarianism Principle is true; then it is an open question why total welfare in this sense can be represented by a sum of real numbers.30 I am not saying that either of these questions is unanswerable. My point is rather that it seems implausible that this line of thought could put the Inequality Aversion Condition beyond controversy, and in any case, an argument that simply presumes the resolution of these difficult issues cannot be satisfactory. Here is a final, less technical worry about the Non-Anti-Egalitarianism Principle, and so derivatively about the Inequality Aversion Condition. The principle concerns cases in which considerations of total welfare, average welfare, and equality point in the same direction. The thrust of the principle is that in these cases no additional considerations can make a difference. But that is not obvious. For example, perhaps it is also relevant how many lives are above a certain level of sufficiency. In particular, in our application of the Inequality Aversion Condition, populations like contain many high-quality lives, while populations like Z contain none. When thinking about the Repugnant Conclusion, a natural idea is that this very fact has overriding axiological significance. (I will describe a toy model with this feature in §4.) More generally, considerations of utility and equality may, in some cases, be overridden by others. This possibility undermines the Non-Anti-Egalitarianism Principle. I can now broaden these remarks to explain why it is not possible to justify the Inequality Aversion Condition on egalitarian grounds alone. Standard ways of thinking about inequality aversion, like the so-called Pigou-Dalton criterion, agree that total utilitarianism is neutral about inequalities in welfare, at least on the assumption that total utility is the relevant measure of total welfare. This is just because total utilitarianism considers populations with the same size and total welfare to be equally good regardless of how equally that total is distributed. Exactly the same point applies to total lexic utilitarianism: on the understanding that it ranks populations by total welfare, it is neutral about inequality. So we cannot rule out TLU as insufficiently egalitarian unless we are willing, controversially, to rule out total utilitarianism on these grounds as well. Therefore the Inequality Aversion Condition is not a necessary condition for an acceptable degree of inequality aversion. This point can be strengthened if we note that total utilitarianism, defined in the very abstract way of this paper, has egalitarian as well as inequality-neutral interpretations. The inequality-neutral interpretation is based on the understanding that increasing someone’s utility by one unit always increases total welfare by the same amount. Instead, we might interpret the utility scale in such a way that the increase in welfare represented by a fixed increase in utility diminishes as we move up the scale. On such an interpretation, it is better to give a fixed quantum of welfare to someone who is badly off than to someone who is better off. According to the Pigou-Dalton criterion, the theory so interpreted is egalitarian. For exactly the same reason, there can be decidedly egalitarian interpretations of TLU. In conclusion, the Inequality Aversion Condition cannot be justified on purely egalitarian grounds. It is not strongly supported by direct intuition. Nor is it, in general, a consequence of the Non-Elitism Condition or of the Non-Anti-Egalitarianism Principle, and the latter principle has problems of its own. 4. Small Steps and indeterminacy Recall the story so far. I have argued that the Inequality Aversion Condition should not be one of the fundamental adequacy conditions of population axiology. On the other hand, this condition follows from the much more compelling Non-Elitism Condition if we accept Small Steps. We have also seen another impossibility theorem, based on the Quantity Condition, which employs Small Steps. I have argued that the assumption of Small Steps is no harmless technicality, nor is it clearly justified. Still, it would be uncomfortable to pin the hopes of population ethics on the falsity of Small Steps. Small Steps follows if the welfare levels are ordered like the real numbers or the integers.31 Many of the quantities we detect in the world around us have that sort of structure, and it is (if nothing else) often assumed that welfare is the same. One can say more in favour of Small Steps. That is not the project of this paper, but here is the kind of argument that I find most compelling. I will give one specific version of the argument, and then indicate how it can be generalized. Suppose for now that welfare depends only on the balance of pleasure and pain in a life. Stipulate that a life would be ‘blissful’ if it consisted of one hundred years of intense pleasure followed by a single neutral minute, completely devoid of pleasure and of pain. Stipulate that a life would be ‘drab’ if it began with one minute of that same intense pleasure, followed by one hundred neutral years. (These stipulations are appropriate as long as the Repugnant Conclusion seems repugnant when understood in terms of these kinds of lives.) Then we find a natural continuum between drab lives and blissful ones, as we lengthen the initial period of pleasure from one minute to one hundred years. Now consider two lives on this continuum that differ by only one millisecond’s worth of pleasure. (Or one nanosecond’s worth; use as tiny an interval as you like.) The difference in welfare between two such lives is surely ‘small’ in the relevant sense. But then Small Steps holds, because there are finitely many milliseconds between one minute and one hundred years. Let me sketch how to generalize this argument away from considerations of pleasure and pain. The key claim is that, whatever the nature of well-being, we can find a continuum of possible lives beginning with some drab life and ending with a blissful one. By a ‘continuum’ I mean technically that these lives can be parameterized by a bounded interval of real numbers. In the specific version of the argument above, the continuum involved variations in the duration of some pleasure. But we could instead vary any of the attributes on which welfare depends, such as, at bottom, the configurations of particles or fields across spacetime. At any rate, this continuum is required to satisfy two further conditions. First, the lives must get better and better as we go along the continuum. Second, they must do so continuously, in the sense that, for any life along the continuum, any other life that is sufficiently close to it along the continuum will differ from it in welfare by only a small amount.32 The structure of the real numbers ensures that we can get from one end of the continuum to the other in a finite sequence of such sufficiently small steps (this is the Heine-Borel Theorem mentioned in fn. 31). Given the plausibility of such arguments for Small Steps, the impossibility theorems do pose genuine difficulties for population axiology. We should presumably aim for some kind of reflective equilibrium between basic intuitions and more theoretical considerations. In concluding this paper, I want to highlight one possible ingredient in this equilibrium that has not been widely addressed in the literature: the possibility of vague or otherwise indeterminate axiologies. Such indeterminacy has been considered before, but only in a limited way. For example, Broome (2004) advocates a version of total utilitarianism with a vague critical level. As he recognizes, this move only partly mitigates the impact of the impossibility theorems. I suggest that vagueness has a more general role to play in balancing competing intuitions. Why is vagueness relevant at all? Let me begin with an analogous case. Suppose I believe that Fred—whom I have never met—is tall; I know precious little else about him. I walk into a room, certain that Fred will be there. But there are two men present. Which one is Fred? The first man I see is determinately not tall. If the second man were determinately tall, I would infer that he was Fred. But the second man is only borderline tall. Still, all else being equal, I will be inclined to think that the second man is Fred. This matches my prior beliefs and my new evidence better than the alternative. Moreover, some borderline tall people are taller than others. Some are borderline tall but almost determinately tall. The closer the second man is to being determinately tall, the more inclined I will be to believe that he is Fred. So too in the case of population axiology. If I think the Quantity Condition (for example) is compelling, then, all else being equal, I should be inclined to favour a theory according to which that condition is borderline, but almost determinately, true over a theory according to which it is determinately false. This picture is strengthened if we observe that the impossibility theorems that use Small Steps are structurally similar to sorites arguments.33 The impossibility theorem I discussed in §2 repeatedly invokes the Quantity Condition to derive the Repugnant Conclusion. Similarly, a sorites argument might claim to prove that every tree is tall by repeatedly invoking The Tolerance Condition: Suppose that a and b are heights, that b is lower than a, and that the difference between a and b is small (less than one millimetre, say). Then it cannot be the case that a is tall for a tree and b is not. Theories of vagueness that respect classical logic must accept that there are counterexamples to the Tolerance Condition. But they must also explain the strong intuition in its favour. A typical explanation is that the Tolerance Condition has no determinate counterexamples. Every instance of the Tolerance Condition is at least borderline true, and indeed close to determinately true.34 If this kind of story explains why the Tolerance Condition is compelling, then it may help with the Quantity Condition and the Non-Elitism Condition as well. Even if these conditions admit counterexamples, they need not admit determinate counterexamples. That may go some way towards explaining their attraction. Let me now illustrate these general considerations with a toy model.35 In this axiology, welfare levels are represented by integers. Let us suppose that 0 represents the neutral level, 1 and 2 represent drab lives, and 100 represents a blissful life. Small Steps is bound to hold, assuming that the difference between consecutive welfare levels counts as ‘small’. The ranking of populations will have a sufficientarian flavour. There is some positive welfare level S, the level of sufficiency, above which life is ‘very good’; lives below – S are ‘very bad’. Populations are ranked, in the first instance, by the number of very good lives minus the number of very bad lives. Then ties are broken by total utility, the sum of integers. Does such an axiology entail the Repugnant Conclusion? No—not as long as the blissful lives are above S and the drab lives are below it. By the first impossibility theorem (§2), we know that the Quantity Condition must fail. Indeed, it fails when, and only when, the small decrease in welfare from a to b brings us from a life that is very good to one that is not. But this is where vagueness can soften the blow. If the level of sufficiency is vague, then there are no consecutive welfare levels a and b such that, determinately, a is very good and b is not. Thus the Quantity Condition has no determinate counterexamples. Each instance is at worst borderline true, failing on at most one of the many possible precisifications of S. For the same reason, the Non-Elitism Condition has no determinate counterexamples. Indeed, of the adequacy conditions appearing in Arrhenius’s theorems, only one is entirely invalidated by this axiology. That is the Inequality Aversion Condition, which, I have already argued, we should not accept on its own merits. 5. Conclusion The main point of this paper is just how much the impossibility theorems rely on the background assumption of Small Steps. I gave a toy example—total lexic utilitarianism—which invalidates Small Steps but satisfies all but one of the main adequacy conditions. The same example helps us see why the remaining adequacy condition, the Inequality Aversion Condition, is not particularly compelling. One possibility, then, is to deny Small Steps. It is a possibility worth considering too: on its face, it is less painful than denying transitivity or giving up, say, the Non-Elitism Condition. Certainly Arrhenius’s justification for the assumption is inadequate, and finding a better justification is important to his project. Moreover, Small Steps and the Inequality Aversion Condition, if they can be justified at all, rest on relatively subtle considerations about the structure of the welfare scale. This necessarily takes us beyond the austere formal framework of the theorems onto more controversial ground, and perhaps we can find a way forward. However, I am not really optimistic about this possibility. As I explained in §4, consideration of how well-being depends on underlying continuous parameters suggests that the welfare scale is enough like a continuum to justify Small Steps. But the reliance of the impossibility theorems on Small Steps opens up a final possibility: the conflict of intuitions might be mitigated by axiological indeterminacy. I have introduced here the main idea, which I will explore more adequately in future work.36 Footnotes 1 There are other common ways of expressing this idea. In particular, some prefer to say that a population with one distribution of welfare would be better than a population with another distribution, all else being equal. I prefer my formulation, but nothing is supposed to hang on it here. 2 I say only ‘seems to entail’ because I will later consider a theory of total welfare that does not entail the Repugnant Conclusion. The well-known ‘critical-level’ theories (for which see Blackorby, Bossert and Donaldson 1995) are arguably also of this kind. Of course, one may wonder what it means to ‘total’ welfare at all; I will raise a related issue in §3. 3 Examples include Ng (1989), Carlson (1998), Kitcher (2000), Tännsjö (2002), and especially Parfit (1984), from which most of the arguments of this type ultimately derive. It is at least arguable that the same problems arise if if we skip axiology and deal directly with the question of which populations one ought to bring about (Arrhenius 2005). But in this paper I will focus on axiology. 4 Arrhenius’s book (forthcoming), is well known in draft form. In fact, the theorems themselves and much of the relevant discussion have been published in previous work (subject to some irrelevant revisions). I will refer to the theorems as they are enumerated in the manuscript, but cite the published discussions. The first four theorems are essentially those developed in Arrhenius (2000a); the fifth is from Arrhenius (2003); the sixth is from Arrhenius (2009, 2011). I note that the proof of his favoured sixth theorem contains an error in the derivation of the Restricted Quality Addition Condition (Arrhenius 2011, Lemma 1.3). As far as I know, one has to slightly strengthen the premisses of the theorem, in a way unlikely to cause further controversy. This will not affect my discussion. 5 In this paper, I just take it for granted that the main adequacy conditions meet this criterion (with the exception of the egalitarian conditions I discuss in §3). There is lively disagreement about whether the Repugnant Conclusion itself is truly repugnant; see especially Huemer (2008), who invokes (for one thing) the kind of argument for the Repugnant Conclusion that I discuss. It is worth noting that the more nuanced fifth and sixth theorems involve intuitive strengthenings of the Repugnant Conclusion, which strike many, including me, as more problematic. For example, the fifth invokes the ‘Very Repugnant Conclusion’: any large population of blissful lives is worse than one consisting of (say) ten times as many people in terrible agony as well as a lot of others whose lives are barely worth living. But such strengthenings would not change the main points I will make, and in general I will avoid irrelevant complications. 6 I will develop this idea much more fully in forthcoming work based on Thomas (2016, ch. 2). 7 The distinction between anonymous and non-anonymous axiologies is also (at least arguably) irrelevant if we stick to comparisons between populations that have no people in common. As the referees pointed out to me, this provides one way to extend the discussion of anonymous axiologies to non-anonymous ones. 8 Of course, one might also be interested in infinite populations, but these raise sui generis problems; see, for example, Bostrom (2011). 9 How exactly to understand the neutral level is one of the key substantive questions; I will say nothing about it here. 10 My use of integers here and below, instead of arbitrary real numbers, is unnecessary but convenient: it will help with my discussion of Small Steps, and it means that once I have specified that 0 represents the neutral level, the utility of every other welfare level is completely determined—for example, there must be a welfare level immediately above the neutral one, and it must get utility 1. 11 In this sense, love is ‘superior’ to money. The superiority of some welfare components over others is best known from Mill (1863, II.5), when he considers two pleasures such that one ‘would not resign [the first pleasure] for any quantity of the other’. See Arrhenius and Rabinowicz (2015) for a critical overview of different types of superiority, including—more relevantly to TLU as such—the superiority of blissful lives over drab ones. 12 To make this point more vivid, observe that we could use single real numbers instead of pairs of integers to represent the order of welfare levels. (For example, instead of the pair (a1, a2), we could use the real number . One can show that these real numbers are ordered in the same way as the corresponding pairs.) With such a representation in mind, there is no temptation to think of welfare as having two components. 13 More formally: there is a finite decreasing sequence of welfare levels such that the difference between consecutive terms is small. Recently, Arrhenius (2016) has adopted the name ‘Finite Fine-grainedness’ for essentially this condition. Erik Carlson (forthcoming) independently raises some very similar objections to Small Steps. 14 See Arrhenius (2000a, §10.3). His argument (including his version of the Quantity Condition) is more nuanced than the version I give here, as he is keen to make his premisses as weak as possible. I have eschewed certain subtleties in the interests of clarity, while preserving the features of the argument that I wish to discuss. A similar comment applies to my discussion of his other theorems. 15 This line of thought was first suggested to me by John Broome; essentially the same point is made by Binmore and Voorhoeve (2003). To be clear, Arrhenius’s main reason for rejecting Theory is that it violates a condition called ‘Weak Non-Sadism’. As I mentioned, his later, preferred theorems do not rely on the Quantity Condition. 16 Thus Arrhenius (2013, §6.4) is wrong to claim that Welfarist Superitarian theories like TLU must violate the Quantity Condition. To see that the Quantity Condition applies, suppose that and are positive welfare levels whose difference is small. A population A of m people at level a has aggregate welfare (mx, my). If x > 0, then a population B of m + 1 people at level b has aggregate welfare ; this is better than A. Or if x = 0, then y and z must both be positive. If we choose a number n such that nz > my, then a population B of n people at level b is better than A, as the Quantity Condition requires. 17 My discussion here refers to Arrhenius (2011, §1.2), as well as to parallel sections in his other cited works. I have slightly simplified his formulation of Discreteness. A more standard term than ‘discrete’ would be ‘locally finite’. 18 As alternatives to Discreteness, a few other technical conditions have been erroneously proposed to me as entailing Small Steps. In this footnote I discuss them briefly in order to forestall further misunderstanding. To begin with, in some of his discussion Arrhenius appears to think that welfare, if not satisfying Discreteness, must be ‘dense’: for any welfare levels a and b, if b is better than a, then there is a welfare level that is better than a and worse than b. Two anonymous referees likewise suggested to me that Small Steps follows automatically if the welfare levels, in addition to being dense, have no isolated points. Now even if this were true, the issue would only be pushed back: why accept the conjunction of denseness and no isolated points? TLU satisfies neither conjunct. More importantly, the proposed conjunction does not entail Small Steps: a counterexample is the lexicographic order on pairs (a1, a2), where a1 is an integer and a2 a real number, and, as in TLU, two pairs differ by a ‘small’ amount if they have the same first component. Another possible condition is continuity. Assuming for simplicity that there is no incomparability, the standard meaning of continuity is that, if a and b are welfare levels and a is better than b, then any sufficiently small perturbation of a is better than b, and any sufficiently small perturbation of b is worse than a (see, for example, Mehta 1998, Definition 2.18 for a rigorous definition). It has been suggested to me that continuity in this sense entails Small Steps. But this is not right either. For example, the preorder on welfare levels in TLU does not satisfy Small Steps, but it is continuous with respect to the natural (discrete) topology on pairs of integers. Heuristically, Small Steps is more closely related to the mathematical condition of compactness rather than denseness or continuity. The argument I give in §4 uses the fact that a closed interval of real numbers is compact (the Heine-Borel Theorem). 19 See Arrhenius (2000a, §10.5). Again, I have made some harmless simplifications in order to focus on the key issues. 20 The theorem replaces the Mere Addition Principle with the Dominance Addition Condition. While ‘mere addition’ simply adds the population B of positive lives, ‘dominance addition’ (or ‘benign addition’, in the terminology of Huemer 2008) simultaneously improves the lives in A. Curiously, Kitcher’s impossibility theorem (Kitcher 2000, p. 567) includes an adequacy condition (‘DVA’) that directly denies the Mere Addition Principle as applied here: he insists that if the Repugnant Conclusion is false, then adding drab lives to a large, blissful population decreases its value. This significantly reduces the interest of his theorem, since the Mere Addition Principle is widely seen as (at least) the default hypothesis, or even ‘obviously true’ (Tännsjö 2002, p. 357). Kitcher (2000, §9) also relies on Small Steps, recognizing, however, that this may be problematic. 21 Indeed, if again a is the blissful level and z and b are drab levels, then the population is always better than the population Z, according to total lexic utilitarianism. 22 A referee pointed out that one might appeal to prioritarian rather than egalitarian ideas to justify the Inequality Aversion Condition. At the level of this discussion, there is not much difference between prioritarianism and egalitarianism, so what I say will apply either way. To justify the Inequality Aversion Condition we need further assumptions, like Small Steps, which are neither egalitarian nor prioritarian in their motivation. 23 For Arrhenius’s discussion of this and related issues, see Arrhenius (2013, §6.6). 24 Arrhenius has two versions of the Non-Elitism Condition (one of them ‘General’), but the difference between either of them and the version I have given here is nugatory. Parfit’s arguments (1984, §142 ff.) also use a version of the Non-Elitism Condition: small losses to some are compensated with at least as large gains to others. (Parfit justifies such compensation using heuristics about utility and equality akin to the Non-Anti-Egalitarianism Principle, discussed below; these heuristics inspired Ng’s work.) He does not derive the Inequality Aversion Condition per se, but my objection applies to his argument as well, since it relies on a series of small steps. The second and third arguments for the Repugnant Conclusion in Tännsjö (2002) are variations on Parfit. (Tännsjö’s first argument uses the Quantity Condition as in §2, following Arrhenius.) 25 Elaborations of this argument appear as lemmas in the proofs of the fourth, fifth and sixth theorems. See Arrhenius (2000a, Lemma 5.1.1; 2003, Lemma 1; 2011, Lemma 1.1.1). 26 Thus Arrhenius wrongly takes it for granted that Welfarist Superitarian theories like TLU must violate the Non-Elitism Condition, since they violate the Inequality Aversion Condition. For example, he writes, ‘Given that the Non-Elitism Condition is such a plausible condition, I think there are only two options here: accept the Inequality Aversion Condition or reject transitivity. The latter move is, of course, quite counterintuitive and … amounts to giving up the project of finding an acceptable population axiology’ (Arrhenius 2013, §6.7). He does not properly recognize the option of denying Small Steps—on the face of it, a much less extreme option than rejecting transitivity. 27 The motivation for the Non-Anti-Egalitarianism Principle does not require talk of ‘total’ or ‘average’ welfare. (I thank Ralf Bader for emphasizing this point to me.) The idea is that the betterness relation might combine two values—let us call them ‘general welfare’ and ‘equality’. The principle is that a population that is better with respect to general welfare and better with respect to equality is better overall. This formulation makes sense whether or not general welfare is conceptualized as the sum of individual welfare levels. However, this more abstract version of the Non-Anti-Egalitarian Principle only slightly ameliorates the issues raised below. 28 See, for example, Huemer (2008) and the ‘first trilemma’ of Carlson (1998). Carlson’s second trilemma uses a similar argument to derive the ‘Reverse Repugnant Conclusion’: for any population of truly awful lives, there is a worse one consisting of lives only just below the neutral level. The derivation is a simple adaptation of Ng’s to deal with negative welfare levels, and so faces the same worries. In fact, Carlson must appeal to an adequacy condition even stronger than Non-Anti-Egalitarianism: one population is better than another if it has higher total and higher average welfare. 29 The argument proceeds as follows. Suppose that population A has m people with welfare a, and B has n people with welfare b. Then the total welfare of is ma + nb, while that of Z is mz + nz. Thus the latter has higher total utility (and the Non-Anti-Egalitarianism Principle says it is better than the former) so long as . If a, z and b are real numbers (or more generally, if the Archimedean axiom holds) then this inequality will hold for all sufficiently large n. 30 More specifically, the key question is why the relevant notion of total welfare (or ‘general welfare’, as I called it in fn. 27) is governed by the Archimedean axiom of measurement theory; see Krantz et al. (1971, §3.2, Definition 1). The axioms given by Krantz et al. are sufficient to derive a representation of general welfare as the sum of real numbers (their subsequent Theorem 1). However, without the Archimedean axiom, we still get an additive representation of general welfare, with values in what Krantz et al. (1971, §2.2.5) call an ‘ordered group’—the set of lexicographically ordered pairs of integers being but one example. See Carlson (2007), Pivato (2014) and Thomas (forthcoming) for discussions of this last point. 31 For the integers, I assume that the welfare difference corresponding to consecutive welfare levels counts as ‘small’. For the real-number case, I assume that, for any real number x, the real numbers that differ from x by a ‘small’ amount include all those in some open interval around x. In other words, any sufficiently small change from x counts as small. The Heine-Borel Theorem says that any closed, bounded interval of real numbers is contained in the union of finitely many of these small intervals. Thus any closed, bounded interval can be traversed in a finite number of small steps. Note that this argument depends on the assumption that all real numbers in an appropriate interval correspond to welfare levels; it will not work if there are gaps. 32 The usual mathematical notion of a continuous function would require that this criterion holds for any standard of smallness (assuming, technically, that the welfare levels that differ from a given one by a small amount form a topological neighbourhood). Here we only need it to hold for some standard of smallness with respect to which the relevant adequacy conditions (the Quantity Condition, the Non-Elitism Condition, or both) are true. 33 I will develop and defend this analogy in other work. For a critical view, see Temkin (2012, ch. 9). Here I rely only on a broad similarity to amplify the considerations of the preceding paragraph. In my informal survey, a few philosophers resist the very idea of moral vagueness. But many others agree that there is, at least, a strong prima facie case for it: see Constantinescu (2014), Dougherty (2014) and Schoenfield (2015) for some recent examples. 34 See, for example, Keefe (2000, pp. 185–6) in the case of supervaluationism. Note that for Keefe, as for many supervaluationists, plain old truth is what I have called determinate truth. For a theory that emphasizes closeness to determinate or ‘clear’ truth, see Edgington (1996). 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doi: 10.1093/mind/fzw078pmid: N/A

Abstract Expressivists have a problem with collectives. I initially illustrate the problem against the background of Allan Gibbard’s expressivist theory, where it is especially stark. I then argue that the problem generalizes. Gibbard’s account entails that judgments about what collective agents ought to do are contingency plans for what to do if one is in the circumstances facing the relevant collective agent. So, for example, my judgment that the United States ought not to have invaded Iraq is a contingency plan for what to do if I find myself in the circumstances facing the United States on the eve of the Iraq war. I argue that, given plausible functionalist assumptions in the philosophy of mind expressivists would struggle to reject, such contingency plans are impossible for individual agents. Since normative judgments about collectives are possible, Gibbard’s theory is unacceptable. Having demonstrated the basic problem for Gibbard’s view, I then argue that the problem has a much wider scope. In particular, I argue that traditional forms of expressivism cannot simultaneously provide a plausible account of both agent-relative normative judgments and judgments about what collectives ought to do. Fortunately, all is not lost; hybrid or ‘ecumenical’ forms of expressivism can disarm the dilemma, or so I argue. I conclude by briefly sketching some further challenges ecumenical expressivism must overcome for its treatment of judgments about collectives to be fully satisfactory and indicate possible lines of argument to be pursued in future work on these challenges. 1. Introduction Expressivists aspire to make sense of ordinary normative thought and discourse. They therefore need an account of normative judgments about collective agents, as such judgments are commonplace. People routinely express their moral outrage at the actions of nation-states, corporations and non-governmental organizations. Collective agents are often held responsible for their actions. On the eve of the United States invasion of Iraq, people said things like ‘The United States ought not to invade Iraq’. Purely prudential normative judgments about collectives are also frequently made. Anti-war activists and foreign policy experts said things like ‘The United States should not invade Iraq—overextending our military would be a strategic blunder’. Ordinary people argue about what corporations like Microsoft ought to do about some problem with their software, what direction a Philosophy department ought to take in its next set of hires, whether the Mets should trade one of their players, and so on. Even though such judgments are commonplace, there has so far been no discussion of what an expressivist should say about them. One might be forgiven for assuming this is because expressivism faces no distinctive problems from this quarter, but this is not the case. My initial presentation of the problem arising here focuses on Allan Gibbard’s theory in Thinking How to Live. With this problem on the table, I argue that expressivists more generally struggle to deal with such judgments while at the same time adequately making sense of agent-relative normative judgments (§2). I then consider what I take to be the best replies to this problem within the framework of a traditional form of expressivism and argue that they fail (§3). Finally, I argue that a hybrid or ‘ecumenical’ form of expressivism can disarm this dilemma, providing a satisfying account of normative judgments about collectives while still making good sense of agent-relative normative judgments (§4). I conclude by discussing residual problems for this solution. 2. The problem I first clarify what I mean by ‘expressivism’, as this term has been used to refer to a variety of views. By ‘expressivism’ I mean a view which explains the meanings of items in a target area of discourse by adverting to distinctive states of mind expressed by claims made with that discourse. Moreover, these states of mind are not to be understood, in the first instance, as representing the world as being a certain way. In the context of normative discourse, the states of mind are instead traditionally understood in the first instance as desire-like, or anyway at least partially constituted by desire-like states. On some versions of expressivism, it is a view entirely within ‘meta-semantics’, but on other versions of the view it also takes on non-trivial commitments in semantics.1 For the purposes of this paper, I can remain neutral on this point. I am, however, excluding views which locate their expressivism entirely in pragmatics.2 Expressivism in my sense therefore must provide an account of what is distinctive about normative judgments, and then explain the meanings of normative sentences in terms of expressing such judgments.3 I initially focus on Allan Gibbard’s theory in Thinking How to Live. Gibbard there provides an account of judgments about the ‘thing to do’—more commonly glossed as the all-things-considered ‘ought’. Since Gibbard’s theory provides one of the most impressive and systematically worked out versions of expressivism in the literature, demonstrating that the problem is a stark one for his view should already be of some interest. Gibbard reminds us that ethics ‘concerns what to do’, and argues that various forms of moral realism ‘drive what to do out of ethics’.4 Suppose reductive naturalism were true. Whatever natural property N the naturalist privileges as normative, one can intelligibly admit that an action is N but still wonder whether it is the thing to do. Nor does non-naturalist realism obviously do any better. Clearly this is not the place to rehearse these familiar arguments and their many epicycles.5 Gibbard argues that judging that an action is the thing to do in a given circumstance just is planning to perform it if in that circumstance, and that this explains how normative judgments settle the thing to do. Of course, we make normative judgments about what other people ought to do, but Gibbard has a ready account of this. In addition to forming plans for circumstances we anticipate facing, we form contingency plans for circumstances we ‘fully know we may never face’. My judgment about what someone else should do is constituted by my planning what to do if in circumstances precisely like those facing that person. Here is Gibbard: What is Holmes doing when he thinks that in Mrs. Hudson’s situation, the thing to do is to project the silhouette and stay in? … Holmes is planning, hypothetically, we might say, what to do if in Mrs. Hudson’s shoes … How much of her plight is Holmes planning for, hypothetically, when he comes to a view as to what the thing for her to do is? All of it, I answer. (Gibbard 2003, p. 50, emphasis added) Obviously more could be said about Gibbard’s view, but this is enough to set up the basic problem. Consider a seemingly obvious corollary of Gibbard’s view when it comes to judgments about collective agents. I judge that the United States ought not to have invaded Iraq in 2003. On Gibbard’s account, this judgment is constituted by a contingency plan for what to do if in circumstances precisely like those facing the United States on the eve of the 2003 invasion of Iraq. These include being a massive nation-state that can declare and wage war. This is just plain weird. Granted, I may plan for all sorts of wild possibilities. I may, in the right frame of mind, deliberate about what I would do if I won the lottery or even if I were Superman. However, forming a contingency plan for what to do if I were in precisely the circumstances facing the United States on the eve of the Gulf war is radically different. Explaining precisely how the case of collectives differs relevantly from these other cases is not trivial, though. It is important at the outset to put an initially tempting objection to one side. One might appeal to the intuitive weirdness of this corollary of Gibbard’s theory to argue that it contradicts the phenomenology of normative judgment and should therefore be rejected. This objection is unconvincing. Expressivists must anyway argue that the phenomenology of normative judgment, insofar as there is such a thing, can be misleading. After all, it probably does not seem ‘from the inside’ that I am planning what to do if in circumstances just like those facing Superman when he is facing down a giant robot, when I judge that he ought to use his heat vision. Indeed, it is part of the point of expressivism that normative judgments are different from factual judgments in ways that are superficially invisible. Rather than drawing plausibility from its fit with the phenomenology of making normative judgments, expressivism draws plausibility from its explanatory power. Objecting to expressivism on these grounds is no more promising than objecting to functionalism on the grounds that it does not seem ‘from the inside’ that my belief that it is raining outside is such-and-such a functional state.6 A better objection begins with a weaker transparency assumption. Granted, we have no robustly privileged access to the underlying nature of our judgments. However, the following much weaker transparency thesis about intention is plausible, as Richard Holton has argued in Holton (1993): For all rational agents X, unless we have contrary evidence we are entitled to believe: X intends to Φ if and only if X believes that he intends to Φ. I here briefly rehearse Holton’s argument. According to functionalism, we characterize a given mental state with a set of biconditionals which specify a functional role associated with that state. Someone who is in the state need not satisfy all these biconditionals, but he must satisfy enough of them or we lose our grip on the idea that he occupies that state. How many is enough? There is no precise answer to this question, which raises broader questions about functionalism I cannot explore here. What are the biconditionals which characterize intending to Φ? Holton plausibly suggests that one such biconditional is that X intends to Φ if and only if X believes he intends to Φ. Obviously there is a lot more that could be said about this, but we are already in a position to see how this might frame an objection to Gibbard’s theory. Because Gibbard’s theory identifies judgments about what one ought to do with intentions (I assume that ‘intention’ and ‘plan’ are interchangeable), it would be a problem for him if people who judged that someone ought to Φ in C did not also in general believe that they intended to Φ if they found themselves in circumstances C.7 Note how this differs from the problematic argument from phenomenology I sketched above. The person making the judgment does not need to realize that in judging that A ought to Φ in C he thereby formed an intention to Φ in C. He need not realize Gibbard’s theory is true, after all. Rather, having successfully formed what is in fact an intention to Φ in C, he must believe he intends to Φ in C. Or at least, there is a presumption that he so believes; otherwise he must satisfy enough of the other biconditionals. This is also plausible as applied to the case of our normative judgments about other individuals, including individuals in radically different circumstances from our own. Suppose I assert that Frankenstein ought not to have created his monster. You are not sure you heard me correctly, and so you ask ‘Are you saying if you were in Frankenstein’s shoes, you wouldn’t have created the monster?’ It certainly would not be weird or surprising for me to say something like, ‘That’s right—although I don’t expect it ever to come up!’ Unfortunately for Gibbard, the corresponding view does sound crazy when transposed to judgments about collectives: Jones: ‘The United States ought to invade Iraq.’ Smith: ‘Are you saying that you plan, if in circumstances just like those the United States is in right now, to invade Iraq?’ Jones: ‘What? No, of course not. What a weird thing to ask! I don’t have any plans for what to do if I were a nation-state! Obviously it is impossible for me to be in those circumstances. You must think I have bizarre delusions of grandeur!’ In the case of judgments about other individuals in weird circumstances, it is not crazy to think that people who make such judgments in a normal sort of case will indeed believe that they intend to act as they judge the individual in question ought to act if they were ever in identical circumstances. By contrast, in the case of our judgments about collectives, we do not expect people making such judgments to believe they plan to act in a certain way if they turn out to be in that collective’s exact circumstances. Indeed, we rightly think that normal people do not form intentions about what to do if they were collectives. One important piece of evidence for this, given functionalism, is that they do not believe they have any such intentions. In particular, they do not believe this in circumstances which Gibbard’s theory plus the functionalist theory predicts they would.8 Of course, someone might intend to do what they can to bring it about that a collective would act as they judge it ought. If I judge the United States invasion of Iraq would be immoral then I might well intend to do what (little) I can to prevent this from happening. This, though, is simply not the same as judging that the United States ought not to invade. As I explain below, given that our normative judgments are sometimes agent-relative, one can coherently judge both that the United States ought not to invade Iraq and at the same time that the President ought to bring it about that the United States invades Iraq. Given a theory like egoism, for example, the ends the President ought to pursue (popularity) and the ends the United States ought to pursue (the national interest) can come apart. One might worry that because contingency plans by individuals for what to do if they were collectives are so weird, the normal connection to believing one so intends is systematically broken. This reply is somewhat ad hoc, without some deeper explanation of the supposed systematic failure of this particular biconditional. In fact, the challenge can be sharpened in a way that further undermines this reply. Consider what the other biconditionals might be that partially define the functional role of intention. Here is a very plausible one: For all rational agents X, X intends to Φ in C if and only if X would try to Φ if he believed himself to be in C. It is hard to imagine a plausible functionalist treatment of intention which did not somehow advert to the role of intention in controlling action. Of course, it is not constitutive of intention that it leads one to do what one intends. More plausibly, intention will normally lead an agent at least to try to act accordingly when the opportunity presents itself. We do perhaps sometimes suffer from weakness of will so severe that we do not even try to do what we intend even when the opportunity arises. That, though, is simply to allow that the relevant biconditionals need not be satisfied all the time for a state to count as intention. The right-hand side of this biconditional should be understood as a counterfactual conditional. If it were construed as a material conditional then it would produce too many false positives—cases in which the antecedent just happens to be false but in which we would not think of the agent as thereby intending accordingly. The counterfactual conditional also fits better with the idea that we can advert to intentions to explain how agents would behave in different merely possible circumstances. If we read the right-hand side in this way, though, we have to ask what the nearest possible worlds in which the agent believes himself to be the relevant collective are like—and in particular, whether the agent tries to do what he believes the collective ought to do. Suppose I believe the United States should have gone to war with Germany in 1940. On Gibbard’s account this means I have a contingency plan to go to war with Germany if I find myself in circumstances just like those facing the United States in 1940. On the biconditional we are considering, we need to see whether I would try to go to war with Germany in the nearest possible worlds in which I believe I am the United States in 1940—or, more accurately, in which I believe I am in circumstances precisely like those facing the United States in 1940, including my being a massive nation-state. The problem is that the nearest possible worlds in which I believe this are most likely worlds in which I am suffering from a delusion. Would I try to go to war with Germany in those worlds? It is not even clear what would constitute my trying to go to war with Germany, just for a start. Even if we can get around the non-trivial conceptual questions about just what would make it true that some individual is literally trying to go to war with Germany, who knows if I would try to do this in the nearest possible worlds in which I am deluded enough to believe I am the United States. All bets are off, it seems, in circumstances in which I suffer from such a bizarre delusion. Plausibly the truth of such biconditionals is far too haphazard to make good sense of my here and now having the relevant weird contingency plan. One might worry that this argument proves too much. I want to allow that I can, for example, plan what to do if I am in circumstances just like those facing Superman or an android or an intelligent dolphin. The problem is that in the nearest possible worlds in which I believe I am in those circumstances I will also be deluded—in which case the preceding argument has proven too much. At least, it has proven too much for me to have shown that collectives pose a special problem for Gibbard. Moreover, in my view, it would have proven too much in any case since I think it is plausible that we can form contingency plans for such weird scenarios. It is, though, worth noting that even if this objection cannot be met, the argument on offer here would still provide a challenge to Gibbard’s view. The problem would simply not be one unique to judgments about collectives, but would also arise in cases involving radically different agents—perhaps any sort of agent which is such that it would be metaphysically impossible for a person making the normative judgment to be identical to an agent of that kind. However, in my view the problem is unique to collectives. How, then, do these cases differ from those involving collectives like a nation-state? Here is one relevant difference. There are at least some epistemically possible worlds in which I could, without delusion, judge that I am in circumstances just like those facing Superman (and so on). To see this, all one has to do is think about radical sceptical scenarios. Drafting this paper right now might be a dream I am having, and I might awaken to find myself in Superman’s circumstances, for example, or those of an android or an intelligent dolphin. Granted that, given the facts as we take them to be, it would be metaphysically impossible for me to have been a dolphin, the point is that this is not the relevant form of possibility. Instead we should focus on what is epistemically possible. Gibbard is admirably clear about this: We might worry that it is metaphysically impossible for me to be Caesar. Since I am not the same person as Caesar, there is no way the world might have been that would have constituted my being Caesar … I answer that … the possibilities we are speaking of are epistemic. I might for all I know for utterly certain, be the genetic son of someone other than my seeming father Harold Gibbard. This, I am fully convinced, is a metaphysical impossibility, since I am his genetic son and the genetic son of anyone else wouldn’t be me—but still, it may just conceivably be the case. It is an epistemic possibility, although utterly remote. I can form a contingency plan for this epistemic possibility, deciding whether, in that case, to honour my purported father who raised me or the man who sired me and left. In a like vein, I’m virtually as certain as certain can be that I’m not Julius Caesar, but still, being he is a remote epistemic possibility for which I can plan. (Gibbard 2012, p. 177) By contrast, there is no epistemically possible scenario in which I find myself in circumstances just like those facing the US.9 Why? Because there is no ‘what it is like’ for a nation-state like the US. All the other scenarios I just floated involved rational agents who presumably have some sort of phenomenology. This assumption is essential to the intelligibility of the sceptical scenarios which make it intelligible to suppose that there are epistemologically possible worlds in which I believe without being delusional that I am in the relevant circumstances. While I have some idea of what it might be like to wake from a dream and find myself in the circumstances of Superman facing down Lex Luthor, I have no idea what it could even mean for me to wake from a dream and find myself in the circumstances of the United States on the eve of the Gulf War. How might this difference help sharpen the challenge for Gibbard? There are two options. We could stick with the biconditional given above, but hold that what counts as ‘close’ when it comes to evaluating possible worlds is context-sensitive, and in particular relative to our theoretical interests. In this context, we might argue that one world is closer than another insofar as I am not deluded in that world but I am deluded in the other world. We could instead alter the content of the biconditional so that the relevant possible world is defined as one in which the agent reasonably believes he or she is in the relevant circumstances. This would also sort the cases appropriately. Here is a straightforward way of developing this into an argument against Gibbard’s view. First, as common sense assumes, it is possible for individuals to make judgments about what a collective agent ought to do in a given set of circumstances. Second, if Gibbard’s theory were correct then, necessarily, an individual could make a judgment about what a collective agent in a given set of circumstances ought to do only if the agent could form a contingency plan for what to do if in the circumstances facing the collective. This is an obvious corollary of Gibbard’s theory. Third, it is not possible for an individual to form a contingency plan for what to do if in the circumstances facing a collective agent. This is an upshot of the discussion of functionalism above. Therefore, Gibbard’s theory is incorrect. The key premise of this argument is the last one (that individuals cannot form contingency plans for being a collective), and I do not pretend to have given a knock-down argument for it. Indeed, I have not even given a knock-down argument that it follows from the most plausible form of functionalism. However, I think I have done enough to make this premise plausible insofar as one is a functionalist, thus putting pressure on Gibbard’s view. Suppose this argument’s central premise is false—suppose we can make sense of the very idea of contingency plans by individuals for what to do if they were in the circumstances facing some collective. The idea would be that we just have to accept that such plans are weird, and that having such intentions depends on what one would try to do if one were deluded in various ways. Even granting this much, there would still be a powerful challenge for Gibbard’s theory in this vicinity. Insofar as we bite the bullet and allow for such bizarre intentions, it becomes implausible that there will be a necessary co-extension between people who make judgments about what collectives ought to do and people who have the corresponding contingency plans. I think the United States ought to have gone to war with Germany in 1940, but am I such that if I were mad enough to believe I was the United States in 1940 I would try to go to war with Germany? Perhaps, but if so that would presumably just be a lucky accident, since I would be quite different in many ways if I were mad enough to harbour such a belief, after all. If Gibbard’s theory were correct, though, then that theory plus the functionalist account of intentions we are now considering would entail that my normative judgment entails that I would try to go to war in such scenarios (and that here and now I would believe that I so intend—our first argument above), and so on. It certainly at least seems possible for me to make a normative judgment about what the United States ought to do without such counterfactuals being true of me—and hence without having the needed intention, on the account of intentions under consideration. The problem is getting two things to line up in the right way: (a) when people intuitively make the relevant normative judgments; and (b) when the relevant weird counterfactuals are true of them. It seems unlikely that these two things will align, much less align in all possible cases.10 We therefore now have the following (third) argument against Gibbard’s theory. First, if Gibbard’s theory were correct then, necessarily, an individual makes a judgment at time t about what a collective agent in a given set of circumstances ought to do only if the agent at t has a contingency plan for what to do if in the circumstances facing the collective. Second, necessarily, someone counts at t as having a contingency plan for what to do if in the circumstances facing a given collective only if he is such that, if he believed himself to be in C, he would try to act as he judges the collective ought to act in C (where C includes all the features of the collective’s situation, including its being the relevant collective). This is just an implication of the theory of intentions discussed above. Third, it is possible for someone to make a judgment at a time about what a collective agent in a given set of circumstances ought to do, without at the same time being such that, if he believed himself to be in C, he would try to act as he judges the collective ought to act in C (where C includes all the features of the collective’s situation, including its being the relevant collective). This is plausible in light of how haphazard the truth of such counterfactuals would be, depending on random facts about what the nearest worlds in which the person is mad in the right way would be like. Therefore, Gibbard’s theory is incorrect. So far, my arguments have been entirely directed at Gibbard’s theory in Thinking How To Live. So much the worse for Gibbard’s theory, one might respond, but why think this indicates anything about expressivism more generally? I concede that judgments about collectives are problematic only for a certain class of expressivist theories. The problem as I have so far formulated it relies heavily on the functional role of planning/intending. The problem therefore seems not to generalize to paradigmatic expressivists who understand normative judgments in terms of some other desire-like state. For example, A.J. Ayer famously explained moral judgment in particular in terms of feelings or emotions (Ayer 1952). Charles Stevenson’s theory was couched in terms of ‘approval’, where this was also understood in terms of emotions (Stevenson 1944). Simon Blackburn emphasizes the idea of a ‘staircase of emotional ascent’, also suggesting an emphasis on emotion rather than intention (Blackburn 1998). Indeed, Gibbard’s own account of specifically moral judgment, as developed in Wise Choices, Apt Feelings, is immune to the problem, at least with a minor modification. To a first approximation, Gibbard there understood the judgment that someone’s action is morally wrong as the judgment that it would be rational for him to feel guilty for doing it and for others to resent him for doing it (Gibbard 1990, p. 42). He then argued that to make a judgment about when guilt or resentment are rational is to accept a norm which prescribes that others feel resentment towards the agent for performing the action and that the culprit feel guilty for having performed it. It is not entirely clear that it makes sense to think of collective agents like the United States as ‘feeling guilty’, but we can charitably modify Gibbard’s account to accommodate this. Instead of insisting that to judge that an action is wrong is to deem rational both guilt on the part of the culprit and resentment on the part of others, we can instead hold that one counts as judging that an action is wrong if one either deems guilt on the part of the culprit rational or deems resentment on the part of others rational. Since there is nothing obviously impossible or irrational about resenting the actions of collective agents, this lightly modified version of Gibbard’s theory seems to handle judgments about collectives easily enough.11 It might now seem as though the problem arising from judgments about collective agents is a problem only for a narrow range of expressivist theories. However, the features of Gibbard’s theory which make it vulnerable to this problem are not so easily abandoned. In particular, the features of Gibbard’s theory which lead to this problem are arguably features which are essential to any adequate account of judgments about agent-relative norms. The easiest way to see the connection to agent-relativity is to consider an initially tempting strategy for accommodating judgments about collective agents within a framework that is very similar to Gibbard’s in Thinking How to Live. Instead of understanding judgments about others as contingency plans for what to do if in their circumstances, we could instead understand such judgments as intentions to do whatever one can to bring it about that anyone in the circumstances facing the person being judged performs the relevant action. This approach avoids any reliance on contingency plans for what to do if one finds oneself in the circumstances of a collective agent of the relevant kind. It thereby neatly avoids the problems arising from the very idea of such plans. However, any theory with this structure faces another problem. In particular, the proposed approach only works for agent-neutral normative judgments, according to which a reason for anyone to do something is a reason for anyone else to promote that person’s doing it. Given agent-neutrality, whenever I judge that someone else ought to do something I will be rationally motivated to promote that person’s doing it if I can. Crucially, making an agent-relative normative judgment that someone ought to do something does not commit one to thinking that anyone who can promote the person performing the action has reason to do so—even a tiny reason. Agent-relative norms index reasons to individuals. Egoism is a simple and familiar agent-relative norm, but the point applies to any agent-relative judgment about the thing to do. Deontological norms, for example, are very commonly understood as being agent-relative, as are the norms corresponding to our ‘special obligations’ to our nearest and dearest, and what Nagel famously called ‘reasons of autonomy’.12 Suppose I am playing chess and I judge that my opponent, Jones, ought to move his knight. Plausibly my normative perspective on the reasons germane to our game will be agent-relative—I have reason to do what would promote my winning the game and Jones has reason to do what would promote Jones’ winning the game. Does this mean I thereby take myself to have reason to promote Jones’ moving the knight? Obviously not! It is not as if I would be rationally motivated by my normative judgment to offer Jones some friendly advice. To be sure, I might do that (for example, to make the game more interesting), but the agent-relative judgment that he ought to move the knight should not rationally motivate me to do this—not even a teeny bit. The problem is that the proposed expressivist theory entails that I would be rationally motivated to tell Jones to move his knight. On that theory, my judgment in this case would be identical to my intending to do whatever I can to promote anyone in Jones’ circumstances moving their knight. Since I can easily promote Jones’ doing so by pointing out that he needs to move his knight to avoid checkmate, this intention would rationally motivate me to do so. This, though, is perverse. Moreover, this is precisely why Gibbard’s theory is formulated as it is. Normative judgments need to be understood as contingency plans for what to do if I were in the person’s circumstances, and not as plans to promote anyone’s performing the action in the relevant circumstances insofar as I can. Here is Gibbard: Suppose I disagree with Caesar on whether, if in his shoes, to go to the Senate on the Ides of March. What sort of disagreement is this? To disagree with his decision I don’t need to be against it. Brutus too, after all, may disagree with Caesar on this. For though Brutus plots desperately to ensure that Caesar comes to the Senate that morning, he may nonetheless say to himself, ‘If I am Caesar in Caesar’s shoes this morning, let me stay home’. (Brutus, in technical jargon, thinks Caesar to have agent-centered reason, all told, to stay home. At the same time, he thinks himself to have agent-centered reason, all told, to ensure that Caesar leave home and come to the Senate). (Gibbard 2003, p. 68) Interestingly, the same objection can be lodged against versions of expressivism which eschew intentions and analyse normative judgment in terms of some other pro-attitude, like desire or preference. Insofar as these pro-attitudes are irreducibly de se, they will likely face a version of the problem posed for Gibbard. In that case, the relevant pro-attitudes are still conditional, judgments concerning what the agent would want if they found themselves in the circumstances of the relevant collective. If, on the other hand, they are not irreducibly de se, but are instead impersonal desires to promote anyone’s acting in accordance with the relevant norm, they will face the objection that they do not adequately accommodate agent-relativity. The problem I have laid out here is at least this general, then: any expressivist theory which aspires to give an account of the nature of judgments about what one ought to do, all things considered, will either be unable to account for normative judgments about collectives or be unable to provide a plausible account of agent-relative normative judgments. It is worth noting that it is not very plausible to construe judgments about what one ought to do, all things considered, as judgments about the rationality of some reactive attitude like guilt or resentment. After all, the norms a given agent takes to settle what one ought to do all things considered need not be moral. Since many of the arguments for expressivism in the moral case are comparably good arguments for expressivism about the all-things-considered ‘ought’, the dilemma is a pressing one for a wide range of expressivist theories. 3. Objections and replies The arguments in §2 rely on functionalism about intentions—that is, a functionalist account of what it is to have an intention with a given content. An initially tempting reply is therefore simply to reject functionalism. In fact, it is not entirely clear that abandoning functionalism will help, though. Although I motivated the biconditionals about intention in §2 via a functionalist framework, those biconditionals are independently plausible. One might, therefore, reasonably endorse those biconditionals even if one rejects functionalism about intentions. In that case, the argument of §2 can survive the rejection of functionalism about intentions. Second, abandoning functionalism about intentions is dialectically problematic for expressivists. A core motivation for expressivism is to avoid the problems facing realists by starting, not with a metaphysical account of normative facts or states of affairs, but instead with our practice of making normative judgments. In particular, expressivists urge us to notice the distinctively practical functional role that these judgments play. On the basis of this functionalist account of normative judgments, the expressivist argues that we should understand them as broadly desire-like states (or, anyway, partly constituted by such states; see §4). Insofar as the expressivist understands normative judgments as reducible to intentions (or ‘planning states’ in Gibbard’s sense), they are thereby committed to giving a functionalist account of intentions. Moreover, the characterization of normative judgments in functional terms fits best with a broader functionalist approach to the nature of mental states. Expressivists could in principle abandon functionalism. In that case, though, it would be unclear how their account of the functional role of normative judgment tells us anything about the nature of normative judgments. To get an idea of just how central functionalist ideas are to paradigm expressivists, consider Simon Blackburn’s Ruling Passions, a landmark book in expressivist theorizing. The first chapter is all about the functional role of ethical judgment. Section 2 of that chapter is entitled ‘Inputs and Outputs’ and contrasts the practical functional role of ethical judgments with ordinary factual judgments (Blackburn 1998, chapter 1). Here is a representative passage: We can usefully compare the ethical agent to a device whose function is to take certain inputs and deliver certain outputs. The input to the system is a representation … The output, we are saying, is a certain attitude, or pressure on attitudes, or favouring of policies, choices and actions. Such a device is a function from input to output: an ethical sensibility. (Blackburn 1998, p. 5, emphasis in original) Blackburn goes so far as to claim that quasi-realism just is a form of functionalism: ‘A full-dress title [for my view] might be “non-descriptive functionalism” or “practical functionalism”’ (Blackburn 1998, p. 77). Gibbard is equally explicit about this. In his more recent book he identifies expressivism as a local form of functionalism: We can say that such a strategy [expressivism] amounts to ‘functionalism’ as the term is used in the philosophy of mind for a theory of mental content. (Gibbard 2012, p. 111) He adds in the footnote to this passage that ‘Jason Stanley pointed out to me that what I had been calling “expressivism” amounts to functionalism as the term is understood in the philosophy of mind’. At least on the face of it, rejecting functionalism is not a very promising strategy for expressivists here. The two most influential expressivists of the latter part of the second half of the twentieth and first part of the twenty-first century consider it a core part of their view. Another reply is simply to deny that we really make judgments about what collectives ought to do. Admittedly we often speak that way, but on this account such claims are always elliptical for claims about what some privileged agent or agents who partly constitute the collective ought to do. For example, perhaps in my toy example of a judgment about whether the United States ought to go to war with Iraq, one could maintain that such a judgment is really about what the President or members of Congress ought to do—namely, not sign a declaration of war, and so on. On the face of it this is rather ad hoc. Why, apart from the pressure it puts on the expressivist theory, should we not take the claims of ordinary people at face value?13 Granted, we may have an interesting philosophical conversation about whether any ‘ought’ claims are true of collective agents, but the arguments of §2 require only the modest claim that people make such judgments. Moreover, in many contexts of utterance there may be no salient individual in a privileged position.14 Suppose I judge that the United States ought to pass a gas tax. Which individuals do I think ought to vote in favour of such a tax? All the members of Congress? Perhaps, but this does not seem to be part of the semantic content of my judgment. The following conversation is intelligible: Jones: ‘The United States should pass a gas tax’. Smith: ‘Oh, so you think everybody in Congress should vote in favour of such a tax?’ Jones: ‘No, actually. My own Senator repeatedly promised not to vote for any new taxes when he was campaigning, and I am a Kantian about promise-keeping. Anyway, all I said was that the United States should pass a gas tax—I didn’t say that the United States should pass such a tax unanimously’. Perhaps the advocate of this line of argument could posit some sort of massive semantic indeterminacy about which agent(s) are being targeted, but again this seems ad hoc. In fact, agent-relative normative perspectives provide an even deeper objection to this proposal. Suppose I am a thoroughgoing egoist, and I also believe that the interests which agents ought to promote are fixed by their ends. I also take nation-states to be agents with their own ends, so I consistently think that they ought to do whatever promotes those ends. This view certainly seems coherent, even if it is not all that plausible. Insofar as this is a possible view, though, the proposal under consideration is doomed. A view like this will make it possible for there to be cases in which an agent can coherently judge that a collective agent ought to perform a given action at a time while at the same time thinking that none of the agents who stand in the right sort of privileged position ought to do their part to make it the case that the collective performs the action. The egoist might think that the United States ought to pass a gas tax because it is in the national interest—however we fix the goals of the United States, these include avoiding catastrophic global warming, let us suppose. At the same time, this egoist denies that the President should vote for a gas tax and also denies that any individual member of Congress should vote for such a tax. Why? Because he believes (perhaps truly) that the overriding end for each of these politicians is to remain popular and electable. Since a gas tax would be extremely unpopular, none of them ought to vote for such a tax by the egoist’s lights. This does bring out a weird implication of egoism when applied in such antagonistic cases, and it may even provide a kind of argument against egoism and other forms of agent-relativity.15 Regardless of whether anything like that follows from reflection on such cases, such a view does at least seem possible to hold. Insofar as it is a possible view, though, the suggestion that seeming judgments about what collectives ought to do are always really judgments about what some privileged individual members of the collective ought to do is hopeless. For here we have an egoist sincerely judging that a collective ought to do something while at the same time judging that none of the relevant individuals ought to do their part to bring it about that the agent performs the relevant action. Yet another reply would be to understand normative judgments about collectives as plans one adopts within a fiction. The idea would be that we somehow imaginatively take up the point of view of the relevant collective agent and within that pretence form a plan about what to do. Note that the view is not that I here and now form a real plan for what to do when engaging in such a fiction. That plan would, on Gibbard’s view, constitute my judgment about what I ought to do if I pretend to be (for example) the United States in such and such circumstances. Instead, the view trades on the idea that when one engages in some sort of pretence, one in some sense adopts plans within that pretence. On at least some views, though, plans within a pretence are not really plans in the same sense that ordinary plans are. If I am playing ‘Star Wars’ with my son then my plan to blow up the Death Star is in one obvious sense not a plan—at least not if we take the fictional plan’s content at face value—that is, as being a plan to blow up the Death Star. One can, of course, try to reduce plans within a fiction to plans for what to do when engaging in such a fiction, but such views do not seem entirely true to the phenomenology and they also seem overly intellectual in the case of the role-playing activities of young children.16 In any event, this reply will work only if we understand such ‘plans’ as not reducible to ordinary plans for what to do when engaging in a fiction, since in that case they will constitute judgments about what an individual should do when pretending to be a collective, rather than a judgment about what a collective ought to do. The reply should then appeal to ‘i-plans’—the imaginative counterparts of plans.17 This reply has some plausibility. When thinking about what a collective ought to do, it is tempting to anthropomorphize the collective and try to take up its ‘point of view’ even though one at some level realizes it does not really have a point of view in any phenomenological sense. However, understanding normative judgments about collectives in these terms as a way of salvaging an expressivist theory like Gibbard’s runs into other serious problems. First, the theory makes false predictions in simple cases of pretence. Returning to my previous example, when playing ‘Star Wars’ with my son and pretending to be Darth Vader, I might well i-plan to destroy a planet inhabited by billions of people. Do I thereby count as judging that someone in Vader’s circumstances should commit mass murder? Obviously not! Similarly, when playing a war game, I may take up the point of view of the United States and i-plan to drop nuclear weapons on Berlin, say. This is consistent with my judging that it would be morally wrong ever to use such weapons on civilian targets.18 A second problem is that there will likely be new forms of the ‘Frege-Geach’ problem arising from this approach. After all, on the proposed view normative judgments about ordinary individuals express plans, whereas normative judgments about collectives express mere i-plans. This looks like a problematic shift in meaning between contexts in which individuals are being evaluated and contexts in which collectives are being evaluated. Third, the expressivist will now need a plausible and independently motivated theory of disagreement which can explain why people who engage in different pretences when engaging in a fictional perspective thereby disagree. It is one thing to agree with Gibbard that when two people plan to act in different and incompatible ways they thereby disagree on the thing to do; that has some independent plausibility. By contrast, it does not seem so plausible to suppose that two people who i-plan to act differently within the same fictional framework disagree. If I i-plan to act one way when pretending I am Darth Vader and you i-plan to act in another (incompatible) way when you are pretending you are Darth Vader, then we simply prefer different forms of role-playing. That should not be sufficient for us to count as having a disagreement. Having explained why what I take to be the most tempting replies to the arguments in §2 do not work given traditional forms of expressivism, I now offer a solution. I argue that a hybrid or ‘ecumenical’ form of expressivism can do better because of the indirection it affords. 4. Ecumenical expressivism and collectives What is needed is a form of expressivism which does all of the following: analyses normative judgments as being at least partly constituted by intentions (thus explaining how normative judgment settles the thing to do); does so in a way that smoothly accommodates agent-relativity; is not vulnerable to the arguments of §2 (the arguments from functionalism and the impossibility of contingency plans for what to do if a collective). I argue that a form of ‘hybrid’ or ‘ecumenical’ expressivism manages to do all three of these things. In fact, I expect that a variety of different hybrid forms of expressivism could manage this so long as they all characterize normative judgments as being partly constituted by intentions. I here focus on the version of ecumenical expressivism I have defended at length in Impassioned Belief, not only because it is the version I favour but because it has been worked out in more detail than any other form of ecumenical expressivism. However, it would be interesting to see whether the same moves could not (as I suspect) be made within the structurally similar frameworks of Mark Schroeder’s ‘relational expressivism’ and Teemu Toppinen’s form of hybrid expressivism.19 Very roughly, hybrid theories differ from ‘pure’ forms of expressivism and cognitivism in that their characterization of normative judgment involves both cognitive and conative elements. Not all hybrid theories should be understood as forms of expressivism, though. Some hybrid theories privilege the cognitive element in their theory, providing a meta-normative account of the representational content of normative thoughts. Such theories are still hybrid because they incorporate an element of desire into their account. Because this approach in effect begins its account with normative ways the world might be, and explains normative judgments as representing the world as having certain normative features, it cannot avoid many of the standard worries about realism that expressivism was meant to avoid—the open question argument, moral twin earth, arguments from disagreement, as well as various metaphysical and epistemological worries. To be sure, such views can do better when it comes to arguments from motivational internalism, but this is only one of the reasons to be an expressivist, and arguably not the most powerful one. Ecumenical expressivism, by contrast, does not appeal to normative contents for representational beliefs at all. Rather, to make a normative judgment an agent must have what I call a ‘normative perspective’ and a representational belief with an ordinary descriptive content, where the contents of these are linked in the right way. Normative perspectives are diachronically stable high-level intentions to reject standards of practical reason with certain features and to deliberate and act only in ways that would be allowed by those standards not yet ruled out. The belief component of a normative judgment concerns what any standard of practical reason which is not ruled out (where those not ruled out are ‘acceptable’) would be like in various ways. Ecumenical expressivism pretty clearly achieves (i) and (ii) of the three criteria. Normative perspectives just are high-level intentions, so (i) is trivially met. The account has an irreducibly de se structure, too, in that normative perspectives always concern how the agent making the judgment will act in various circumstances. Because nothing in the account entails that these standards cannot have an agent-relative form, (ii) is also accommodated. The crucial question is how ecumenical expressivism achieves (iii). It is perhaps simplest to see how it does so by working through an example. Suppose I judge that the United States ought to adopt a gas tax. This judgment will be constituted by a normative perspective/belief pair. The normative perspective will rule out a range of standards of practical reason, while the belief will concern what all those standards not ruled out have in common. In particular, the content of the belief will be that all such standards would require the United States to adopt a gas tax. Nothing in this theory involves an agent making a judgment planning what to do if he found himself in precisely the circumstances facing the US. His normative perspective rules out a range of standards of practical reason, so he intends not to adopt any of those, and it also commits him more positively only to act in ways that would be allowed by all of the remaining standards. Once we have this notion of a range of acceptable standards in place, the agent can form beliefs about what those standards would require of other agents—including agents radically different from himself, like collectives. Returning to my example, my normative perspective might rule out all standards of practical reason other than egoism. Crucially, the logical form of the egoist standard I deem acceptable might be a universally quantified standard which ranges over all possible rational agents. As such, the standard would apply equally to collective rational agents, if any there are, as it does to individual rational agents. Insofar as the standards I deem acceptable do have this logical form, they entail prescriptions for collective agents like the US. The agent making the judgment can therefore work out what prescriptions they entail for such collective agents without at any stage planning what to do if he were a collective. So condition (iii) is also satisfied. The reason a hybrid theory like ecumenical expressivism is especially well suited to achieve this is the indirection provided by incorporating both a desire-like element and a belief in the ground-level account of normative judgment. So long as the standards fixed by the agent’s normative perspective have universal scope with regards to all possible rational agents, they will trivially include collective rational agents in their scope. The agent can then rationally form beliefs about what these norms entail for various collectives. Of course, beliefs about collective rational agents do not raise the worries discussed in §2. There is no argument from functionalism that there could be no such thing as the belief about what, for example, the principle of utility would demand of the US. Because the desire-like element (the normative perspective) does not involve planning what to do if one were a collective agent, there is no way for the arguments from §2 to gain purchase against ecumenical expressivism. By ‘offloading’ everything specifically about collectives onto the belief component of the agent’s normative judgment, the arguments can be neatly evaded. This, though, raises an important question about the theory’s resources. The account works smoothly for any judgment where the norms implicated all range over all possible rational agents. What, though, about someone who judges that there are reasons which can apply only to collective rational agents? For example, someone might think that the fact that performing a given action would carry out the ‘general will’ of the individuals who constitute some collective agent A is itself a reason for A to perform that action. Insofar as this sort of reason necessarily applies only to collective rational agents, the account I have just laid out might seem not to deal very easily with cases like this. Insofar as my normative perspective functions to guide my choices, where I am necessarily an individual agent, why would that perspective discriminate between standards which necessarily apply only to collective rational agents?20 This is an interesting worry, which I intend to investigate further in future research. Unfortunately, an adequate discussion of the many issues arising here would go beyond the scope of this paper. However, the worry is also not obviously decisive. One plausible response is to deny that it makes sense to think there could be reasons which necessarily apply only to collective rational agents. Insofar as a suitable Kantian universalizability principle according to which any maxim of practical reason must be possible for all rational agents to accept is sound, this would provide a principled basis for this view. Of course, I do not have the space in this paper to explore the plausibility of such Kantian principles, nor the interesting question of how well they cohere with a broadly expressivist framework.21 Won’t this response sit poorly with the pre-theoretical intuition that normative judgments which seem to rely on principles which can only apply to collectives are coherent and intelligible, though? This is not as obvious as it might seem. Take the example of the reason to implement the ‘general will’. Plausibly this reason should not be understood as fundamental. Rather, it should perhaps be understood as derived from a more basic normative principle of some kind. Perhaps it can be derived from some version of the categorical imperative. Or perhaps it can be derived from a more basic principle which requires agents to act with integrity, since carrying out the general will of the individuals who constitute one as a (collective) agent is intuitively a form of integrity. Indeed, there is a rich and long tradition of drawing on analogies between such reasons of integrity for individuals and for collectives, most famously going back to Plato’s account of justice as the tripartite harmony of the soul in The Republic. More contemporary Kantians like Christine Korsgaard have done a lot to explain how this ‘constitutional model’ of agency fits very well with a broadly Kantian action theory.22 If this is right, and this strategy can be generalized, then the problem of norms which as such apply only to collectives is not so forceful. So long as the relevant norms are not fundamental, but can instead be derived from more basic norms which can apply directly to individuals, the indirect strategy laid out in this section can still succeed. Even so, one might worry that these kinds of arguments can establish only that the relevant norms are not plausibly understood as fundamental. The worry about ecumenical expressivism is that it implies that judgments which endorse such norms as fundamental are simply impossible, whereas pre-theoretically such judgments are possible. In fact, I am not sure we have confident and widely shared intuitions about whether such fine-grained judgments are possible. It is one thing for a theory to entail that normative judgments about collectives are all impossible, as I have argued Gibbard’s theory and others like it do. It is quite another thing for a theory to entail that a certain proper subset of normative judgments one might have thought could be made about collectives turn out to be metaphysically impossible for some subtle reason. Although this may well still be a cost of the view, it is not so obviously a decisive one. Our intuitions on such fine-grained matters may simply not be reliable. Again, though, much more would need to be said to vindicate this theoretical hunch. For present purposes, I shall rest content with having argued that the residual problem facing ecumenical expressivism on this front is, at any rate, much less powerful than the one facing other forms of expressivism. 5. Conclusion Expressivists have a problem with collectives, but perhaps not an insoluble one. Insofar as non-ecumenical expressivism satisfies certain important desiderata, it must offer a problematic account of our judgments about what collective agents ought to do. Gibbard’s theory puts this worry into very sharp relief, but any non-ecumenical expressivist theory which can make sense of agent-relativity will face a similar problem. Fortunately, ecumenical expressivism can do much better in virtue of the indirection afforded by its bifurcated structure. Whether it does well enough, all things considered, depends on delicate issues about the extent to which normative judgments which necessarily apply only to collective rational agents are intelligible. I have only scratched the surface of this important issue, which deserves further attention. However, I hope this article has at least demonstrated that collectives provide a new and interesting problem for expressivists, and that ecumenical expressivism can resolve this problem considerably better than can non-ecumenical expressivism.23 Footnotes 1 For purely meta-semantic interpretations of expressivism, see for example Charlow (2013), Chrisman (2013), Chrisman (2016), Ridge (2014), Sepielli (2012), Silk (2013) and Sinclair (2016). For an argument that expressivism must take on commitments in semantics see Schroeder (2008) and (2010). See also Alwood (2015). Yet another approach is to understand expressivism in terms of the broader framework of dynamic semantics. See, for example Charlow (2015). Compare also Perez Carballo and Santorio (2016). 2 Seth Yalcin, for example, understands expressivism as first and foremost a pragmatic thesis, albeit one which imposes constraints on the semantics for the relevant fragment of discourse. See, for example Yalcin (2012). Yet another view that comes under the heading of ‘expressivism’ is that the target words do not contribute to semantic content at all, but instead act as speech-act modifiers. For a view of this kind with regards to epistemic modals, see Schneider (2010). This sort of speech-act modifier view (or something close to it) can also be seen in many of the classical ethical expressivists, perhaps most notably in Hare’s work; see Hare (1952). See also Stevenson’s account of ‘good’ and in particular his ‘do so as well!’ clause in for example Stevenson (1944). Compare Ridge (2003) and Ayer (1952), chapter 6. More recently, some ‘hybrid theorists’ who call themselves expressivists locate their expressivism in pragmatic phenomena like the implicature of a non-cognitive attitude, though in my view it is confusing to refer to such views as ‘expressivist’ since in an important sense they are more aligned with traditional forms of cognitivism. See, for example, Barker (2000). 3 In this respect, expressivism in my view stands in contrast not only to some of the pragmatic accounts listed in the previous footnote, but also to inferentialist theories of meaning which are also often referred to as forms ‘of expressivism’. In this case, the idea is that we understand meaning in terms of the expression of an inferential role, rather than in terms of the expression of a state of mind. See Brandom (1994). For a discussion of how Brandom’s inferentialist form of expressivism might fruitfully be combined with expressivism in Blackburn’s sense, see Price (2011). 4 Gibbard (2003), pp. 13-20. 5 Because Gibbard’s argument puts so much weight on what is ‘intelligible’, it might seem not to apply to so-called ‘Cornell Style’ realism, but there are familiar ways of extending this general strategy to target those views as well. Readers well stepped in these debates already will be relieved to know that we will not be visiting Cornell, Moral Twin Earth or the island on which Hare’s missionary met the cannibals, though all of those vistas would be essential first steps for anything like a proper survey of the relevant terrain. Those not familiar with this territory might begin with Boyd (1988), Horgan and Timmons (1992) and Hare (1952). 6 For discussion of transparency assumptions and expressivism more generally, see Woods (2014), Toppinen (2014) and Ridge (2009). See also Horgan and Timmons (2006) and Joyce (2010). I discuss the analogy with functionalism more below. 7 In Thinking How to Live Gibbard presents himself, at least initially, as merely offering a ‘possibility proof’ that normative language could work as his expressivist theory predicts—that such a language is at least possible. It is clear, though, that Gibbard is ultimately trying to convince the reader that this is not only possible, but that in fact it is the best construal of our actual discourse. Insofar as this is correct, we should, at the end of the day, identify normative judgments with the relevant planning states. This is fairly clear from the Preface where he remarks ‘The hypothesis of this book is easy to state: Thinking what I ought to do is thinking what to do’ (p. x, emphasis in original). Given that thinking what to do just is planning what to do, it is clear that Gibbard’s ultimate conclusion is about the nature of normative judgment itself. This conclusion is therefore presumably modally robust—that is, what Gibbard really wants to establish is the essential nature of normative judgment. 8 One might object that in these cases we have immediate evidence that misleads us about our own intentions, namely the mere fact that the relevant circumstances involve being a collective agent, which is weird even if possible. If it were just the weirdness of the intention, though, then we would be just as quick to balk at the attribution of contingency plans for what to do if weird individual agents, which we don’t—or anyway, not to the same extent. Moreover, the fact that the circumstances include being a collective agent presumably would reliably count as good evidence that the individual has no such contingency plan only if it is impossible to form intentions for such a contingency. In that case, though, Gibbard’s theory is sunk anyway. Thanks to an anonymous referee for pressing me on this point. 9 This suggests another objection, namely, that intention presupposes not being certain you cannot fulfil the intention. If someone is absolutely certain they will never face the relevant contingency (as in the case of an individual planning for being a collective agent), then there is a sense in which they should be certain they will never fulfil the intention, save perhaps in a vacuous sense. In the relevant sense, I do not fulfil my intention to try curry if in London by blowing up London, though that does ensure that I am never both in London and not trying curry. Developing this objection would, however, require more controversial commitments than the arguments in the text. 10 This problem is related in interesting ways to Gibbard’s discussion of planning for circumstances in which you know your plan will almost certainly not be efficacious, as with the alcoholic who plans not to drink on Saturday when he craves a drink. Here too, the relevant counterfactuals will not be satisfied. See Gibbard, (2003, pp. 51-2). In these cases, though, at least the agent will characteristically satisfy some of the other biconditionals associated with intending—for example, he will believe that he intends not to drink on Saturday. Also, we would expect someone with such a plan to do things, in advance of being tempted, to make it less likely that he will succumb to temptation or to avoid temptation altogether. In the case of planning for being a collective, none of these counterfactuals make sense either, which makes the idea that we can plan for such circumstances more obscure. Thanks to an anonymous referee for prompting me to discuss the analogy between the case discussed in the text and these sorts of cases. 11 Thanks to an anonymous referee for pressing me to discuss this point. 12 For a classic discussion of these species of agent-relative norms, see Nagel (1986, chapter 9). 13 It might be objected that expressivism already essentially involves not taking the claims of ordinary people at face value, in which case this is an odd or even hypocritical complaint from the expressivist. This objection would be forceful against ‘old school’ expressivists like A.J. Ayer who explicitly reject the self-understanding of ordinary speakers. It is, however, much less obviously forceful against quasi-realist expressivists who try to accommodate all the realist-sounding things ordinary people say, including their claims of mind-independence, normative truth and normative knowledge, in a broadly expressivist framework. Rather than denying that there are normative beliefs, or that people make normative assertions, for example, the quasi-realist insists that these theses are compatible with their theory when properly understood. Whether quasi-realism, if successful, ultimately implies that the thoughts of ordinary folks (as opposed to moral realist philosophers) are misguided is a difficult question which probably depends on the extent to which ordinary folks are committed to various arguably theory-laden assumptions (for example, that normative belief has the same ‘direction of fit’ as descriptive belief). I will not try to resolve this question decisively here, but my own view is that insofar as quasi-realism succeeds it will allow us to take the claims of ordinary folks at face value. Thanks to one of the editors of Mind for raising this natural concern. 14 Here I in effect elaborate on the discussion of egoism and the Iraq example in §2 above. 15 I discuss this at length in Ridge (2005). See also Copp (2007). 16 For an attempt to defend a standard Humean belief-desire account of pretence, see Funkhauser and Spaulding (2009). For an opposing view which insists on the irreducibility of belief-within-a-fiction and desire-within-a-fiction, see Velleman (2000). 17 Thanks to an anonymous referee for encouraging me to discuss this reply. 18 In the text I focus on an appeal to imagined planning which has the agent making the judgment imagining him or herself as a collective, but at the same time pretending such collectives have a phenomenological point of view. An alternative version of the appeal to imagined planning would be to imagine oneself as an individual but an individual in precisely the circumstances facing the United States (for example) apart from being a collective—in effect, pretending that the United States is an individual rather than pretending that it is a collective with a phenomenology. One might then plan for such circumstances in an ordinary sense of ‘planning’ but against the backdrop of a merely imagined possibility, which would be different from the sort of i-planning discussed in the text. This is an interesting alternative, but it is not clear to me that it is possible to imagine an individual who is literally just like the United States in all respects apart from being an individual. An individual, for example, cannot literally ‘go to war’—though they might bring it about that the United States goes to war. (Cf. my discussion in the text of the attempt to understand judgments about collectives as disguised judgments about privileged individuals.) One could instead imagine an individual who is ‘as similar as possible’ to the United States while still being an individual, but it is far from obvious that such similarities will be sufficient to ensure that what one judges the United States ought to do is what such an individual should do. Much more could no doubt be said about all this, but until a worked-out version of the expressivist appeal to planning within a fiction of some kind has been developed it strikes me as premature to go into great detail discussing the potential problems of such a view. Thanks to an anonymous referee and an editor of Mind for pressing me on this point. 19 See Ridge (2014), Schroeder (2013) and Toppinen (2013). For an earlier and somewhat different version of ecumenical expressivism, see Ridge (2006) and Ridge (2007). 20 See Ridge (2005) for related discussion. 21 R.M. Hare, of course, famously argued that his form of expressivism fit well with a strong form of universalizability, from which he then tried to derive substantial normative conclusions. See Hare (1952). 22 See Korsgaard (2009), especially chapter 7. 23 Thanks for helpful comments to Matthew Chrisman, Guy Fletcher, Allan Gibbard, Sebastian Kohler, Elinor Mason, Debbie Roberts, two anonymous referees for Mind and audiences at the Global Expressivism Conference in Szczecin and the New Directions For Expressivism Conference in Sheffield. I am especially grateful to Matthew Chrisman as it was a conversation with him which gave me the idea for this paper in the first place. References Alwood A. 2015 . ‘Should Expressivism Be a Theory at the Level of Meta-Semantics’ , Thought : pp. 13 – 22 . Ayer A. 1952 . 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doi: 10.1093/mind/fzw065pmid: N/A

Abstract Epistemic Permissivists face a special problem about the relationship between our first- and higher-order attitudes. They claim that rationality often permits a range of doxastic responses to the evidence. Given plausible assumptions about the relationship between your first- and higher-order attitudes, I show that you can't be on the edge of the range, so there can't be a range at all. Permissivism, in its traditional form, can't be right. I consider new ways of developing Permissivism to avoid my argument, but they have problems of their own. 1. Introduction Matt and Abby are members of a jury for a murder case. They have all the same evidence and review it separately. When they convene to discuss their conclusions, they discover that they disagree. Matt is confident that Jones is innocent; Abby is confident that Jones is guilty. When they learn of their disagreement, what do they discover about themselves? Clearly, they learn that one of them is confident in a falsehood: either Jones is guilty or he isn’t. But do they also learn that one of them has been less than fully rational, that one has failed to properly assimilate the evidence before him? Proponents of Epistemic Uniqueness say yes: given your total evidence, there is a unique rational doxastic attitude that you can take to any proposition.1 Matt and Abby have the same evidence, but have different levels of confidence in the proposition that Jones is guilty (Guilty). Uniqueness entails that at most one of them is fully rational. Proponents of Epistemic Permissivism say no. Matt and Abby may simply have different standards of reasoning. For example, Matt may tend to favour simple hypotheses, and Abby may tend to favour complex, more explanatory hypotheses. A permissivist thinks both standards of reasoning may be perfectly rational, even though they sanction very different responses to the evidence.2 Permissivists paint a simple, attractive picture of rationality. There are some general, justifiable rules—for instance, Conditionalization, Probabilism, and the Principal Principle—and a wide range of permissible starting points. So long as you begin at one of these, and you follow the rules, you’re doing fine. Permissivists charge that Uniquers paint a much more complicated, and metaphysically loaded, picture of rationality.3 Uniquers must say everything Permissivists say, and much more—that there is a unique rational starting point, a unique rational credence in Guilty, and so forth. I argue that Permissivists face a special challenge about the interaction between our first- and higher-order attitudes. They claim that rationality often permits a range of credences in a certain proposition. Yet, given certain plausible assumptions about the relationship between our first- and higher-order attitudes, you cannot adopt a credence on the edge of that range. But Permissivism says that for some such range, any credence in that range is rational. So Permissivism is false. I consider new ways of developing Permissivism to avoid this argument, but they have problems of their own.4 Conclusion: Permissivism is not as simple as advertised, and without new motivations, it’s not very attractive either. On to the argument. 2. Dominance Suppose that Permissivism is true, and that Matt's and Abby’s evidence rationalizes any credence between, say, 0.3 and 0.7 in Guilty. Quite plausibly, Matt is not always in a position to discern the exact boundaries of the permissible range.5 Compare: he isn’t able to determine the exact height of a tree some distance off just by looking—his eyesight is nowhere near that good. Similarly, by reflection alone, he can’t reliably determine the value of the upper and lower bounds of the permissible range to the nearest (say) 0.01 degrees of confidence—the evidence is too complex, and his powers of reasoning are nowhere near that good. Even if he truly believes that the lower bound is 0.3, he’s merely guessing—for all he knows, the lower bound is 0.31 or 0.29. He can’t reliably distinguish the actual case from one in which the lower bound is slightly higher or slightly lower. Matt ought to know this about himself. He ought to know that if he were to guess the exact values of the upper and lower bound, he’d likely err. Compare: since you know that you can’t reliably guess the exact height of the tree some distance off, you shouldn’t be certain that the tree is exactly 667 inches tall, even if it is—you should recognize that it might be slightly taller or slightly shorter. Similarly, Matt should acknowledge that the lower bound might well be slightly greater than 0.3. So what should Matt believe about the boundaries of the permissible range? That, it seems, depends on what they actually are. If the lower bound is 0.3, then he should believe that it is roughly 0.3—he should believe it is between (say) 0.2 and 0.4. For even though rational requirements are not wholly transparent, they shouldn’t be completely opaque to those who reflect carefully. After all, we regard careful reflection on our evidence as valuable precisely because it helps us form rational beliefs—beliefs that better reflect the force of our evidence. If the requirements of rationality were wholly inaccessible, what would justify such a practice? So if Matt is rational, he believes that the permissible range of credences in Guilty runs from roughly 0.3 to roughly 0.7.6 But if he believes that, it would be irrational for him to adopt credence 0.3. Why? Because Matt is not certain that a credence of 0.3 is rational, but there are other credences whose rationality Matt does not doubt—he is certain that a credence of (say) 0.5 is rational. But when you are certain that a given credence is rational, it is irrational to adopt any other credence that you are not certain is rational: it is irrational to adopt credences that are, what I’ll call, weakly rationality dominated. A bit more precisely. Let an evidential situation be a complete specification of which credences are rational responses to one’s evidence. Then where c and are credences that a subject S might adopt, Weak Rationality Dominance: c weakly rationality dominates for S iff for every evidential situation that S rationally treats as a live option and in which is rational, c is too, and in some evidential situation that S rationally treats as a live option, c is rational, but is not. Matt believes that the lower bound is roughly 0.3. To believe that the lower bound is roughly 0.3 is just to believe that it might be slightly higher or slightly lower than 0.3. Let’s make a simplifying assumption that Matt treats three evidential situations as live options: that the lower bound is 0.2, that it is 0.3, and that it is 0.4. In each of these evidential situations in which it is rational to assign 0.3 to Guilty—that is, when the lower bound is 0.2 or 0.3—it is rational to assign 0.4 to Guilty. But in the evidential situation in which the lowest rational credence is 0.4, assigning 0.4 to Guilty is rational, and assigning 0.3 to Guilty is not. Hence, in some evidential situation that Matt rationally treats as as a live option, assigning 0.4 to Guilty is rational, but assigning 0.3 to Guilty is not. So assigning 0.3 to Guilty is weakly rationality dominated by assigning 0.4 to Guilty for Matt. But dominated options aren’t rational: it’s not rational to adopt a credence that’s risky by your own lights when you know of a safer option. It follows that it is not rational for Matt to assign 0.3 to Guilty. But the Permissivist’s hypothesis was that it’s rationally permissible to adopt any credence between 0.3 and 0.7. We’ve now contradicted that assumption. Given what Matt ought to believe about the permissible range, it is irrational for Matt to adopt a credence on the edge of that range.7 The argument generalizes. For any range of putatively permissible credences in a proposition P, it is irrational to assign to P the lowest or highest value in that range— that is, it is irrational to adopt any credence on the edge of the permissible range.8 But Permissivism says that there is some range such that any credence in that range is permissible. Contradiction.9 (Perhaps you wonder why we should care about rationality dominance: our ultimate epistemic goal is not rationality per se, but accuracy. Even if we grant this, we ought to recognize that epistemic rationality is a good guide to accuracy—in general, more rational credences are more accurate. On this view, we should avoid credences that are rationality dominated because we should do what we can to be most accurate. I return to this issue in my reply to Objection 5.10) In the remainder of the paper, I explore various objections to my argument and find them wanting. The upshot is that Permissivism faces a special challenge about the interaction between our first- and higher-order attitudes. Answering the challenge requires taking on new, unattractive commitments about how we form higher-order beliefs or about what it is permissible to do in the face of higher-order uncertainty. Perhaps we will conclude in the end that those commitments are worth carrying to save Permissivism. But if we do accept Permissivism, we should do so in full knowledge of those commitments. We should know what burdens we shoulder. 3. Objections and Replies Objection 1: Your argument exploits the vagueness of epistemic permissibility. It relies on the premiss that if a certain credence is not rational, then no credence sufficiently close to it is rational either. But any premiss of that form is soritical, and so ought to be rejected. Reply: That premiss is indeed soritical, but my argument doesn’t rely on it. I do not say that since 0.3 is irrational, so too is 0.31. If my argument did rely on this premiss, it would have the (absurd) consequence that there are no rational credences. But it has no such consequence. To see this, take the limiting case, where there is just one permissible credence in Guilty—say, 0.5. If 0.5 is the unique rational credence in Guilty, then Matt ought to believe that it is roughly 0.5 (reflection doesn’t get us all the way to the truth, but it gets us somewhere). Now, if Matt believes that the rational credence is roughly 0.5, then if he assigns 0.5 to Guilty, he won’t be certain that his own credence is rational. But that’s not itself irrational: although Matt is not certain that his credence is rational, he is not certain, of any particular credence, that it is rational. There is no other credence Matt thinks would be better than his own.11 When the rationality of everything is in doubt, assigning 0.5 credence to Guilty will not be rationality dominated for Matt. Like clear-eyed Permissivists, clear-eyed Uniquers are uncertain about the rationality of their credences; unlike clear-eyed Permissivists, they are not sure that any other credences are rational. (By ‘clear-eyed Permissivist’, I mean someone who believes, of a certain case, that it is a permissive one. By ‘clear-eyed Uniquer’, I mean someone who believes that there are no permissive cases.) The dominance argument works against Permissivism because if there is a wide range of credences, Matt can be sure that certain credences in the middle of the range are rational—being in the middle will be safer, by Matt’s lights, than being on the edge. But if you think there’s just one rational credence, nothing will be perfectly safe by your lights. Matt may assign 0.5 credence to Guilty, because this credence will not be rationality dominated by any other credence. Objection 2: Ideally rational agents know exactly what rationality permits. So, in particular, if Matt is ideally rational, he is certain that the permissible range of credences in Guilty runs from exactly 0.3 to exactly 0.7, and so he is no victim of the dominance argument. Reply: Maybe.12 But Epistemic Permissivism is not just a view about ideally rational agents, but about ordinary agents like you and me, with all our human limitations. Indeed, Permissivists often tout their view as the only alternative to an objectionably demanding epistemology. Try to imagine yourself in Matt’s shoes, they say. You’re faced with a mess of evidence. Jones’s glove was found on the scene, but another suspect’s fingerprints were there too. Three witnesses claim that Jones owned a gun and was prone to violence. Two others deny this. And so on. Could it really be that the only rational response to his evidence is for Matt to become (say) 0.6453 confident in Guilty? Surely not, the Permissivist says. Rationality does not require us to do the impossible— typically there is a wide range of responses to our evidence that would be rational.13 If the Permissivist embraces this motivation, then surely when she says that it is permissible to hold any credence between 0.3 and 0.7, she means that it is permissible for someone like Matt—a non-ideal, cognitively limited agent— to hold any credence between 0.3 and 0.7. But I’ve argued that this can’t be. A non-ideal agent ought not to be certain of the exact boundaries of the permissible range, so he cannot adopt a credence on the edge of that range. But even if the Permissivist eschews this motivation, I don’t think she’s much better off. To be sure, the dominance argument does not apply to those who are certain of the exact boundaries of the permissible range. So, for any credence between 0.3 and 0.7 in Guilty, perhaps there is an ideally rational agent who holds that credence. But the argument still applies to ordinary agents—their options will be much more constrained. This leaves us with quite a surprising account of rationality, one that affords ideally rational agents many options, and limits ordinary agents to just one. This is exactly the opposite of what we should expect from a Permissivist who recognizes a distinction between ideal and non-ideal rationality. Permissivism is populist epistemology, a view for ordinary folk. Impermissivists ignore the realities of our actual cognitive lives. Permissivists don’t. If the Permissivist grants that any form of rationality is impermissive, it should be an idealized notion, one that abstracts away from our actual cognitive limitations, and so, by their lights, has little relevance for people like us. Absent a suitable story about why things would be reversed—why it would be ideal rationality that is permissive and non-ideal rationality that is impermissive—we should be suspicious of an appeal to ideal rationality as a way of evading the dominance argument. Objection 3: Matt should believe that he is in the middle of the permissible range. Suppose we grant that it is impermissible to adopt dominated options. Then we must say that, if Matt believes that the boundary of the permissible range is roughly 0.3, it is irrational for him to be 0.3 confident in Guilty. Matt shouldn’t regard himself as taking an unnecessary risk. But that doesn’t mean the 0.3 credence has to go, as I’ve argued. Rather, it’s Matt’s higher-order beliefs that should change: Matt should believe that his 0.3 credence is close to the middle of the range of permissible credences in Guilty, so that he is certain that 0.3 is rational. Reply: If you pursue this strategy, you need a story about how we form higher-order beliefs which explains why agents on the edge of the permissible range must always believe falsely that they are in the middle. To be sure, agents can form false beliefs about what rationality permits if they have misleading higher-order evidence. Matt may get misleading higher-order evidence suggesting that the permissible range of credences in Guilty runs from roughly 0.1 to roughly 0.5. I don’t doubt that it would then be permissible for him to assign 0.3 to Guilty. But Epistemic Permissivism is not just a view about what we are permitted to believe when we are misled. We need an account of how we form higher-order beliefs which explains how it can be rational for agents on the edge to believe falsely that they are in the middle, even in the absence of misleading higher-order evidence. The kind of story about higher-order belief formation that we are interested in is one that tells Matt and Abby to believe that they are in the middle of the permissible range. So, since Matt assigns 0.3 to Guilty, he ought to believe that the range of permissible credences in Guilty is roughly 0.1–0.5, and since Abby assigns 0.7 to Guilty, she ought to believe that the range of permissible credences is roughly 0.5–0.9. What kind of method must Matt and Abby be using to form these higher-order beliefs? It must be one that takes into account their own credences in Guilty. Perhaps the story goes like this. In general, you are rationally entitled to believe that your own credences and beliefs are rational. So when Matt examines the evidence and adopts a credence of 0.3, he is thereby permitted to infer that a credence of 0.3 is rational. Similarly, when Abby examines the evidence and adopts a credence of 0.7 credence, she is thereby permitted to believe that a credence of 0.7 is rational. Now, the story can’t stop there, for since Matt and Abby are clear-eyed Permissivists, they think other credences are rational too. Which ones? A natural thought: those that are sufficiently close to their own! Matt reasons, ‘I know that a credence of 0.3 is rational. So any credence as low as 0.1 or as high as 0.5 is probably rational too’, and Abby reasons, ‘I know that a credence of 0.7 is rational, so anything as low as 0.5 and as high as 0.9 is rational too’. Can this procedure explain how Matt and Abby could rationally believe that they are in the middle of the range? I think not. For if your credence is sufficiently close to the edge, this procedure will lead you astray about the upper and lower bounds of the permissible range, as it does for Matt and Abby. Now, the unreliability of the method is not itself the problem—perhaps it is sometimes rational for us to use unreliable methods. What is worrying is that a clear-eyed Permissivist is in a position to know that the method is unreliable. To see why, it will be instructive to compare Permissivism to Uniqueness on this issue. Suppose that I am a clear-eyed Uniquer. In that case, I know that, if my first-order belief or credence is rational, then if I come to believe that my own credence is rational, my belief will be true. In short, if Uniqueness is true, then the method I've discussed guarantees that rational agents will form true beliefs about rationality, and clear-eyed Uniquers are in a position to rationally believe this about themselves. Things are different for Permissivism. Matt is a clear-eyed Permissivist. He believes that his credence in Guilty is rational, and infers that all credences close to his are rational. That’s how Matt comes to believe that the range of permissible credences in Guilty is roughly 0.1 to roughly 0.5. But although being rational guarantees that you will form true beliefs about the rationality of your own credence, it does not guarantee that you will form true beliefs about the upper and lower bounds of the permissible range of credences—it doesn’t guarantee that you will form true beliefs about what other credences are rational. But Matt in a position to know this about the method he is using. Matt should be highly confident that he is on the edge of the permissible range of credences in some propositions, and, for all he knows, Guilty is one of them. So, Matt should recognize that, for all he knows, his credence is on the edge of the range of permissible credences in Guilty. Matt should doubt the conclusion of the method he is using: he should think, ‘Even if my credence in Guilty is rational, I might be on the edge of the permissible range, in which case my belief that all credences close to my own are rational will be false!’ But it can’t be rational to use a method whose conclusions one doubts. If I am in a position to know a priori that a conclusion I’ve drawn could easily be false, I shouldn’t believe it. Pending a suitable story about higher-order belief formation, we ought to be suspicious of a view that says that we must always believe that our credences are close to the middle of the permissible range. Objection 4: You assume that if Permissivism is true, then Matt can rationally believe he is in a permissive case. But some Permissivists deny this. For example, Stewart Cohen (2013) is a Permissivist who defends Doxastic Uniqueness, the claim that a subject cannot rationally hold one credence while believing that some other credence is just as rational. That is, a subject can never rationally believe that she is in a permissive case. If Matt doesn’t believe that there is a range of permissible credences in Guilty, the threat of dominance evaporates. Reply: Granted. But the traditional motivations for Permissivism strongly suggest that if Permissivism is true, then we can, at least sometimes, rationally believe that we are in a permissive case.14 Permissivists usually motivate their view, at least in part, by reflection on particular cases—cases of disagreement among jurors about whether Jones is guilty, among palaeontologists about what killed off the dinosaurs, and among philosophers about whether we have free will. But if we can know that a particular case is permissive when we’re doing epistemology, what could stop us from continuing to know that a particular case is permissive when we’re in one? A second way of motivating Permissivism, the ‘competing theoretical virtues’ argument, also suggests that we often know that we’re in a permissive case. Permissivists say that what it’s rational for us to believe depends not just on the content of our evidence, but on how we balance certain theoretical virtues against each other—things like simplicity, predictive strength, and explanatory power. There are many different yet equally rational ways of balancing these virtues against one another, and they will often yield different levels of confidence in various hypotheses.15 But surely we can tell, at least sometimes, how simple, predictive and explanatory a certain hypothesis is. If we can, then we can also determine, say, that balancing simplicity and predictive power in this way would yield high credence in Guilty, and weighing them in that way would yield lower credence in Guilty. But if we also know that both these ways of balancing the theoretical virtues are rational, we can put two and two together, and conclude that high credence and low credence in Guilty are both rational.16 Objection 5: It can be permissible for Matt to hold on to a credence that is rationality dominated. Matt’s credence has something else going for it: he expects it to be most accurate. Why? Because Matt’s credence is recommended by his own epistemic standards, which he endorses: Matt expects the credences recommended by his standards to be more accurate than those recommended by any other standards. This argument is not new: it’s Schoenfield’s (2014) response to White’s (2005) charge that if Permissivism is true, then it should be fine to switch arbitrarily from one permissible credence to another.17 We can think of Schoenfield’s brand of Permissivism as a kind of Intrapersonal Epistemic Uniqueness: there are many, equally permissible sets of epistemic standards, but once you’ve settled on one, you have reason to adopt the credences your standards recommend. (For Schoenfield, that’s because if you’re rational, you expect your standards to maximize expected accuracy.)18 So, contra White, it is never rational to switch arbitrarily from one permissible credence to another. If we’re convinced by Schoenfield’s reply to White, might we use it to reply to my challenge as well? Reply: There are two ways of understanding Schoenfield’s reply on behalf of the Intrapersonal Epistemic Uniquer, one weaker, one stronger: the weaker, though plausibly an effective response to White’s challenge, is no objection to mine; the stronger is indeed an objection to the dominance principle, but intuitively it is far too strong.19 The weaker version of Schoenfield’s reply says that expecting some credence to be most accurate is sometimes a reason to prefer it—in particular, it is a reason to prefer it when the rationality of the various credences you’re considering is not in doubt. This is in fact the thought that motivates Schoenfield's reply to White (see footnote 21 below). Plausibly, Schoenfield has answered White’s challenge—she has explained why, when you know that some other credence is just as rational as yours, you still have reason to prefer your own. But the weaker version of Schoenfield’s reply does not help the Permissivist answer my challenge—Schoenfield does not (nor does she intend to) explain why it would be permissible to hold on to credences that are rationality dominated. After all, cases in which your credence is rationality dominated are precisely those cases in which the rationality of one of the credences you are considering is in doubt. The stronger version of Schoenfield’s reply says that expecting your credence to be most accurate is always a reason to prefer it—in particular, it is a reason to prefer it even when the rationality of that credence is in doubt. This is indeed an objection to the dominance principle, the principle that it is always irrational to adopt weakly dominated credences. The stronger version of Schoenfield’s reply says that you should stick to your credence when it is rationality dominated because you expect it to be most accurate. But the Permissivist should not be happy to pursue the stronger version of Schoenfield's reply. It implies that we should never be moved to revise our credences by evidence that we’ve been less than fully rational. This is not a welcome consequence. Those who refuse to revise their beliefs in the face of evidence that they are irrational seem over-confident, indeed dogmatic—they seem paradigmatically irrational. Suppose Jill has examined all the evidence and becomes highly confident that the Warriors, her favourite NBA team, will win the championship. A trusted friend tells her that she always overestimates the likelihood of favourable outcomes. The Permissivist we are considering says that Jill should remain highly confident that the Warriors will win, despite her friend’s warning. Since she expects her high credence to be most accurate, she needn’t be worried by evidence that she has been irrational. This doesn’t seem right. When she has reason to believe her credence is irrational, Jill shouldn’t be able to appeal to the perceived accuracy of her credence as a reason to hold on to it. Compare this to a case of all-out beliefs. Suppose that Jill simply believes that the Warriors will win, and her friend tells her that the evidence doesn't support belief. Jill couldn’t reply to her friend’s concern, ‘Well, I must have got lucky—even though the evidence supports lower confidence, I’ve wound up with a true belief!’20 Return to the case of credences. Jill can’t respond to her friend’s concern about the rationality of her credence with ‘Well, I must have got lucky— even though my evidence supports a lower credence, my credence is more accurate!’ Evidence that she has been irrational should make her doubt the accuracy of her credences and beliefs, and she should lower her confidence accordingly. Similar things can be said of Matt’s credence in Guilty. He worries that his credence might be too low. But he’s sure that it’s not too high—he’s certain that it would be rational to assign a credence of 0.4 to Guilty. The Permissivist we’re considering says that he needn’t be moved by doubts about the rationality of his 0.3 credence in Guilty because he expects it to be most accurate. But again, this seems wrong. Matt cannot appeal to the perceived accuracy of his credence as a reason to maintain that credence when its rationality is in doubt.21 This is connected to a worry I mentioned earlier: don’t rational agents care about rationality only as a guide to accuracy, and not for its own sake? If so, accuracy always comes first. But then my dominance principle is false: because Matt expects his credence to be more accurate than any other credence, he should stick with a credence of 0.3 even if he isn’t sure it is rational and he is sure that a credence of (say) 0.4 is rational. To shift from 0.3 to 0.4 in order to ensure rationality—at the cost of accuracy, by Matt’s lights—would be irrational. But I deny that it can be rational for Matt to expect his credence to be most accurate when he has reason to believe that his credence might be irrational and he is sure that some other credence is rational. If Matt were sure that his credence was rational, then perhaps it would be rational for him to expect it to be most accurate. But the moment he starts doubting the rationality of his credence, continuing to assume that it is most accurate seems overly self-confident and dogmatic. Even if we don’t care about rationality for its own sake, it is a good guide to accuracy—in general, more rational credences are more accurate than less rational ones. But then we ought to see it that way—if we expect one credence to be more rational than another, we should also expect it to be more accurate, and so we should prefer it. Since Matt expects a credence of 0.4 to be more rational than one of 0.3—he is sure that 0.4 is rational, but he is not sure that 0.3 is—he should also expect 0.4 to be more accurate than 0.3, and Matt should revise his credence accordingly. On this view, avoiding dominated credences is just part of doing what we can to be most accurate. Let’s take a step back. As we’ve seen, I’m not the first to object to Permissivism. White argued that if you know that you’re in a permissive case, then it should be permissible to switch credences arbitrarily. As we saw in Objection 4, some Permissivists simply deny that we ever know that we are in a permissive case, and such Permissivists escape my dominance argument. But the Permissivists who endorse the traditional motivations for Permissivism—such as competing theoretical virtues—say that you can know that you are in a permissive case, but it is nonetheless impermissible to switch arbitrarily. These Permissivists must say that rational agents have some reason to privilege their own credences even when they know that some other credence is just as rational. Perhaps the reason is that the standards of a rational agent maximize expected accuracy for that agent, as Schoenfield argues. Or perhaps it’s simply that we should be (diachronically) consistent; we shouldn’t change our minds for no reason.22 But whatever the reason is, we must ask the question that I asked in response to Schoenfield: what is the force of the reason? Do we always have reason to adopt the credences that our standards recommend? Or rather, can it be defeated by evidence that our credences (and so our standards too) are irrational? As we have seen, the Permissivist should accept that if you have reason to believe that your standards are irrational, then whatever reason you had to adhere to your standards is defeated—when the rationality of a certain credence is in doubt, that it is recommended by your standards is no reason to prefer it. The thought that you shouldn’t change your mind for no reason is a far cry from the thought that you shouldn’t change your mind even when you have reason to believe that your present attitude is irrational. But I have argued that this is the predicament of the clear-eyed Permissivist on the edge of the permissible range. It’s not that he believes that some other credence is just as rational as his. No, it’s that he expects some other credence to be more rational than his. (Matt is sure that a credence of 0.5 is rational, but he is not sure that one of 0.3 is rational.) To privilege your credence when the rationality of that credence is not in doubt is one thing; to do so when you have reason to believe it might be irrational, and you’re sure that some other credence is rational, is quite another. The dominance argument goes through as long as you admit that it is rational to revise your credence when you’re not sure that your credence is rational but you are sure that some other credence is rational. And any Permissivist should admit this much. 4. Conclusion I have argued that if you are on the edge of the permissible range of credences in a certain proposition, your credence will be rationality dominated by certain credences closer to the middle. Since dominated options aren’t rational, it’s not rational to adopt a credence on the edge of the permissible range. But Permissivism says that, for some such range, any credence in that range is rationally permissible. I have considered some objections to my argument and found them wanting. Permissivism, in its traditional form, cannot be right.23 Footnotes 1 This formulation is from White (2005). 2 See Greco and Hedden (2015), Horowitz (2013), and White (2005) for arguments against versions of Epistemic Permissivism. See Ballantyne and Coffman (2012), Douven (2009), Kelly (2014), Kopec (2015), Meacham (2014), and Schoenfield (2014) for defences. See Kopec and Titelbaum (2015) for an overview of various arguments for and against. 3 See, for example, Kelly (2014) and Schoenfield (2014) for this criticism. 4 Strictly speaking, someone could be a Permissivist yet deny that there is ever a range of permissible credences in any proposition—you might think, say, that there are just two permissible credences in the proposition that Jones is guilty, 0.3 and 0.7. But the standard motivations—that there are some general, justifiable rules, and a wide range of starting points—strongly suggest that there will be a wide range of permissible credences in most propositions. If the Permissivist denies this, she owes us a general story about why there can never be such a range. Since no story like this has been told, I ignore this complication in this paper. 5 See, for instance, Christensen (2010), Elga (2013), Horowitz (2014), and Williamson (2000) for sympathetic discussion of similar claims. 6 Note that this point is not specific to Permissivism. If Epistemic Uniqueness is true, and the unique rational credence in Guilty is (say) 0.5, then Matt is not in a position to know that it is exactly 0.5, and so he too should believe that the rational credence is roughly 0.5. In my reply to the first objection, I’ll show why this does not pose problems for the proponent of Uniqueness. Thanks to an anonymous referee for bringing this to my attention. 7 I should note that the dominance argument does not apply to an extreme version of subjective Bayesianism that says that our priors must be probabilistically coherent, but there are no other constraints on what they should look like. If any probabilistically coherent prior is permissible, the range of permissible credences in (almost) any proposition will be [0, 1]— any credence will be rationally permissible. And if that’s right, we can be sure that our credences are rational, and so they won’t be weakly rationality dominated. But for many, this extreme version of subjective Bayesianism will seem too permissive. (It doesn’t rule out counter-inductivists, for example.) My argument targets any moderate Permissivist—that is, any Permissivist who wants to carve out a space between (extreme) subjective Bayesianism and Uniqueness. 8 The dominance argument actually shows something stronger. If it is impermissible to take dominated options, then it will be irrational to adopt any credence that is close enough to the edge that you believe that it might fall just outside of the permissible range. This means that the argument goes through even if the range of permissible credences has no lowest or highest value. 9 The Permissivist might object that I oversell the force of the dominance argument. If the range of permissible credences in Guilty is narrow, so narrow that Matt is not certain that any particular credence is rational, then his 0.3 credence in Guilty will not be rationality dominated. Granted. But the Permissivist shouldn’t rest content. For the guiding motivations for Permissivism—for instance, that different people can rationally come to opposite conclusions about an issue—strongly suggest that the permissible range of credences will often be very wide. See Rosen (2001) and Schoenfield (2014). 10 Thanks to an anonymous referee for bringing this to my attention. 11 Christensen (2010) gives an example of what seems to be a fully rational agent who is uncertain about what the rational credence is. Ava is considering the possibility that the next US President will be a Democrat (D). Christensen says, ‘Ava gives D some particular credence, say, 0.7; this reflects a great deal of her general knowledge, her feel for public opinion, her knowledge of possible candidates, etc. But given the possibility that her credence is affected by wishful thinking, protective pessimism, or just failure to focus on and perfectly integrate an unruly mass of evidence, Ava very much doubts that her credence is exactly what her evidence supports. This seems only natural; indeed, eminently reasonable’ (2010, p. 121) 12 Why ‘maybe’? Because it isn’t clear that even ideally rational agents are certain about which credences are licensed by their evidence. Here’s one reason to think they aren’t. Ideally rational agents aren’t always in a position to know exactly what they know and don't know. In particular, knowledge does not obey negative introspection: ideally rational agents can fail to know P without also knowing that they don’t know P. But if, following Williamson (2000), we accept that our evidence just is our knowledge, then even ideally rational agents won’t know exactly what their evidence is—sometimes they will be rationally uncertain about which credences are rational. 13 See Schoenfield (2014) for arguments like this. 14 See Ballantyne and Coffman (2012), Douven (2009), Kelly (2014), Schoenfield (2014), and Kopec and Titelbaum (2015) for defences of clear-eyed Permissivism, the view that Permissivism is true and we are sometimes in a position to know, of a certain case, that it is permissive. 15 See, for example, Douven (2009), Schoenfield (2014), and Titelbaum (2015a) for arguments along these lines. 16 Thanks to an anonymous referee for suggesting this point. 17 White presents many arguments against Permissivism, but I take this to be the central objection unifying all of them. 18 Kelly (2014), Meacham (2014), and Kopec and Titelbaum (2015) also defend Intrapersonal Uniqueness, and discuss how this view helps us respond to White. 19 Thanks to Bernhard Salow for discussion on the arguments of this section. 20 For defences or sympathetic discussion of the claim that it is irrational to maintain some credence or belief when you acquire evidence that it is irrational, see Christensen (2010), Elga (2013), Greco (2014), Horowitz (2014), Sliwa and Horowitz (2015), Smithies (2012), and Titelbaum (2015b). For criticism, see Coates (2012), Lasonen-Aarnio (2014), Lasonen-Aarnio (2015), and Williamson (2011). 21 Schoenfield’s discussion of irrelevant influences on belief makes it explicit that she endorses only the weaker version of Intrapersonal Uniqueness. She is interested in cases where you learn that your belief was influenced by an irrelevant factor. In cases like this, it seems we should revise our earlier beliefs. Schoenfield explains this intuition by saying that we should revise our beliefs when we have reason to believe that they are irrational (2014, pp. 203–6). Schoenfield accepts that if you have evidence that you’ve picked standards in a way that was unlikely to leave you with rational ones, then you ought to change them. It’s a short step from this thought to my dominance principle. 22 See Kopec and Titelbaum (2015) for a discussion of how appealing to certain norms of diachronic consistency helps us reply to White. 23 Thanks to David Boylan, Alex Byrne, Cosmo Grant, Dan Greco, Sophie Horowitz, Matt Mandelkern, Miriam Schoenfield, Kieran Setiya, Jack Spencer, Roger White, and, especially, Kevin Dorst, Milo Phillips-Brown, and Bernhard Salow for many helpful discussions. References Ballantyne Nathan , Coffman E. J. 2012 : ‘ Conciliationism and Uniqueness ’. Australasian Journal of Philosophy , 90 , pp. 657 – 70 . Google Scholar CrossRef Search ADS Christensen David 2010 : ‘ Rational Reflection ’. Philosophical Perspectives , 24 , pp. 121 – 40 . Google Scholar CrossRef Search ADS Christensen David , Lackey Jennifer (eds.) 2013 : The Epistemology of Disagreement: New Essays . Oxford : Oxford University Press . Coates Allen 2012 : ‘ Rational Epistemic Akrasia ’. American Philosophical Quarterly , 49 , pp. 113 – 24 . Cohen Stewart 2013 : ‘ A Defense of the (Almost) Equal Weight View ’. In Christensen and Lackey 2013 , pp. 98 – 119 . Dougherty Trent (ed.) 2011 : Evidentialism and Its Discontents . Oxford : Oxford University Press . Douven Igor 2009 , ‘ Uniqueness Revisited ’. American Philosophical Quarterly , 46 , pp. 347 – 61 . Elga Adam 2013 : ‘ The Puzzle of the Unmarked Clock and the New Rational Reflection Principle ’. Philosophical Studies , 164 , pp. 98 – 120 . Google Scholar CrossRef Search ADS Gendler Tamar Szabó , Hawthorne John (eds.) 2015 : Oxford Studies in Epistemology , Vol. 5 . Oxford : Oxford University Press . Greco Daniel 2014 : ‘ A Puzzle about Epistemic Akrasia ’. Philosophical Studies , 167 , pp. 201 – 19 . Google Scholar CrossRef Search ADS Greco Daniel , Hedden Brian 2015 : ‘ Uniqueness and Metaepistemology ’. Forthcoming in Journal of Philosophy . Horowitz Sophie 2013 : ‘ Immoderately Rational ’. Philosophical Studies , 167 , pp. 1 – 16 . Horowitz Sophie 2014 : ‘ Epistemic Akrasia ’. Noûs , 48 , pp. 718 – 44 . Google Scholar CrossRef Search ADS Kelly Thomas 2014 : ‘ Evidence Can Be Permissive ’. In Steup, Turri and Sosa (eds), Contemporary Debates in Epistemology , pp. 298 – 311 . Wiley-Blackwell . Kopec Matthew 2015 : ‘ A Counterexample to the Uniqueness Thesis ’. Philosophia , 43 , pp. 403 – 09 . Google Scholar CrossRef Search ADS Kopec Matthew , Titelbaum Michael G. 2015 : ‘ The Uniqueness Thesis ’. Forthcoming in The Philosophical Compass . Lasonen-Aarnio Maria 2014 : ‘ Higher-Order Evidence and the Limits of Defeat ’. Philosophy and Phenomenological Research , 88 , pp. 314 – 45 . Google Scholar CrossRef Search ADS Lasonen-Aarnio Maria 2015 : ‘ New Rational Reflection and Internalism about Rationality ’. In Hawthorne and Gendler 2015 , pp. 145 – 71 . Meacham Christopher J. G. 2014 : ‘ Impermissive Bayesianism ’. Erkenntnis , 79 , pp. 1185 – 1217 . Google Scholar CrossRef Search ADS Rosen Gideon 2001 : ‘ Nominalism, Naturalism, and Epistemic Relativism ’. Philosophical Perspectives , 15 , pp. 69 – 91 . Schoenfield Miriam 2014 : ‘ Permission to Believe: Why Permissivism Is True and What It Tells Us About Irrelevant Influences on Belief ’. Noûs , 48 , pp. 198 – 218 . Google Scholar CrossRef Search ADS Sliwa Paulina , Horowitz Sophie 2015 : ‘ Respecting all the Evidence ’. Philosophical Studies , 172 , pp. 2835 – 58 . Google Scholar CrossRef Search ADS Smithies Declan 2012 : ‘ Moore’s Paradox and the Accessibility of Justification ’. Philosophy and Phenomenological Research , 85 , pp. 273 – 300 . Google Scholar CrossRef Search ADS Titelbaum Michael G. 2010 : ‘ Not Enough There There: Evidence, Reasons, and Language Independence ’. Philosophical Perspectives , 24 , pp. 477 – 528 . Google Scholar CrossRef Search ADS Titelbaum Michael G. 2015a : ‘ Continuing On ’. Canadian Journal of Philosophy , 45 , pp. 670 – 91 . Google Scholar CrossRef Search ADS Titelbaum Michael G. 2015b : ‘ Rationality’s Fixed Point (or: In Defense of Right Reason) ’. In Gendler and Hawthorne 2015 , pp. 253 – 94 . White Roger 2005 : ‘ Epistemic Permissiveness ’. Philosophical Perspectives , 19 , pp. 445 – 59 . Google Scholar CrossRef Search ADS Williamson Timothy 2000 : Knowledge and Its Limits . Oxford : Oxford University Press . Williamson Timothy 2011 : ‘ Improbable Knowing ’. In Dougherty 2011 , pp. 149 – 64 . © Schultheis 2017 This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

doi: 10.1093/mind/fzx043pmid: N/A

1. Epistemic Friction: Constraints on Knowledge from the World and from the Mind Gila Sher’s Epistemic Friction is a bold and ambitious book, with many interesting things to say not only about knowledge, truth, and logic (the three topics mentioned in her subtitle) but also about matters ontological. It often requires the reader (this reader, anyway) to construe it hermeneutically, but repays the effort of doing so. She coins the expression ‘epistemic friction’ to refer to constraints on a system of knowledge, coming from both the world and the mind. She says, ‘The world as the object or target of our theories restricts what we can truly say about it, and the mind restricts our theories both voluntarily and involuntarily’ (p. 3). Borrowing terminology from Shapiro (1991), she describes her project as foundation without foundationalism. ‘The key idea’, she says, ‘… is that there is no inherent connection between grounding our system of knowledge in reality and doing so in a strictly ordered manner … . Foundation-without-foundationalism is committed to avoiding vicious circularity/regress, but since not all non-strictly-ordered grounding is viciously circular/regressive, the road is open to a non-foundationalist yet foundational methodology’ (p. 23). Here I will focus on just a few central elements in her rich and broad-ranging articulation and defence of this epistemological approach. 2. Creative Intellect and the Dynamic Centre/Periphery Model of Knowledge Sher is very critical of epistemological empiricism, as she construes this position. She interprets Quine as a (radical) empiricist, and opposes him in this regard. But although she regards Quine’s centre/periphery model of knowledge as too empiricist and too static, she does embrace a variant of it—a dynamic variant. So, how is she construing empiricism, and how does this connect to her dynamic centre/periphery model of knowledge? In the preface, she says the following about Quine’s model of knowledge: Quine’s model has a significant interface with both reality and mind (periphery and centre); it is a rich holistic model, with an elaborate network of connections between diverse units of knowledge; and it rejects the traditional divisions of units of knowledge into those grounded in reality and those grounded solely in the mind. But while I adopt these elements of Quine’s model, I renounce others … . [Its] periphery is limited to observational sentences and its center to pragmatic considerations and conventional postulations … . There is no room in Quine’s model for a veridical challenge to logic and mathematics as branches of knowledge in their own right. This limited view of abstract knowledge is closely connected to Quine’s deep, and quite radical, empiricism—another target of my criticism. Not only is Quine’s conception of center and periphery relatively narrow, but so is his conception of mind and world. Quine never asks whether objects in the world have abstract features, nor does he ask whether humans have resources for cognizing such features. To me, it is inconceivable that humans would reach the level of knowledge they have without a significant contribution of intellect (as something distinct both from sensory perception and from pragmatic conventions), but Quine completely neglects the role of intellect in knowledge. He considers, and rightly rejects, supernatural means of discovery and justification, but human intellect is not supernatural. Human intellect cannot be identified with either telepathy or clairvoyance, nor is it related to Greek deities, or the like. In the entire Quinean corpus there is no consideration of intellect as a crucially, or even potentially, significant cognitive corpus … . (pp. ix-x, emphasis in original) I sympathize with the spirit of these remarks. Creative intellect contributes significantly to the acquisition of knowledge about the world, and the ‘friction’ from the mind-independent world that we humans encounter when seeking to know about the world is hardly limited to the immediate deliverances of sensory-perceptual experience. For one thing, knowledge generation is a richly abductive matter, and the concepts that get invented and deployed in the course of abductive theorizing in science draw heavily on the creative work of the human intellect. Explanatory understanding of the world is a much richer phenomenon than simply being able to predict upcoming sensory stimulations; and explanatory understanding requires very rich input from intellect and its capacities. But in what sense, if at all, does Quine completely neglect the role of intellect, as something distinct from pragmatic conventions? I take Sher to mean that for Quine, the reifications of intellect do not really contribute anything to human knowledge beyond successful predictions of potential upcoming observations. In a text that she herself does not cite or quote, Quine writes: [I]f we transform the range of objects of our science in any one-to-one fashion, by reinterpreting our terms and predicates as applying to new objects instead of the old ones, the entire evidential support of our science would remain undisturbed … . The conclusion is that there can be no evidence for one ontology as over against another, so long anyway as we can express a one-to-one correlation between them … . Certainly we are dependent on a familiar ontology of middle-sized bodies for the inception of reification, on the part both of the individual and of the race; but once we have an ontology, we can change it with impunity … . The very notion of object, or of one and many, is indeed as parochially human as the parts of speech; to ask what reality is really like, however, apart from human categories, is self-stultifying. It is like asking how long the Nile really is, apart from parochial matters of miles or meters. Positivists were right in branding such metaphysics as meaningless. (Quine 1992, pp. 8-9, emphases in original) As against this radically empiricist conception of both the meaning of the sentences that collectively constitute a body of knowledge and of the nature of that knowledge itself, I take Sher to be claiming that some posits of human intellect figure in sentences that correspond to what reality is really like, whereas other posits of human intellect do not—even if those other posits can be deployed in some body of sentences that is empirically equivalent to the body of knowledge-constituting sentences. In this I applaud her. When engaging in epistemic projects like seeking explanatory understanding, quite a lot other than Quinean observation sentences and their contents can move to the periphery of a centre/periphery structure of knowledge—something that Sher emphasizes by offering us a dynamic variant of Quine’s own centre/periphery model. As she puts it, My own model … is a dynamic model: center and periphery are job descriptions rather than fixed locations, and each discipline moves from periphery to center and vice versa according to the task at hand. (p. x) This too seems very plausible. Consider, for instance, theorizing in cosmology about the large-scale spatio-temporal structure of the universe. One’s abductively best theoretical account here might well turn out to be one according to which, say, the cosmos is finite in spatial extent and yet unbounded—with the large-scale geometry, say, of the three-dimensional surface of a temporally expanding four-dimensional hyper-sphere. One way to dynamically bring such a theoretical hypothesis to the periphery of our knowledge-system is to point out, as a putative mark against it, that we humans are not capable of literally imagining—literally forming a mental image of—a four-dimensional hypersphere. But then other considerations can be brought to bear at this current periphery, pulling in the other direction and arguably outweighing the evidential significance of this unimaginability phenomenon—for instance, the fact that higher-dimensional generalizations of non-Euclidean geometry are mathematically natural and straightforward, and the fact that if we try to understand the large-scale geometrical structure of the cosmos in a purely Euclidean way we run smack into Kantian antinomy. Or consider, for another example, debates in philosophy about what kind of logic and semantics is best for accommodating vagueness—which, among other things, requires finding a way to block the infamous sorites paradox. One way to dynamically bring competing proposed systems of logic for vagueness to the periphery of our knowledge system is by noting certain commitments of the different systems and then asking how well these commitments conform with ordinary common-sense thought and talk. Take supervaluationism, for example. Concerning a statement like ‘For every n, if an n-grained pile of sand is a heap then an n-1 grained pile of sand is a heap’, a supervalutionist will affirm the statement’s classical negation, and will also affirm the following statement, which is logically equivalent (both under classical two-valued semantics and under supervaluationist semantics) to that classical negation: ‘There exists an n such that an n-grained pile of sand is a heap and an n-1 grained pile of sand is not a heap’. The supervaluationist will also say that although this existential claim is true, it has no true instances. Well, one important count against supervaluationism, while we are holding it at the periphery of the knowledge system, is this: claiming that the existential statement is true despite the fact that none of its instances are true goes deeply contrary to what we ordinarily would take ourselves to mean in affirming that existential statement. Other proposed approaches to the logic and semantics of vagueness can perhaps do better in this respect—perhaps without encountering comparably powerful objections themselves. At the beginning of Chapter 5 Sher further elaborates her dynamic centre/periphery model as follows. Our model is characterized by: A broad and open-ended conception of reality, neither Platonist nor nominalist, one that affirms both experiential and abstract features of reality—one reality—and regards them as interconnected. A view of human intellect as playing a central role in knowledge, both abstract and empirical. Intellect’s role is central not just to the conceptual or pragmatic aspects of knowledge, but also, and significantly, to its veridicality. By affirming the central role of intellect in knowledge, however, the model does not affirm apriorism, nor does it identify non-apriorism with empiricism. The model is neither apriorist nor empiricist, regarding intellect and sensory perception as two essential, yet interconnected, elements of knowledge. ‘Basic’ realism: A realism which is more robust than most other forms of realism in regarding reality as both the target and ground of all human knowledge (including abstract, e.g., logical and mathematical, knowledge), yet is more flexible than most other forms of realism with respect to the ways in which a theory can be (substantially) connected to reality. (p. 73, emphasis in original) Here she appears to be using the term ‘empirical’ and the label ‘empiricism’ in such a way that the category ‘empirical’ largely or completely excludes the operation of what she calls ‘intellect’ in human knowledge. Thus, she also appears to be construing empiricism as an epistemological orientation that also largely or completely excludes the operation of intellect (which fits with her remarks in an above-quoted passage about Quine’s radical empiricism). This way of understanding her is further underwritten by the following remarks: Knowledge of the world, or of various aspects of the world, is attained, in our model, by a combination of activities, ranging from sensory perception to conceptualization, abstraction, generalization, reflection, combinatorics, analysis, figuring out, model building (scientific and logical), experiment design, mathematical intuition, and so on. In this essay I place these activities with the exception of sensory perception, under ‘intellect’. Intellectual activity, in the sense intended here, is thus any non-sensory cognitive activity, i.e., any cognitive activity that does not principally rely on any of our five senses. I also use ‘reason’ as a synonym for ‘intellect’ in this sense. (p. 84, emphasis added) Her ‘basic realism’, I take it, affirms (as against the above-quoted passage from Quine), both that it does make sense to ask what reality is really like, and also that humans can indeed obtain knowledge about what reality is really like. Such knowledge, of course, would not be something ‘apart from human categories’ (as Quine put it), but instead would deploy certain human categories to frame claims that correspond to what reality is really like. (Cf. §3 below.) Her rejection of what she calls ‘empiricism’, I take it, really amounts to a rejection of the kind of verificationism about meaning that leads to the contention that metaphysical questions about what reality is really like are meaningless. Now, admittedly, words like ‘empirical’ and ‘empiricist’ are terms of art in philosophy (and in science). But although Quine and the positivists embraced a radical empiricism that asserts in effect that meaning is exhausted by matters observational (with Quine treating the whole of science as the unit of meaning, rather than the individual sentence), nonetheless the words ‘empirical’ and ‘empiricism’ often are used in philosophy much more broadly—‘empirical’ for something like ‘not a priori’, and ‘empiricism’ for the view that there is no a priori synthetic knowledge (or, if one rejects the analytic/synthetic distinction, for the view that there is no a priori knowledge at all). Moreover, Sher herself rejects the analytic/synthetic distinction, and is very dubious about the category of the pure a priori. (She holds that neither logic nor mathematics is purely a priori.) In addition, her dynamic version of the centre/periphery model allows that components of one’s system of knowledge which Quine treated as always at or near the centre actually can, and sometimes do, get dynamically brought to the periphery in the course of inquiry—thereby becoming more thoroughly subject to ‘friction’ from reality than in Quine’s own centre/periphery model of knowledge. In these respects, her position is arguably even more thoroughly ‘empiricist’ than is Quine’s—even though hers is neither a radical, verificationist, empiricism about meaning itself nor a foundationalist empiricism that treats all knowledge as an inferentially strictly-ordered superstructure built upon the foundation of sensory experience. 3. Manifold Correspondence and Minimal Realism Sher argues that truth is correspondence to reality, and also that this correspondence takes many forms. She says: [A] core, universal principle of truth concerns the connection between mind and reality inherent in it. Traditionally, this principle is called ‘correspondence’, but the form it takes in the present theory differs in several ways from its traditional form(s). In particular, our version of correspondence allows it to take multiple forms, including highly intricate forms, in contrast to the single and simple form—copy (picture, mirror) or isomorphism—that most traditional conceptions of this relation demand … . To signal both the similarities and the differences between traditional correspondence and the one proposed here, I will call the latter ‘manifold correspondence’. As a starting point, we can briefly formulate the principle of manifold correspondence as follows: (M-COR) Truth is a matter of a substantial and systematic connection between thought and reality, a connection that has to do both with the way the world is and the way our mind operates. This connection might be quite intricate and take different forms in different fields. The forms it takes depend both on what aspect of reality a given thought targets and on the cognitive resources available to us for reaching it. Abstracting from differences, this connection holds between a given thought and reality when the aspect of reality it targets is, directly or indirectly, yet systematically, as it says it is. (p. 186, emphasis in original) While I sympathize strongly with these remarks, again I find myself reading them hermeneutically—and more particularly, as conforming with my own approach to truth. (In Chapter 8, Sher explicitly compares her views about truth to mine (Horgan 2001), and also to those of Aristotle, Frege, Quine, Field, and Yablo.) First, I construe M-COR in a way that includes an explicitly ontological understanding of the distinction between direct correspondence, on the one hand, and the various kinds of indirect correspondence on the other. Only when the pertinent kind of correspondence is direct do one’s claims carry genuine ‘ontological commitment’ regarding what reality is really like. Only then do one’s claims embody commitments regarding the items (objects, events, properties, tropes—whatever) that belong to the correct ontology. (This of course is a realist use of Quine’s expression ‘ontological commitment’—a use which he himself presumably would have repudiated as belonging to meaningless metaphysics.) As one might put it, when the contextually operative kind of correspondence is indirect rather than direct, a true statement’s grammatical ‘ontological commitments’ (by Quinean criteria) need not be robust ontological commitments. Second, I construe M-COR as identifying truth with correct affirmability under contextually operative, and contextually variable, semantic-affirmability standards. Generically, truth normally is a joint product of (a) the contextually operative semantic-affirmability standards and (b) how things are with reality. But direct correspondence and indirect correspondence are distinct species of this genus. Sometimes, the contextually operative standards work in such a way that the statements they govern are ontologically committal in the metaphysical-realist sense; these are direct-correspondence semantic standards. But in many contexts the operative semantic standards instead operate differently: although they do impose certain requirements upon reality in order for a given statement to count as semantically correctly affirmable (that is, as true), they do not require the correct ontology to include items answering to the statement’s posits. These are indirect-correspondence semantic standards. As a plausible example of a statement that I claim would normally be governed by indirect-correspondence standards of semantically correct affirmability (that is, of truth), consider this: ‘Arizona has exactly three public universities’. We all know well enough what kinds of evidence would be required to justify this claim, and such evidence would not suffice to justify the contention that the right ontology includes putative entities like states, nations, or public universities. And although the positivists were mistaken in regarding truth as a matter of epistemic correctness, they were on to an important fact even so: often there is a comparatively small gap between epistemic correctness and truth (that is, between epistemic correctness and contextually operative semantic correctness). Such small gap-size, in the context of a given discourse, typically is an indicator that in that context, truth is a matter of indirect correspondence. On Sher’s ‘minimal realism’, truth is indeed correspondence to reality; thus—contra Quine—true statements really do say ‘how reality really is’. As I understand M-COR, however, when the contextually operative kind of correspondence is indirect rather than direct, true statements say how reality is in such a way that the posits they employ need not necessarily pick out denizens of the correct ontology; that is, their grammatical ontological commitments need not be robust ontological commitments. Of the innumerable ways reality might be, the actual way-reality-is is a There-are-exactly-three-public-universities-in-Arizona way—even though the right ontology need not contain such putative items as public universities, nations, or the State of Arizona. (The grammatical ontological commitments of the statement that Arizona has exactly three public universities are not robust ontological commitments.) And, again contra Quine, once our thought and discourse employ posits like public universities and the State of Arizona, it is not the case that we can change them ‘with impunity’ so long as the class of entailed observation sentences remains unaltered; for, such impunity would go contrary to the indirect-correspondence affirmability standards that are actually operative in prosaic thought and prosaic discourse about universities and States of the Union. Sher advocates substantivism about truth, as against deflationism—an attitude with which I wholeheartedly concur. She says: Substantivists (advocates of a substantive theory of truth) differ from deflationists on multiple points: Where deflationists say that ‘truth is entirely captured by the … triviality … that each proposition specifies its own condition for being true’, substantivists say that it is far from being fully captured by this triviality; where deflationists say that ‘the truth predicate exists solely for the sake of a certain logical need’ (Horwich [1990/8]: p. 2), substantivists say that it exists for other needs as well; where deflationists say that truth is not a deep notion, substantivists say it is; and where deflationists say that a theory of truth cannot be, or need not be, genuinely explanatory, substantivists say it can and should be. (p. 132) But just what are the other needs served by the notion of truth, and just how can claims about the truth or falsity of first-order claims be explanatory in ways that differ from the explanatory potential of the first-order claims themselves? Once again, I find myself reading Sher hermeneutically. As I understand M-COR, it is a construal of truth that allows us to fend off quietism about substantive metaphysical debates in philosophy. Deflationists tend to go minimalist across the board about a host of conceptually interconnected notions: truth, property/relation, fact, correspondence, and so on. They also tend to think that there is no real subject-matter-neutral notion of existence. So they are apt to say that there is no substantive issue whether numbers exist, since (for example) it follows from the Peano axioms that there is a natural number greater than 2. And they are apt to say that there’s no substantive question whether moral properties or moral facts exist, since (for example) murder is wrong—from which it follows that murder instantiates the property wrongness, that murder’s being wrong is a fact, and that the statement ‘Murder is wrong’ corresponds to that fact. Crucial to M-COR, as I interpret it, is the contextual variability of semantic correct-affirmability standards. On one hand, this feature allows the approach to accommodate what is right in deflationist or minimalist approaches: the truth-predicate often is governed by contextually operative semantic standards under which truth-talk runs smoothly, disquotationally, in tandem with first-order talk; likewise, the semantically operative semantic standards governing property-talk, fact-talk, correspondence-talk, and existence-talk often work in this same minimalist way vis-à-vis first-order talk. On the other hand, (a) often those contextually operative semantic correct-affirmability standards will be indirect correspondence standards of one kind or another, and (b) the possibility is always there of shifting the contextually operative ‘score in the language game’ (Lewis 1979) to direct correspondence standards, thereby posing and addressing substantive metaphysical issues. As the currently fashionable saying goes, the possibility is always there of speaking and thinking in the manner appropriate for being in the ‘ontology room’—that is, the manner governed by direct correspondence semantic standards, in which the grammatical ontological commitments of one’s thought and discourse constitute genuine, robust ontological commitments. (Indeed, the possibility is always there of shifting the language-game score in such a way that although the newly operative semantic-affirmability standards are still indirect-correspondence standards, nonetheless in pertinent respects they are closer to direct-correspondence standards than before. For instance, we can debate moral realism and moral irrealism—in contexts of detached metaethical dispute, as distinct from contexts of engaged first-order moral dispute—while still helping ourselves to posits like universities and the State of Arizona.) So much the worse for metaphysical quietism, and so much the better for metaphysics. 4. Analyticity, Mathematical Truth and Epistemic Friction My own construal of M-COR leaves room for the possibility that some statements are analytic, at least sometimes and under some contextually operative language-game scores. Indeed, it leaves room for the possibility that some existence claims are analytic—for example, the statement that there is a natural number greater than 2. I find it very plausible that the truths of pure mathematics are analytic—existence claims included—that is, that these mathematical claims are semantically correctly affirmable under the contextual semantic-affirmability standards that normally govern thought and talk deploying mathematical posits—and are correctly affirmable solely by virtue of those standards themselves, apart from any ‘friction’ from reality. This view is attractive epistemologically, with respect to understanding the nature of mathematical knowledge. And it is attractive metaphysically, since it is entirely compatible with saying the following after shifting the language-game score into direct-correspondence semantic standards: numbers and other putative mathematical entities do not exist. Sher, as I noted above, sides with Quine in repudiating analyticity altogether—including in the case of pure mathematics. Against my own approach to mathematical truth, she says that on this view, ‘[o]rdinal and cardinal terms, like any other mathematical terms, are not connected to reality at all. Instead, they are connected (exclusively) to pure conventions, i.e., in our terminology to the mind’ (p. 215). I lack the space to rehearse here her arguments against analyticity and my reasons for finding them unpersuasive. Instead, let me conclude my discussion of her rich and provocative book by briefly replying to the just-quoted charge against me. The charge seems to assume, in effect, that if the true claims of pure mathematics are analytic, then the mathematical concepts that figure in these claims cannot figure in any claims that are subject to friction from reality—that is, claims that are subject to being rendered either true or false by how things really are in our world. But that assumption seems to me eminently deniable. Even if some claims deploying ordinal and cardinal terms are analytic (including some existence claims), it hardly follows that all claims deploying such terms are analytic. The claim that the earth has exactly one moon is empirical; the claim that Arizona has exactly three public universities is empirical; and so on for numerous other claims employing ordinal and cardinal terms. Imagine a ‘deductive savant’ (I do not say a mathematical savant) who is marvellously good at applying rules of deductive logic to certain axioms—for example, the Peano axioms and the axioms of Euclid—to derive theorems. Suppose this person also confidently mouths the axioms and theorems and confidently embraces them, but has no capacity to count and has no idea what you are talking about if you ask, for example, ‘How many siblings do you have?’ Although the axioms and theorems the person mouths and embraces are, in fact, truths of pure mathematics, this person has no capacity at all to deploy mathematical concepts in framing any claims that are subject to friction from reality. Would this person possess mathematical concepts, or possess knowledge of analytically true mathematical claims qua mathematical? I would say no, and I think this response is entirely consistent with my contention that the truths of pure mathematics are all analytic. Two morals emerge. First, analytic truths in pure mathematics can constrain the correct use of mathematical concepts in claims that are subject to friction from reality, just as purely analytic truths about bachelorhood can constrain the correct use of the concept BACHELOR in claims that are subject to friction from reality—for example, the claim that Isaac Newton was a lifelong bachelor. (That empirical claim could not be true unless Newton was never married.) Second, a person utterly unable to appreciate such constraints would not really possess mathematical concepts—however good the person might be at mouthing sentences that happen to express analytic mathematical truths, or at deriving theorems from axioms. References Horgan Terence 2001 , ‘Contextual Semantics and Metaphysical Realism: Truth as Indirect Correspondence’, in Lynch M. (ed.), The Nature of Truth . Cambridge, MA : MIT Press , 67 – 95 . Horwich Paul 1990 /8, Truth . Oxford : Oxford University Press . Lewis David 1979 , ‘ Scorekeeping in a Language Game’ , Journal of Philosophical Logic 8 : 339 – 359 . Google Scholar CrossRef Search ADS Quine Willard Van Orman 1992 , ‘Structure and Nature’ , The Journal of Philosophy 89 : 5 – 9 . Google Scholar CrossRef Search ADS Shapiro Stewart 1991 , Foundationalism without Foundations . Oxford : Oxford University Press . © Mind Association 2018 This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

doi: 10.1093/mind/fzx031pmid: N/A

Elliott Sober’s first book, Simplicity (1975), defends the view that the simplicity of a theory or hypothesis is a measure of its informativeness – roughly, simpler theories require less new information to be added to them to answer relevant questions of interest. While this measure of simplicity is question-relative, it is still what you might call a global view of simplicity – simplicity means the same thing across different scientific problems and it is always an epistemic virtue. Ockham’s Razor is just good scientific reasoning. Sober’s 1988 book Reconstructing the Past: Parsimony, Evolution, and Inference argues against this global conception of simplicity and replaces it with a local one. Here, in one context parsimony (now roughly synonymous with simplicity) means one thing while in another context it may mean something different. Similarly, whether the more parsimonious hypothesis is to be preferred is also a local matter; it depends on various background assumptions in play, something which can differ between contexts. Ockham’s Razor is not a universally valid inference rule. Sober’s 1990 ‘Let’s Razor Ockham’s Razor’ pushes this view even further by suggesting that perhaps there is no reason to continue using Ockham’s Razor at all. The basic reason is that parsimony is not a sui generis epistemic virtue. When parsimony goes along with something of basic epistemic value, then the parsimonious theory is to be preferred. If it does not, then parsimony is of no value. Sober’s most recent book Ockham’s Razors: A User’s Manual brings together much of his previous work on parsimony, substantially expands his previous arguments and presents a host of new ones. It continues the localist and reductionist traditions of Reconstructing the Past. As Sober puts it, ‘If parsimony contributes to the achievement of some more fundamental epistemic goal, I am all for it. If it does not, I am not’ (p. 149). However, in this work, Sober argues that there is no need to ‘razor the razor’ as he previously suggested. Just because parsimony is not itself a fundamental theoretical virtue, it does not follow that it is not valuable to understand and study it: ‘The epistemic relevance of parsimony does not require that parsimony be an end in itself’ (p. 149). On this point, I believe that Sober is correct. Parsimony could be a relevant consideration even if it always reduces to something else. But it is still a relevant question to ask whether in fact it does always reduce to something else. Sober argues yes, it always does (or perhaps when it doesn’t, then it is not of any value). Sober’s reductionism entails that we could razor the razor if we wished without changing which inferences were good ones. I am not so sure that we could do so and I will return to this point near the end of this review. As well as reinforcing some of his previous arguments, Sober frames his discussion within a larger historical and philosophical context. He also argues for a number of substantial theses which are important and interesting regardless of how they relate to discussions about Ockham's Razor. It is an impressive work – well worth reading for philosophers and scientists from a number of different fields and essential reading for philosophers of science interested in scientific epistemology. Let’s begin with the basic question of just what Ockham’s Razor actually is. According to Sober, ‘Ockham’s Razor, the principle of parsimony, says that a theory that postulates fewer entities, processes, or causes is better than a theory that postulates more, so long as the simpler theory is compatible with what we observe’ (p. 2). Despite this seemingly clear definition, Sober goes on to say that ‘different thinkers have meant different things by parsimony and different justifications for principles of parsimony have been constructed. My goal in this book is to describe this diversity and to determine when parsimony is relevant and when it is not’ (p. 2). By equating Ockham’s Razor with a kind of quantitative and ontological parsimony in this way, Sober is immediately setting aside discussion of various aspects of simplicity, such as the beauty and elegance of a theory which might be called ‘syntactic simplicity’ (Sober 2001). I do not think it is a problem for Sober that he ignores these kinds of uses, but it is worth noting that his pluralistic conclusions about the varieties of ways in which the razor can be used could easily be broadened. Having got clear about what the principle of parsimony actually says, it is time to ask whether it is justified. To cut to the chase, Sober says in his introduction that ‘[p]arsimony arguments that draw conclusions from the fact that one theory is more parsimonious than another differ from each other at two levels. First, some of them succeed while others fail. Second, the successful arguments succeed for different reasons, and the unsuccessful arguments go wrong in different ways’ (p. 3). The book goes on to make a few general claims about Ockham’s Razor, but each claim is justified by a detailed look at a variety of special cases examined in their local context. Chapter 1 features a collection of short historical examples including Aristotle, William of Ockham, Copernicus, Descartes, Leibniz, Newton, Hume, Kant, Mill, Whewell, Maxwell, and Morgan. In looking at a variety of uses of Ockham’s Razor, we can see right away some important differences between them. To help categorize the uses, Sober splits the principle of parsimony into two principles: the ‘razor of silence’ and the ‘razor of denial’. The distinction is supposed to parallel the difference between agnosticism and atheism. The stated purpose of the chapter is not just to look at historical cases where a principle of parsimony has been used, but to look at the various attempts to justify such a principle. While the justifications differ across these cases, theological justifications are common, as is the idea that the principle is justified because nature itself is simple. Sober argues that neither of these traditional justifications is acceptable. Chapter 2 moves the discussion to the twentieth century where discussions of simplicity take a ‘probabilistic turn’. Sober argues that we can find two distinct ‘parsimony paradigms’, which show that parsimony is epistemically relevant. One is the Bayesian paradigm on which parsimony can be justified when it lines up with likelihood – that is, the probability of the observations given the hypothesis. A second paradigm is frequentist. Here parsimony can play a role in model selection criteria such as the Akaike Information Criterion, where parsimony counts the number of adjustable parameters in a model. Since reducing the number of adjustable parameters in a model reduces overfitting, parsimony in this sense is relevant to the predictive accuracy of a model. Understanding these paradigms requires understanding some technical details, so the chapter features a very short introduction to probability theory, Bayes’ Theorem, models and model selection theory. An example of the likelihood justification for parsimony is examined through the lens of Reichenbach’s common cause principle, where Sober considers the common cause hypothesis for two correlated events to be more parsimonious than the hypothesis of two separate causes. Sober then investigates the conditions under which the more parsimonious hypothesis matches the one with the higher likelihood. (The likelihood of a hypothesis H is P(O|H) – the probability that the hypothesis confers on the data.) It turns out that they often (but not always) match. Sober (2001) describes a third parsimony paradigm: sometimes parsimony is a stand-in for prior probability. This would also be a kind of Bayesian justification. In fact, it is sometimes treated as ‘the standard’ Bayesian justification for Ockham’s Razor (Earman 1992). While in one footnote Sober suggests that this paradigm ‘plays third fiddle’ (p. 141), in his more comprehensive discussion of the connection between simplicity and prior probability, Sober argues that this potential justification for Ockham’s Razor is fatally flawed. Siding with Popper, Sober argues that it is impossible for simpler hypotheses always to have higher probabilities than more complex ones for the reason that simpler hypotheses often entail more complex ones and so therefore the more complex ones cannot have lower probabilities (though he does not accept Popper’s claim that simpler hypotheses are more falsifiable). Chapter 3 looks at the connection between parsimony and likelihood much more deeply through an investigation of the problem of phylogenetic inference and the inference methods of cladistic parsimony and maximum likelihood which are frequently used in such problems. Reconstructing the Past provided an in-depth look at this connection. Here Sober reiterates a number of previous points, including how to think about which background assumptions are sufficient or necessary for the two methods to favour the same phylogenetic trees. He also updates the reader by pointing to a number of new discoveries about this relationship that have been made in the intervening time. Chapter 4 is a fascinating look at the scientific question of whether chimpanzees are mind-readers – that is, whether they form mental representations of the mental states of others. To some authors, it seems that there is a kind of default presumption in favour of the view that they have no such abilities. That this is the default follows from Morgan’s Canon: ‘In no case may we interpret an action as the outcome of the exercise of a higher psychical faculty, if it can be interpreted as the outcome of the exercise of one which stands lower in the psychological scale’ (Morgan 1894, p. 53). This is plausibly an instance of the principle of parsimony, though as Sober points out, Morgan actually thought that positing the higher faculties was the simpler theory but wanted to warn against it. This idea that one theory might be simpler than another on one set of grounds and less simple on some other set has important consequences. Researchers have performed a number of different experiments which seem to indicate that chimpanzees can mind-read. What we observe are the environments in the experimental setup and the behaviours that the chimpanzees exhibit. This leaves open the question of the psychological mechanisms leading to the behaviours and so is an instance of what Sober calls ‘black-box inference’. Povinelli and Vonk (2004) argue that there is a logical problem with positing an ability of the chimpanzees that we can’t directly observe: it is possible that the chimpanzees are predicting the behaviour of the other chimpanzees directly based on the environmental stimuli they can see. Positing mind-reading is positing an extra intervening variable (namely, representations of mental states) between the environmental features and the chimpanzees’ predictions of other chimpanzees’ behaviours and, therefore, mind-reading is an unnecessarily complex hypothesis. Tomasello and Call (2006) argue that positing that chimpanzees can mind-read allows us to explain the results of different experiments with a single unifying explanation. Unification and parsimony often go hand in hand and it is natural to think that on this basis, mind-reading is actually the simpler explanation. Another way to view this issue is to argue, as Whiten (1996) does, that the mind-reading hypothesis gives us a natural way to represent the causal story in a more economical way with fewer causal arrows. Sober ultimately rejects Whiten’s arrow counting argument and argues instead that when we think about the two hypotheses as models, mind-reading has an extra adjustable parameter and so is less parsimonious. Of course, mind-reading is still more unifying and so Sober treats the case as one where parsimony and unification are in conflict. While I agree that parsimony and unification can conflict, it seems to me that it is very important to recognize that parsimony considerations can conflict with each other and not just considerations having to do with Ockham's Razor broadly understood. In other words, not only is it not clear what the epistemological impact is when one theory is simpler than another, it is often not clear which theory is simpler in the first place. This case seems a perfectly good example of this. If Tomasello and Call had argued that mind-reading hypothesis is better on the grounds of simplicity, rather than explicitly citing unification, it would make just as much sense. This dispute over parsimony and unification has led to something of a stand-still in the debate over whether chimpanzees can mind-read. Rather than fighting over methodological principles, Sober proposes a new type of experiment that he hopes will shed some light on the debate. In chapter 5, Sober discusses Ockham's Razor in connection with debates in philosophy, including debates about: the existence of God, the mind-body problem, the causal efficacy of the mental, moral realism, Plantinga’s evolutionary argument against naturalism, nominalism about mathematics, and solipsism. Apropos the above discussion, when I saw this list in the contents I naturally assumed that solipsism was the parsimonious hypothesis. What could be more ontologically parsimonious than getting rid of the external world?! But Reichenbach himself argued that there was a common cause argument for the existence of the external world and harking back to the arguments of chapter 2, Sober treats this as a parsimony argument. As it turns out, Sober argues that this particular common cause argument fails since even if we assume there is a common cause, it may well be internal to our minds. In addition to any common cause considerations in favour of solipsism, like the chimpanzee mind-reading hypothesis, the external world hypothesis is more unifying, which makes it seem simpler in certain respects. The problem of the external world does seem precisely the kind of problem that is not settled on empirical grounds. This is exactly where Ockham’s Razor is supposed to shine. But since there are multiple, competing parsimony considerations in this case, we have good reasons for thinking that Ockham’s Razor will not solve this particular problem for us. What about the existence of God? Sober focuses only on the problem of evil. As he sees it, atheism is more parsimonious than theism and the law of likelihood shows that the observations of evil in this world evidentially favour no PKG (all-powerful, all-knowing, and perfectly good) God over the existence of a PKG God. Thus, this is one of the justified uses of the principle of parsimony, since it falls under one of the parsimony paradigms. Perhaps the most common argument against the existence of God is the problem of evil. But a close competitor is undoubtedly some version of Ockham’s Razor. When asked ‘Why not believe in God’, atheists such as Hitchens (2007) sometimes recount the story (likely apocryphal) involving the great French physicist and mathematician Pierre-Simon Laplace. Laplace is asked by Napoleon why his book Treatise on Celestial Mechanics made no mention of God. He is supposed to have replied ‘Je n'avais pas besoin de cette hypothèse-là’. (‘I had no need of that hypothesis'.) The atheist’s move from ‘God is not needed’ to ‘God doesn’t exist’ is the razor of denial in action. But like chimpanzee mind-reading and the external world, the hypothesis that there is a God has often been thought to be unifying and, in fact, a more simple hypothesis than atheism (Swinburne 2004). Once we start looking, it is easy to find cases where it is unclear which of two competing hypotheses is actually simpler. Often this is because we tend to associate particular features with simplicity (the paucity of types of entities and unification, for example) and if we do this, it is easy to see that these can come into conflict. All we need to do is simply introduce a new entity which allows a unification between two previously distinct explanations. Of course if the entity introduced is clearly ad hoc, the ‘unifying’ hypothesis will not be a serious one. But if there is some reason to think it is plausible (as in the case of chimpanzee mind-reading or God) we have the recipe for a serious debate. These kinds of trade-off cases cannot be decided a priori; they must be looked at on a case-by-case basis. Sober’s detailed discussions of apparently unrelated cases is of great philosophical and scientific interest and ultimately justifies his view in the ‘localness’ of the value of Ockham’s Razor. But direct arguments like this one lead to the same conclusion. Now let’s look at some of the more global conclusions in the book. As I mentioned earlier, Sober splits the principle of parsimony into two principles: the ‘razor of silence’ and the ‘razor of denial’. The distinction is supposed to parallel the difference between agnosticism and atheism. The exact statements of the principles can be found in Sober (2009, p. 128): Razor of denial: If your evidence does not discriminate between ‘X exists’ and ‘X does not exist’, you should deny the former and affirm the latter. Razor of silence: If your evidence does not discriminate between ‘X exists’ and ‘X does not exist’, you should suspend judgment about both. Since they give incompatible recommendations in the same cases, the principles themselves are incompatible. When discussing whether some application of Ockham’s Razor is justified, Sober often points out whether it is an application of the razor of silence or of the razor of denial. So which, if either, of these principles is justified? Sober suggests that the razor of silence has an obvious justification. For any probability function and any X and Y, Pr(Y&X) ≤ Pr(Y). (I have made a few trivial notational changes for readability.) Therefore, ‘slicing away’ X by declining to assert or deny it will not decrease probability and will often increase it. As Sober puts it, ‘silence reduces your risk of error. The razor of silence has a simple Bayesian rationale’ (p. 71). I disagree. First, Y&X and Y are not actually competing hypotheses. Why shouldn’t I believe both? Or neither? While Sober himself is not a Bayesian and makes no recommendations in the book about what we ought to believe, Sober implies that this basic fact about probability tells us that if you are a Bayesian, then rather than believing Y&X you should believe Y and should suspend judgment on X. But what if X is actually true? Then by suspending judgment on X rather than believing it, you are believing fewer true things. Whether it is rational to believe X obviously depends on the evidence that you have for it. In some sense, suspending judgment on any of your beliefs at all would increase probability (namely, by increasing the probability that the conjunction of all your beliefs is true). It certainly doesn’t follow that there is a Bayesian rationale for doing so. The razor of silence is a principle about rational belief (or rational acceptance). Thus, in order to provide a rationale for this razor (or the razor of denial), you need a theory of rational belief. Bayesianism is not such a theory. Now, it might seem as though there is an obvious connection between Bayesianism and rational belief: Bayesianism tells us that we should have a degree of belief in every proposition and then we can simply accept some version of the Lockean thesis which connects degrees of belief to beliefs. For example, a simple version of this might be ‘It is rational to believe anything with probability > .5, rational to disbelieve anything with probability < .5 and rational to suspend judgment on propositions with probability = .5’. I am not claiming that this is a good principle of rationality, merely that it is the kind of principle which could relate to the razors of silence and denial. So, can such a principle justify the razor of silence? Of course, the key here is the antecedent: ‘your evidence does not discriminate between “X exists” and “X does not exist”’. But what exactly does this mean? If it means that Pr(X exists) = Pr(X does not exist) = .5 then it does seem reasonable to suspend judgment on X and our Lockean principle would entail this. However, this has nothing to do with the probabilities of conjunctions and it seems odd to call this a ‘Bayesian rationale’ for the razor. In addition, equal probability as an interpretation of ‘the evidence does not discriminate’ is problematic, since Sober often rejects the use of prior probabilities as unjustified. Sober’s favoured principle of evidence is The Law of Likelihood. It says that O favours H1 over H2 to the extent that P(O|H1) > P(O|H2). The natural consequence is that ‘evidence doesn’t discriminate between X and ∼X’ is P(E|X) = P(E|∼X). This equality is consistent with X having any probability between 0 and 1. For example, my evidence doesn’t discriminate between this ticket winning this large, fair lottery versus any other ticket winning. But in such a lottery, it is perfectly reasonable for me to have a very low degree of belief that this ticket will win. It therefore seems unreasonable that I should suspend judgment on this proposition. Instead, I should believe that I will lose. While this example doesn’t immediately deal with the existence of entities, it is easy to construct parallel cases that are about ontological matters. For a Soberesque example, despite its high likelihood, I should not believe that there are gremlins bowling in my attic (Sober 2008). In fact, I think that it is appropriate that I believe there are not gremlins rather than merely suspending judgment. For a plausible example that moves from low to high probability, my degree of belief that there is currently at least one ant within 100 feet of the front door of my house is extremely high – though it isn’t clear that my current evidence actually discriminates between the two relevant hypotheses. I have some inductive evidence about the past, plus a very general understanding of how common ants are where I live. But I have no direct evidence at all about whether there is right now an ant in that location. After all, I am in my office away from my home and my belief is not sensitive in any way to whether or not there is an ant within 100 feet of the front door of my house. Now, certainly, Bayesianism by itself doesn’t recommend that I suspend judgment on whether there are gremlins in my attic or ants near my front door. Contra Sober, the razor of silence has no Bayesian justification. What about the razor of denial? Unlike the razor of silence, Sober never suggests that the razor of denial has any kind of general justification. Since it is directly incompatible with the razor of silence, any justification for silence is thereby an argument against the razor of denial (and vice versa). In its full generality, the principle has serious problems. For example, if ‘the evidence doesn’t discriminate’ means that P(X) = P(∼X) = .5, it is certainly sometimes reasonable to suspend judgment rather than believe ∼X. If we take ‘the evidence doesn’t discriminate’ to mean P(O|X) = P(O|∼X), then we have cases where P(X) is quite high. But instead of thinking of the principle in full generality, we can instead consider special cases of it. Consider completely superfluous hypotheses. One clear conclusion is that our best scientific theories should not include such entities. Sometimes a theory doesn’t mention some particular entity and we take that merely to mean that the theory is silent on the question of whether the entity exists. But this is not always true. Consider the famous case of Einstein’s theory of special relativity, which is more parsimonious than Lorentz’s theory since special relativity denies the existence of the aether. Sober (1981) uses this example to argue that the razor of silence is incorrect since it conflicts with the razor of denial, which is sometimes justified! In the case of God, as mentioned before, it is common for atheists to cite Ockham’s Razor-like justifications. Why not believe in God? Sober considers the Problem of Evil – one common reason people cite for being an atheist. But here is one way out of that particular problem: ‘God’ is not actually perfectly good. Now I myself do not believe that there is an all-powerful, all-knowing being. (Set aside whether he is perfectly good.) What exactly justifies my belief that there is no such being? To bring out the puzzle clearly, imagine that such a being might not ever actually causally intervene in the world. On a purely likelihoodist understanding of evidential discrimination, it is hard to see how my evidence discriminates between this kind of God existing versus not existing. Perhaps the best thing to say is that the likelihoods are inscrutable rather than equal, but this does not give us a reason to deny this God’s existence. At this point, a reader might suggest that I don’t need Ockham’s Razor to justify my disbelief in such an entity. The prior probability of such a thing existing is so low that when combined with the fact that I have no evidence for or against it, it is rational to believe such a thing does not exist. I agree, though Sober (2008) is sceptical that prior probabilities for the existence of beings like this can be justified. If we do accept that the prior probability should be low, the obvious next question is: Why does the existence of such a being have a low probability in the first place? I suggest that whatever the answer to that question is, it will be a pretty good summary of (some version of) Ockham's Razor. In chapter 2, Sober points out that sometimes we call an explanation the ‘simplest’ when we mean that it is the best or most probable explanation. But where does this high probability come from? In standard cases, such as asking whether a patient has a rare or more common disease, simple induction based on past frequencies gives us rational justification for these priors. Sober makes the distinction between ‘first priors’ and ‘non-first priors’, which (I think) is meant to capture the idea that there is nothing necessarily unparsimonious about the hypotheses that have low prior probabilities if they are based on conditioning on past evidence. But what about first priors? This is precisely where Bayesians have thought that simplicity can matter. For example, Swinburne concludes his 2009 book Simplicity as Evidence for Truth with the following: ‘To summarise the claims in a nutshell: either science is irrational (in the way it judges theories and predictions probable) or the principle of simplicity is a fundamental synthetic a priori truth’ (p. 56). In some cases, I agree. I just disagree with Swinburne when he says that the God hypothesis is simple. I think it is much simpler to deny the existence of God and our respective beliefs about simplicity in part ground our prior probabilities for the existence of God. If you don’t like the God example, think of the mysterious creatures that I just made up: ‘can’t see ums’. If they did exist, I wouldn’t expect to have any evidence for their existence. After all, they are scared of humans and incredibly good at hiding. It seems to me completely appropriate to believe that they don’t exist rather than just suspending judgment. Evidence is a tricky notion, but I am inclined to say that I do not have any evidence that such creatures do not exist. Rather, there is a default presupposition of rational thinking that you should assume that totally ad hoc hypotheses with nothing to count in their favour can be summarily dismissed. With cases such as these, we are getting closer to understanding why the razor of denial sometimes seems justified. First, following Barnes (2000), let’s distinguish between a mere anti-quantity principle (positing fewer entities is better) and the weaker anti-superfluity principle, which says that theories should not contain superfluous components. (This is weaker since there are often theories with more components than another theory, but none of the components are superfluous.) Add to this another common distinction in the literature: the distinction between qualitative and quantitative parsimony. Lewis (1973, p. 87) distinguishes between qualitative and quantitative parsimony where qualitative parsimony is a matter of keeping down the number of kinds of entities while quantitative parsimony is a matter of minimising the number of entities within a kind. Lewis holds that while qualitative parsimony is a good thing in a philosophical or empirical hypothesis, quantitative parsimony is not relevant. There is a lively debate about the status of quantitative parsimony, but the authors all seem to agree with Lewis that there is a basic presumption in favour of qualitative parsimony (Baker 2016, Jansson and Tallant 2016, Nolan 1997). There is a clear pattern from the history of science: when a special type of entity is shown to be explanatorily superfluous, it is eliminated from scientific theories. There are numerous examples, such as privileged spatial and temporal locations, absolute space and time, phlogiston, the aether, vital forces, the soul and God. Many of these apparently led to specific predictions, which then turned out false. But at some point, all were posited in such a way that we don’t have direct observational evidence that they do not exist. But when they are thought to be explanatorily impotent and superfluous it is claimed that they do not exist. When someone wants to dispute this conclusion, they argue that in fact these entities are not superfluous. Rather, they are explanatorily powerful and therefore we do have evidence for their existence. No one ever responds in the following way: ‘You are correct, we have no evidence for vital forces. However, we should remain agnostic. Perhaps they exist, perhaps not’. When we do not know whether to believe in a special type of entity or not (for example, we aren’t sure if substance dualism is true) it is because we are not sure whether or not non-physical substances are in fact superfluous. These ‘denial inferences’ seem to me completely justified. Specifically, I would argue that conditionals such as ‘If the soul is explanatorily superfluous, then it doesn’t exist’ are justified. This seems to me a clear use of Ockham’s Razor. But here parsimony does not mirror likelihood or predictive accuracy. In chapter 5, Sober argues that we can use model selection techniques to see why the mind-body identity theory would be more predictively accurate than substance dualism: it uses fewer adjustable parameters. He might then suggest that similar considerations will work in the ‘undetectable God’ case and other cases of explanatorily superfluous entities. But even if he is right about dualism (and I don’t think he is, though reasons of space prevent me from arguing about this here), model selection techniques and statistical theorems such as Akaike’s theorem are not sufficiently broad to cover all the kinds of cases that the anti-superfluity principle will apply to. Perhaps there is some other fundamental epistemic virtue that parsimony mirrors in these cases. Sober leaves open that there may well be other parsimony paradigms. But I don’t know what they are. Sober is certainly correct that there are a wide variety of uses and justifications (good ones and bad ones) for Ockham’s Razor. But Sober also concludes that there is no non-reductive justification for the principle in any case. If we split cases finely so that we are looking at qualitative parsimony and cases of superfluous entities, I am not so sure. Here, perhaps Sober’s pluralism should make room for one more parsimony paradigm – a non-reductive one. References Baker Alan 2016 , ‘Simplicity’, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2016/entries/simplicity/>. Barnes E. C. 2000 , ‘Ockham’s Razor and the Anti-Superfluity Principle’ , Erkenntnis 53 , pp. 353 – 374 . Google Scholar CrossRef Search ADS Earman John 1992 , Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory ( Cambridge, MA : The MIT Press ). Hitchens Christopher 2007 , God is not Great: How Religion Poisons Everything ( New York : Twelve ). 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