The Haecceitic Euthyphro problem

The Haecceitic Euthyphro problem Abstract Haecceitism is the thesis that, necessarily, in addition to its qualities, each thing has a haecceity or individual essence. The purpose of this paper is to expose a flaw in haecceitism: it entails that familiar cases of fission and fusion either admit of no explanation or else only admit of explanations too bizarre to warrant serious consideration. Because the explanatory problem we raise for haecceitism closely resembles the Euthyphro problem for divine command theory, we refer to our objection as the haecceitic Euthyphro problem, or the Haecceitic Euthyphro for short. We conclude that the objection is decisive against haecceitism. 1. Introduction: Haecceitism Haecceitism is the thesis that, necessarily, in addition to its qualities, each thing has a haecceity or individual essence – an irreducible property the having of which is both necessary and sufficient for being identical to a specific individual. As an example, consider Socrates. Socrates has certain qualities: he is pale, snub-nosed and wise. Haecceitists hold that, in addition to qualities like these, there is a feature – call it ‘socraticity’ – which Socrates necessarily has and which nothing else could ever possibly have. Necessarily, anything that has socraticity is numerically identical to Socrates, and necessarily, anything that is numerically identical to Socrates has socraticity. Socrates cannot exist without socraticity nor can he share it with anything else. Haecceitists believe that every individual has a property that is as essential and particular to it as socraticity is to Socrates.1 2. The Haecceitic Euthyphro problem Consider a case of fission: a single amoeba, Maude, splits into two distinct amoebae: Rod and Todd. Put aside traditional questions about which of the two new amoebae, if either, is identical to the original – for our purposes, it doesn’t matter. The important fact is that where there used to be one individual, there are now two. So according to the haecceitist, it used to be the case that one haecceity was instantiated, but now two haecceities are instantiated instead. Our question is the following: did the amoeba split in two because two haecceities came to be instantiated, or did two haecceities come to be instantiated because the amoeba split in two? Between the change in the haecceities and the change in amoebae, which explains the other?2 Now consider a case of fusion: two amoebae, Rod and Todd, merge into a single amoeba, Maude. Again, put aside traditional questions of identity and focus on the fact that, where there used to be two individuals, there is now one. So according to the haecceitist, there used to be two instantiated haecceities, but now there is only one instantiated haecceity. Our question is this: did the two amoebae merge because their haecceities ceased to be instantiated, or did the haecceities cease to be instantiated because the two amoebae merged? Again, between the change in haecceities and the change in amoebae, which explains the other?3 For the haecceitist, cases of fission and fusion give rise to the question of whether facts about haecceities explain, or are explained by, facts about concrete individuals. Like the rest of us, the haecceitist believes in the generation and destruction of concrete individuals. But unlike the rest of us, the haecceitist takes such events to be accompanied by changes in the instantiation of individual essences. The problem arises when we ask which explains the other. Are individual essences instantiated because concrete individuals come into being? Or do concrete individuals come into being because their individual essences are instantiated? Do individual essences cease to be instantiated because concrete individuals are destroyed? Or are concrete individuals destroyed simply because their individual essences cease to be instantiated? Between the changes in haecceities and the changes in concrete individuals, which explains the other? There are only two possible responses to the Haecceitic Euthyphro, one of which is quite sensible but violates the principles of haecceitism, the other of which is consistent with haecceitism but thoroughly absurd. What the Haecceitic Euthyphro shows is that haecceitism comes at the cost of absurdity, namely that facts about perfectly ordinary physical events are due to obscure changes in purely abstract entities. To show why this is so, let us consider each option in turn. 3. Option 1: Generation and destruction explain instantiation One response to the Haecceitic Euthyphro is to claim that changes in haecceities are explained by the generation and destruction of things that have them. If this is correct, haecceities are instantiated as a result of concrete individuals' existing, and they cease being instantiated as a result of the concrete individuals’ ceasing to exist.4 This first option has the virtue of explaining obscure haecceitic facts in terms of more familiar facts about objects. Haecceities, after all, are mysterious. They contribute nothing to the qualitative character of their possessors, so their presence cannot be seen, smelt, or directly detected in any way.5 Even when instantiated they have no spatial location, since having a spatial location requires extension and size. Haecceities are obscure. If we must accept them – and the haecceitist says that we must – we’d like to understand them in more familiar terms. Just as immaterial mental states are easier to accept as epiphenomena, or as dependent by-products of physical changes, so is haecceitic instantiation easier to accept as a result of the generation and destruction of concrete individuals. In our initial case, there was nothing mysterious about how Rod and Todd came into existence; we already knew what fission is. If the instantiation of new haecceities is just a result of that, then the change in instantiation loses some of its mystery, and haecceitism becomes all the more agreeable. However, this response is incompatible with a particular argument for haecceitism, which goes something like this: consider a world W that contains a perfectly spherical object A, which is one mile in diameter and made of chemically pure iron, and a perfectly spherical object B, which is one mile in diameter and made of chemically pure iron (Black 1952).6 In W, A and B have exactly the same features. So how, asks the haecceitist, could they ever be distinct? In other words, what explains the fact that exactly similar objects are numerically different? Since A and B are exactly similar, we cannot show their distinctness by pointing out a quality that one has and the other lacks. Just stipulating that they are two does not make it so, and saying that one could exist without the other is just more stipulation. We could distinguish A and B by their relation to points in absolute space, but this commits us to points in space, which, intrinsically, are just as indiscernible as the spheres. Attempting to individuate them by the matter that constitutes them does not help either, since we still have to provide a criterion for distinguishing exactly similar materials – unless, of course, we smuggle haecceities in at the level of matter as we would at the level of property instances by appealing to tropes (Rosenberg 1996). Nor is it enough to point out that each sphere has the property of being a certain distance from an iron sphere, since a single sphere can be a certain distance from itself if space is curved (Hacking 1975), or if one and the same sphere is multiply located in the way an immanent universal is (O’Leary-Hawthorne 1995; Zimmerman 1997). For real numeric distinctness between exactly similar objects, concludes the haecceitist, we must posit haecceities as primitive individuators. A and B are distinct in virtue of the fact that they have distinct haecceities. A alone has the individual essence of A-ness, while B alone has the individual essence of B-ness. Call this the Diversity of Indiscernibles argument. Its conclusion is that haecceities are needed in order to explain the numeric distinctness between objects which, like A and B, are exactly similar in every respect. Haecceitists who accept the Diversity of Indiscernibles argument – including Adams, Rosenkrantz, and originally Scotus – explain the numeric distinctness of ordinary objects in terms of the instantiation of haecceities.7 By their lights, we have two spheres precisely because two sphere haecceities are instantiated, and if we have two amoebae, then the amoebae are two precisely because two amoeba haecceities are instantiated. Thus, in a chapter entitled ‘Haecceity: a metaphysical explanation of diversity', Gary Rosenkrantz writes that ‘we are entitled to infer the existence of non-qualitative haecceities as a plausible hypothesis which helps to explain the diversity of particulars at a time' (Rosenkrantz 1993: 130). Haecceities do their metaphysical work by being explanatorily prior to the numeric distinctness of the objects that have them. Even if someone accepts haecceities on the basis of a different argument – something other than the Diversity of Indiscernibles argument – a haecceitist will nonetheless likely appeal to haecceities in order to explain the possibility of two qualitatively similar objects. And that is all that is needed to make our point – once haecceities are introduced as an explanation for why it is that there can be numerically distinct, exactly similar objects, the haecceitist cannot then maintain that changes in haecceities are explained by the generation and destruction of things that have them. Returning to our original case of fission, in which Maude splits into Rod and Todd, we find the haecceitist explaining the resultant diversity in terms of haecceities. But what about the event of Maude’s splitting? In other words, what about the process which resulted in there being two amoebae? Must the haecceitist explain this in terms of haecceities as well? We think she does. Here’s why. The very idea of splitting presupposes numeric diversity. Maude could not have split unless doing so resulted in additional individuals. To even say ‘Maude is splitting’ presupposes this resultant diversity. If we ask what makes it true that Maude is splitting, as opposed to doing something else, like dancing or thinking, part of the answer must cite the fact that more than one individual is involved. Maude’s splitting, in other words, is made possible by the phenomenon of numeric diversity. This is reason enough to think that numeric diversity is part of the metaphysical explanation of fission, rather than something that is explained by it. Returning now to our original case, suppose for reductio that both (i) the changes in haecceitic instantiation are explained in terms of Maude’s splitting and that (ii) the diversity that results from Maude’s splitting is explained in terms of the instantiation of haecceities. The problem is that Maude’s splitting is itself explained in terms of numeric diversity. Maude’s splitting is made possible by numeric diversity, which is to say that numeric diversity is part of the metaphysical explanation of the splitting. But because such diversity is itself explained in terms of the instantiation of haecceities, it follows that, contrary to (i), the event of Maude’s splitting is explained in terms of haecceitic instantiation. Therefore, it cannot be that generation and destruction explain changes in haecceities; rather, it must be that changes in haecceities explain generation and destruction. On pain of circularity, then, the haecceitist cannot explain the instantiation of individual essences in terms of the generation and destruction of concrete individuals. She cannot remove haecceities’ mystery by grounding them in more familiar phenomena. So the most plausible response to the Haecceitic Euthyphro, which is to claim that two haecceities are instantiated as a result of Maude's splitting, is unavailable to the haecceitist. There is only one other response to the Haecceitic Euthyphro, which is to say that Maude splits as a result of two haecceities coming to be instantiated. As we will see, this second option is no better than the first. 4. Option 2: Instantiation explains generation and destruction Suppose, then, that Maude's splitting is due to activity at the level of haecceities – that the generation and destruction of concrete individuals is explained by changes in their individual essences. If this is correct, objects begin to exist because their haecceities come to be instantiated, and they cease to exist because their haecceities cease being instantiated. The idea that generation and destruction is due to activity among abstract entities is not a new one; its roots go back to Plato, who in the Phaedrus describes how immaterial souls, in their desire to know the Forms, inadvertently descend from the abstract realm and acquire bodies. Once embodied, they retain only vague recollections of their former residence, and, whether aware of it or not, strive in overwhelming ignorance to return. Later Platonists like Apuleius symbolise this account with the tale of Psyche and Eros, lovers whom the gods separated when the former broke her promise to remain blindfolded in the presence of the latter. However, mythology is one thing, metaphysics another, and although systematic thinkers like Proclus have attempted to provide non-metaphorical accounts of instantiation in terms of logical and intentional relations, the resulting story of curiosity and lost love is thematically the same. However poetic, the Platonic account of haecceitic instantiation is, at best, severely underdeveloped, and at worst absurd. It will not do. Unfortunately, other accounts of haecceitic activity have yet to appear in the literature. We can imagine how a few such options would go, but ultimately, they appear to fare no better than the Platonic account. They are as follows: 4.1 Splitting haecceities In the case of Maude, two haecceities came to be instantiated in the same way that two new amoebae came into existence. The original haecceity, like the original amoeba, split, leaving two new haecceities in its place. 4.2 Objection to splitting haecceities This response requires haecceities to be capable of fission, yet fission is something that only happens to extended bodies. Simple abstracta cannot split. If you tell us that a certain thing, Tim, was created when it split off from Tom, and that Tom was not thereby diminished in any way, it will no longer be clear what you mean by ‘split’. We might speak of splitting a conjunction into its conjuncts, or of splitting an angle by bisecting it, or of splitting a quantity by dividing it by two, but such operations can only be understood within the well-defined procedures of logic and mathematics. Splitting a haecceity in this sense is completely different from bisecting an angle; there is no abstract science of haecceities with rules for splitting and combining haecceities in the way that there is an abstract science of splitting and combining angles and any attempt to produce one is likely to assume, rather than explain, the phenomenon of splitting in question. Here, we maintain that haecceities are mereologically simple, but one might disagree with this assumption, and instead claim that the parts of a thing’s haecceity are just the haecceities of that thing’s parts.8 On this proposal, a material object such as a table, t, may have a table leg, l, as a part; and since l and t are distinct, each will have a distinct haecceity. The leg l has a haecceity, hl, and t has a haecceity, ht, where hl≠ ht. One might then claim that the following principle is intuitive: l is part of t iff hl is part of ht. In other words, the parts of the table’s haecceity are just the haecceities of the table’s parts. It seems like an elegant idea. Moreover, unlike Armstrong’s (1986) allegedly ‘mereological’ relations, which unite structural universals, this relation among haecceities would obey extensionality. Why not accept it?9 Here’s why: to solve the Haecceitic Euthyphro, it is not enough to explain how a haecceity could have parts. One also needs an explanation for why these parts behave as they do – i.e. splitting and joining. In other words, to make sense of the idea that Maude’s haecceity splits in half, we not only need to make sense of what half her haecceity would be (it’s the haecceity of her half!); we also need to make sense of why and how a haecceity would split in the first place. What kind of force, or what kind of causal chain, could be responsible, here? Why would haecceities be splitting and joining, if not because of the splitting and joining of their possessors? Again, philosophical history has already witnessed answers, which, though beautiful, fall short of explanatory adequacy: do haecceities split as a result of crashing down from heaven, as Plato’s allegory in the Phaedrus, and Apuleius’ Tale of Psyche and Eros, would suggest? Certainly not, unless we discover some literal meaning to the central metaphor of descent. Do haecceities split as a result of evaluative differences among their parts, as McTaggart would have souls split across his C-series? Certainly not, lest we attribute qualities to haecceities, and endow every case of fusion or fission with value. Do haecceities split as a result of theurgic forces, as Proclus would suggest? Certainly not, for that is literal magic. Nor should we suppose that haecceities split as a result of physical force, lest we turn haecceities into a mysterious kind of material object – one which, though invisible, is always co-located with its possessor, and which must be split apart for its possessor to be split apart. For the theory of splitting haecceities to work, in other words, there must be an answer for why they split. There must be an explanation for how change is effected among haecceities, and it must fare better than existing proposals. Splitting haecceities is therefore no solution to the Haecceitic Euthyphro. Let us examine another. 4.3 Intensive diminution The new haecceities come into existence from the old one, but not by splitting. Rather, the new ones come into being through a diminution of the old one’s intensity, as when one incredibly bright light source splits into two dimmer light sources of the same size. 4.4 Objection to intensive diminution What exactly is this feature of haecceities, whose magnitude, modelled on light, increases with the fusion of their possessors and decreases with their fission? What exactly is the ‘brightness’ of haecceities? Whatever it is, a haecceity’s intensity will have to vary in proportion to the degree that its possessor is composite. A simple item that is incapable of splitting would be dim, combinations of them would get increasingly brighter and the whole cosmos would be at maximum brightness. But such elaborations still proceed analogically. Just as we demand an account of splitting from the previous proposal, so do we demand an account of dimming from this one. Both the splitting and the intensive diminution accounts of haecceitic activity raise more questions – and harder ones! – than the one they purport to answer. The Platonic account is either absurd or severely underdeveloped. Yet unless the haecceitist can produce another one, she is committed to one of the three. We take this as a reductio against haecceitism. What the Haecceitic Euthyphro shows is that ordinary cases of fission and fusion either admit of no explanation at all or else admit of explanations too bizarre to take seriously. 5. A third option? We close our discussion by considering just one more view – one which answers the Haecceitic Euthyphro but which no haecceitist would want to accept, namely the idea that a concrete individual is identical to its instantiated haecceity. According to this view, Maude just is the instantiation of her individual essence, and the event of her destruction just is the event of her haecceity’s ceasing to be instantiated. In general, this view holds that the generation and destruction of concrete individuals is identical to the instantiation and – for lack of a better word – uninstantiation of individual essences, respectively. By identifying a concrete individual with the instantiation of its individual essence, the haecceitist can avoid having to answer the troublesome question of which one explains the other’s existence. Under such an account, the question makes no sense; one may as well ask whether a certain astral body is the Morning Star because it is the Evening Star, or whether it is the Evening Star because it is the Morning Star. Since the Morning Star just is the Evening Star, the question of which explains the other does not arise. So there is indeed one view that circumvents the Haecceitic Euthyphro. Why shouldn’t the haecceitist take it? The reason why the haecceitist should not take it is that it turns the Diversity of Indiscernibles argument into an exercise in question begging. What makes it the case that there are two spheres instead of one? The haecceitist says that there are two spheres instead of one because two haecceities are instantiated instead of one. But if each sphere is identical to the instantiation of its haecceity, then the haecceitist’s claim amounts to nothing more than a reassertion that there are two spheres. In other words, to identify concrete individuals with the instantiation of their essences would be to give up the idea that haecceities explain numeric diversity; the claim ‘there are two spheres because there are two instantiated haecceities’ becomes ‘there are two spheres because there are two spheres’. And this, like all circular explanations, is repugnant to the intellect.10 Footnotes 1 Following Lewis (1986: 221), we might define haecceitism differently, as the denial of a supervenience thesis rather than as an existence claim. We’ll call Lewis's version, which he defines but does not accept, independence haecceitism, and the version accepted by Rosenkrantz (1993) and Plantinga (1974: 62–7), full-blown haecceitism. Independence haecceitists agree with full-blown haecceitists that the qualitative character of a world does not settle the question of which things exist in it – i.e. they agree that two worlds can be exactly similar but differ with respect to which individuals exist in them – but unlike full-blown haecceitists, independence haecceitists do not defend the existence of individual essences. In other words, independence haecceitists hold that individuality is brute; nothing makes two exactly similar individuals distinct from one another. Full-blown haecceitists hold that individuality is not brute; haecceities are needed precisely to account for numeric differences between individuals. Contemporary independence haecceitists include Lycan (1994: 95–127) and Hofweber (2005). Adams (1979) argues that his ‘moderate haecceitism’ is of the independent variety, but his use of haecceities as truthmakers in the philosophy of time Adams (1986) strongly suggests otherwise, especially since the sort of use to which he puts them is exactly the sort that commits Plantinga (1974) to full-blown haecceitism.  Because the Haecceitic Euthyphro concerns the relationship between a thing and its individual essence, it does not arise for independence haecceitists unless independence haecceitism entails its full-blown counterpart. Whether it does is a question that will not be taken up in this article. 2 If you think Maude survives the split, just ask the question this way: did the amoeba split because a new haecceity came to be instantiated alongside the old one, or did a new haecceity come to be instantiated alongside the old one because the amoeba split? 3 If you think either Rod or Todd survives the merge, just ask the question this way: did the amoebae merge because of one of their haecceities ceased to be instantiated, or did one of their haecceities cease to be instantiated because they merged? 4 This ‘resulting’ is not temporal; it does not require haecceities to be instantiated some moment after the generation of the things that have them. Rather, the dependence between haecceity and object, like the dependence between the love of Euthyphro’s gods and the piety of the actions they love, is atemporal. This makes our challenge to the haecceitist somewhat obscure, but no more obscure than Socrates’ own challenge to Euthyphro. Since the latter is easily grasped by professional philosophers and undergraduates alike, we claim that our challenge is legitimate. 5 Rosenkrantz (1993: 184–241), however, holds that every self-conscious individual can detect its own haecceity. 6 Scotus’s original presentation of the problem appeals to examples of rocks and rays of sunlight rather than to iron spheres (Spade 1994: 61, 65). 7 There may be some debate as to whether Adams (1979) explicitly endorses Diversity of Indiscernibles argument (or something like it). Nonetheless, Adams clearly endorses haecceities as an explanation for the possibility of numerically distinct, exactly similar objects, and that is all that is needed to make our point. See below. Thanks to an anonymous referee for raising this issue. 8 An object is mereologically simple iff it has no proper parts. 9 Thanks to an anonymous referee for raising this issue. A relation obeys extensionality if it prohibits any whole from having the same part ‘many times over’, and if it allows any collection of parts to compose at most one whole. 10 We would like to thank the anonymous referees at Analysis for their helpful comments. References Adams R.M. 1979. Primitive thisness and primitive identity. Journal of Philosophy  76: 5– 26. Google Scholar CrossRef Search ADS   Adams R.M. 1986. Time and thisness. Midwest Studies in Philosophy  11: 315– 29. Google Scholar CrossRef Search ADS   Armstrong D.M. 1986. A defense of structural universals. Australasian Journal of Philosophy  64: 85– 9. Google Scholar CrossRef Search ADS   Black M. 1952. The identity of indiscernibles. Mind 61: 153– 164. Hacking I. 1975. The identity of indiscernibles. Journal of Philosophy  72: 249– 56. Google Scholar CrossRef Search ADS   Hofweber T. 2005. Supervenience and object-dependent properties. Journal of Philosophy  102: 5– 32. Google Scholar CrossRef Search ADS   Lewis D. 1986. On the Plurality of Worlds . Oxford: Oxford University Press. Lycan W.G. 1994. Modality and Meaning . New York: Springer. Google Scholar CrossRef Search ADS   O’Leary-Hawthorne J. 1995. The bundle theory of substance and the identity of indiscernibles. Analysis  55: 191– 6. Google Scholar CrossRef Search ADS   Plantinga A. 1974. The Nature of Necessity . Oxford: Oxford University Press. Rosenberg J.F. 1996. On a certain antinomy: properties, concepts, and items in space. Philosophical Perspectives  10: 357– 83. Rosenkrantz G. 1993. Haecceity: An Ontological Essay . New York: Springer Academic Publications. Google Scholar CrossRef Search ADS   Spade P.V. 1994. Five Texts on the Mediaeval Problem of Universals: Porphyry, Boethius, Abelard, Duns Scotus, Ockham . Indianapolis: Hackett. Zimmerman D. 1997. Distinct indiscernibles and the bundle theory. Mind  106: 305– 9. Google Scholar CrossRef Search ADS   © The Authors 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: journals.permissions@oup.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis Oxford University Press

The Haecceitic Euthyphro problem

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Abstract

Abstract Haecceitism is the thesis that, necessarily, in addition to its qualities, each thing has a haecceity or individual essence. The purpose of this paper is to expose a flaw in haecceitism: it entails that familiar cases of fission and fusion either admit of no explanation or else only admit of explanations too bizarre to warrant serious consideration. Because the explanatory problem we raise for haecceitism closely resembles the Euthyphro problem for divine command theory, we refer to our objection as the haecceitic Euthyphro problem, or the Haecceitic Euthyphro for short. We conclude that the objection is decisive against haecceitism. 1. Introduction: Haecceitism Haecceitism is the thesis that, necessarily, in addition to its qualities, each thing has a haecceity or individual essence – an irreducible property the having of which is both necessary and sufficient for being identical to a specific individual. As an example, consider Socrates. Socrates has certain qualities: he is pale, snub-nosed and wise. Haecceitists hold that, in addition to qualities like these, there is a feature – call it ‘socraticity’ – which Socrates necessarily has and which nothing else could ever possibly have. Necessarily, anything that has socraticity is numerically identical to Socrates, and necessarily, anything that is numerically identical to Socrates has socraticity. Socrates cannot exist without socraticity nor can he share it with anything else. Haecceitists believe that every individual has a property that is as essential and particular to it as socraticity is to Socrates.1 2. The Haecceitic Euthyphro problem Consider a case of fission: a single amoeba, Maude, splits into two distinct amoebae: Rod and Todd. Put aside traditional questions about which of the two new amoebae, if either, is identical to the original – for our purposes, it doesn’t matter. The important fact is that where there used to be one individual, there are now two. So according to the haecceitist, it used to be the case that one haecceity was instantiated, but now two haecceities are instantiated instead. Our question is the following: did the amoeba split in two because two haecceities came to be instantiated, or did two haecceities come to be instantiated because the amoeba split in two? Between the change in the haecceities and the change in amoebae, which explains the other?2 Now consider a case of fusion: two amoebae, Rod and Todd, merge into a single amoeba, Maude. Again, put aside traditional questions of identity and focus on the fact that, where there used to be two individuals, there is now one. So according to the haecceitist, there used to be two instantiated haecceities, but now there is only one instantiated haecceity. Our question is this: did the two amoebae merge because their haecceities ceased to be instantiated, or did the haecceities cease to be instantiated because the two amoebae merged? Again, between the change in haecceities and the change in amoebae, which explains the other?3 For the haecceitist, cases of fission and fusion give rise to the question of whether facts about haecceities explain, or are explained by, facts about concrete individuals. Like the rest of us, the haecceitist believes in the generation and destruction of concrete individuals. But unlike the rest of us, the haecceitist takes such events to be accompanied by changes in the instantiation of individual essences. The problem arises when we ask which explains the other. Are individual essences instantiated because concrete individuals come into being? Or do concrete individuals come into being because their individual essences are instantiated? Do individual essences cease to be instantiated because concrete individuals are destroyed? Or are concrete individuals destroyed simply because their individual essences cease to be instantiated? Between the changes in haecceities and the changes in concrete individuals, which explains the other? There are only two possible responses to the Haecceitic Euthyphro, one of which is quite sensible but violates the principles of haecceitism, the other of which is consistent with haecceitism but thoroughly absurd. What the Haecceitic Euthyphro shows is that haecceitism comes at the cost of absurdity, namely that facts about perfectly ordinary physical events are due to obscure changes in purely abstract entities. To show why this is so, let us consider each option in turn. 3. Option 1: Generation and destruction explain instantiation One response to the Haecceitic Euthyphro is to claim that changes in haecceities are explained by the generation and destruction of things that have them. If this is correct, haecceities are instantiated as a result of concrete individuals' existing, and they cease being instantiated as a result of the concrete individuals’ ceasing to exist.4 This first option has the virtue of explaining obscure haecceitic facts in terms of more familiar facts about objects. Haecceities, after all, are mysterious. They contribute nothing to the qualitative character of their possessors, so their presence cannot be seen, smelt, or directly detected in any way.5 Even when instantiated they have no spatial location, since having a spatial location requires extension and size. Haecceities are obscure. If we must accept them – and the haecceitist says that we must – we’d like to understand them in more familiar terms. Just as immaterial mental states are easier to accept as epiphenomena, or as dependent by-products of physical changes, so is haecceitic instantiation easier to accept as a result of the generation and destruction of concrete individuals. In our initial case, there was nothing mysterious about how Rod and Todd came into existence; we already knew what fission is. If the instantiation of new haecceities is just a result of that, then the change in instantiation loses some of its mystery, and haecceitism becomes all the more agreeable. However, this response is incompatible with a particular argument for haecceitism, which goes something like this: consider a world W that contains a perfectly spherical object A, which is one mile in diameter and made of chemically pure iron, and a perfectly spherical object B, which is one mile in diameter and made of chemically pure iron (Black 1952).6 In W, A and B have exactly the same features. So how, asks the haecceitist, could they ever be distinct? In other words, what explains the fact that exactly similar objects are numerically different? Since A and B are exactly similar, we cannot show their distinctness by pointing out a quality that one has and the other lacks. Just stipulating that they are two does not make it so, and saying that one could exist without the other is just more stipulation. We could distinguish A and B by their relation to points in absolute space, but this commits us to points in space, which, intrinsically, are just as indiscernible as the spheres. Attempting to individuate them by the matter that constitutes them does not help either, since we still have to provide a criterion for distinguishing exactly similar materials – unless, of course, we smuggle haecceities in at the level of matter as we would at the level of property instances by appealing to tropes (Rosenberg 1996). Nor is it enough to point out that each sphere has the property of being a certain distance from an iron sphere, since a single sphere can be a certain distance from itself if space is curved (Hacking 1975), or if one and the same sphere is multiply located in the way an immanent universal is (O’Leary-Hawthorne 1995; Zimmerman 1997). For real numeric distinctness between exactly similar objects, concludes the haecceitist, we must posit haecceities as primitive individuators. A and B are distinct in virtue of the fact that they have distinct haecceities. A alone has the individual essence of A-ness, while B alone has the individual essence of B-ness. Call this the Diversity of Indiscernibles argument. Its conclusion is that haecceities are needed in order to explain the numeric distinctness between objects which, like A and B, are exactly similar in every respect. Haecceitists who accept the Diversity of Indiscernibles argument – including Adams, Rosenkrantz, and originally Scotus – explain the numeric distinctness of ordinary objects in terms of the instantiation of haecceities.7 By their lights, we have two spheres precisely because two sphere haecceities are instantiated, and if we have two amoebae, then the amoebae are two precisely because two amoeba haecceities are instantiated. Thus, in a chapter entitled ‘Haecceity: a metaphysical explanation of diversity', Gary Rosenkrantz writes that ‘we are entitled to infer the existence of non-qualitative haecceities as a plausible hypothesis which helps to explain the diversity of particulars at a time' (Rosenkrantz 1993: 130). Haecceities do their metaphysical work by being explanatorily prior to the numeric distinctness of the objects that have them. Even if someone accepts haecceities on the basis of a different argument – something other than the Diversity of Indiscernibles argument – a haecceitist will nonetheless likely appeal to haecceities in order to explain the possibility of two qualitatively similar objects. And that is all that is needed to make our point – once haecceities are introduced as an explanation for why it is that there can be numerically distinct, exactly similar objects, the haecceitist cannot then maintain that changes in haecceities are explained by the generation and destruction of things that have them. Returning to our original case of fission, in which Maude splits into Rod and Todd, we find the haecceitist explaining the resultant diversity in terms of haecceities. But what about the event of Maude’s splitting? In other words, what about the process which resulted in there being two amoebae? Must the haecceitist explain this in terms of haecceities as well? We think she does. Here’s why. The very idea of splitting presupposes numeric diversity. Maude could not have split unless doing so resulted in additional individuals. To even say ‘Maude is splitting’ presupposes this resultant diversity. If we ask what makes it true that Maude is splitting, as opposed to doing something else, like dancing or thinking, part of the answer must cite the fact that more than one individual is involved. Maude’s splitting, in other words, is made possible by the phenomenon of numeric diversity. This is reason enough to think that numeric diversity is part of the metaphysical explanation of fission, rather than something that is explained by it. Returning now to our original case, suppose for reductio that both (i) the changes in haecceitic instantiation are explained in terms of Maude’s splitting and that (ii) the diversity that results from Maude’s splitting is explained in terms of the instantiation of haecceities. The problem is that Maude’s splitting is itself explained in terms of numeric diversity. Maude’s splitting is made possible by numeric diversity, which is to say that numeric diversity is part of the metaphysical explanation of the splitting. But because such diversity is itself explained in terms of the instantiation of haecceities, it follows that, contrary to (i), the event of Maude’s splitting is explained in terms of haecceitic instantiation. Therefore, it cannot be that generation and destruction explain changes in haecceities; rather, it must be that changes in haecceities explain generation and destruction. On pain of circularity, then, the haecceitist cannot explain the instantiation of individual essences in terms of the generation and destruction of concrete individuals. She cannot remove haecceities’ mystery by grounding them in more familiar phenomena. So the most plausible response to the Haecceitic Euthyphro, which is to claim that two haecceities are instantiated as a result of Maude's splitting, is unavailable to the haecceitist. There is only one other response to the Haecceitic Euthyphro, which is to say that Maude splits as a result of two haecceities coming to be instantiated. As we will see, this second option is no better than the first. 4. Option 2: Instantiation explains generation and destruction Suppose, then, that Maude's splitting is due to activity at the level of haecceities – that the generation and destruction of concrete individuals is explained by changes in their individual essences. If this is correct, objects begin to exist because their haecceities come to be instantiated, and they cease to exist because their haecceities cease being instantiated. The idea that generation and destruction is due to activity among abstract entities is not a new one; its roots go back to Plato, who in the Phaedrus describes how immaterial souls, in their desire to know the Forms, inadvertently descend from the abstract realm and acquire bodies. Once embodied, they retain only vague recollections of their former residence, and, whether aware of it or not, strive in overwhelming ignorance to return. Later Platonists like Apuleius symbolise this account with the tale of Psyche and Eros, lovers whom the gods separated when the former broke her promise to remain blindfolded in the presence of the latter. However, mythology is one thing, metaphysics another, and although systematic thinkers like Proclus have attempted to provide non-metaphorical accounts of instantiation in terms of logical and intentional relations, the resulting story of curiosity and lost love is thematically the same. However poetic, the Platonic account of haecceitic instantiation is, at best, severely underdeveloped, and at worst absurd. It will not do. Unfortunately, other accounts of haecceitic activity have yet to appear in the literature. We can imagine how a few such options would go, but ultimately, they appear to fare no better than the Platonic account. They are as follows: 4.1 Splitting haecceities In the case of Maude, two haecceities came to be instantiated in the same way that two new amoebae came into existence. The original haecceity, like the original amoeba, split, leaving two new haecceities in its place. 4.2 Objection to splitting haecceities This response requires haecceities to be capable of fission, yet fission is something that only happens to extended bodies. Simple abstracta cannot split. If you tell us that a certain thing, Tim, was created when it split off from Tom, and that Tom was not thereby diminished in any way, it will no longer be clear what you mean by ‘split’. We might speak of splitting a conjunction into its conjuncts, or of splitting an angle by bisecting it, or of splitting a quantity by dividing it by two, but such operations can only be understood within the well-defined procedures of logic and mathematics. Splitting a haecceity in this sense is completely different from bisecting an angle; there is no abstract science of haecceities with rules for splitting and combining haecceities in the way that there is an abstract science of splitting and combining angles and any attempt to produce one is likely to assume, rather than explain, the phenomenon of splitting in question. Here, we maintain that haecceities are mereologically simple, but one might disagree with this assumption, and instead claim that the parts of a thing’s haecceity are just the haecceities of that thing’s parts.8 On this proposal, a material object such as a table, t, may have a table leg, l, as a part; and since l and t are distinct, each will have a distinct haecceity. The leg l has a haecceity, hl, and t has a haecceity, ht, where hl≠ ht. One might then claim that the following principle is intuitive: l is part of t iff hl is part of ht. In other words, the parts of the table’s haecceity are just the haecceities of the table’s parts. It seems like an elegant idea. Moreover, unlike Armstrong’s (1986) allegedly ‘mereological’ relations, which unite structural universals, this relation among haecceities would obey extensionality. Why not accept it?9 Here’s why: to solve the Haecceitic Euthyphro, it is not enough to explain how a haecceity could have parts. One also needs an explanation for why these parts behave as they do – i.e. splitting and joining. In other words, to make sense of the idea that Maude’s haecceity splits in half, we not only need to make sense of what half her haecceity would be (it’s the haecceity of her half!); we also need to make sense of why and how a haecceity would split in the first place. What kind of force, or what kind of causal chain, could be responsible, here? Why would haecceities be splitting and joining, if not because of the splitting and joining of their possessors? Again, philosophical history has already witnessed answers, which, though beautiful, fall short of explanatory adequacy: do haecceities split as a result of crashing down from heaven, as Plato’s allegory in the Phaedrus, and Apuleius’ Tale of Psyche and Eros, would suggest? Certainly not, unless we discover some literal meaning to the central metaphor of descent. Do haecceities split as a result of evaluative differences among their parts, as McTaggart would have souls split across his C-series? Certainly not, lest we attribute qualities to haecceities, and endow every case of fusion or fission with value. Do haecceities split as a result of theurgic forces, as Proclus would suggest? Certainly not, for that is literal magic. Nor should we suppose that haecceities split as a result of physical force, lest we turn haecceities into a mysterious kind of material object – one which, though invisible, is always co-located with its possessor, and which must be split apart for its possessor to be split apart. For the theory of splitting haecceities to work, in other words, there must be an answer for why they split. There must be an explanation for how change is effected among haecceities, and it must fare better than existing proposals. Splitting haecceities is therefore no solution to the Haecceitic Euthyphro. Let us examine another. 4.3 Intensive diminution The new haecceities come into existence from the old one, but not by splitting. Rather, the new ones come into being through a diminution of the old one’s intensity, as when one incredibly bright light source splits into two dimmer light sources of the same size. 4.4 Objection to intensive diminution What exactly is this feature of haecceities, whose magnitude, modelled on light, increases with the fusion of their possessors and decreases with their fission? What exactly is the ‘brightness’ of haecceities? Whatever it is, a haecceity’s intensity will have to vary in proportion to the degree that its possessor is composite. A simple item that is incapable of splitting would be dim, combinations of them would get increasingly brighter and the whole cosmos would be at maximum brightness. But such elaborations still proceed analogically. Just as we demand an account of splitting from the previous proposal, so do we demand an account of dimming from this one. Both the splitting and the intensive diminution accounts of haecceitic activity raise more questions – and harder ones! – than the one they purport to answer. The Platonic account is either absurd or severely underdeveloped. Yet unless the haecceitist can produce another one, she is committed to one of the three. We take this as a reductio against haecceitism. What the Haecceitic Euthyphro shows is that ordinary cases of fission and fusion either admit of no explanation at all or else admit of explanations too bizarre to take seriously. 5. A third option? We close our discussion by considering just one more view – one which answers the Haecceitic Euthyphro but which no haecceitist would want to accept, namely the idea that a concrete individual is identical to its instantiated haecceity. According to this view, Maude just is the instantiation of her individual essence, and the event of her destruction just is the event of her haecceity’s ceasing to be instantiated. In general, this view holds that the generation and destruction of concrete individuals is identical to the instantiation and – for lack of a better word – uninstantiation of individual essences, respectively. By identifying a concrete individual with the instantiation of its individual essence, the haecceitist can avoid having to answer the troublesome question of which one explains the other’s existence. Under such an account, the question makes no sense; one may as well ask whether a certain astral body is the Morning Star because it is the Evening Star, or whether it is the Evening Star because it is the Morning Star. Since the Morning Star just is the Evening Star, the question of which explains the other does not arise. So there is indeed one view that circumvents the Haecceitic Euthyphro. Why shouldn’t the haecceitist take it? The reason why the haecceitist should not take it is that it turns the Diversity of Indiscernibles argument into an exercise in question begging. What makes it the case that there are two spheres instead of one? The haecceitist says that there are two spheres instead of one because two haecceities are instantiated instead of one. But if each sphere is identical to the instantiation of its haecceity, then the haecceitist’s claim amounts to nothing more than a reassertion that there are two spheres. In other words, to identify concrete individuals with the instantiation of their essences would be to give up the idea that haecceities explain numeric diversity; the claim ‘there are two spheres because there are two instantiated haecceities’ becomes ‘there are two spheres because there are two spheres’. And this, like all circular explanations, is repugnant to the intellect.10 Footnotes 1 Following Lewis (1986: 221), we might define haecceitism differently, as the denial of a supervenience thesis rather than as an existence claim. We’ll call Lewis's version, which he defines but does not accept, independence haecceitism, and the version accepted by Rosenkrantz (1993) and Plantinga (1974: 62–7), full-blown haecceitism. Independence haecceitists agree with full-blown haecceitists that the qualitative character of a world does not settle the question of which things exist in it – i.e. they agree that two worlds can be exactly similar but differ with respect to which individuals exist in them – but unlike full-blown haecceitists, independence haecceitists do not defend the existence of individual essences. In other words, independence haecceitists hold that individuality is brute; nothing makes two exactly similar individuals distinct from one another. Full-blown haecceitists hold that individuality is not brute; haecceities are needed precisely to account for numeric differences between individuals. Contemporary independence haecceitists include Lycan (1994: 95–127) and Hofweber (2005). Adams (1979) argues that his ‘moderate haecceitism’ is of the independent variety, but his use of haecceities as truthmakers in the philosophy of time Adams (1986) strongly suggests otherwise, especially since the sort of use to which he puts them is exactly the sort that commits Plantinga (1974) to full-blown haecceitism.  Because the Haecceitic Euthyphro concerns the relationship between a thing and its individual essence, it does not arise for independence haecceitists unless independence haecceitism entails its full-blown counterpart. Whether it does is a question that will not be taken up in this article. 2 If you think Maude survives the split, just ask the question this way: did the amoeba split because a new haecceity came to be instantiated alongside the old one, or did a new haecceity come to be instantiated alongside the old one because the amoeba split? 3 If you think either Rod or Todd survives the merge, just ask the question this way: did the amoebae merge because of one of their haecceities ceased to be instantiated, or did one of their haecceities cease to be instantiated because they merged? 4 This ‘resulting’ is not temporal; it does not require haecceities to be instantiated some moment after the generation of the things that have them. Rather, the dependence between haecceity and object, like the dependence between the love of Euthyphro’s gods and the piety of the actions they love, is atemporal. This makes our challenge to the haecceitist somewhat obscure, but no more obscure than Socrates’ own challenge to Euthyphro. Since the latter is easily grasped by professional philosophers and undergraduates alike, we claim that our challenge is legitimate. 5 Rosenkrantz (1993: 184–241), however, holds that every self-conscious individual can detect its own haecceity. 6 Scotus’s original presentation of the problem appeals to examples of rocks and rays of sunlight rather than to iron spheres (Spade 1994: 61, 65). 7 There may be some debate as to whether Adams (1979) explicitly endorses Diversity of Indiscernibles argument (or something like it). Nonetheless, Adams clearly endorses haecceities as an explanation for the possibility of numerically distinct, exactly similar objects, and that is all that is needed to make our point. See below. Thanks to an anonymous referee for raising this issue. 8 An object is mereologically simple iff it has no proper parts. 9 Thanks to an anonymous referee for raising this issue. A relation obeys extensionality if it prohibits any whole from having the same part ‘many times over’, and if it allows any collection of parts to compose at most one whole. 10 We would like to thank the anonymous referees at Analysis for their helpful comments. References Adams R.M. 1979. Primitive thisness and primitive identity. Journal of Philosophy  76: 5– 26. Google Scholar CrossRef Search ADS   Adams R.M. 1986. Time and thisness. Midwest Studies in Philosophy  11: 315– 29. Google Scholar CrossRef Search ADS   Armstrong D.M. 1986. A defense of structural universals. Australasian Journal of Philosophy  64: 85– 9. Google Scholar CrossRef Search ADS   Black M. 1952. The identity of indiscernibles. Mind 61: 153– 164. Hacking I. 1975. The identity of indiscernibles. Journal of Philosophy  72: 249– 56. Google Scholar CrossRef Search ADS   Hofweber T. 2005. Supervenience and object-dependent properties. Journal of Philosophy  102: 5– 32. Google Scholar CrossRef Search ADS   Lewis D. 1986. On the Plurality of Worlds . Oxford: Oxford University Press. Lycan W.G. 1994. Modality and Meaning . New York: Springer. Google Scholar CrossRef Search ADS   O’Leary-Hawthorne J. 1995. The bundle theory of substance and the identity of indiscernibles. Analysis  55: 191– 6. Google Scholar CrossRef Search ADS   Plantinga A. 1974. The Nature of Necessity . Oxford: Oxford University Press. Rosenberg J.F. 1996. On a certain antinomy: properties, concepts, and items in space. Philosophical Perspectives  10: 357– 83. Rosenkrantz G. 1993. Haecceity: An Ontological Essay . New York: Springer Academic Publications. Google Scholar CrossRef Search ADS   Spade P.V. 1994. Five Texts on the Mediaeval Problem of Universals: Porphyry, Boethius, Abelard, Duns Scotus, Ockham . Indianapolis: Hackett. Zimmerman D. 1997. Distinct indiscernibles and the bundle theory. Mind  106: 305– 9. Google Scholar CrossRef Search ADS   © The Authors 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: journals.permissions@oup.com

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