Restricted Causal Relevance

Restricted Causal Relevance Abstract Causal selection and priority are at the heart of discussions of the causal parity thesis, which says that all causes of a given effect are on a par, and that any justified priority assigned to a given cause results from causal explanatory interests. In theories of causation that provide necessary and sufficient conditions for the truth of causal claims, status as cause is an either/or issue: either a given cause satisfies the conditions or it does not. Consequently, assessments of causal parity and priority require more resources, which can either be in addition to or part of the causal analysis itself. While adding resources has been standard, here we develop a unified conceptual analysis that includes a range of different, precise causal concepts that allow for the assessment of causal priority in terms of different kinds of causal relevance. 1 Introduction 2 The Minimal Notion of Causal Relevance 3 Direct, Mediated, and Actual Causation as Restricted Causal Relevance 4 Normality Restrictions and Redundant Causes 4.1 Normality and norm restrictions 4.2 Redundant, non-redundant, and contextually necessary causes 5 Applications in Philosophy of Biology 5.1 Non-redundancy and redundancy in molecular biology of the nervous system 5.2 Normality in biology 5.3 Miscommunication and extrapolation 5.4 Circularity and non-substantial distinctions 6 Causal Parity Claims Refined 7 Conclusion 1 Introduction Distinctions between causes are invoked both in scientific and everyday causal judgements and reasoning. We often hear claims that some causes are stronger or more relevant than others. For example, genetic factors are referred to as causes in a sense not ascribed to other factors in development (Waters [2007]), and norm-violating actions are ascribed a causal status not shared by norm-abiding actions (Knobe and Fraser [2008]). How are such differences in causal judgements best understood? In this article we develop a pluralistic—though unified—analysis of causal concepts that accounts for numerous causal distinctions. On our account, causal concepts differ due to specific quantifier restrictions in their definitions. All concepts defined are unified by being, in various ways, stronger versions of a minimal definition of causal relevance. Different interests and explanatory aims contextually trigger different causal concepts, and we provide resources to spell out their precise contents. Pragmatic features—like aims and interests—determine what causal claims we make and investigate, while the causal claims themselves have objectively assessable truth conditions. Our approach contrasts with standard approaches, which provide analyses of causation in terms of necessary and sufficient conditions for the truth of canonical causal claims like ‘X is a cause of Y’. Examples of this include Lewis’s counterfactual dependence analysis of causation (Lewis [1973], [2004a]), and Woodward’s interventionist analysis of causation (Woodward [2003]). Lewis ([1973]) defines causation as the ancestral of causal dependence, where causal dependence between events is defined in terms of counterfactual dependence between a pair of propositions about the occurrence of these events. Event e depends causally on event c if and only if were c to occur, then e would occur; and if c were not to occur, then e would not occur. Lewis appeals to pragmatic-explanatory interests when discussing selection and priority among causes (Lewis [1986], [2004b]). On Woodward’s theory, causation is a relation between variables that can take any number of different values, and the central interventionist idea is that variable X is a cause of variable Y if and only if it is possible to change the value of Y by interventions on X (Woodward [2003], p. 59). In his core definition, Woodward defines both direct and contributing cause, so his view is not obviously monistic in the same sense as Lewis’s. However, when accounting for distinctions among causes, his strategy is to invoke his theory of causal explanation (Woodward [2010]), rather than his conceptual analysis and core definition. Woodward discusses how degrees of invariance (Woodward [2003]) and the notions of proportionality, specificity, and stability (Woodward [2010]) provide resources for drawing distinctions when it comes to the explanatory relevance and force of causes. In contrast, we explore how a pluralistic conceptual analysis can provide resources to distinguish between different kinds of causal relevance. We focus on distinctions having to do with actuality, redundancy, normality, and norm-sensitivity, and how these can function as restrictions on a minimal definition, thereby giving rise to stronger—restricted—concepts of causal relevance. Even if there are such differences in approach and focus, the view developed here bears close resemblance to, and is strongly inspired by, Woodward’s work. The argument for the pluralistic approach is based on discussions of causal selection and priority in biology, and a brief discussion of the norm-sensitivity of causal judgements. Moreover, the way our framework unifies existing and new causal concepts provides philosophical understanding—an additional consideration in its favour. We do not deny that additional resources can be used to make further distinctions between causes of the same kind. Correlation coefficients, measures of variance, and relative frequencies are examples of such additional resources (see, for instance, Wright et al. [1992]), and various rankings of normality, invariance, and specificity may be too (Halpern [2008]; Halpern and Hitchcock [2015]; Griffiths et al. [2015]). The present discussion is situated within a broadly interventionist framework. More precisely, we assume three core ideas as our point of departure: (i) that truth conditions for causal claims can be formulated in terms of behaviour under certain specific hypothetical changes (interventions) to causal systems; (ii) that type-causation is analytically fundamental, meaning that a philosophical analysis should start with type-causal relations, and from these derive token (event or actual) causal notions; and (iii) that causal claims essentially are part of, or derive from, larger causal representations, and that both truth and verification conditions for causal claims must make reference to the larger causal representations in which they are embedded. These ideas will become clearer as we spell out the framework. Our approach exemplifies a meta-philosophy where philosophical analyses answer to challenges and insights from outside academic philosophy. In the case of causal concepts, such external inputs include challenges in interdisciplinary communication in science, scientific accounts of human causal cognition, and alignment with scientific methodology. This is not to give up on the idea that causal concepts track objective relations; rather, it is to extend the input to philosophical inquiry beyond intuitions, thought experiments, and metaphysical theorizing. In recent contributions, approaches similar to parts of our account are developed in (Halpern and Pearl [2005]; Halpern [2008]; Gendler Szabó and Knobe [2013]; Halpern and Hitchcock [2015]; Kaiserman [2016]). We remark on most of these contributions along the way. These accounts mainly focus on actual causation and defaults having to do with norms (Hitchcock and Knobe [2009]; Gendler Szabó and Knobe [2013]) or typicality (Halpern [2008]). Our restrictions are closely related to the idea of defaults (Halpern [2008]; Halpern and Hitchcock [2015]), but our account is more liberal since it includes type-level causal relevancies, and allows for a whole range of different restrictions. Also, on our account, the restrictions figure directly in the definitions of specific causal concepts. First, we define a minimal notion of causal relevance by quantifying over interventions, over variables describing the system of interest, and over the values these variables might take. Various restrictions on these quantifiers give rise to stronger concepts of causal relevance; what we call ‘restricted causal relevance’ (or a related discussion, see Strand and Oftedal [2013]). The minimal notion gives a necessary condition for all kinds of causal relevance captured by the framework. In consecutive sections, we use this framework to define direct, mediated, and actual causes, and then normality-restricted and redundant causes. We present several examples of redundant and non-redundant causes in molecular biology of the nervous system, and show how truth conditions for causal claims can be specified in particular examples. We then present several biological understandings of normality and discuss normality restrictions and their role in conceptualizing causes in biology. Next, we discuss how our framework can facilitate the communication of causal claims and how relevant conceptual distinctions can helpfully frame the issue of extrapolation. Finally, we argue that causal parity theses should be restated as several different precise claims. 2 The Minimal Notion of Causal Relevance The framework developed here relies on core commitments of the interventionist framework (in particular, see Woodward [2003]). Causal relevance among types is analysed in terms of dependence among variables under interventions.1 Variables are representational devices that range over a set of values. The values in the value range of a variable are mutually exclusive. Value assignments to all or to a subset of the variables in a causal model are, respectively, points or regions in the state-space of the model, and these represent possible scenarios or sets of possible scenarios. Binary variables can represent properties being instantiated or not. Events can be represented by variables taking certain values. Variables used in causal representations should be distinct, which means that, ideally, any correlations among them should be due to causal dependencies. Causal claims are parts of representations of reality. Causal relations and structures are typically represented by causal claims, graphical representations, or structural equation models. The representations used in this article are causal concepts, distinct variables with specified value ranges, and directed graphs. Directed graphs consist of nodes representing variables and directed arrows representing direct causal dependence (to be defined). Against this backdrop, we define a minimal notion of causal relevance by quantifying over interventions, variables, and values2. In contrast to interventionist analyses in terms of fixed sufficient and necessary conditions (for example, Woodward [2003], p. 59), our notion allows for specifications of many different causal concepts by specifying various restrictions on the domains of the quantifiers. Definition 1: X is a cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y when some subset of variables (allowing this set to be empty) in M are fixed at some values. Here, M is a representation consisting of a set of distinct variables with specified value ranges, and an intervention on X relative to Y is a change in X that does not backtrack, that is, that changes X independently of X’s other causes, and that does not change Y directly.3 The following version of Definition 1 makes the quantifiers explicit, and thus marks the points at which restrictions can be introduced: Definition 1*: X is a cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y (quantifier over interventions on X: Q1) when some subset of variables (allowing this set to be empty) in M (quantifier over subsets of variables in M excluding X and Y: Q2) are fixed at some values (quantifier over the values of the variables: Q3). 3 Direct, Mediated, and Actual Causation as Restricted Causal Relevance By introducing restrictions on the quantifiers over variables and values in Definition 1, we can define several varieties of causal relevance. First, direct cause (Woodward [2003]; Strand and Oftedal [2013]): Definition 2: X is a direct cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y, when all other variables in M are fixed at some value. The concept of direct cause captures the idea of proximate cause, whose influence on the effect is not mediated by other variables. This aspect is captured by the requirement that all variables in M, except X and Y, are held fixed, since mediated causal relevance would be masked when fixating intermediary variables. Whether a causal relation between X and Y is direct or not is relative to M. A direct causal relation in M may be a mediated causal relation relative to a different representation, M*, that includes intermediary variables. The concept of direct cause is especially helpful since it can be used to define causal paths. A causal path is a sub-structures of a causal graph, representing a connected series of direct causal relationships. Consider a simple case of a switch, S, directing electrical current from battery B to either resistor R1 or resistor R2, represented in a causal graph as shown in Figure 1. Figure 1. View largeDownload slide Causal graph. Figure 1. View largeDownload slide Causal graph. Sub-structures B → S → R1 and B → S → R2 represent causal paths. With this notion we can define mediated causal relevance: Definition 3: X is a mediated cause of Y relative to M if and only if there is a path, P, between X and Y such that there is a possible intervention on X that would result in a change of Y when all variables in M not on path P between X and Y are fixed at some values, and X is not a direct cause of Y relative to M. While useful, Definition 3 does not capture mixed cases where X is a cause of Y along several paths, where one of these paths is direct.4 The simplest such case is shown in Figure 2. Figure 2. View largeDownload slide Mixed case. Figure 2. View largeDownload slide Mixed case. Mixed cases are tricky because causal relevance along the direct path cannot be controlled for and is therefore difficult to separate from causal relevance along other paths. Suppose that there are interventions on X that would result in changes to Y in Figure 2. The task is to isolate a further condition that states when this causal relevance distributes across both paths, and when there is no relevance via Z. A concept of path-specific cause enables such distinctions by imposing restrictions on the direct causal relationships constituting the path in question.5 The idea is to ensure that there are possible changes brought about in Y by interventions on X that are at least partly mediated along the path in question. More generally, X is a path-specific cause of Y along path P{X, Z1, […], Zn, Y} if and only if there is a possible intervention IX on X such that path P composes under IX: Path P {X, Z1, Z2, …, Zn, Y} in M composes under intervention IX on X if and only if there is a set of hypothetical interventions, {IZ1, …, IZn}, such that IX would bring about a change from value z11 to z12 in Z1 when all variables in M, except X and Z1, are fixed at some value; IZ1 would change Z1 from z11 to z12 and thereby bring about a change from z21 to z22 in Z2 when all variables in M, except Z1 and Z2, are fixed at some value; IZ2 would change Z2 from z21 to z22 and thereby bring about a change … from zn1 to zn2 in Zn when all variables in M, except Zn-1 and Zn, are fixed at some value; and IZn would change Zn from zn1 to zn2 and thereby change Y when all values in M, except Zn and Y, are fixed at some value. This requirement rules out failures of composition along the path in question. Failures of composition are counterexamples to causal transitivity where there is a causal path from X to Y, but where interventions on X only bring about changes in intermediate variables that are irrelevant for changes in Y.6 Definition 3 does not fully capture causal relevance along path P. There might be cases where a direct path from an intermediate variable to Y secures the existence of the required intervention, even if the mediating path we are interested in does not compose under that intervention. On the other hand, X might be a path-specific cause of Y along path P even if there are no possible interventions on X that would change Y when we hold all variables in M not on path P fixed. This might seem counterintuitive, but such cases arise if there is a direct link between X (or some intermediate variable on P) and Y that cancels out the influence along P. For this reason, one might think that the requirement that path P composes under some intervention is too weak for establishing mediated causal relevance between X and Y along path P. If so, one can introduce an additional requirement of dependence under intervention: X is a path-mediated cause of Y along path P{X, Z1, …, Zn, Y} in M if and only if there is a possible intervention, IX, on X such that path P composes under IX, and IX would result in a change of Y, when all variables in M not on path P are fixed at some value. Such a concept of path-mediated cause would allow for various restrictions on IX and on the values at which the other variables are held fixed. The distinction between direct and mediated cause is representation-dependent. That is, causal dependencies that are direct relative to a simple representation will typically qualify as mediated dependencies if we expand the representations to explicitly represent mediating factors. Most of the definitions in this article are formulated as direct causal dependencies, but there will be corresponding concepts of mediated causal dependence. We will point this out when it affects the discussion. A much-discussed version of restricted causal relevance is actual cause. Actual causation has received a lot of attention in the literature (see Hitchcock [2001]; Woodward [2003]; Collins et al. [2004]; Halpern and Pearl [2005]; Halpern [2008]; Halpern and Hitchcock [2015]). Many subtle problems with actual causation are thoroughly discussed in these contributions. We do not give an elaborate account of actual causation here, but we provide a definition that indicates how actual causation fits into our framework. Definition 4: X is a direct actual cause of Y relative to M if and only if there is a possible intervention on X that changes X from its actual value, resulting in a change of Y from its actual value, when all other variables in M are fixed at their actual values. This is intended to capture the notion of proximate event causation, where a cause is a difference-maker in a given actual situation. There are, however, notorious counterexamples to dependence analyses of actual causation. In particular, it has proven difficult to get idealized versions of both symmetric overdetermination and late pre-emption cases right. In Section 5.1 we discuss redundant causes and show how our framework can at least handle scientifically relevant cases of redundant causation. Kenneth Waters ([2007]) defines a causal concept that captures the notion of an actual difference-maker in a population, based on an interventionist framework. He introduces a distinction between actual difference-makers and potential difference-makers, and suggests that actual difference-makers are those factors or variables that, in most cases, we pick out as causes, while potential difference-makers are those factors or variables we frequently consider as background conditions. Actual difference-making causes are special because they actually vary in the population, while potential difference-makers do not. Waters argues that his distinction illuminates causal selection in general, and causal selection in classical and molecular genetics in particular. For example, he suggests that genetic factors had a distinguished causal status in relation to variation in eye colour in Morgan’s fruit fly experiments, due to the fact that they actually varied in the population. From our perspective, this causal concept can be captured by requiring the values of the variables to be instantiated in the population. An actuality restriction on the interventions (Q1) and on the values of the other variables (Q3) gives: Definition 5: X is a direct actual diference-making cause of Y in population P relative to M if and only if there is a possible intervention on X that changes the value of X among actually occurring values x1 and x2 in P, resulting in a change of Y among its actually occurring values in P, when all other variables in M are fixed at joint-value assignments actually occurring in combination with both x1 and x2 in P. Corresponding concepts of mediated actual causes and mediated actual diference-makers can be defined. Further restrictions can be formulated in terms of actual values in other populations; what scientists take their normal, expected, or most frequent values to be; in terms of what interventions are of clinical interest in medical research; or in terms of what we take to be normal or norm-respecting values in everyday contexts. We discuss some of these in the next section. 4 Normality Restrictions and Redundant Causes Redundancy and sensitivity to normality together with normative considerations give rise to interesting causal concepts. We show how these concepts are useful for understanding scientific practice and for analysing important features of causal reasoning. Some additional terminology will be useful at this point. A pair of counterfactual scenarios ‘witness' a causal dependence when they fulfil the truth conditions for the corresponding causal claim. Similar terminology is used in (Halpern [2008]) and (Halpern and Hitchcock [2015]) for possible worlds that demonstrate actual causal relationships; Halpern and Hitchcock ([2015]) formulate normality rankings of witnesses relative to the actual world. Our use of the term ‘witness’ is more liberal, but it is inspired by and trades on the same idea as these authors. A ‘hypothetical intervention’ can be thought of as an operation that creates a contrast between hypothetical scenarios (or between an actual and a hypothetical scenario in the case of actual causation). The existence of such contrast scenarios that differ in the right way witnesses the truth of causal claims. Experiments mimic such hypothetical contrasts by controlling for other factors and inducing a change in the cause factor of interest. 4.1 Normality and norm restrictions A number of recent contributions discuss the relevance of normality considerations and norm-sensitivity for causal judgement (Halpern [2008]; Hitchcock and Knobe [2009]; Gendler Szabó and Knobe [2013]; Halpern and Hitchcock [2015]; Kaiserman [2016]; Weber [forthcoming]). In these accounts, normality and norms enter as constraints on the counterfactual scenarios relevant for causal judgement. Some of these accounts also develop rankings of counterfactual scenarios in terms of normality (Halpern [2008]; Halpern and Hitchcock [2015]). Within the present framework, however, normality (or normality thresholds) figure as quantifier restrictions that specify distinct normality-restricted causal concepts. In the case of normality, one can generate a range of different concepts since we have three quantifiers that can be restricted and since there are several ways of specifying normality. The interest of these definitions will vary, and we will only consider a few that we think are interesting here. Definition 6: X is a normality-restricted direct cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y when all other variables in M are fixed at some normal, joint-value assignment. This definition does not include a normality restriction on the values set by interventions, and thereby allows for abnormal interventions. Such a concept might be of use, for example, when reasoning about the effect of medical interventions. Concepts with normality restrictions on the values set by interventions are relevant in other contexts, as suggested by Weber ([forthcoming]) (see brief discussion in Section 4.2). Normality can be specified objectively, in terms of frequency or relative frequency. It can also be specified in more subjective or human-centred terms, for example, as compatibility with norms or expectations. We discuss notions of normality relevant for biology in Section 5.2. In particular, Knobe and Frasers’ ([2008]) results on the norm-sensitivity of folk-causal judgement have sparked recent philosophical debate (see Hitchcock and Knobe [2009]; Gendler Szabó [2013]). According to Hitchcock and Knobe ([2009]), norms make certain counterfactual scenarios salient in causal judgement about actual cases. This suggestion can be cashed out in a slightly different way within the present framework. Rather than norms acting directly on causal judgement by making certain counterfactual scenarios salient, they are contextual factors that play a part in determining what causal concepts are expressed in the context. When people make asymmetric causal judgements about norm-violating and norm-abiding actions, they actually employ a norm-sensitive concept of cause. Definition 7: X is a norm-restricted, direct actual cause of Y relative to M if and only if there is a possible intervention on X that takes X from its actual value, which violates a norm, to a value that does not violate the norm, and that would result in a change of Y when all other variables in M are held fixed at their actual values. In the case discussed by Hitchcock and Knobe ([2009]), and first presented by Knobe and Fraser ([2008]), a member of faculty takes a pencil despite the norm that the pencils are for administrators only. An administrator also takes a pencil. The respondents are then asked who caused the consequent lack of pencils. According to their surveys, the faculty member who violated the norm is judged as a cause, while the administrator who did not violate the norm is not. On our account, this is explained by the hypothesis that many people reason with a norm-restricted concept of cause in such contexts.7 4.2 Redundant, non-redundant, and contextually necessary causes The distinction between redundant and non-redundant causes shows up in discussions of robustness and functional stability in philosophy of biology (Strand and Oftedal [2009], [2013]). There are also extensive philosophical discussions of late pre-emption and overdetermination cases (Woodward [2003]; Collins et al. [2004]; Lewis [2004a]), which are regarded as counterexamples to dependence analyses of causation. In the following, we distinguish between redundant causes, trigger-redundant causes, non-redundant causes, and contextually necessary causes. We do not discuss idealized counterexamples like trumping and late pre-emption here; instead, we focus on how our approach can account for redundant causes in scientifically relevant cases. The core idea is that a cause is redundant if its causal relevance only is witnessed by pairs of counterfactual scenarios where one is somehow abnormal. Two concepts of redundant cause can be distinguished. First, in cases similar to late pre-emption cases, backups are not triggered by interventions on the redundant cause but are latent and ready to bring about the effect if the redundant cause does not. Second, in cases similar to early pre-emption, backup causes are triggered by interventions on the redundant cause. Corresponding concepts of redundant causes differ in terms of the kind of abnormalities required to witness the causal dependence. Definition 8: X is a latent-redundant cause of Y relative to M if and only if there is a possible intervention on X that would change the value of Y only when some other variables in M are fixed at values that are abnormal in combination with the pre-intervention value of X. Definition 9: X is a trigger-redundant cause of Y relative to M if and only if there is a possible intervention on X that would change the value of Y only when some other variables in M are fixed at values that are abnormal in combination with the post-intervention value of X. A cause is redundant if it is latent or trigger-redundant. The kind of normality involved in these definitions will presumably vary with context, and we suspect that both norm-based and typicality-based normality restrictions figure in everyday causal reasoning about pre-emption and overdetermination cases. However, our focus will be on selected biological examples of redundant causes, which are discussed in the next section. A non-redundant cause is a cause whose relevance is witnessed by normal counterfactual scenarios. In other words, it is a normality-restricted cause. Intuitively, X is a non-redundant cause of Y if X’s causal influence on Y does not have a backup for at least some normal, joint-value assignments of the other variables. To illustrate, only a small percentage of individual genes are non-redundant causes of phenotypic traits. Gene-knockout experiments reveal widespread genetic redundancy of single genes (Gu et al. [2003]; Wagner [2005]), and such causal relevance is only witnessed in multiple knockout scenarios or in abnormal environments. Finally, we define a direct contextually necessary cause: Definition 10: X is a direct, contextually necessary cause of Y relative to M if and only if, for all normal, joint-value assignment of values to all other variables in M, there is a possible intervention on X that would change the value of Y. An example of a direct contextually necessary cause is an enzyme necessary for catalysing some biological process (Rabus et al. [1999]; Vincents et al. [2004]). 5 Applications in Philosophy of Biology Causal locutions and terms like ‘cause’, ‘proximate cause’, ‘contributing factor’, and so on express causal concepts, but different locutions can express different causal concepts, and even different occurrences of the same locution can express different concepts in different contexts. Which concept is being expressed is sometimes determined by context, but sometimes it is underdetermined in the given context, which may result in ambiguity and possible miscommunication. In the following, we discuss non-redundancy, redundancy, and normality in biology, and suggest how to precisely understand corresponding causal concepts by introducing relevant restrictions on causal relevance. 5.1 Non-redundancy and redundancy in molecular biology of the nervous system The examples in this section illustrate the distinction between redundant and non-redundant causes as they figure in molecular biology. Additionally, the examples show how a dependence-based account of causation can handle scientific examples of redundancy. We thus give a more hands-on take on pre-emption problems, in contrast to how idealized pre-emption and overdetermination cases are often presented when discussing counterexamples to dependence analyses of causation. A non-redundant cause in molecular biology is a cause that has no backup mechanisms in normal contexts. Consequently, the functionality of the system is affected if a non-redundant cause is perturbed. Receptors are small molecules on the surface of cells that receive and bind to external chemical signals. Plexin receptors can be found on the surface of neuronal cells and are receivers of small protein signals called semaphorins. By inhibiting or enhancing axonal growth, the binding of semaphorin to plexin receptors influences how the neural system develops. Several studies suggest that genes involved in the formation of plexin receptors are non-redundant in several neuronal processes (see, for example, Worzfeld et al. [2004]). For instance, mice in which the Plexin-B2 gene was knocked out showed defects in neural tube closure in the development of the embryonal nervous system. Significant impairment such as exencephaly (brain located outside the scull) and prenatal death resulted (Deng et al. [2007]; Friedel et al. [2007]). In these cases, no backup genes or processes replaced the knocked out Plexin-B2 gene, with devastating developmental results. Under these experimental conditions, Plexin-B2 was a non-redundant cause of a range of effects. The concept of non-redundant cause that is in play here is captured by the concept of a normality-restricted cause. More precisely, the truth conditions for the claim that Plexin-B2 is a non-redundant cause of axonal growth are: Plexin-B2 is a non-redundant cause of axonal growth relative to M (set of factors represented in the given context) if and only if there is a possible intervention on Plexin-B2 that would change axonal growth when all other factors not on the causal paths between Plexin-B2 and axonal growth are fixed at some normal, joint-value assignment. We have deliberately not specified the notion of normality in play, which presumably will vary with context. In Section 5.2, we discuss various notions relevant in biology. Redundancy is frequent in living systems and contributes to system robustness. If several causal factors ensure the same effect, the system may survive and perform equally well if one or several parts of the system are changed, destroyed, or removed (Kafri et al. [2009]). Biological causal redundancy can be realized by at least three different mechanisms: duplication, degeneracy, and distributed robustness (Edelman and Gally [2001]; Wagner [2005]). Duplication occurs when several copies of a factor, typically genes, are present and one or more copies act as backups if the original cause is perturbed. Degeneracy occurs in situations where structurally different parts can do the same causal job. For instance, when different genes contribute to proteins with the same function, or when different enzymes catalyse the same processes. The case of distributed robustness concerns more complex system adjustments as a response to the perturbation of a factor. The idea is that several components and processes jointly act as backup for a causal factor. In all these versions of redundancy, the causal dependence between the redundant cause and its effect is not witnessed by normal scenarios. Rather, in normal circumstances, when a factor is perturbed, another factor compensates and there is no difference-making relationship between the alleged cause and the effect.8 Under abnormal conditions, however—when, for example, all the existing backups are knocked out—the causal relation is witnessed. An example is the genetic contribution to the production of calmodulin (CaM), a calcium sensor protein important for signalling in the nervous system. Calcium ions (Ca2+) act as intracellular messengers because their concentration decides neuronal excitability. When increasing in concentration, Ca2+ ions bind to CaM proteins and start signalling cascades, which play important roles in a range of processes such as learning, memory, and other cognitive activities, as well as in stress responses. Having this central role, living organisms secure the production of CaM proteins through causal redundancy. In vertebrates, there is a whole family of genes placed at different locations in the chromosome that encode an identical CaM protein thus ensuring a high level of robustness of the CaM-dependent processes (Toutenhoofd and Strehler [2000]). Under normal conditions, if a CaM-producing gene is not working for some reason, one or several other genes are lined up to step in. Thus, knocking out a gene under normal conditions will not (significantly) affect the CaM-dependent processes. In abnormal conditions, however, where backup genes are out of play, the dependence between the CaM processes and the gene in question is witnessed (Panina et al. [2012]). Models of CaM-gene redundancy may include both latent redundancy and trigger redundancy. An example of latent redundancy is a case where the knocking out of a CaM-related gene is compensated by other CaM-related genes without their expression being affected by the knockout. Simultaneous stable expression of several CaM-related genes may overdetermine CaM production, so that already existing CaM production is sufficient to compensate for the lacking gene. Using the previously defined concept of latent redundant cause, we can spell out the truth conditions for the claim that a CaM gene is a latent redundant cause of calmodulin production: A CaM gene is a latent redundant cause of calmodulin relative to M if and only if there are possible interventions on the CaM gene that would change calmodulin production only when some variables in M are fixed at values that are abnormal in combination with the CaM gene not being knocked out. In cases where knocking out a CaM-related gene affects the regulation of other genes through feedback mechanisms, the gene is a trigger-redundant cause. The counterfactual dependence will only be witnessed in scenarios where backup mechanisms are fixed at values that are abnormal given that the gene is knocked out. Normally, backup mechanisms will compensate when a gene is knocked out, but under abnormal conditions (for example, multiple knockouts) they are kept from compensating. Using the previously defined concept of trigger-redundant cause, we can spell out the truth conditions for the claim that a CaM gene is a trigger-redundant cause of calmodulin production: A CaM gene is a trigger-redundant cause of calmodulin relative to M if and only if there are possible interventions on the CaM gene that would change calmodulin production only when some variables in M are fixed at values that are abnormal given that the CaM gene is knocked out. Whether a particular CaM-related gene is a latent redundant or a trigger-redundant cause is an empirical question when the relevant kind of normality is specified, and investigating particular redundancy types may require distinct research designs. Another example of redundancy is found in the spliceosome. The spliceosome consists of splicing factors, including small nuclear RNAs and protein complexes in the cell nucleus that remove parts of the RNA sequence before it becomes mature messenger RNA (mRNA) ready to serve as a template for protein production. Thus, splicing factors influence how premature RNA sequences are cut and spliced to constitute final templates for proteins. An RNA sequence can be cut and spliced in many different ways. Such alternative splicing greatly increases the repertoire of mRNA and proteins in multicellular organisms. Typically, environmental and/or epigenetic factors influence the spliceosome, enabling the cell to make different proteins from the same gene depending on environmental demands. For example, adrenaline-producing cells in the human nervous system respond to stress by altering the construction of calcium (Ca2+) channels in the cell membrane to better accommodate stress conditions compared to standard Ca2+ channels (Liu et al. [2012]). The modified channels open more easily and respond more quickly to stress. The stress-induced channels are different because splicing factors include an extra RNA part in the mRNA called STREX (stress exon) in the template for the relevant channel protein. Splicing redundancy occurs when several different splicing agents can perform the same addition or subtraction of premature RNA. A recent study has shown that two different splicing factors, hnRNP L and hnRNP LL, act redundantly in the modulation of the STREX exon in response to depolarization of the cell (Liu et al. [2012]). Inclusion of STREX under stress conditions is thereby secured via causal redundancy of factors in the splicing process. Knocking down a splicing factor did not stop the inclusion of STREX into the mRNA and subsequently into the channel protein. Knocking down both hnRNP L and hnRNP LL at the same time, however, stopped this particular stress response in cell membrane channels (Liu et al. [2012], p. 22711). Using our concept of latent redundant cause, and assuming that STREX is overdetermined by the two splicing factors, we can spell out the truth conditions for the claim that hnRNP L is a latent-redundant cause of STREX: hnRNP L is a latent-redundant cause of STREX relative to M if and only if there are possible interventions on hnRNP L that will change STREX production only when some variables in M are fixed at values that are abnormal in combination with hnRNP not being knocked down. 5.2 Normality in biology In this section we discuss three understandings of biological normality, and indicate how they can generate concepts of restricted causal relevance. The three are function-based normality, statistical normality, and normality in terms of natural occurrence.9 Concepts of normality can be applied to different size and time scales of biological systems, and can be indexed with respect to particular environments. Understandings of normality in biology often link to the concept of function. A normal heart is a heart that functions biologically. There is a large philosophical debate about the notion of biological function. Roughly, function is either analysed as an etiological concept (Millikan [1984]) or as a causal role concept (Cummins [1975]). In etiological theories, a biological function is understood in terms of its evolutionary history, which explains why the function is there; while in causal role accounts, statements about biological functions are merely used to explain how components of a structure contribute to a capacity of the system. We will not enter this debate except to note that a concept of biological normality more easily links up to etiological accounts, as these allow for malfunction. Many differences between hearts are permitted within the range of normal functioning, but not those that are associated with malfunctioning (Wachbroit [1994]). Statistical normality or typicality is frequently invoked in biology and often overlaps with, and is used as an indicator of, function-based normality. Statistical normality can be represented by a normal distribution of some trait, process or state, or it can be defined as the mean, median, or most frequent (Wachbroit [1994], p. 580). Still, non-functional biological processes or states sometimes occur rather frequently in populations (for example, obesity), thus what is statistically normal is not always functionally normal. Causal concepts with statistical normality restrictions seem to be in play in causal reasoning when we ignore hypothetical scenarios that include statistically very atypical possibilities. For example, we do not judge the absence of a meteorite fall as a cause of the development of a lake trout population. In Woodward’s terminology, statistical normality restrictions can exclude scenarios that are not serious possibilities. We also distinguish a third kind of normality within biology in terms of what exists in naturally occurring systems, where the salient contrast is systems that are affected in some way by human interventions. Non-natural systems would typically be experimental systems or systems that are changed via technology or medication. Causal analysis of medicated systems, for example, may need different conceptualizations of cause than for natural systems. Drugs, for instance, add to the causal repertoire of a system and may introduce novel redundancies. Many drugs work by binding to receptors that, normally (understood in terms of naturally occurring), are reserved for components that already exist in the system. In the examples of redundancy described in the previous section, normality restrictions in terms of natural occurrence are relevant since, typically, abnormal scenarios that include multiple knockouts are induced by human experimental interventions on the system. Normality is relative to different size scales or graining; abnormalities at smaller scales may not be relevant at larger scales. Backup mechanisms often secure full organismal functionality, and in cases without backups, where a mechanism is dysfunctional, the dysfunction may constitute only a small contribution to how the organism copes as a whole. There are also cases where fine-grained dysfunction is clearly detrimental to organismal functionality. In a recent paper, Marcel Weber ([forthcoming]) suggests an account of what he calls ‘biologically normal interventions’. On his view, biologically normal interventions are such that they (i) could be brought about by natural biological processes and (ii) are compatible with survival of the organism (see also discussion in Griffiths et al. [2015], p. 543). From our perspective, this is a way of introducing a normality restriction on relevant causal interventions in terms of normality at the organismal scale. Weber’s definition appeals to a combination of normality in terms of natural occurrence and function-based normality, as discussed above. He introduces the concept of a normal intervention to isolate a set of interventions that are compatible with survival of the system, and these are the biologically relevant subset of all possible interventions in living systems. According to Weber, such restrictions capture an important feature of causal explanatory practice in biology, namely, that only biologically normal interventions are found relevant in most explanatory contexts. Weber’s definition enters the discussion of specificity of DNA–RNA–protein relations (Waters [2007]; Woodward [2010]; Griffiths et al. [2015]; Weber [forthcoming]), where specificity is understood as fine-grained influence. A causal relation is specific when there are several different values of the cause variable that roughly correspond one-to-one with values of the effect variable (Woodward [2010], p. 305). Sequences of DNA are considered specific causes of sequences of RNA in virtue of the large number of possible combinations of DNA bases that correspond in a one-to-one manner to combinations of RNA bases. As pointed out by Weber ([forthcoming]), however, it is only a small number of such combinations that are actually consistent with a viable system. For Weber, the number of viable combinations, rather than the number of merely possible combinations of DNA and RNA sequences, is the relevant basis for the specificity of their causal relation. From the perspective of our framework, Weber’s suggestion is a special version of a normality restriction on interventions. Normality can also be understood in relation to different time scales. The normal functioning of a molecular mechanism is often manifested over a short time scale, while normality in development and functioning over longer time scales includes the normality of organs, lifespans of organisms, and cycles of populations. Analogous to size scales, normal development over a longer timespan can often be sustained despite disruption over shorter timespans. In many cases, what is normal is relative to variations in background conditions (Dussault and Gagne-Julien [2015]). Many organisms have a high degree of phenotypic plasticity, allowing growth and functioning to vary with the organism's environment. For example, at varying altitudes, plants of the same species often look and function very differently. Thus, what is normal for many plants at high altitudes is not normal at lower altitudes. Such context-dependent normality is also a basis from which one can formulate relevant restrictions. The variety of understandings of normality indicates a need to be specific about what kind of normality restrictions are in play in a given context. We take it to be a virtue of the present account that it allows for the specification of different causal concepts corresponding to different normality restrictions, depending on their importance in various contexts. 5.3 Miscommunication and extrapolation Differences between the precise meaning of causal claims in experimental contexts and the interpretation of these claims in other contexts are possible sources of miscommunication (Oftedal and Parkkinen [2013]). Explicating restrictions on causal concepts in play can be used to specify variations in the precise content of causal claims across contexts. Extrapolation involves the transportation of causal claims from one setting to another, assuming the relevance of the causal claim despite changes in background conditions. Such extrapolations are often undertaken from research on animal models to claims about human physiology, but extrapolation is important in most fields of research. Our account provides tools for explicating precisely what separates causal claims in the contexts we are extrapolating between, by explicating conceptual differences potentially triggered by the different contexts. Separating these conceptual issues from the issue of how extrapolation can be justified when the causal claims have stable meaning across contexts is necessary for getting traction on this issue. When transporting causal claims across contexts, the extent to which different causal concepts are in use, or the extent to which different assumptions are being made about background conditions, will vary. One often finds that various restrictions on background conditions are made explicit if miscommunication is suspected.10 Combined with the fact that restricted causal claims entail claims of minimal causal relevance, complex communicative situations are created. An example is found in the debates over evidence-based medicine. Even if assumptions bridging the inferential gap from trial population to target population can be justified, stronger assumptions are needed for clinical decisions concerning individual treatments—for example, that the actual condition of the individual in question is relevantly similar to the trial subpopulations in which the treatment had positive effect. Population- and individual-level perspectives differ in terms of what restrictions are salient; causal information sufficient to justify population-level guidelines is not sufficient to justify particular clinical decisions (Strand and Parkkinen [2014]). By focusing on differences between causal concepts in terms of variations in the truth-conditions for corresponding causal claims, we suggest a procedure for mending this situation. Whenever miscommunication seems likely, we should be precise about the restrictions in play. In such cases, it is crucial that information about restrictions and assumptions are explicitly stated along with the causal information. This requirement is exemplified by the CONSORT guidelines for medical publications.11 These guidelines are developed to alleviate problems arising from inadequate reporting of randomized controlled trials (RCTs). It includes a check list and a flow diagram that recommend how to report design, analyses, and interpretations of RCTs. A focus on the appropriate assumptions and restrictions is important for the interpreter too, because it is generally not valid to infer restricted causal relevancies from evidence for other kinds of causal relevance. 5.4 Circularity and non-substantial distinctions If a variable is defined in terms of other variables, including its typical effects, there is an immediate potential for circularity in causal explanations involving that variable (and violations of independence assumptions like the causal Markov condition). One example is a dispositional feature like water solubility: if water solubility is defined as a tendency to dissolve in water, the solubility of a given drug will not causally explain that it dissolves in water. In short, causes and effects should not be conceptually related in this way in order to provide informative explanations and make explanations empirically falsifiable. Such worries have been a recurrent theme in criticisms of belief–desire explanations in empirical psychology (see, for example, Rosenberg [1985]). If normality-restricted causal concepts are defined in terms of causal functionality, then a related circularity might arise. A causal role definition of a function specifies the function in terms of its causal role, that is, in terms of what output it creates in response to certain inputs. For example, a loudspeaker has the function of transforming electrical signals into sound waves. If normal scenarios are defined as the scenarios where the functioning of the loudspeaker accords with the causal role description of the loudspeaker, then whether the loudspeaker is a normality-restricted cause of the sound or not becomes a matter of definition. The worry is that some function-based normality restrictions will introduce circularity for cases where the relevant cause and effect figure in the causal role definition of the function. If the normality restriction restricts counterfactual scenarios to the ones where the loudspeaker functions properly, then the electrical input will be appropriately correlated with sound waves in those scenarios, by definition. After all, we are only considering scenarios where that is the case. Such functional-normality-restricted causal concepts will thus be problematic for causal explanations of effects figuring in the analysis of the function. Whether a restricted cause–effect relationship obtains should be a matter of empirical fact, not a matter of definition. Such restrictions and concepts might still be useful as heuristics for gaining relevant understanding about causal structures, but one should be aware of the potentially problematic circularities they introduce. Against this background, it becomes an interesting issue whether such functional-normality-restricted causal concepts actually are in play in causal explanatory practice. If so, it should be checked whether they give rise to problematically circular explanations, and whether the claims in which they figure are empirically testable. 6 Causal Parity Claims Refined Discussions of causal parity in the philosophy of biology concern the apportioning of causal responsibilities to genetic and environmental causes. Different versions of the parity thesis have been invoked to argue that genetic and environmental causes are on a par (see, for example, Griffiths and Stotz [2013]), while others argue on the basis of particular characteristics of the DNA–RNA–protein relation that these causes are not on a par (Waters [2007]; Woodward [2010]). Discussions of causal parity are found both in the causation literature and in the developmental systems theory (DST) literature. Stegmann ([2012]) provides a helpful discussion of the various claims that surface in the DST literature and their connections to the causation literature. In particular, he spells out a Millean parity thesis applied to the relation between genetic and environmental causes (Stegmann [2012], p. 906), based on John Stuart Mills’s general causal parity claim. Millean Parity: Genetic and non-genetic factors are on a par insofar as both are causes and causes constitute a uniform ontological category (specifically, there is no ontological difference between causes and conditions). From our perspective, the ontological differences between different kinds of causes discussed by Stegmann and several participants in this debate is better understood as an objective difference in causal status. On our view, cause is not an ontological category; whether something is a cause is a question of whether it relates to a given effect in certain ways. Causes can be variables, properties, property instances, objects, activities, and so forth. Causes can cause effects by being absent, by transferring momentum, by depolarizing, and so forth. There seems to be neither ontological nor physical unity to all causes and causal relations. For these reasons, we reinterpret Millean parity in the DST context as: Millean Parity*: Genetic and non-genetic factors are on a par insofar as they are causes of the same kind in development. On a monistic view of causation, Millean parity* will be close to trivial, since there is only one kind of causal status. For this reason, DST discussions of parity have often focused on other kinds of objective (sometimes denoted ‘ontological’) differences between genes and non-genetic causal factors in development. Examples are distinctions between information carriers and other causes, between replicators and interactors, and between specific and non-specific causal factors. On the pluralistic framework developed here, however, we can distinguish several different causal parity claims. The minimal notion of causal relevance (Definition 1) gave us a template for defining precise causal concepts that enable qualitative comparisons of causes. Given the resulting pluralism of related but distinct causal concepts, we can straightforwardly reject strong causal parity theses holding that all causes are on a par. Weaker causal parity theses should thus be considered. Minimal Causal Parity: Any cause is a cause in the minimal sense. This claim is correct for all the causal concepts discussed here. However, we do not rule out that there can be legitimate uses of causal locutions that are not captured by our framework. Notions of agent causation in philosophy of action are candidates. Another causal parity claim, which can be formulated in terms of restricted causal relevance, is that any two causes that fulfil a given restriction are on a par. This, however, is not true in general. The reason is that such causes can be asymmetric relative to other restrictions. For example, of two direct actual causes of a given effect, only one might fulfil a normality restriction. Consequently, we get two different parity claims relativized to restrictions: Local Restricted Causal Parity: Any cause that fulfils any given restriction is on a par with any other cause of the same kind, with respect to that restriction. Global Restricted Causal Parity: Any two causes that fulfil all the same restrictions are on par. Based on several learning studies in mice, an example of local restricted causal parity can be constructed. Suppose there is a mouse population where some mice (Doogie mice) have an enhanced NMDA receptor function, resulting in improved memory and learning due to foreign genes being inserted into their genome (Tang et al. [1999]). In addition, suppose that the population members vary with respect to anxiety levels (Deacon [2013]), which also affect memory and learning (Darcet et al. [2014]). In such a case, the causes (genes and anxiety levels) are on a par with respect to the first set of restrictions (actuality) but not with respect to the second set of restrictions (natural occurrence). NMDA-genes and anxiety levels actually vary in the population, while only variation in anxiety levels is naturally occurring. Global restricted causal parity appears to follow directly from our definitions, and in a sense it does. However, if normality restrictions can be graded (in terms of more-or-less normal value assignments), then causal parity would be a graded phenomenon. Causal parity would come in degrees, and causes could be more or less on a par. If we assume that there is a partial order on scenarios (points or regions in the state space of the relevant causal model) in terms of normality, we can get an ordering on the causes for a given effect in terms of how normal the scenarios that witness dependence under interventions are. (Halpern and Hitchcock [2015]) is an interesting development of this approach for actual causation (see also Halpern [2008]). We do not take a stand here on whether such developments should be incorporated into the definitions of causal concepts or figure as part of a theory of causal explanation. 7 Conclusion We have developed the interventionist framework into a unified, though conceptually pluralistic, account of causation. Our minimal definition serves as a template for a range of causal concepts generated from different sets of restrictions. We have discussed how concepts of restricted causal relevance can be used to clarify causal claims, to disentangle conceptual and substantial issues, and to facilitate communication of causal information across contexts. Further developments of this account are worthwhile and in progress. In particular, we would like to assess whether relaxing the distinctness requirement on the variables and/or the requirements on interventions can accommodate various forms of non-causal explanation, including constitutive explanation, grounding, and functional and teleological explanations. Other developments include accounts of invariance and causal specificity. Various aspects of invariance can be captured by specifying under what ranges of variation the causal dependence obtains. There are several dimensions to invariance (see Woodward [2003]). They concern which other factors can vary, how much they can vary, and the range of interventions on the cause variable that result in changes on the effect variable. Invariance cannot be captured by simple restrictions on the quantifiers in our minimal definition. Rather, degrees of invariance can be captured by the (relative) size of the subdomains of these quantifiers where the dependence under interventions obtains. As with the normality rankings discussed above, it is an interesting question whether degrees of invariance should enter directly into the semantics of causal concepts, or whether they are better accounted for by a theory of causal explanation. Similarly, various forms of causal specificity might be defined in terms of the relative size of partitions of possible changes in the effect variable that are bijectively related to partitions of possible changes in the cause variable. Whether some forms of specificity—and degrees of specificity in particular—are better accounted for by a theory of causal explanation is a question we leave unanswered here. Acknowledgements We would like to thank Henrik Forssell for early discussions of the idea that the relevant definitions can be formulated using quantifiers and quantifier restrictions. We would also like to thank Torfinn Huvenes and William Wimsatt for helpful comments on earlier drafts. We are very grateful to two anonymous referees, who gave exceptionally valuable feedback that led to significant improvements. This work is part of the project ‘Causation and Reduction in Systems Biology’, funded by the Norwegian Research Council and the University of Oslo (grant no. 231106), and hosted by the Department of Philosophy, Classics, History of Art and Ideas, University of Oslo. Footnotes 1 There are subtle but philosophically important issues concerning the relata of causal relations. They can be literally taken as variables, that is, as representations of factors; or they can be taken as the referents of these representational devices. For the purposes of this article, we do not take a stand on this issue. 2 See (See (Strand and Oftedal [2013], p.180) for a preliminary version of this minimal notion of causal relevance. 3 See (Woodward [2003], Section 3.1.3) for a more elaborate and precise description of interventions. 4 Such cases have been discussed in the context of the faithfulness condition (Spirtes et al. [2000]; Woodward [2003], pp. 49–50) and counterexamples to transitivity (Hitchcock [2001]; Hall [2003]). 5 See (Pearl [2001]) for a definition along similar lines and a discussion concerning the possibility of deactivating causal paths and direct links. 6 Hitchcock ([2001]) discusses counterexamples to transitivity, including failures of composition and the notion of an active causal route. In contrast to his discussion in that paper, our definitions focus on type-level relevancies rather than event causation. Notice that counterexamples to causal transitivity based on failures of composition are ruled out if we are restricted to binary variables in M. This might explain the widespread acceptance of causal transitivity in the literature on event causation (for example, Lewis [1973]). 7 The results were seemingly robust, but many respondents still judged the norm-abiding action of the administrator also to be a cause. On our take, this is explained by these respondents not employing a norm-restricted causal concept in that context (of course, some respondents might also just be mistaken in their reasoning). 8 We here assume relative coarse-grained and temporally limited representations. More fine-grained models and/or models with long time-scales may reveal differences in many actual cases. 9 We considered evaluative normality involving norms above. 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Woodward J. [ 2003 ]: Making Things Happen: A Theory of Causal Explanation , Oxford : Oxford University Press . Woodward J. [ 2010 ]: ‘ Causation in Biology: Stability, Specificity, and the Choice of Levels of Explanation ’, Biology and Philosophy , 25 , pp. 287 – 318 . Google Scholar CrossRef Search ADS Worzfeld T. , Püschel A. W. , Offermanns S. , Kuner R. [ 2004 ]: ‘ Plexin-B Family Members Demonstrate Non-Redundant Expression Patterns in the Developing Mouse Nervous System: An Anatomical Basis for Morphogenetic Effects of Sema4D During Development ’, European Journal of Neuroscience , 19 , pp. 2622 – 32 . Google Scholar CrossRef Search ADS PubMed Wright E. O. , Levine A. , Sober E. [ 1992 ]: ‘Causal Asymmetries’, in Wright E. O. , Levine A. , Sober E. (eds), Reconstructing Marxism: Essays on Explanation and the Theory of History , New York : Verso , pp. 129 – 76 . © The Author 2017. Published by Oxford University Press on behalf of British Society for the Philosophy of Science. 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Restricted Causal Relevance

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Oxford University Press
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© The Author 2017. Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. For Permissions, please email: journals.permissions@oup.com
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0007-0882
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10.1093/bjps/axx034
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Abstract

Abstract Causal selection and priority are at the heart of discussions of the causal parity thesis, which says that all causes of a given effect are on a par, and that any justified priority assigned to a given cause results from causal explanatory interests. In theories of causation that provide necessary and sufficient conditions for the truth of causal claims, status as cause is an either/or issue: either a given cause satisfies the conditions or it does not. Consequently, assessments of causal parity and priority require more resources, which can either be in addition to or part of the causal analysis itself. While adding resources has been standard, here we develop a unified conceptual analysis that includes a range of different, precise causal concepts that allow for the assessment of causal priority in terms of different kinds of causal relevance. 1 Introduction 2 The Minimal Notion of Causal Relevance 3 Direct, Mediated, and Actual Causation as Restricted Causal Relevance 4 Normality Restrictions and Redundant Causes 4.1 Normality and norm restrictions 4.2 Redundant, non-redundant, and contextually necessary causes 5 Applications in Philosophy of Biology 5.1 Non-redundancy and redundancy in molecular biology of the nervous system 5.2 Normality in biology 5.3 Miscommunication and extrapolation 5.4 Circularity and non-substantial distinctions 6 Causal Parity Claims Refined 7 Conclusion 1 Introduction Distinctions between causes are invoked both in scientific and everyday causal judgements and reasoning. We often hear claims that some causes are stronger or more relevant than others. For example, genetic factors are referred to as causes in a sense not ascribed to other factors in development (Waters [2007]), and norm-violating actions are ascribed a causal status not shared by norm-abiding actions (Knobe and Fraser [2008]). How are such differences in causal judgements best understood? In this article we develop a pluralistic—though unified—analysis of causal concepts that accounts for numerous causal distinctions. On our account, causal concepts differ due to specific quantifier restrictions in their definitions. All concepts defined are unified by being, in various ways, stronger versions of a minimal definition of causal relevance. Different interests and explanatory aims contextually trigger different causal concepts, and we provide resources to spell out their precise contents. Pragmatic features—like aims and interests—determine what causal claims we make and investigate, while the causal claims themselves have objectively assessable truth conditions. Our approach contrasts with standard approaches, which provide analyses of causation in terms of necessary and sufficient conditions for the truth of canonical causal claims like ‘X is a cause of Y’. Examples of this include Lewis’s counterfactual dependence analysis of causation (Lewis [1973], [2004a]), and Woodward’s interventionist analysis of causation (Woodward [2003]). Lewis ([1973]) defines causation as the ancestral of causal dependence, where causal dependence between events is defined in terms of counterfactual dependence between a pair of propositions about the occurrence of these events. Event e depends causally on event c if and only if were c to occur, then e would occur; and if c were not to occur, then e would not occur. Lewis appeals to pragmatic-explanatory interests when discussing selection and priority among causes (Lewis [1986], [2004b]). On Woodward’s theory, causation is a relation between variables that can take any number of different values, and the central interventionist idea is that variable X is a cause of variable Y if and only if it is possible to change the value of Y by interventions on X (Woodward [2003], p. 59). In his core definition, Woodward defines both direct and contributing cause, so his view is not obviously monistic in the same sense as Lewis’s. However, when accounting for distinctions among causes, his strategy is to invoke his theory of causal explanation (Woodward [2010]), rather than his conceptual analysis and core definition. Woodward discusses how degrees of invariance (Woodward [2003]) and the notions of proportionality, specificity, and stability (Woodward [2010]) provide resources for drawing distinctions when it comes to the explanatory relevance and force of causes. In contrast, we explore how a pluralistic conceptual analysis can provide resources to distinguish between different kinds of causal relevance. We focus on distinctions having to do with actuality, redundancy, normality, and norm-sensitivity, and how these can function as restrictions on a minimal definition, thereby giving rise to stronger—restricted—concepts of causal relevance. Even if there are such differences in approach and focus, the view developed here bears close resemblance to, and is strongly inspired by, Woodward’s work. The argument for the pluralistic approach is based on discussions of causal selection and priority in biology, and a brief discussion of the norm-sensitivity of causal judgements. Moreover, the way our framework unifies existing and new causal concepts provides philosophical understanding—an additional consideration in its favour. We do not deny that additional resources can be used to make further distinctions between causes of the same kind. Correlation coefficients, measures of variance, and relative frequencies are examples of such additional resources (see, for instance, Wright et al. [1992]), and various rankings of normality, invariance, and specificity may be too (Halpern [2008]; Halpern and Hitchcock [2015]; Griffiths et al. [2015]). The present discussion is situated within a broadly interventionist framework. More precisely, we assume three core ideas as our point of departure: (i) that truth conditions for causal claims can be formulated in terms of behaviour under certain specific hypothetical changes (interventions) to causal systems; (ii) that type-causation is analytically fundamental, meaning that a philosophical analysis should start with type-causal relations, and from these derive token (event or actual) causal notions; and (iii) that causal claims essentially are part of, or derive from, larger causal representations, and that both truth and verification conditions for causal claims must make reference to the larger causal representations in which they are embedded. These ideas will become clearer as we spell out the framework. Our approach exemplifies a meta-philosophy where philosophical analyses answer to challenges and insights from outside academic philosophy. In the case of causal concepts, such external inputs include challenges in interdisciplinary communication in science, scientific accounts of human causal cognition, and alignment with scientific methodology. This is not to give up on the idea that causal concepts track objective relations; rather, it is to extend the input to philosophical inquiry beyond intuitions, thought experiments, and metaphysical theorizing. In recent contributions, approaches similar to parts of our account are developed in (Halpern and Pearl [2005]; Halpern [2008]; Gendler Szabó and Knobe [2013]; Halpern and Hitchcock [2015]; Kaiserman [2016]). We remark on most of these contributions along the way. These accounts mainly focus on actual causation and defaults having to do with norms (Hitchcock and Knobe [2009]; Gendler Szabó and Knobe [2013]) or typicality (Halpern [2008]). Our restrictions are closely related to the idea of defaults (Halpern [2008]; Halpern and Hitchcock [2015]), but our account is more liberal since it includes type-level causal relevancies, and allows for a whole range of different restrictions. Also, on our account, the restrictions figure directly in the definitions of specific causal concepts. First, we define a minimal notion of causal relevance by quantifying over interventions, over variables describing the system of interest, and over the values these variables might take. Various restrictions on these quantifiers give rise to stronger concepts of causal relevance; what we call ‘restricted causal relevance’ (or a related discussion, see Strand and Oftedal [2013]). The minimal notion gives a necessary condition for all kinds of causal relevance captured by the framework. In consecutive sections, we use this framework to define direct, mediated, and actual causes, and then normality-restricted and redundant causes. We present several examples of redundant and non-redundant causes in molecular biology of the nervous system, and show how truth conditions for causal claims can be specified in particular examples. We then present several biological understandings of normality and discuss normality restrictions and their role in conceptualizing causes in biology. Next, we discuss how our framework can facilitate the communication of causal claims and how relevant conceptual distinctions can helpfully frame the issue of extrapolation. Finally, we argue that causal parity theses should be restated as several different precise claims. 2 The Minimal Notion of Causal Relevance The framework developed here relies on core commitments of the interventionist framework (in particular, see Woodward [2003]). Causal relevance among types is analysed in terms of dependence among variables under interventions.1 Variables are representational devices that range over a set of values. The values in the value range of a variable are mutually exclusive. Value assignments to all or to a subset of the variables in a causal model are, respectively, points or regions in the state-space of the model, and these represent possible scenarios or sets of possible scenarios. Binary variables can represent properties being instantiated or not. Events can be represented by variables taking certain values. Variables used in causal representations should be distinct, which means that, ideally, any correlations among them should be due to causal dependencies. Causal claims are parts of representations of reality. Causal relations and structures are typically represented by causal claims, graphical representations, or structural equation models. The representations used in this article are causal concepts, distinct variables with specified value ranges, and directed graphs. Directed graphs consist of nodes representing variables and directed arrows representing direct causal dependence (to be defined). Against this backdrop, we define a minimal notion of causal relevance by quantifying over interventions, variables, and values2. In contrast to interventionist analyses in terms of fixed sufficient and necessary conditions (for example, Woodward [2003], p. 59), our notion allows for specifications of many different causal concepts by specifying various restrictions on the domains of the quantifiers. Definition 1: X is a cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y when some subset of variables (allowing this set to be empty) in M are fixed at some values. Here, M is a representation consisting of a set of distinct variables with specified value ranges, and an intervention on X relative to Y is a change in X that does not backtrack, that is, that changes X independently of X’s other causes, and that does not change Y directly.3 The following version of Definition 1 makes the quantifiers explicit, and thus marks the points at which restrictions can be introduced: Definition 1*: X is a cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y (quantifier over interventions on X: Q1) when some subset of variables (allowing this set to be empty) in M (quantifier over subsets of variables in M excluding X and Y: Q2) are fixed at some values (quantifier over the values of the variables: Q3). 3 Direct, Mediated, and Actual Causation as Restricted Causal Relevance By introducing restrictions on the quantifiers over variables and values in Definition 1, we can define several varieties of causal relevance. First, direct cause (Woodward [2003]; Strand and Oftedal [2013]): Definition 2: X is a direct cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y, when all other variables in M are fixed at some value. The concept of direct cause captures the idea of proximate cause, whose influence on the effect is not mediated by other variables. This aspect is captured by the requirement that all variables in M, except X and Y, are held fixed, since mediated causal relevance would be masked when fixating intermediary variables. Whether a causal relation between X and Y is direct or not is relative to M. A direct causal relation in M may be a mediated causal relation relative to a different representation, M*, that includes intermediary variables. The concept of direct cause is especially helpful since it can be used to define causal paths. A causal path is a sub-structures of a causal graph, representing a connected series of direct causal relationships. Consider a simple case of a switch, S, directing electrical current from battery B to either resistor R1 or resistor R2, represented in a causal graph as shown in Figure 1. Figure 1. View largeDownload slide Causal graph. Figure 1. View largeDownload slide Causal graph. Sub-structures B → S → R1 and B → S → R2 represent causal paths. With this notion we can define mediated causal relevance: Definition 3: X is a mediated cause of Y relative to M if and only if there is a path, P, between X and Y such that there is a possible intervention on X that would result in a change of Y when all variables in M not on path P between X and Y are fixed at some values, and X is not a direct cause of Y relative to M. While useful, Definition 3 does not capture mixed cases where X is a cause of Y along several paths, where one of these paths is direct.4 The simplest such case is shown in Figure 2. Figure 2. View largeDownload slide Mixed case. Figure 2. View largeDownload slide Mixed case. Mixed cases are tricky because causal relevance along the direct path cannot be controlled for and is therefore difficult to separate from causal relevance along other paths. Suppose that there are interventions on X that would result in changes to Y in Figure 2. The task is to isolate a further condition that states when this causal relevance distributes across both paths, and when there is no relevance via Z. A concept of path-specific cause enables such distinctions by imposing restrictions on the direct causal relationships constituting the path in question.5 The idea is to ensure that there are possible changes brought about in Y by interventions on X that are at least partly mediated along the path in question. More generally, X is a path-specific cause of Y along path P{X, Z1, […], Zn, Y} if and only if there is a possible intervention IX on X such that path P composes under IX: Path P {X, Z1, Z2, …, Zn, Y} in M composes under intervention IX on X if and only if there is a set of hypothetical interventions, {IZ1, …, IZn}, such that IX would bring about a change from value z11 to z12 in Z1 when all variables in M, except X and Z1, are fixed at some value; IZ1 would change Z1 from z11 to z12 and thereby bring about a change from z21 to z22 in Z2 when all variables in M, except Z1 and Z2, are fixed at some value; IZ2 would change Z2 from z21 to z22 and thereby bring about a change … from zn1 to zn2 in Zn when all variables in M, except Zn-1 and Zn, are fixed at some value; and IZn would change Zn from zn1 to zn2 and thereby change Y when all values in M, except Zn and Y, are fixed at some value. This requirement rules out failures of composition along the path in question. Failures of composition are counterexamples to causal transitivity where there is a causal path from X to Y, but where interventions on X only bring about changes in intermediate variables that are irrelevant for changes in Y.6 Definition 3 does not fully capture causal relevance along path P. There might be cases where a direct path from an intermediate variable to Y secures the existence of the required intervention, even if the mediating path we are interested in does not compose under that intervention. On the other hand, X might be a path-specific cause of Y along path P even if there are no possible interventions on X that would change Y when we hold all variables in M not on path P fixed. This might seem counterintuitive, but such cases arise if there is a direct link between X (or some intermediate variable on P) and Y that cancels out the influence along P. For this reason, one might think that the requirement that path P composes under some intervention is too weak for establishing mediated causal relevance between X and Y along path P. If so, one can introduce an additional requirement of dependence under intervention: X is a path-mediated cause of Y along path P{X, Z1, …, Zn, Y} in M if and only if there is a possible intervention, IX, on X such that path P composes under IX, and IX would result in a change of Y, when all variables in M not on path P are fixed at some value. Such a concept of path-mediated cause would allow for various restrictions on IX and on the values at which the other variables are held fixed. The distinction between direct and mediated cause is representation-dependent. That is, causal dependencies that are direct relative to a simple representation will typically qualify as mediated dependencies if we expand the representations to explicitly represent mediating factors. Most of the definitions in this article are formulated as direct causal dependencies, but there will be corresponding concepts of mediated causal dependence. We will point this out when it affects the discussion. A much-discussed version of restricted causal relevance is actual cause. Actual causation has received a lot of attention in the literature (see Hitchcock [2001]; Woodward [2003]; Collins et al. [2004]; Halpern and Pearl [2005]; Halpern [2008]; Halpern and Hitchcock [2015]). Many subtle problems with actual causation are thoroughly discussed in these contributions. We do not give an elaborate account of actual causation here, but we provide a definition that indicates how actual causation fits into our framework. Definition 4: X is a direct actual cause of Y relative to M if and only if there is a possible intervention on X that changes X from its actual value, resulting in a change of Y from its actual value, when all other variables in M are fixed at their actual values. This is intended to capture the notion of proximate event causation, where a cause is a difference-maker in a given actual situation. There are, however, notorious counterexamples to dependence analyses of actual causation. In particular, it has proven difficult to get idealized versions of both symmetric overdetermination and late pre-emption cases right. In Section 5.1 we discuss redundant causes and show how our framework can at least handle scientifically relevant cases of redundant causation. Kenneth Waters ([2007]) defines a causal concept that captures the notion of an actual difference-maker in a population, based on an interventionist framework. He introduces a distinction between actual difference-makers and potential difference-makers, and suggests that actual difference-makers are those factors or variables that, in most cases, we pick out as causes, while potential difference-makers are those factors or variables we frequently consider as background conditions. Actual difference-making causes are special because they actually vary in the population, while potential difference-makers do not. Waters argues that his distinction illuminates causal selection in general, and causal selection in classical and molecular genetics in particular. For example, he suggests that genetic factors had a distinguished causal status in relation to variation in eye colour in Morgan’s fruit fly experiments, due to the fact that they actually varied in the population. From our perspective, this causal concept can be captured by requiring the values of the variables to be instantiated in the population. An actuality restriction on the interventions (Q1) and on the values of the other variables (Q3) gives: Definition 5: X is a direct actual diference-making cause of Y in population P relative to M if and only if there is a possible intervention on X that changes the value of X among actually occurring values x1 and x2 in P, resulting in a change of Y among its actually occurring values in P, when all other variables in M are fixed at joint-value assignments actually occurring in combination with both x1 and x2 in P. Corresponding concepts of mediated actual causes and mediated actual diference-makers can be defined. Further restrictions can be formulated in terms of actual values in other populations; what scientists take their normal, expected, or most frequent values to be; in terms of what interventions are of clinical interest in medical research; or in terms of what we take to be normal or norm-respecting values in everyday contexts. We discuss some of these in the next section. 4 Normality Restrictions and Redundant Causes Redundancy and sensitivity to normality together with normative considerations give rise to interesting causal concepts. We show how these concepts are useful for understanding scientific practice and for analysing important features of causal reasoning. Some additional terminology will be useful at this point. A pair of counterfactual scenarios ‘witness' a causal dependence when they fulfil the truth conditions for the corresponding causal claim. Similar terminology is used in (Halpern [2008]) and (Halpern and Hitchcock [2015]) for possible worlds that demonstrate actual causal relationships; Halpern and Hitchcock ([2015]) formulate normality rankings of witnesses relative to the actual world. Our use of the term ‘witness’ is more liberal, but it is inspired by and trades on the same idea as these authors. A ‘hypothetical intervention’ can be thought of as an operation that creates a contrast between hypothetical scenarios (or between an actual and a hypothetical scenario in the case of actual causation). The existence of such contrast scenarios that differ in the right way witnesses the truth of causal claims. Experiments mimic such hypothetical contrasts by controlling for other factors and inducing a change in the cause factor of interest. 4.1 Normality and norm restrictions A number of recent contributions discuss the relevance of normality considerations and norm-sensitivity for causal judgement (Halpern [2008]; Hitchcock and Knobe [2009]; Gendler Szabó and Knobe [2013]; Halpern and Hitchcock [2015]; Kaiserman [2016]; Weber [forthcoming]). In these accounts, normality and norms enter as constraints on the counterfactual scenarios relevant for causal judgement. Some of these accounts also develop rankings of counterfactual scenarios in terms of normality (Halpern [2008]; Halpern and Hitchcock [2015]). Within the present framework, however, normality (or normality thresholds) figure as quantifier restrictions that specify distinct normality-restricted causal concepts. In the case of normality, one can generate a range of different concepts since we have three quantifiers that can be restricted and since there are several ways of specifying normality. The interest of these definitions will vary, and we will only consider a few that we think are interesting here. Definition 6: X is a normality-restricted direct cause of Y relative to M if and only if there is a possible intervention on X that would result in a change of Y when all other variables in M are fixed at some normal, joint-value assignment. This definition does not include a normality restriction on the values set by interventions, and thereby allows for abnormal interventions. Such a concept might be of use, for example, when reasoning about the effect of medical interventions. Concepts with normality restrictions on the values set by interventions are relevant in other contexts, as suggested by Weber ([forthcoming]) (see brief discussion in Section 4.2). Normality can be specified objectively, in terms of frequency or relative frequency. It can also be specified in more subjective or human-centred terms, for example, as compatibility with norms or expectations. We discuss notions of normality relevant for biology in Section 5.2. In particular, Knobe and Frasers’ ([2008]) results on the norm-sensitivity of folk-causal judgement have sparked recent philosophical debate (see Hitchcock and Knobe [2009]; Gendler Szabó [2013]). According to Hitchcock and Knobe ([2009]), norms make certain counterfactual scenarios salient in causal judgement about actual cases. This suggestion can be cashed out in a slightly different way within the present framework. Rather than norms acting directly on causal judgement by making certain counterfactual scenarios salient, they are contextual factors that play a part in determining what causal concepts are expressed in the context. When people make asymmetric causal judgements about norm-violating and norm-abiding actions, they actually employ a norm-sensitive concept of cause. Definition 7: X is a norm-restricted, direct actual cause of Y relative to M if and only if there is a possible intervention on X that takes X from its actual value, which violates a norm, to a value that does not violate the norm, and that would result in a change of Y when all other variables in M are held fixed at their actual values. In the case discussed by Hitchcock and Knobe ([2009]), and first presented by Knobe and Fraser ([2008]), a member of faculty takes a pencil despite the norm that the pencils are for administrators only. An administrator also takes a pencil. The respondents are then asked who caused the consequent lack of pencils. According to their surveys, the faculty member who violated the norm is judged as a cause, while the administrator who did not violate the norm is not. On our account, this is explained by the hypothesis that many people reason with a norm-restricted concept of cause in such contexts.7 4.2 Redundant, non-redundant, and contextually necessary causes The distinction between redundant and non-redundant causes shows up in discussions of robustness and functional stability in philosophy of biology (Strand and Oftedal [2009], [2013]). There are also extensive philosophical discussions of late pre-emption and overdetermination cases (Woodward [2003]; Collins et al. [2004]; Lewis [2004a]), which are regarded as counterexamples to dependence analyses of causation. In the following, we distinguish between redundant causes, trigger-redundant causes, non-redundant causes, and contextually necessary causes. We do not discuss idealized counterexamples like trumping and late pre-emption here; instead, we focus on how our approach can account for redundant causes in scientifically relevant cases. The core idea is that a cause is redundant if its causal relevance only is witnessed by pairs of counterfactual scenarios where one is somehow abnormal. Two concepts of redundant cause can be distinguished. First, in cases similar to late pre-emption cases, backups are not triggered by interventions on the redundant cause but are latent and ready to bring about the effect if the redundant cause does not. Second, in cases similar to early pre-emption, backup causes are triggered by interventions on the redundant cause. Corresponding concepts of redundant causes differ in terms of the kind of abnormalities required to witness the causal dependence. Definition 8: X is a latent-redundant cause of Y relative to M if and only if there is a possible intervention on X that would change the value of Y only when some other variables in M are fixed at values that are abnormal in combination with the pre-intervention value of X. Definition 9: X is a trigger-redundant cause of Y relative to M if and only if there is a possible intervention on X that would change the value of Y only when some other variables in M are fixed at values that are abnormal in combination with the post-intervention value of X. A cause is redundant if it is latent or trigger-redundant. The kind of normality involved in these definitions will presumably vary with context, and we suspect that both norm-based and typicality-based normality restrictions figure in everyday causal reasoning about pre-emption and overdetermination cases. However, our focus will be on selected biological examples of redundant causes, which are discussed in the next section. A non-redundant cause is a cause whose relevance is witnessed by normal counterfactual scenarios. In other words, it is a normality-restricted cause. Intuitively, X is a non-redundant cause of Y if X’s causal influence on Y does not have a backup for at least some normal, joint-value assignments of the other variables. To illustrate, only a small percentage of individual genes are non-redundant causes of phenotypic traits. Gene-knockout experiments reveal widespread genetic redundancy of single genes (Gu et al. [2003]; Wagner [2005]), and such causal relevance is only witnessed in multiple knockout scenarios or in abnormal environments. Finally, we define a direct contextually necessary cause: Definition 10: X is a direct, contextually necessary cause of Y relative to M if and only if, for all normal, joint-value assignment of values to all other variables in M, there is a possible intervention on X that would change the value of Y. An example of a direct contextually necessary cause is an enzyme necessary for catalysing some biological process (Rabus et al. [1999]; Vincents et al. [2004]). 5 Applications in Philosophy of Biology Causal locutions and terms like ‘cause’, ‘proximate cause’, ‘contributing factor’, and so on express causal concepts, but different locutions can express different causal concepts, and even different occurrences of the same locution can express different concepts in different contexts. Which concept is being expressed is sometimes determined by context, but sometimes it is underdetermined in the given context, which may result in ambiguity and possible miscommunication. In the following, we discuss non-redundancy, redundancy, and normality in biology, and suggest how to precisely understand corresponding causal concepts by introducing relevant restrictions on causal relevance. 5.1 Non-redundancy and redundancy in molecular biology of the nervous system The examples in this section illustrate the distinction between redundant and non-redundant causes as they figure in molecular biology. Additionally, the examples show how a dependence-based account of causation can handle scientific examples of redundancy. We thus give a more hands-on take on pre-emption problems, in contrast to how idealized pre-emption and overdetermination cases are often presented when discussing counterexamples to dependence analyses of causation. A non-redundant cause in molecular biology is a cause that has no backup mechanisms in normal contexts. Consequently, the functionality of the system is affected if a non-redundant cause is perturbed. Receptors are small molecules on the surface of cells that receive and bind to external chemical signals. Plexin receptors can be found on the surface of neuronal cells and are receivers of small protein signals called semaphorins. By inhibiting or enhancing axonal growth, the binding of semaphorin to plexin receptors influences how the neural system develops. Several studies suggest that genes involved in the formation of plexin receptors are non-redundant in several neuronal processes (see, for example, Worzfeld et al. [2004]). For instance, mice in which the Plexin-B2 gene was knocked out showed defects in neural tube closure in the development of the embryonal nervous system. Significant impairment such as exencephaly (brain located outside the scull) and prenatal death resulted (Deng et al. [2007]; Friedel et al. [2007]). In these cases, no backup genes or processes replaced the knocked out Plexin-B2 gene, with devastating developmental results. Under these experimental conditions, Plexin-B2 was a non-redundant cause of a range of effects. The concept of non-redundant cause that is in play here is captured by the concept of a normality-restricted cause. More precisely, the truth conditions for the claim that Plexin-B2 is a non-redundant cause of axonal growth are: Plexin-B2 is a non-redundant cause of axonal growth relative to M (set of factors represented in the given context) if and only if there is a possible intervention on Plexin-B2 that would change axonal growth when all other factors not on the causal paths between Plexin-B2 and axonal growth are fixed at some normal, joint-value assignment. We have deliberately not specified the notion of normality in play, which presumably will vary with context. In Section 5.2, we discuss various notions relevant in biology. Redundancy is frequent in living systems and contributes to system robustness. If several causal factors ensure the same effect, the system may survive and perform equally well if one or several parts of the system are changed, destroyed, or removed (Kafri et al. [2009]). Biological causal redundancy can be realized by at least three different mechanisms: duplication, degeneracy, and distributed robustness (Edelman and Gally [2001]; Wagner [2005]). Duplication occurs when several copies of a factor, typically genes, are present and one or more copies act as backups if the original cause is perturbed. Degeneracy occurs in situations where structurally different parts can do the same causal job. For instance, when different genes contribute to proteins with the same function, or when different enzymes catalyse the same processes. The case of distributed robustness concerns more complex system adjustments as a response to the perturbation of a factor. The idea is that several components and processes jointly act as backup for a causal factor. In all these versions of redundancy, the causal dependence between the redundant cause and its effect is not witnessed by normal scenarios. Rather, in normal circumstances, when a factor is perturbed, another factor compensates and there is no difference-making relationship between the alleged cause and the effect.8 Under abnormal conditions, however—when, for example, all the existing backups are knocked out—the causal relation is witnessed. An example is the genetic contribution to the production of calmodulin (CaM), a calcium sensor protein important for signalling in the nervous system. Calcium ions (Ca2+) act as intracellular messengers because their concentration decides neuronal excitability. When increasing in concentration, Ca2+ ions bind to CaM proteins and start signalling cascades, which play important roles in a range of processes such as learning, memory, and other cognitive activities, as well as in stress responses. Having this central role, living organisms secure the production of CaM proteins through causal redundancy. In vertebrates, there is a whole family of genes placed at different locations in the chromosome that encode an identical CaM protein thus ensuring a high level of robustness of the CaM-dependent processes (Toutenhoofd and Strehler [2000]). Under normal conditions, if a CaM-producing gene is not working for some reason, one or several other genes are lined up to step in. Thus, knocking out a gene under normal conditions will not (significantly) affect the CaM-dependent processes. In abnormal conditions, however, where backup genes are out of play, the dependence between the CaM processes and the gene in question is witnessed (Panina et al. [2012]). Models of CaM-gene redundancy may include both latent redundancy and trigger redundancy. An example of latent redundancy is a case where the knocking out of a CaM-related gene is compensated by other CaM-related genes without their expression being affected by the knockout. Simultaneous stable expression of several CaM-related genes may overdetermine CaM production, so that already existing CaM production is sufficient to compensate for the lacking gene. Using the previously defined concept of latent redundant cause, we can spell out the truth conditions for the claim that a CaM gene is a latent redundant cause of calmodulin production: A CaM gene is a latent redundant cause of calmodulin relative to M if and only if there are possible interventions on the CaM gene that would change calmodulin production only when some variables in M are fixed at values that are abnormal in combination with the CaM gene not being knocked out. In cases where knocking out a CaM-related gene affects the regulation of other genes through feedback mechanisms, the gene is a trigger-redundant cause. The counterfactual dependence will only be witnessed in scenarios where backup mechanisms are fixed at values that are abnormal given that the gene is knocked out. Normally, backup mechanisms will compensate when a gene is knocked out, but under abnormal conditions (for example, multiple knockouts) they are kept from compensating. Using the previously defined concept of trigger-redundant cause, we can spell out the truth conditions for the claim that a CaM gene is a trigger-redundant cause of calmodulin production: A CaM gene is a trigger-redundant cause of calmodulin relative to M if and only if there are possible interventions on the CaM gene that would change calmodulin production only when some variables in M are fixed at values that are abnormal given that the CaM gene is knocked out. Whether a particular CaM-related gene is a latent redundant or a trigger-redundant cause is an empirical question when the relevant kind of normality is specified, and investigating particular redundancy types may require distinct research designs. Another example of redundancy is found in the spliceosome. The spliceosome consists of splicing factors, including small nuclear RNAs and protein complexes in the cell nucleus that remove parts of the RNA sequence before it becomes mature messenger RNA (mRNA) ready to serve as a template for protein production. Thus, splicing factors influence how premature RNA sequences are cut and spliced to constitute final templates for proteins. An RNA sequence can be cut and spliced in many different ways. Such alternative splicing greatly increases the repertoire of mRNA and proteins in multicellular organisms. Typically, environmental and/or epigenetic factors influence the spliceosome, enabling the cell to make different proteins from the same gene depending on environmental demands. For example, adrenaline-producing cells in the human nervous system respond to stress by altering the construction of calcium (Ca2+) channels in the cell membrane to better accommodate stress conditions compared to standard Ca2+ channels (Liu et al. [2012]). The modified channels open more easily and respond more quickly to stress. The stress-induced channels are different because splicing factors include an extra RNA part in the mRNA called STREX (stress exon) in the template for the relevant channel protein. Splicing redundancy occurs when several different splicing agents can perform the same addition or subtraction of premature RNA. A recent study has shown that two different splicing factors, hnRNP L and hnRNP LL, act redundantly in the modulation of the STREX exon in response to depolarization of the cell (Liu et al. [2012]). Inclusion of STREX under stress conditions is thereby secured via causal redundancy of factors in the splicing process. Knocking down a splicing factor did not stop the inclusion of STREX into the mRNA and subsequently into the channel protein. Knocking down both hnRNP L and hnRNP LL at the same time, however, stopped this particular stress response in cell membrane channels (Liu et al. [2012], p. 22711). Using our concept of latent redundant cause, and assuming that STREX is overdetermined by the two splicing factors, we can spell out the truth conditions for the claim that hnRNP L is a latent-redundant cause of STREX: hnRNP L is a latent-redundant cause of STREX relative to M if and only if there are possible interventions on hnRNP L that will change STREX production only when some variables in M are fixed at values that are abnormal in combination with hnRNP not being knocked down. 5.2 Normality in biology In this section we discuss three understandings of biological normality, and indicate how they can generate concepts of restricted causal relevance. The three are function-based normality, statistical normality, and normality in terms of natural occurrence.9 Concepts of normality can be applied to different size and time scales of biological systems, and can be indexed with respect to particular environments. Understandings of normality in biology often link to the concept of function. A normal heart is a heart that functions biologically. There is a large philosophical debate about the notion of biological function. Roughly, function is either analysed as an etiological concept (Millikan [1984]) or as a causal role concept (Cummins [1975]). In etiological theories, a biological function is understood in terms of its evolutionary history, which explains why the function is there; while in causal role accounts, statements about biological functions are merely used to explain how components of a structure contribute to a capacity of the system. We will not enter this debate except to note that a concept of biological normality more easily links up to etiological accounts, as these allow for malfunction. Many differences between hearts are permitted within the range of normal functioning, but not those that are associated with malfunctioning (Wachbroit [1994]). Statistical normality or typicality is frequently invoked in biology and often overlaps with, and is used as an indicator of, function-based normality. Statistical normality can be represented by a normal distribution of some trait, process or state, or it can be defined as the mean, median, or most frequent (Wachbroit [1994], p. 580). Still, non-functional biological processes or states sometimes occur rather frequently in populations (for example, obesity), thus what is statistically normal is not always functionally normal. Causal concepts with statistical normality restrictions seem to be in play in causal reasoning when we ignore hypothetical scenarios that include statistically very atypical possibilities. For example, we do not judge the absence of a meteorite fall as a cause of the development of a lake trout population. In Woodward’s terminology, statistical normality restrictions can exclude scenarios that are not serious possibilities. We also distinguish a third kind of normality within biology in terms of what exists in naturally occurring systems, where the salient contrast is systems that are affected in some way by human interventions. Non-natural systems would typically be experimental systems or systems that are changed via technology or medication. Causal analysis of medicated systems, for example, may need different conceptualizations of cause than for natural systems. Drugs, for instance, add to the causal repertoire of a system and may introduce novel redundancies. Many drugs work by binding to receptors that, normally (understood in terms of naturally occurring), are reserved for components that already exist in the system. In the examples of redundancy described in the previous section, normality restrictions in terms of natural occurrence are relevant since, typically, abnormal scenarios that include multiple knockouts are induced by human experimental interventions on the system. Normality is relative to different size scales or graining; abnormalities at smaller scales may not be relevant at larger scales. Backup mechanisms often secure full organismal functionality, and in cases without backups, where a mechanism is dysfunctional, the dysfunction may constitute only a small contribution to how the organism copes as a whole. There are also cases where fine-grained dysfunction is clearly detrimental to organismal functionality. In a recent paper, Marcel Weber ([forthcoming]) suggests an account of what he calls ‘biologically normal interventions’. On his view, biologically normal interventions are such that they (i) could be brought about by natural biological processes and (ii) are compatible with survival of the organism (see also discussion in Griffiths et al. [2015], p. 543). From our perspective, this is a way of introducing a normality restriction on relevant causal interventions in terms of normality at the organismal scale. Weber’s definition appeals to a combination of normality in terms of natural occurrence and function-based normality, as discussed above. He introduces the concept of a normal intervention to isolate a set of interventions that are compatible with survival of the system, and these are the biologically relevant subset of all possible interventions in living systems. According to Weber, such restrictions capture an important feature of causal explanatory practice in biology, namely, that only biologically normal interventions are found relevant in most explanatory contexts. Weber’s definition enters the discussion of specificity of DNA–RNA–protein relations (Waters [2007]; Woodward [2010]; Griffiths et al. [2015]; Weber [forthcoming]), where specificity is understood as fine-grained influence. A causal relation is specific when there are several different values of the cause variable that roughly correspond one-to-one with values of the effect variable (Woodward [2010], p. 305). Sequences of DNA are considered specific causes of sequences of RNA in virtue of the large number of possible combinations of DNA bases that correspond in a one-to-one manner to combinations of RNA bases. As pointed out by Weber ([forthcoming]), however, it is only a small number of such combinations that are actually consistent with a viable system. For Weber, the number of viable combinations, rather than the number of merely possible combinations of DNA and RNA sequences, is the relevant basis for the specificity of their causal relation. From the perspective of our framework, Weber’s suggestion is a special version of a normality restriction on interventions. Normality can also be understood in relation to different time scales. The normal functioning of a molecular mechanism is often manifested over a short time scale, while normality in development and functioning over longer time scales includes the normality of organs, lifespans of organisms, and cycles of populations. Analogous to size scales, normal development over a longer timespan can often be sustained despite disruption over shorter timespans. In many cases, what is normal is relative to variations in background conditions (Dussault and Gagne-Julien [2015]). Many organisms have a high degree of phenotypic plasticity, allowing growth and functioning to vary with the organism's environment. For example, at varying altitudes, plants of the same species often look and function very differently. Thus, what is normal for many plants at high altitudes is not normal at lower altitudes. Such context-dependent normality is also a basis from which one can formulate relevant restrictions. The variety of understandings of normality indicates a need to be specific about what kind of normality restrictions are in play in a given context. We take it to be a virtue of the present account that it allows for the specification of different causal concepts corresponding to different normality restrictions, depending on their importance in various contexts. 5.3 Miscommunication and extrapolation Differences between the precise meaning of causal claims in experimental contexts and the interpretation of these claims in other contexts are possible sources of miscommunication (Oftedal and Parkkinen [2013]). Explicating restrictions on causal concepts in play can be used to specify variations in the precise content of causal claims across contexts. Extrapolation involves the transportation of causal claims from one setting to another, assuming the relevance of the causal claim despite changes in background conditions. Such extrapolations are often undertaken from research on animal models to claims about human physiology, but extrapolation is important in most fields of research. Our account provides tools for explicating precisely what separates causal claims in the contexts we are extrapolating between, by explicating conceptual differences potentially triggered by the different contexts. Separating these conceptual issues from the issue of how extrapolation can be justified when the causal claims have stable meaning across contexts is necessary for getting traction on this issue. When transporting causal claims across contexts, the extent to which different causal concepts are in use, or the extent to which different assumptions are being made about background conditions, will vary. One often finds that various restrictions on background conditions are made explicit if miscommunication is suspected.10 Combined with the fact that restricted causal claims entail claims of minimal causal relevance, complex communicative situations are created. An example is found in the debates over evidence-based medicine. Even if assumptions bridging the inferential gap from trial population to target population can be justified, stronger assumptions are needed for clinical decisions concerning individual treatments—for example, that the actual condition of the individual in question is relevantly similar to the trial subpopulations in which the treatment had positive effect. Population- and individual-level perspectives differ in terms of what restrictions are salient; causal information sufficient to justify population-level guidelines is not sufficient to justify particular clinical decisions (Strand and Parkkinen [2014]). By focusing on differences between causal concepts in terms of variations in the truth-conditions for corresponding causal claims, we suggest a procedure for mending this situation. Whenever miscommunication seems likely, we should be precise about the restrictions in play. In such cases, it is crucial that information about restrictions and assumptions are explicitly stated along with the causal information. This requirement is exemplified by the CONSORT guidelines for medical publications.11 These guidelines are developed to alleviate problems arising from inadequate reporting of randomized controlled trials (RCTs). It includes a check list and a flow diagram that recommend how to report design, analyses, and interpretations of RCTs. A focus on the appropriate assumptions and restrictions is important for the interpreter too, because it is generally not valid to infer restricted causal relevancies from evidence for other kinds of causal relevance. 5.4 Circularity and non-substantial distinctions If a variable is defined in terms of other variables, including its typical effects, there is an immediate potential for circularity in causal explanations involving that variable (and violations of independence assumptions like the causal Markov condition). One example is a dispositional feature like water solubility: if water solubility is defined as a tendency to dissolve in water, the solubility of a given drug will not causally explain that it dissolves in water. In short, causes and effects should not be conceptually related in this way in order to provide informative explanations and make explanations empirically falsifiable. Such worries have been a recurrent theme in criticisms of belief–desire explanations in empirical psychology (see, for example, Rosenberg [1985]). If normality-restricted causal concepts are defined in terms of causal functionality, then a related circularity might arise. A causal role definition of a function specifies the function in terms of its causal role, that is, in terms of what output it creates in response to certain inputs. For example, a loudspeaker has the function of transforming electrical signals into sound waves. If normal scenarios are defined as the scenarios where the functioning of the loudspeaker accords with the causal role description of the loudspeaker, then whether the loudspeaker is a normality-restricted cause of the sound or not becomes a matter of definition. The worry is that some function-based normality restrictions will introduce circularity for cases where the relevant cause and effect figure in the causal role definition of the function. If the normality restriction restricts counterfactual scenarios to the ones where the loudspeaker functions properly, then the electrical input will be appropriately correlated with sound waves in those scenarios, by definition. After all, we are only considering scenarios where that is the case. Such functional-normality-restricted causal concepts will thus be problematic for causal explanations of effects figuring in the analysis of the function. Whether a restricted cause–effect relationship obtains should be a matter of empirical fact, not a matter of definition. Such restrictions and concepts might still be useful as heuristics for gaining relevant understanding about causal structures, but one should be aware of the potentially problematic circularities they introduce. Against this background, it becomes an interesting issue whether such functional-normality-restricted causal concepts actually are in play in causal explanatory practice. If so, it should be checked whether they give rise to problematically circular explanations, and whether the claims in which they figure are empirically testable. 6 Causal Parity Claims Refined Discussions of causal parity in the philosophy of biology concern the apportioning of causal responsibilities to genetic and environmental causes. Different versions of the parity thesis have been invoked to argue that genetic and environmental causes are on a par (see, for example, Griffiths and Stotz [2013]), while others argue on the basis of particular characteristics of the DNA–RNA–protein relation that these causes are not on a par (Waters [2007]; Woodward [2010]). Discussions of causal parity are found both in the causation literature and in the developmental systems theory (DST) literature. Stegmann ([2012]) provides a helpful discussion of the various claims that surface in the DST literature and their connections to the causation literature. In particular, he spells out a Millean parity thesis applied to the relation between genetic and environmental causes (Stegmann [2012], p. 906), based on John Stuart Mills’s general causal parity claim. Millean Parity: Genetic and non-genetic factors are on a par insofar as both are causes and causes constitute a uniform ontological category (specifically, there is no ontological difference between causes and conditions). From our perspective, the ontological differences between different kinds of causes discussed by Stegmann and several participants in this debate is better understood as an objective difference in causal status. On our view, cause is not an ontological category; whether something is a cause is a question of whether it relates to a given effect in certain ways. Causes can be variables, properties, property instances, objects, activities, and so forth. Causes can cause effects by being absent, by transferring momentum, by depolarizing, and so forth. There seems to be neither ontological nor physical unity to all causes and causal relations. For these reasons, we reinterpret Millean parity in the DST context as: Millean Parity*: Genetic and non-genetic factors are on a par insofar as they are causes of the same kind in development. On a monistic view of causation, Millean parity* will be close to trivial, since there is only one kind of causal status. For this reason, DST discussions of parity have often focused on other kinds of objective (sometimes denoted ‘ontological’) differences between genes and non-genetic causal factors in development. Examples are distinctions between information carriers and other causes, between replicators and interactors, and between specific and non-specific causal factors. On the pluralistic framework developed here, however, we can distinguish several different causal parity claims. The minimal notion of causal relevance (Definition 1) gave us a template for defining precise causal concepts that enable qualitative comparisons of causes. Given the resulting pluralism of related but distinct causal concepts, we can straightforwardly reject strong causal parity theses holding that all causes are on a par. Weaker causal parity theses should thus be considered. Minimal Causal Parity: Any cause is a cause in the minimal sense. This claim is correct for all the causal concepts discussed here. However, we do not rule out that there can be legitimate uses of causal locutions that are not captured by our framework. Notions of agent causation in philosophy of action are candidates. Another causal parity claim, which can be formulated in terms of restricted causal relevance, is that any two causes that fulfil a given restriction are on a par. This, however, is not true in general. The reason is that such causes can be asymmetric relative to other restrictions. For example, of two direct actual causes of a given effect, only one might fulfil a normality restriction. Consequently, we get two different parity claims relativized to restrictions: Local Restricted Causal Parity: Any cause that fulfils any given restriction is on a par with any other cause of the same kind, with respect to that restriction. Global Restricted Causal Parity: Any two causes that fulfil all the same restrictions are on par. Based on several learning studies in mice, an example of local restricted causal parity can be constructed. Suppose there is a mouse population where some mice (Doogie mice) have an enhanced NMDA receptor function, resulting in improved memory and learning due to foreign genes being inserted into their genome (Tang et al. [1999]). In addition, suppose that the population members vary with respect to anxiety levels (Deacon [2013]), which also affect memory and learning (Darcet et al. [2014]). In such a case, the causes (genes and anxiety levels) are on a par with respect to the first set of restrictions (actuality) but not with respect to the second set of restrictions (natural occurrence). NMDA-genes and anxiety levels actually vary in the population, while only variation in anxiety levels is naturally occurring. Global restricted causal parity appears to follow directly from our definitions, and in a sense it does. However, if normality restrictions can be graded (in terms of more-or-less normal value assignments), then causal parity would be a graded phenomenon. Causal parity would come in degrees, and causes could be more or less on a par. If we assume that there is a partial order on scenarios (points or regions in the state space of the relevant causal model) in terms of normality, we can get an ordering on the causes for a given effect in terms of how normal the scenarios that witness dependence under interventions are. (Halpern and Hitchcock [2015]) is an interesting development of this approach for actual causation (see also Halpern [2008]). We do not take a stand here on whether such developments should be incorporated into the definitions of causal concepts or figure as part of a theory of causal explanation. 7 Conclusion We have developed the interventionist framework into a unified, though conceptually pluralistic, account of causation. Our minimal definition serves as a template for a range of causal concepts generated from different sets of restrictions. We have discussed how concepts of restricted causal relevance can be used to clarify causal claims, to disentangle conceptual and substantial issues, and to facilitate communication of causal information across contexts. Further developments of this account are worthwhile and in progress. In particular, we would like to assess whether relaxing the distinctness requirement on the variables and/or the requirements on interventions can accommodate various forms of non-causal explanation, including constitutive explanation, grounding, and functional and teleological explanations. Other developments include accounts of invariance and causal specificity. Various aspects of invariance can be captured by specifying under what ranges of variation the causal dependence obtains. There are several dimensions to invariance (see Woodward [2003]). They concern which other factors can vary, how much they can vary, and the range of interventions on the cause variable that result in changes on the effect variable. Invariance cannot be captured by simple restrictions on the quantifiers in our minimal definition. Rather, degrees of invariance can be captured by the (relative) size of the subdomains of these quantifiers where the dependence under interventions obtains. As with the normality rankings discussed above, it is an interesting question whether degrees of invariance should enter directly into the semantics of causal concepts, or whether they are better accounted for by a theory of causal explanation. Similarly, various forms of causal specificity might be defined in terms of the relative size of partitions of possible changes in the effect variable that are bijectively related to partitions of possible changes in the cause variable. Whether some forms of specificity—and degrees of specificity in particular—are better accounted for by a theory of causal explanation is a question we leave unanswered here. Acknowledgements We would like to thank Henrik Forssell for early discussions of the idea that the relevant definitions can be formulated using quantifiers and quantifier restrictions. We would also like to thank Torfinn Huvenes and William Wimsatt for helpful comments on earlier drafts. We are very grateful to two anonymous referees, who gave exceptionally valuable feedback that led to significant improvements. This work is part of the project ‘Causation and Reduction in Systems Biology’, funded by the Norwegian Research Council and the University of Oslo (grant no. 231106), and hosted by the Department of Philosophy, Classics, History of Art and Ideas, University of Oslo. Footnotes 1 There are subtle but philosophically important issues concerning the relata of causal relations. They can be literally taken as variables, that is, as representations of factors; or they can be taken as the referents of these representational devices. For the purposes of this article, we do not take a stand on this issue. 2 See (See (Strand and Oftedal [2013], p.180) for a preliminary version of this minimal notion of causal relevance. 3 See (Woodward [2003], Section 3.1.3) for a more elaborate and precise description of interventions. 4 Such cases have been discussed in the context of the faithfulness condition (Spirtes et al. [2000]; Woodward [2003], pp. 49–50) and counterexamples to transitivity (Hitchcock [2001]; Hall [2003]). 5 See (Pearl [2001]) for a definition along similar lines and a discussion concerning the possibility of deactivating causal paths and direct links. 6 Hitchcock ([2001]) discusses counterexamples to transitivity, including failures of composition and the notion of an active causal route. In contrast to his discussion in that paper, our definitions focus on type-level relevancies rather than event causation. Notice that counterexamples to causal transitivity based on failures of composition are ruled out if we are restricted to binary variables in M. This might explain the widespread acceptance of causal transitivity in the literature on event causation (for example, Lewis [1973]). 7 The results were seemingly robust, but many respondents still judged the norm-abiding action of the administrator also to be a cause. On our take, this is explained by these respondents not employing a norm-restricted causal concept in that context (of course, some respondents might also just be mistaken in their reasoning). 8 We here assume relative coarse-grained and temporally limited representations. More fine-grained models and/or models with long time-scales may reveal differences in many actual cases. 9 We considered evaluative normality involving norms above. 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Published: Sep 1, 2017

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