The Exclusion Problem Meets the Problem of Many Causes Matthew C. Haug The College of William & Mary

The Exclusion Problem Meets the Problem of Many Causes Matthew C. Haug The College of William & Mary Abstract In this paper I develop a novel response to the exclusion problem. I argue that the nature of the events in the causally complete physical domain raises the problem of many causes : there will typically be countless simultaneous low-level physical events in that domain that are causally sufficient for any given high-level physical event (like a window breaking or an arm raising). This shows that even reductive physicalists must admit that the version of the exclusion principle used to pose the exclusion problem against nonreductive physicalism is too strong. The burden is on proponents of the exclusion problem to provide a reason to think that any qualifications placed on the exclusion principle will solve the problem of many causes while ruling out causation by irreducible mental events. 1. Introduction The exclusion problem has long been the bane of non-reductive physicalists. Proponents of the exclusion problem claim that non-reductive physicalists must give up either the causal efficacy of mental properties and events or their irreducibility, on pain of abandoning at least one of three claims that any physicalist must allegedly endorse: the completeness of physics, the exclusion principle the claim that there cannot be two or more simultaneous sufficient causes of a given event, except in cases of overdetermination, and non-overdetermination the claim that mental causation does not involve systematic overdetermination. 1 Although many different responses to the exclusion problem have been offered, there is no consensus about which is best or if any of them succeeds. Probably the most popular direct response to this problem is to endorse what is often called causal compatibilism and deny the exclusion principle, by claiming that there are cases where two simultaneous events are causally sufficient for a given event without overdetermining that event (e.g. Horgan 1997; Bennett 2003, 473; Yablo 1992). Others deny nonoverdetermination and claim that overdetermination is ubiquitous and unproblematic (e.g., Sider 2003). 2 Many causal compatibilists motivate their denial of the exclusion principle by attempting to show that mental events are related to physical events in such a way that they do not compete as sufficient causes (say, as determinables are related to their determinates). Thus, it is open to the proponent of the exclusion 1

problem to challenge the details of this response, by questioning either the proposed account of the mental/physical relation or the implications of that relation. Many non-reductive physicalists also want to use exclusion-based reasoning the so-called causal argument for physicalism to argue for their view and against substance or property dualism (e.g. Papineau 2001, cf. Bennett 2008). (In Haug forthcoming, I attempt to show that non-reductive physicalists can do so consistently.) Such philosophers will be reluctant to deny non-overdetermination and to treat all cases of (broad sense) overdetermination equally. Further, they will also be reluctant merely to deny the strict version of the exclusion principle stated above without replacing it with some appropriately qualified version. This is because they seek to use the causal argument (which, again, relies on some form of the exclusion principle) to rule out interactionist forms of dualism that also endorse the completeness of physics. Any physicalist would seem to be committed to claiming that these forms of dualism involve an unacceptable form of systematic overdetermination. In this paper, I offer a novel defense of the claim that the exclusion principle, as stated above, is false. Considerations that are analogous to the problem of the many (see Unger 1980) show that even the proponent of the exclusion problem must admit that there are apparently countless simultaneous physical causes of a given physical effect. Hence, the exclusion principle, as stated above, is unacceptable even from within a reductive physicalist framework. Many physicalists (both reductive and nonreductive) will want to accept a weaker, qualified version of the exclusion principle in order to show that the many causes are an acceptable case of overdetermination. However, it is likely that any principle that does so will also deem as acceptable causation by simultaneous mental and physical events that are related in an appropriate way. In Section 2, I point out that proponents of the exclusion problem assume that completeness applies only in the low-level physical domain. In Section 3, I follow Kim in assuming that this lowlevel physical domain is closed under the formation of micro-based properties and includes aggregates of fundamental physical entities. 3 I then argue that the problem of many causes shows that the strong version of the exclusion principle, which generates the exclusion problem, is false. In Section 4, I argue 2

that the exclusion problem can be blocked even if we drop Kim s assumptions about the low-level physical domain. Compositional nihilists who deny the existence of aggregate objects and micro-based properties either neglect to include properties of pluralities of low-level physical objects in the low-level physical domain, in which case completeness is false, or they include such properties, and now either the problem of many causes again arises or the exclusion principle fails to apply at all. 2. Formulating the Exclusion Problem Philosophers have long known that there are at least two notions of physical at play in the literature (see, e.g., Feigl 1958). Contemporary accounts typically contrast low-level physical entities with a disjoint set of high-level physical or ordinary physical entities (e.g., Chalmers 1996, 33). For example, low-level physical properties, according to Chalmers, are the fundamental properties that are invoked by a completed theory of physics. Perhaps these will include mass, charge, spatiotemporal position; properties characterizing the distribution of various spatiotemporal fields, the exertion of various forces, and the form of various waves; and so on (ibid.). High-level physical properties and events plausibly include arm movements, earthquakes, and being a toaster. High-level physical events supervene on low-level physical events, and the inclusive physical domain can be taken to be the union of the lowlevel and high-level physical domains. The completeness of physics is roughly the claim that every physical event has a physical sufficient cause. Authors who discuss completeness claim that only the low-level physical domain is causally complete. For example, Kim writes: It is only when we reach the fundamental level of microphysics that we are likely to get a causally closed domain (2003, 173; see also Baker 1993, 79). 4 Given this, the exclusion problem can be posed in terms of the following five mutually inconsistent theses: Completeness: For every inclusive physical event and every time t, if that event has a sufficient cause at t, then it has a low-level physical sufficient cause at t. Causal efficacy: Mental events are causally sufficient for some inclusive physical events. Exclusion principle: For every time t, there cannot be two or more sufficient causes at t of an inclusive physical event, except for cases of overdetermination. 3

Non-overdetermination: Instances of mental causation are not, in general, cases of overdetermination. Irreducibility: Mental events are not identical to low-level physical events. Kim provides some reason to think that completeness is plausible only if complex, aggregate objects and their micro-based properties are included in the low-level physical domain: Plainly the physical domain must also include aggregates of basic particles, aggregates of these aggregates, and so on, without end; atoms, molecules, cells, tables, planets, computers, biological organisms, and all the rest must be, without question, part of the physical domain. It is important that these [objects and their] micro-based properties are counted as physical, for otherwise the physical domain won't be causally closed. (Kim 1998, 113-4) 5 These aggregate objects and their micro-based properties are arguably needed as causes of some inclusive physical events. For example: The shattering of the glass was caused by the baseball and certainly not by the individual particles composing it (Kim 2003, 167). 6 I will follow Kim in making this assumption until Section 4. 3. The Exclusion Problem Meets the Problem of Many Causes If the low-level physical domain includes aggregate objects and their properties, then completeness may well be true. But in that case, I argue that the exclusion principle is false, even by reductionists lights. So, the exclusion problem does not arise. Given a high-level physical event E, say, my arm moving, what does one of the low-level physical events that are causally sufficient for E look like? As noted above, it is not a simple microphysical event like an electron being excited to a higher energy level. Rather, it is an immensely complicated micro-based low-level physical event me (or my brain) instantiating a micro-based property involving countless low-level physical objects propertied and related in certain ways. Call such an event C. 7 Neuroscience suggests that other events that occur in my brain simultaneously with C are also causally sufficient for E. For instance, an event C that is exactly like C but in which a particular neuron fails to fire (or in which it still fires but the firing involves an influx of three fewer sodium ions) will also be causally sufficient for E. In fact, there will apparently be countless such low-level, micro- 4

based physical events C, C, etc. that actually occur and differ only minutely from C but are still causally sufficient for E. We are faced with a situation analogous to the problem of the many countless sufficient causes where the proponents of the exclusion problem claim there can only be one, just as the problem of the many raises the prospect of countless objects where there is intuitively only one. What should the friends of the exclusion problem say about C, C, C, etc.? One way to respond to this scenario is to reject what Jonathan Schaffer (2003) calls individualism with respect to the apparent (broad sense) overdeterminers (cf. note 2) and adopt collectivism. That is, one could claim that none of the individual Cs is a sufficient cause of E but that only their mereological sum (or disjunction) is. Schaffer himself provides some strong arguments for individualism and against collectivism. However, even if it collectivism were plausible, it is clear that proponents of the exclusion problem cannot endorse collectivism, for they in effect assume individualism as part of their reductio against non-reductive physicalism. So, given individualism, the defenders of exclusion problem must claim that only one of C, C, C, etc. is a sufficient cause of E. How can they support this claim? It seems that they would need to provide a reason for choosing one of C, C, C, as the sufficient cause. If one of these Cs is the sufficient cause of E and the others are not, then there it seems that there must be something that makes it the case that that low-level physical event is the sufficient cause and the others are not. This kind of causal fact does not seem to be entirely arbitrary. One family of responses to the problem of the many denies this. It claims that although there is no principled reason for choosing one of the many over the others as the ordinary object, there is in fact only one ordinary object. Proponents of the exclusion problem could make the analogous claim: that there is no principle that determines which of the Cs is the sufficient cause but that, nevertheless, only one is the sufficient cause. This could be done in several ways. First, they could claim that it is a brute metaphysical fact about causation that one of the Cs is the sufficient cause of E, a position analogous to mereological brutalism. Alternatively, they could claim that it is a brute semantic fact, which is in principle impossible for us to know, that, say, C, satisfies is a sufficient cause of E and thus adopt an 5

epistemicist solution. Finally, they could adopt a supervaluationist solution. On this approach they would admit that there is no fact of the matter about whether C or C or C or lie in the extension of sufficient cause of E, but they would claim that this is consistent with exactly one of the Cs falling in that extension. 8 However, in the context of the exclusion problem one cannot turn to any of these solutions. For the proponents of exclusion problem recognize that they need to provide a reason for choosing one purported sufficient cause over another. 9 Completeness was supposed to serve as such a principle, as giving us a reason to choose the physical event over the mental one as the sufficient cause. But the friends of the exclusion problem obviously cannot turn to completeness to choose between the Cs at this point because they are all within the smallest physical domain of which completeness is held to be true. Put another way, if one ultimately needs to appeal to arbitrary or brute facts in order to meet the challenge posed by physical causes like the Cs, why bother with completeness as a component of the exclusion problem at all? Why not just stipulate that there can be only one low-level physical cause of a physical event at a given time and that only low-level physical events can be causes of physical events? This may be an argument against non-reductive physicalism, but it is a very different line of thought than the exclusion problem and would need to be supported by different arguments. Proponents of the exclusion problem may respond by asking why they need to provide a principle to choose among the Cs. Granted, they use completeness to rule out unreduced mental events as causes, but why think that the same principle, or indeed any principle, is needed to solve the problem of many causes? Why can t the reductive physicalist adopt one of the strategies proposed above for solving the problem of many causes, and then, with this solution in hand, proceed to pose the exclusion problem (with the completeness of physics as a component) as a challenge to non-reductive physicalists? 10 Reductive physicalists who take this route must still claim that one of these brute fact strategies works in the low-level physical domain but not in a more inclusive domain that includes mental properties. According to this move, completeness is still needed in the latter domain. This disjunctive treatment is unmotivated. The reductive physicalist has in effect been forced to make a distinction 6

between two exclusion problems : one, the problem of many causes that I have raised, is claimed to arise only in the low-level physical domain and is supposedly resolved via some version of the brute fact approach; the other incorporates completeness and is used to rule out causation by unreduced mental events. But the reductive physicalist has given no reason why such a distinction should hold, other than that it leads to the result she wants. Thus, I think that this move begs the question against non-reductive physicalism. The exclusion principle, and the apparent problem of which it is a part, should apply universally. Why would simultaneous events compete as sufficient causes simply because one was high-level physical and the other low-level physical but be compatible if both were low-level physical? Whatever plausibility the exclusion principle has derives from general considerations about causation considerations that also apply in the low-level physical domain. For instance, Kim suggests that the principle is supported by the general claim that there is usually not more than one independent causal chain or process leading to the same event (see Kim 1993, 243 n.15). Events like C and C plausibly do not violate this claim, although they do violate the exclusion principle as stated above. The Cs are only minutely different from each other and thus there is plausibly some physiological causal process of which they are both part that is sufficient for E. Hence, it is plausible that they in fact do not compete with one another for causal sufficiency, contra the above formulation of the exclusion principle. Thus, even the reductionist should admit that this strong, unrestricted version of the exclusion principle should be rejected. Of course, one obvious response that the proponent of the exclusion problem might make is to claim that the exclusion principle can be qualified so that there is no competition between multiple simultaneous low-level physical causes but mental causes are still screened off or excluded by low-level physical ones. A related worry is that the non-reductive physicalist might seem to be in a worse position than she was before. After all, if she simply rejects the exclusion principle, isn t she accepting the existence of many simultaneous sufficient low-level physical causes as well as a sufficient mental cause? This is closely related to the problem I mentioned above for those who deny non-overdetermination and claim that all forms of overdetermination are ubiquitous and unproblematic. The non-reductive 7

physicalist should ultimately seek to explain why causation by the Cs and by certain mental and physical events count as acceptable cases of overdetermination and why causation by sui generis mental events and physical events is unacceptable (especially if she wants to use a causal argument for her view, as against dualism and emergentism). In other words, the non-reductive physicalist will also need to propose appropriate qualifications to the overly strict exclusion principle stated above. However, unlike the proponent of the exclusion problem, she will claim that any qualified exclusion principle that counts simultaneous low-level physical causes, like the Cs, as acceptable will also countenance mental causes that are appropriately related to simultaneous low-level physical events. At this point, it is important to keep the dialectical state of play clearly in mind. A successful response to the exclusion problem needs only to establish parity between mental causes and (low-level) physical causes. The non-reductive physcialist needs to show merely that there is no more problem with mental causation of physical events than there is with low-level physical causation. This is what I have attempted to do in this paper to argue that a crucial reductive physicalist assumption is false. At any given time, there is plausibly more than one low-level physical sufficient cause of a given high-level physical event, so reductive physicalists must adopt some version of causal compatibilism. Even they must reject the exclusion principle stated above. Arguably, the non-reductive physicalist must do so as well, which allows her to consistently endorse causal efficacy, irreducibility, completeness, and nonoverdetermination. In effect, this has shifted the burden of proof to proponents of the exclusion problem to show that a plausible qualified exclusion principle allows only simultaneous sufficient causes like the Cs and excludes mental causes. Further, it appears unlikely that they can accomplish this task. For, the obvious plausible candidates that count the Cs as acceptable e.g., allowing overdetermination by simultaneous causes that are part of the same causal process or those that are not wholly distinct from one another are ones that the non-reductive physicalist will claim also allow for mental sufficient causes. 11 4. What If There Are No Aggregate Objects? Until now I have followed Kim in assuming that the low-level physical domain includes aggregates of individual low-level physical entities and that the low-level physical domain is closed under 8

the formation of micro-based properties. However, these assumptions have been challenged by those who endorse compositional nihilism. According to this view, there are no aggregate objects; only simples exist (cf. Hossack 2000). On the nihilist view, there are no baseballs or baseball-like aggregates but only particles arranged baseball-wise. And the nihilist would claim, contra Kim, that these individual particles, together, do cause windows to shatter. To reach this conclusion, one needs to argue that plural quantification and predication can be used to state all of the causal facts in the physical domain and that plural quantification and predication does not commit one to the existence of any entities other than those one is already committed to by the use of first-order quantifiers. 12 One way to motivate such a view is to use considerations about causal overdetermination to claim that aggregate objects and their properties are causally redundant (cf. Merricks 2001). According to this perspective, completeness is true of the low-level physical domain restricted to individual low-level objects, and the exclusion principle rules out all alleged instances of causation involving aggregates; only events involving individual low-level physical objects or pluralities of such objects cause anything (if any causation occurs at all). 13 One might think that this result is absurd and that the fact that the exclusion problem generalizes in this way is a reductio of exclusion-based arguments (cf. Noordhof 1999, among many others). However, as Kim has argued, even if this result is absurd, pointing this out does not show where the exclusion problem goes wrong (2003, 165). Fortunately, one can show where the exclusion problem goes wrong while avoiding the unfortunate bruiting of conflicting intuitions regarding whether or not causal drainage is an absurd consequence. For, the nihilist about macro and aggregate objects agrees that events involving changes in individual microphysical objects are not enough to provide a domain in which completeness is true. In addition to these atomic events, we need certain relations between simple objects properties picked out by such expressions as arranged baseball-wise, which are not truly predicated of individual objects but only of some of them taken together. (After all, the same token particles would not have broken the window if they were dispersed like a gas.) Given this, the nihilist view faces the following dilemma. Even if pluralities are not objects (semantic values of first-order 9

singular terms), either they can be counted, or they cannot. And, in either case, the exclusion problem does not get off the ground. If token pluralities are similar enough to objects that they can be counted, then the nihilist view faces the problem of many causes outlined above. Assume that some plurality of particles is causally sufficient for the breaking of a window (where, again, talk of pluralities does not commit one to aggregate objects). In most cases, some slightly different actual arrangement of particles (e.g., one involving a couple fewer particles) of which arranged baseball-wise is true, is also causally sufficient for the window breaking. 14 So, anyone who holds this view must also recognize that the exclusion principle as stated above is too strong. On the other hand, if token pluralities cannot be counted, then the exclusion principle no longer has any force because there are never two (or more) apparently competing simultaneous sufficient causes of a given event. In other words, in this case the nihilist perspective may give us reason to be reductive physicalists, but it is distinct from the line of thought behind the exclusion problem. 5. Concluding Remarks Many philosophers think that something is wrong with the exclusion problem. Most have focused their criticism on the exclusion principle or non-overdetermination; they have claimed either that mental causation involves acceptable simultaneous, non-overdetermining causes (e.g. Bennett 2003, Yablo 1992) or that overdetermination is in general acceptable (e.g. Sider 2003). However, prominent defenses of the former strategy embroil its proponents in controversies about their account of the mental/physical relation (e.g. Funkhouser 2006), and the latter strategy prevents non-reductive physicalists from using the powerful causal argument for physicalism. I have offered a new defense of the claim that the strict exclusion principle, which plays a crucial role in the exclusion problem, is false. For, completeness is true only if the causally complete physical domain includes events that involve micro-based properties of composite objects (or at least properties of pluralities of physical simples). Given this, even the proponent of the exclusion problem must admit that there are countless simultaneous sufficient physical causes of a given physical event. Thus, the exclusion principle, as stated above, is too 10

strong. Further, it is likely that any plausible modification to it will not rule out causation by irreducible mental events. Non-reductive physicalism may face genuine difficulties (e.g. specifying the precise nature of the relation between the physical and the mental), but the exclusion problem is not one of them. Notes 1 For a defense of the exclusion problem, see Kim 1993, 2003. I assume that an event is an object instantiating a property at a time. If one adopted a different view of events, then the terms of the debate change but not its substance. E.g., if one adopted a Davidsonian view of events and thought of causation as an extensional relation over them, then the exclusion problem shifts to a debate about what Terence Horgan (1989) has called quausation. 2 There may not be much difference between these responses in the end. They merely disagree on how best to understand overdetermination. The former adopts a narrow reading of overdetermination, according to which two simultaneous events, A and B, overdetermine a given event only if A and B are (metaphysically or nomologically) independent. The latter interprets overdetermination broadly, so that any two numerically distinct simultaneous sufficient causes of a given event overdetermine that event. 3 A micro-based property is the property of having proper parts propertied and related in certain ways. I will say that an event is micro-based if its constituent property is a micro-based property. 4 However, Sturgeon (1998) has claimed that it is not part of science or commonsense that mental events have low-level physical effects. In effect, Sturgeon claims that the plausibility of completeness and of the causal efficacy of the mental trade on distinct senses of physical. I will set aside this kind of objection to the exclusion problem here, since others have addressed it (e.g. Witmer 2000). That is, I will grant the proponents of the exclusion problem the strong claim that the low-level physical domain contains a sufficient cause for every inclusive physical event. 5 Note that Kim s reasoning need not automatically lead to the collapse of the distinction between highlevel and low-level physical domains, for high-level physical properties plausibly include more than just micro-based properties of aggregate objects. Further, it is somewhat misleading to continue to use the 11

term low-level, since the low-level physical domain includes molecules, cells, organisms, etc. and their micro-based properties. However, as Kim notes, in Oppenheim and Putnam s scheme, the only levels scheme that has been worked out with some precision the bottom level of elementary particles is in effect the universal domain that includes molecules, organisms, and the rest (2003, 173 n.23). 6 Here Kim seems to assume that baseballs and other macro-objects are identical to aggregates of microscopic entities. In this paper, I do not make this stronger assumption, as it is arguably not needed to generate the exclusion problem. 7 An anonymous referee wondered why the micro-based neurophysiological property involved in C counts as low-level physical. There are likely to be difficult issues involved in developing a coherent, general metaphysical account of levels, and I offer no such account here. I am merely following Kim s assumption that the low-level physical domain must be closed under the formation of micro-based properties if completeness is to be true of the low-level physical domain. I drop that assumption in Section 4. 8 What about other approaches to the problem of the many? Clearly, nihilism about sufficient causes is not an option for the defenders of the exclusion problem nor is claiming that constitution is not identity. One might try the relative identity approach and claim that although C and C are not the same low-level physical event, they are the same sufficient cause. In addition to the standard objections to relative identity, this approach cannot simply say that C and C are the same sufficient cause, for in some contexts their differences are causally relevant. Rather, it must say that they are the same sufficient cause of E, and thus make identity relative to very narrowly construed, ad hoc sortals. Partial identity is not a plausible option either. While it may be that we count by almost identity when we talk about everyday things like cats and clouds, it is ad hoc to claim that we do so when talking about low-level physical causes. This is related to a key difference between the problem of the many and the problem that faces the defender of the exclusion problem. In the former we are trying to defend a commonsense belief, in the latter a theoretical view to which the defender of the exclusion problem is driven. 12

9 Note that Kim sets up the exclusion problem in terms of choosing the physical cause over the mental one (2003, 158). He does so for good reason. The reductionist is trying to argue that non-reductive physicalism is inconsistent. So he must assume for the sake of argument that there are two simultaneous sufficient causes, one physical and one mental and attempt to show that this leads to a conflict with completeness and the exclusion principle, giving us reason to conclude that the mental event is not a cause (unless it just is the physical event under another name). Thanks to Brian Weatherson for discussion of this point. 10 Thanks to Andy Egan for suggesting this response. 11 Filling in the details of this claim overlaps with the non-reductive physicalist project of spelling out the relation between mental and physical events. For example, is it determination, realization, or some other asymmetric determination relation? However, if the arguments in this paper are correct, then doing so is not necessary to show where the exclusion problem goes wrong as an attack on non-reductive physicalism. 12 There are reasons to doubt whether plural quantification is ontologically innocent i.e. whether it commits one to any entities in addition to the individuals quantified over in first-order logic (see, e.g., Resnik 1988). For broadly scientific reasons to reject nihilism about composite objects, see Early 2006. I set these aside for the sake of argument. 13 Of course, this is not Merricks view, for he rejects the completeness of physics (2001, 140ff.). 14 Karen Bennett has also recently argued that Unger s original problem of the many faces the compositional nihilist as well as the believer in composite objects. According to Bennett: Where the believer has many mostly overlapping objects of the same kind, the nihilist has many mostly overlapping instantiations of the same property (2009, 67). Thanks to an anonymous referee for directing me to this discussion. 13

Acknowledgements Some of the ideas in this paper descend from an unpublished essay titled A Novel Solution to the Exclusion Problem, which I presented at the 2004 meeting of the Creighton Club in Skaneateles, NY. Thanks to the audience on that occasion and especially to my commentator, Gregory Fowler, for helpful questions and comments. I am also grateful to Richard N. Boyd, Sydney Shoemaker, Nicholas Sturgeon, and two anonymous referees for discussion about, or comments on, previous versions of this paper. Some of this material is based upon work supported under a National Science Foundation Graduate Research Fellowship. Additional funding was provided by a Faculty Summer Research Grant from The College of William and Mary. I thank both institutions for their support. References Baker, L.R. (1993). Metaphysics and mental causation. In Mental Causation, ed. J. Heil and A. Mele, 75-95. New York: Clarendon. Bennett, K. (2003). Why the exclusion problem seems intractable, and how, just maybe, to tract it. Noûs 37: 471-497. ---. (2008). Exclusion again. In Being Reduced, ed. J. Hohwy and J. Kallestrup. Oxford: Oxford UP. 280-305. ---. (2009) Composition, colocation, and metaontology. In Metametaphysics, ed. D. Chalmers, D. Manley, and R. Wasserman, 38-76. New York: Clarendon. Chalmers, D. (1996). The Conscious Mind. New York: Oxford. Early, J. (2006). Chemical substances that are not chemical substances. Philosophy of Science 73: 841-852. Feigl, H. (1958). The mental and the physical. in Minnesota Studies in the Philosophy of Science. Vol. 2, ed. H. Feigl, M. Scriven and G. Maxwell, 370-497. Minneapolis: U of Minnesota Press. Funkhouser, E. (2006). The determinable-determinate relation. Nous. 40: 548-569. Haug, M. (Forthcoming). Two kinds of completeness and the uses (and abuses) of exclusion principles. Southern Journal of Philosophy. 14

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