Is Metaphysical Dependence Irreflexive?1

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Is Metaphysical Dependence Irreflexive?1 Carrie Jenkins

Draft only; please do not quote or cite without permission If reality has a structure, then perhaps that structure is (at least in part) created by the obtaining of relations of metaphysical dependence or grounding2 between objects, states of affairs, facts, and/or other things. It’s not in my remit here to ask or answer any substantive questions about the nature of dependence relations. However, I do want to raise to prominence, and challenge, a common assumption about the kind of relation metaphysical dependence is (and correspondingly, about the kind of structure – if any – that it gives rise to). It is very commonly asserted that metaphysical dependence or grounding is an irreflexive relation: that is to say, it never holds between an item and itself. And it seems very natural to think of dependence this way. How could anything be metaphysically dependent upon itself? If we want to know in what S’s pain is grounded, it may be illuminating to be told it is grounded in a certain state of the brain. But to say that S’s pain is grounded in S’s pain itself just sounds silly. Similarly, while it may be interesting to suggest that the truth of a sentence is metaphysically dependent upon the existence of some truthmaking entity, if we tried to claim that the truth of sentence is metaphysically dependent upon the truth of that very sentence, we would get very short shrift. The irreflexivity of dependence or grounding is espoused or assumed without comment by Correia (2008, p. 1023), Rosen (forthcoming), Schaffer (e.g. 2009, pp. 364 and 376), Fine (2001, p. 15), McLaughlin and Bennett (2005, §3.5), and many others. Irreflexivity matters to reality’s structure. If reality is structured by the obtaining of dependence relations, irreflexivity has consequences for the nature of that structure and the individuation of structured entities. If nothing depends upon itself, then the structure (if any) generated by dependence is a structure that relates non-‐identical entities, and the entities that depend and/or are depended upon must be individuated accordingly. If, on the other hand, irreflexivity is rejected, it may be necessary to postulate other (perhaps unexpected) structural features in the world 1

I am grateful to members of my audiences at the Colorado Dependence Conference in 2009, the Carolina Metaphysics Workshop 2010 and the Joint Session of the Mind Association and the Aristotelian Society 2010, in particular Tim Button and Brian King. Thanks also to Mark Barber, Michael Clark, Matthew Slater, two Monist referees and especially Daniel Nolan for comments on earlier drafts.

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I assume for the purposes of this paper that there is one notion of metaphysical dependence in this vicinity, variously expressed by philosophers using words like ‘grounding’, ‘dependence’, and other cognate terms.

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to accommodate the obtaining and non-‐obtaining of dependence relations. (More on this below.) Convincing though it seems at first glance, I am not sure that the irreflexivity assumption is appropriate. Suppose I say that S’s pain is metaphysically dependent upon some brain state. What happens if I then go on to identify the pain state with the brain state? Am I forced to go back and reject the dependence claim? The purpose of this paper is to investigate views on which I am not; views on which it might be acceptable to say things like: “Of course S’s pain depends on S’s brain state. They are one and the same.” I will grant, for the sake of argument, that ‘dependence’ (the word, not the relation) is ‘quasi-‐irreflexive’. By that I mean that it always sounds bad to say ‘x metaphysically depends on x’ or ‘x metaphysically grounds itself’. This could, I think, be resisted; consideration of some of the cases considered in this paper might give rise to contexts where such utterances really don’t sound bad at all. But let’s pretend that it’s established. Quasi-‐irreflexivity could perhaps be taken to motivate the irreflexivity of the dependence relation. Of course, any argument which moves straight from quasi-‐ irreflexivity to irreflexivity will be invalid: sometimes the truth sounds bad. But in the absence of deliberate consideration, it is not hard to see how the fact that it always sounds bad to say ‘x metaphysically depends on x’ could lead people to think that dependence is irreflexive. After all, in many cases where ‘x Φs x’ always sounds bad (and most of the kinds of case that spring readily to mind when one considers this symptom) this is properly attributable to irreflexivity. Of course, irreflexivity assumptions might be based on something else, or on nothing in particular. I shall consider another argument for irreflexivity towards the end of this paper, as well as ways of claiming that no argument for irreflexivity is required by those who assume it. But some sort of move from quasi-‐irreflexivity strikes me as the most plausible explanation of the irreflexivity assumption in the majority of cases where that assumption is made without discussion, so I shall focus on this move for most of the paper. It is natural to take it that the reason claims of the form ‘x depends on x’ always sound bad is because they are always false, and hence conclude that nothing stands in the dependence relation to itself. In suggesting that grounding may not be irreflexive I still want to accommodate the prima facie inappropriateness of such utterances. But we can accommodate this inappropriateness in any of three ways: (1) By saying that these utterances they are always false because dependence is irreflexive. (2) By saying that these utterances are sometimes prima facie inappropriate but nevertheless true. (Perhaps they sound bad only because they are misleading in most contexts, for example.)

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(3) By saying that these utterances are always false even though dependence is not irreflexive. The third strategy is the one considered here, though of course those not convinced by irreflexivity have the option of defending (2), as well as the aforementioned option of denying quasi-‐irreflexivity. What could be appealing about option (3)? Why might one want to leave open the possibility that dependence is not irreflexive? One reason is that if we wish to maintain irreflexivity while preserving the truth of certain dependence claims, we will need to make sure we individuate the items that are supposed to stand in the relation in a sufficiently fine-‐grained way. For example, if we wish to maintain irreflexivity and that S’s pain is dependent upon brain state B, we had better divide up the world with sufficient fineness of grain to make S’s pain and brain state B come out as distinct states. Certain conceptions of what exists, namely conceptions which would look to identify those two states, are not now an option. If we even want to make the dependence claim while staying neutral on other metaphysical issues such as the identity of the states under consideration, we had better not assume that dependence is irreflexive. A defender of irreflexivity could perhaps argue that dependence claims are not, and should not be, neutral with respect to individuation in the way envisaged. That is to say, she could argue that in claiming that S’s pain depends upon S’s brain state B, you immediately commit yourself to the non-‐identity of the pain state and the brain state. However, considering some further cases may help to motivate the thought that it is at least a little uncomfortable to think of dependence claims as thus committal. It’s pretty plausible that fusions depend metaphysically on their parts; but if that’s true then the irreflexivity of dependence entails that I am not identical to the fusion of myself, since I am a part of that fusion (albeit an improper one). It’s pretty plausible that statues depend metaphysically on the matter of which they are composed; but if that’s true then the irreflexivity of dependence entails that no statue is identical to its matter. For all I’ll argue here it could be that these plausible-‐sounding dependence claims are false, and/or that the things they entail are true. But cases like these should, I think, at least raise some doubts as to whether it is always appropriate to think of dependence claims as committing one immediately to the non-‐identity of the dependent and depended-‐upon entities. If so, then neutrality can be methodologically desirable, and that for this reason alone it is worth considering the possibility that dependence is not irreflexive. However, that the project of investigating whether the commonplace assumption of irreflexivity is correct need not be motivated by anything more than caution, and specifically the desire to avoid making unwarranted – and/or unnecessary – assumptions. So although I think there are considerations of methodological

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neutrality which speak against assuming irreflexivity, I think these are not the only reason the issue is worth considering. To stress, I don’t intend to argue that it is a mistake to say that dependence is an irreflexive relation, but simply that it is a mistake to assume there are no alternatives. The motivating thought that ‘x depends on x’ always sounds bad – and indeed, the further claim that it is always false – can be accommodated without going irreflexive. We have the option of treating the semantics of the phrase ‘depends on’ as hyperintensional. To say that ‘depends on’ is hyperintensional is to say that it creates contexts into which one cannot always substitute necessarily co-‐extensive terms salva veritate. The verb ‘believes’ is often thought to be like this. We can have all-‐true triads of the following form:3 i. The Sherriff of Nottingham believes that Robin Hood is wicked. ii. The Sherriff of Nottingham does not believe that Robin of Locksley is wicked. iii. Robin Hood is identical to Robin of Locksley. Similarly, I suggest, one might think that there can be all-‐true triads of the following form: a) S’s pain depends on S’s brain state B. b) S’s pain does not depend on S’s pain. c) S’s brain state B is identical to S’s pain. This option is, importantly, compatible with ontologies states that identify brain states with pain states. We are free to identify S’s pain with the brain state that grounds it, should we wish (for reasons of parsimony, say) to do so. The hyperintensionality option is in that respect less metaphysically committing than the irreflexivity option. Similarly, were we to take the things that stand in dependence relations to be facts or states of affairs or objects (or whatever), the hyperintenstionality option enables us to be less metaphysically committed with respect to identifications among those things. What are we to think about the relation of dependence (assuming there is one), as opposed to the phrase ‘depends on’, if we decide to take this route? It now seems quite difficult to say whether or not the relation is irreflexive. One the one hand, ‘x depends on itself’ is always false. But on the other, sometimes ‘x depends on y’ is true where x=y, which, it seems, ought to mean that sometimes x does depend on itself. Yet in saying that x does depend on itself, I will have said something false.4 3 Thanks to Daniel Nolan for this example. 4 This situation is, naturally, rather like that surrounding ‘belief’-‐talk. Consider the classic case of

Pierre (Kripke 1979). Pierre is shown pictures of a pretty place called ‘Londres’ and holds a belief which he expresses by ‘Londres est jolie’. One day he finds himself in an ugly part of a city called ‘London’ and forms a belief which he expresses by ‘London is ugly’. He does not realize

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One can of course think of the dependence relation as hyperintensionally individuated, but that won’t solve this problem. Some may regard this as contradictory (saying that relations are by definition extensional), but even those who are happy for relations to be individuated hyperintensionally (allowing that, for example, the relation of being-‐a-‐trilateral-‐to-‐the-‐left-‐of and being-‐a-‐triangle-‐to-‐the-‐ left-‐of are different relations) will not admit that this makes sense of how a single relation of dependence, once specified, can hold between two things and also not hold between the same two things. Hyperintensional individuation just enables us to make finer distinctions between different relations.5 One option for accommodating triads like a-‐c is to construe the dependence relation as more-‐than-‐two-‐place, despite the surface appearances created by the way the phrase ‘depends on’ works. For instance, we could think of the dependence relation as holding between a state of affairs, a (possibly identical) state of affairs, a feature or aspect of the first state of affairs and a feature or aspect of the second state of affairs. We could then say that in order to get a true sentence of the form ‘x grounds y’, one must present the referents of ‘x’ and ‘y’ in such a way that the relevant aspects of them, i.e. the things which stand in the relation’s third and fourth places, are sufficiently evident (in context). This is one way in which denying irreflexivity could lead to the postulation of (perhaps previously unexpected) structure in the world to accommodate the obtaining and non-‐obtaining of dependence relations. On this option, dependence trades upon the structure created by the possession of different aspects or features by one and the same thing. For example, suppose S’s pain depends upon and is identical to S’s brain state B. The relation of metaphysical dependence could then be said to hold between 1. 2. 3. 4.

S’s pain (which is identical to brain state B) Brain state B The pain-‐y aspect of the state in question The brain-‐y aspect of the state in question

It could then be argued that ‘S’s pain depends on S’s pain’ is false because the brain-‐ y aspect of B is not sufficiently evident in the second presentation of B in that sentence. That is to say, when you utter ‘S’s pain depends on S’s pain’, your second presentation of B as ‘S’s pain’ means that context supplies the pain-‐y aspect of B in the fourth argument-‐place. Since the fourth argument needs to be the brain-‐y aspect of B in order for the sentence is to come out true, the sentence will come out false. Londres is London, so does not revise his earlier belief. Does Pierre believe that London is pretty? On the one hand saying so seems false; he believes London is ugly, and would dissent if you asked him whether London is pretty. But on the other, he believes Londres is pretty, and Londres is as in fact identical to London. 5

I am grateful to Dan Korman for helping me to be clearer in this part of the paper.

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By contrast, ‘S’s pain depends on S’s brain state B’ is true because the brain-‐y aspect of B is sufficiently evident in the second presentation of B in this sentence. That is to say, when you utter ‘S’s pain B depends on S’s brain state B’, your second presentation of B means that context supplies the brain-‐y aspect of B in the fourth argument-‐place, and hence the sentence comes out true. Is the dependence relation correctly described as irreflexive if this is what’s going on? It seems not. Assuming that reflexivity and irreflexivity are both properties of two-‐place relations, then if the relation is really four-‐place it is not appropriate to describe it is irreflexive. At best – if, for example, all that was meant was that it is not a reflexive relation – calling it irreflexive would be misleading. (NB: Although it is not my focus here, the relation is also, contrary to popular assumption, neither transitive nor asymmetric if it is four-‐place.) There need, I think, be no concern to the effect that grounding is “not metaphysical enough” just because the mode of presentation of the grounding and grounding entities matters to the truth value of a grounding claim. The reason mode of presentation matters, on the example view just sketched, is because of the roles played by certain aspects or features of the relevant states of affairs. One can hold that it is a substantive, metaphysical matter that these features play these roles, and that our language is simply respecting the importance of these metaphysical roles by rendering ‘depends on’ hyperintensional in the way described. Another kind of objection to the four-‐place view of dependence is that an obviously-‐ preferable alternative will always be available.6 The envisaged alterative is that grounding is two-‐place and irreflexive, and holds between the aspects labelled 3 and 4 above. But I don’t agree that this is obviously preferable. The surface appearance is of a two-‐place relation holding between items labelled 1 and 2, not between aspects thereof. So it seems that the two options being compared here are: to reject the surface appearance that the relation is two-‐place, or: to reject the surface appearance that the relation has the things we expected as relata. It’s not obvious to me that one is preferable to the other. A second irreflexivity-‐denying option is to deny that ‘depends on’ expresses a relation at all (or at least, to deny that it expresses any metaphysically interesting relation). While ‘x depends on y’ may appear to assert that a relation of dependence holds between x and y, it could be that something quite different is going on. Perhaps, for example, in using the locution ‘x depends on y’ one is simply providing a certain kind of explanation of y, one which might be underwritten by but does not consist in any of a number of different metaphysical relations between x and y. Personally I’m happy to be abundant enough with (metaphysically interesting) relations to regard this as unnecessarily parsimonious, but the option is there for those who want it. (There are, of course, other no-‐relation options besides this one.)

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Thanks to my Joint Session audience for suggesting I discuss this objection.

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This obviously has consequences for the structure of reality. A view that fits naturally with this line is that we have been mislead by our structured ‘dependence’-‐ talk into thinking that reality is structured by some kind of dependence relation, whereas in fact nothing of the kind is true. A third option is to maintain that dependence is two-‐place, just as it appears to be, but argue that ‘depends upon’ is nevertheless hyperintensional in such a way that irreflexivity can be denied without rejecting quasi-‐irreflexivity. One might suggest, taking inspiration from Lewis 2003, that (for example) S’s pain qua pain state depends on B qua brain state. One could then argue that dependence is a two-‐place relation, but since it holds between S’s pain qua pain state and the same state qua brain state, it is false to say ‘S’s pain depends on S’s pain’. One must present the object in a way that makes evidence the appropriate qua aspects in order to get a true reading. Whether or not these qua aspects constitute structure in the world or whether they are merely shadows our ways of representing it will, I imagine, be a matter for serious debate among those who pursue this sort of line. These are not the only strategies one could try for challenging irreflexivity without denying quasi-‐irreflexivity. Alternatives include taking the truth-‐value of the English sentence ‘x depends on y’ to be sensitive to things besides the relation expressed by ‘depends’ and the referents of ‘x’ and ‘y’, though I doubt this sort of approach will have wide appeal unless extra semantic elements can be found in ‘x’, ‘y’ and ‘depends’, so that we can avoid being committed to a non-‐compositional semantics for the whole sentence. Let me now turn to another argument in favour of irreflexivity,7 which does not rely upon quasi-‐irreflexivity but rather on the asymmetry of dependence. The argument runs as follows: suppose A depends on B, to which it is also identical. Then it follows, by a simple substitution, that B depends on A. But dependence is asymmetric. So it must be irreflexive. It should be clear from the preceding discussion that this argument makes assumptions which those who want to remain neutral on irreflexivity do not have to make. The substitution of ‘B’ and ‘A’ for ‘A’ and ‘B’ respectively in ‘A depends on B’ is not guaranteed to preserve truth if ‘depends’ is hyperintensional. And the dependence relation might not be correctly classified as asymmetric, if for example it is four-‐place, or if a state qua pain state can bear that relation to itself qua brain state and the relation is transitive. Maybe the irreflexivity assumption doesn’t require argument?8 Perhaps it is reasonable just to assume it, in the absence of arguments to the contrary? There 7

Thanks to a Monist referee for suggesting I discuss this argument.

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Thanks to a Monist referee for suggesting I discuss this possibility.

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are (at least) three possible ways to back up this suggestion. One could take the irreflexivity claim to be 1. 2. 3.

stipulative, intuitive, or too basic to require justification (at least in the relevant contexts).

If it is taken to be stipulative (i.e. if one takes it to be true by definition that dependence is irreflexive), one runs the risk of discussing something that isn’t what everyone else meant by ‘dependence’, or of discussing something that is less interesting that schmependence (a nearby non-‐irreflexive relation). One can mean whatever one likes by ‘dependence’, of course, but these risks are to be treated with respect by any serious philosopher. If one merely takes irreflexivity to be intuitive, however, one is open to the possibility that its intuitiveness might be explained away as being due merely to quasi-‐irreflexivity. What about taking irreflexivity to be too basic to require justification in the relevant contexts?9 After all, one must start somewhere if one is to make any progress; one can’t argue for all one’s assumptions. But one can assert that dependence appears to be irreflexive, or exhibits some features suggestive of irreflexivity, almost as quickly as one can assert that it is irreflexive. Now that the irreflexivity assumption has been questioned and one obvious motivation for it undermined, it is not good philosophical practice to sweep the challenge back under the carpet.

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It is sometimes claimed that dependence is unanalyzable or (conceptually) primitive (see e.g. Cameron 2008, p. 3). This doesn’t immediately entail that the irreflexivity claim requires no justification, but it might be taken to suggest that the dependence notion is so basic that we shouldn’t aspire to such a justification.

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References Cameron, R. 2008. ‘Turtles All The Way Down: Regress, Priority and Fundamentality’, in Philosophical Quarterly 58, pp. 1-‐14. Correia, F. 2008. ‘Ontological Dependence’, in Philosophy Compass 3, pp. 1013-‐32. Fine, K. 2001. ‘The Question of Realism’, in Philosophers Imprint 1, pp. 1-‐30. Kripke, S. 1979. 'A Puzzle about Belief', in A. Margalit (ed.) Meaning and Use. Dordrecht: Reidel, pp. 239-‐83. Lewis, D. 2003. ‘Things Qua Truthmakers’, in H. Lillehammer and G. Rodriquez-‐ Pereyra (ed.s) Real Metaphysics: Essays in Honour of D. H. Mellor, London: Routledge, pp. 25-‐38. McLaughlin, B. and Bennett, K. 2005. ‘Supervenience’, in E. Zalta (ed.) The Stanford Encyclopedia of Philosophy (Summer 2010 Edition). Retrieved 28th August 2010 from http://plato.stanford.edu/entries/supervenience/. Schaffer, J. 2009. ‘On What Grounds What’, in D. Chalmers, D. Manley and R. Wasserman (ed.s), Metametaphysics, Oxford University Press, pp. 347-‐83.

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