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Instantiation is not partial identity

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Abstract

In order to avoid the problems faced by standard realist analyses of the “relation” of instantiation, Baxter and, following him, Armstrong each analyze the instantiation of a universal by a particular in terms of their partial identity. I introduce two related conceptions of partial identity, one mereological and one non-mereological, both of which require at least one of the relata of the partial identity “relation” to be complex. I then introduce a second non-mereological conception of partial identity, which allows for both relata to be simple. I take these three conceptions to exhaust the plausible ways of construing two entities as being partially identical. I then argue that there is no analysis (including those offered by Baxter and Armstrong) of a universal and a particular as being partially identical consistent with any of these three conceptions that (i) is coherent, (ii) is consistently realist, (iii) does not lead to absurd consequences, and (iv) offers a “solution” to the problem of instantiation that avoids the problems with the other standard realist responses. In so arguing, I offer a criticism of the analysis of instantiation as partial identity that is independent of the standard criticism that it entails the necessity of predication.

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Notes

  1. For the purposes of this paper I use ‘realist’ as a label for anyone who recognizes the existence of both universals and particulars as the two fundamental kinds of entity. This does not include those who recognize universals as the only fundamental kind of entity—such philosophers fall within the scope of the label ‘universalist’. ‘Nominalist’ applies to those who recognize the existence of particulars (be they tropes or otherwise) as the only fundamental kind of entity.

  2. The accusation is that the realist analyzes the monadic predication ‘a is F’ in terms of another monadic predication, ‘a instantiates F’, which she in turn takes to be unanalyzable. It would be preferable, according to this objection, to dispense with the additional ontology (the universal F) and leave the original predication unanalyzed, for such an account would be just as explanatorily powerful as the realist’s. See, e.g., Devitt (1980) and Lewis (1983, pp. 352–354).

  3. Armstrong has since given up this view.

  4. While I find the necessity of predication resulting from Armstrong’s theory absurd, this is not one of the consequences to which I will appeal.

  5. Note the following way of characterizing mereological proper parthood: x is a mereological (proper) part of y iff x ≠ y and there exists some z such that y is a mereological composite of x and z, and z ≠ x.

  6. The definition of non-mereological constituency seems to require the following qualification: x is a non-mereological constituent of y iff x ≠ y and there exists some z such that y is a non-mereological composite of x and z, and x ≠ z. Compare to the definition of mereological (proper) parthood in my footnote 5.

  7. It seems that a general definition of partial identity can be constructed that allows for a non-mereological composite and a mereological composite to be partially identical: x and y are partially identical iff (i) they are mereologically partially identical, (ii) they are non-mereologically partially identical, or (iii) there exists some z such that z is a non-mereological constituent of x and z is a mereological (proper) part of y.

  8. Ignore, for the sake of argument, how “simple” (atomic) states of affairs are supposed to combine to form a “complex” (i.e. molecular) state of affairs. One can simply focus on the case in which a thin particular instantiates only one universal (and thus composes a thick particular identical to an atomic state of affairs).

  9. Some universals (i.e. complex and structural universals) do have parts for Armstrong (1997), but I’m only considering “basic” universals here. (Besides, the complexity of these sorts of universals can’t be exploited to explain their instantiation, for one must still explain the instantiation of such a universal’s parts—even if there is “supervenience all the way down”, the possibility of which Armstrong allows for.)

  10. This may be because his view changes throughout these works. Even so, each version of the view he holds is represented by one of the views I discuss in Sects. 5 and 6.

  11. See, e.g., Lewis (1991, pp. 81–87).

  12. Unless, of course, composition is characterized as a “relation” that holds of something just in virtue of its being self-identical. But this would render all objects—even non-composite ones—composite, which is obviously absurd.

  13. I say ‘something resembling monism’ because it is not clear that the result would be monism, strictly speaking. Suppose there are universals F and G, particulars b and c, b instantiates (only) F, and c instantiates (only) G. F and b are thus identical, and G and c are identical, but b and c are distinct because they do not instantiate any of the same universals (likewise for F and G with regard to being instantiated by particulars). Thus, there are two distinct entities (the b-F entity and the c-G entity). Now, if these entities stand in relations, how does one analyze their instantiation of a relation? Construing this instantiation in the same way that Baxter construes monadic instantiation seems to result in a thoroughgoing monism, which was Bradley’s way of avoiding instantiation at the cost of refusing to recognize relations. If this instantiation is not so construed, then one still faces the problem of instantiation.

  14. This is Baxter’s (2001, p. 455) own characterization of nominalism.

  15. “Thus we might say of two particulars that each has an aspect in which it is identical with the other. But we might as well just say of a universal that it has aspects in which it is distinct from itself” (Baxter 2001, p. 455).

  16. See, e.g., Campbell (1990, pp. 130–133).

  17. See, e.g., Stout (1952, pp. 77–81).

  18. See, e.g., Maurin (2002, pp. 109–115).

  19. Obviously, I haven’t exhausted all the responses to these difficulties that trope theorists offer, nor was it my intent to do so.

  20. Distinguishing between two such relations seems to amount to essentially the same thing as distinguishing between “multiple sorts of numerical identity” (i.e. the p-“count” and u-“count”) as Underwood (2010, p. 267, fn. 1) does. So, if Underwood were to dispense with the appeal to aspects, it seems to me that his view would be essentially the same as the one I am now describing.

  21. There are two oddities that result from this theory. One is that u 1 and u 2 are u-identical with each other (from either (B3) and (B4) or (B5) and (B6)), but this doesn’t preclude them from being p-distinct, which is all that is required for their numerical distinctness. The second is that there may not be grounds for drawing the universal-particular distinction given the apparent symmetry of u-identity. This might be avoided by asserting that the relation of u-identity is asymmetrical (or even, perhaps, non-symmetrical). I merely note these points here: filling in the details of this sort of theory is beyond the scope of this essay.

  22. The use of the word ‘relation’ here is not meant to indicate that numerical distinctness is somehow reified by realists or nominalists. Nominalists accept that there are distinct particulars and (typically) offer no analysis of this fact: distinct particulars just are distinct. Likewise, realists accept that there are distinct particulars and distinct universals and (typically) offer no analysis of this fact: distinct entities just are distinct. This is the sense in which both realists and nominalists accept a primitive “relation” of distinctness.

  23. This is how, e.g., Lewis (1991) construes the relationship between an individual and its singleton.

  24. That is, insofar as it is invoked as a response to the problem with (2).

  25. By transitivity of identity.

  26. I have in mind someone who applies a view like Markosian’s (1998) to the view in question.

  27. See footnote 24.

  28. This is assuming, of course, that such a view is coherent. There seems to be good reason to think that it isn’t: after all, if a composite is supposed to be identical to its constituents (taken collectively), then it seems that it must exist whenever they do.

  29. I have in mind a variant of Markosian’s view. See footnote 26.

  30. See footnote 24.

  31. I use ‘proper part’ here, but I note that ‘constituent’ could just as easily be used: pace Armstrong, one could accept that non-mereological composition is governed by a principle of unrestricted composition.

  32. Given Baxter’s examples of aspects (e.g. a’s-being-F), this seems tantamount to taking a state of affairs to be the constituent the sharing of which establishes the instantiation of a universal by a particular rather than that which is composed when a universal is instantiated by a particular. Armstrong, in the early formulations of his view (2004a, pp. 140–143; 2004b, pp. 46–48; 2005a, p. 317), seems to hold something like this, although I think that he is best interpreted as holding that universals and particulars are both simple (thus facing the objections I make in Sect. 6). If, however, he thinks they’re both complex, his view is subject either to the objections I’ve made in the first part of this section (if he accepts restricted composition for the constituents of a universal and particular), or else to the objections I make against option (I) (if he accepts unrestricted composition).

  33. Furthermore, suppose that particular a instantiates only universal F (and F is instantiated only by a). In this case, it seems that a and F are identical, which no realist should want to admit.

  34. See Lewis (1983, pp. 344–348).

  35. Paul (2002) takes herself to accept unrestricted composition of “properties” while being able to distinguish between actual fusions (i.e. “objects”) and non-actual ones. She distinguishes them “by defining a primitive predicate which as a matter of contingent fact applies only to fusions that are actual and to no other fusions” (2002, p. 580). As I see it, this is just to say that there is an unanalyzable difference between the case in which some universals compose an object (or, for my purposes, a particular) and the case in which they don’t, which gives rise to the problems with (1a) (as an explanation of (2)). So, this sort of maneuver doesn’t seem to help.

  36. Armstrong, in the later formulations of his view (2005b, p. 274; 2006, pp. 242–243), seems to hold something like this, although, again, he seems best interpreted as holding that universals and particulars are both simple rather than complex. If, however, a particular is taken to be complex, his view is subject either to the objections I make at the beginning of this section (if he accepts restricted composition for the constituents of a particular), or else to the objections I make against option (II) (if he accepts unrestricted composition).

  37. This is the necessity of predication that follows from Armstrong’s view, and for which it has been both criticized (Simons 2005, pp. 258–260) and praised (Mumford 2007, pp. 183–194).

  38. See, e.g., Lewis (1983, pp. 344–348).

  39. See, e.g., Stout (1952) for a moderate version and Rodriguez-Pereyra (2002) for an extreme version.

  40. See footnote 32.

  41. See footnote 36.

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Acknowledgments

I’d like to thank Herb Hochberg, Rob Koons, and those present at the 5th and 49th meetings of the eidos Center for Metaphysics at the University of Geneva for their helpful comments on and criticisms of various versions of this paper.

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Mantegani, N. Instantiation is not partial identity. Philos Stud 163, 697–715 (2013). https://doi.org/10.1007/s11098-011-9840-0

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