Abstract
Some people object to realism about universals because they think that instantiation, the connection between something and the universals that characterize it, is too mysterious. Baxter and Armstrong try to make instantiation less mysterious by taking it to be a kind of partial identity. However, I argue that their accounts of instantiation, and any similar ones, fail.
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Notes
Here and throughout, I use “thing” broadly. Both particulars and universals are things.
The reduction fails if there are necessarily uninstantiated universals. For other potential problems with it, see MacBride (2005).
Mantegani (2013) also argues that their accounts fail, but our objections are independent. Mantegani argues that Baxter abandons realism for something like trope theory and that Armstrong either abandons realism, cannot distinguish particulars from universals, or has a version of realism that is explanatorily idle. For discussion, see Baxter (2013).
Instantiation is reflexive just in case everything instantiates itself.
Instantiation is irreflexive just in case nothing instantiates itself.
Instantiation is symmetric just in case everything instantiates everything that instantiates it.
Instantiation is asymmetric just in case nothing instantiates something that instantiates it.
Instantiation is nonreflexive just in case it is neither reflexive nor irreflexive; it is nonsymmetric just in case it is neither symmetric nor asymmetric.
Armstrong mentions one way that his notion is non-classical: some pluralities do not compose anything (A plurality composes something just in case each of them is a part of it and each part of it overlaps at least one of them; one thing overlaps another just in case something is a part of the former and a part of the latter). Another difference is that distinct things can have exactly the same parts. In correspondence with Armstrong, John Hawthorne points out further differences. See Armstrong (2004: 143). Since Armstrong also accepts a kind of parthood that satisfies the axioms of classical extensional mereology, Armstrong is a mereological pluralist. See McDaniel (2009).
For an early account of nomic necessitation, see Armstrong (1983). For an early account of comparative naturalness, see Lewis (1983). Both relations are third-order particulars, since they are second-order universals that instantiate something. They are second-order universals, since they are instantiated by some pairs of first-order universals.
Other counterexamples to Ordered Intersection include being triadic, being a relation, having exactly seven parts, having exactly seven constituents, being transitive, being symmetric, being reflexive, and maybe being complex if it is not, itself, complex. Ordered Intersection incorrectly entails that each of these universals instantiates itself.
One possible motivation appeals to the claim that a universal exists only if it is not had essentially by each of it instances. The thought behind this claim is that universals had essentially by each of their instances would not do any philosophical work, since any work they do could be done instead by appealing to their instances’ essential natures. This sort of sparse realism explains some similarities by appealing to the possession of an essential nature rather than to the instantiation of a universal. A realist who accepts that sort of theory might avoid my objection to Ordered Intersection, but she does comparatively worse with respect to ideological economy—essential natures on her view cannot reduce to collections of universals, since not all of the required universals exist—and she sacrifices the unified explanation of similarity available to more abundant versions of realism. Thanks to an anonymous referee for helpful comments on this point.
The change does not actually help. The objection, raised independently by Simons (2005) and McDaniel (2005), goes like this. Suppose that this apple is nutritious and being nutritious is a universal. The apple might have not existed, but its nonexistence would not be a small, local matter if Armstrong’s original account is right. If the apple did not exist, then being nutritious would not exist either, since the apple and being nutritious are partially identical. At best, some diminished counterpart of being nutritious would exist instead. But, if being nutritious did not exist, then none of the nutritious things would exist either, since being nutritious is partially identical to each of them. Likewise, no property of anything nutritious would exist, nor would anything that instantiates those properties, and so on. Armstrong’s new account is supposed to help stop the nonexistence of a single particular from spreading globally in this way. However, it does not. All the work is done by Armstrong’s claim that removing from existence a particular does not also remove from existence its constituents. It does not matter whether the constituents are universals, as with the new account, or merely common parts, as with the old account. The objection relies on a version of mereological essentialism that Armstrong rejects, and it is this rejection, not a new view about what the constituents are, that lets him reply to Simon’s and McDaniel’s objection.
Armstrong (1978a: 114; 1997: 123–126) distinguishes between a thick and a thin conception of particulars and identifies the former, particulars thought of along with all of their non-relational properties rather than abstracted from them, with states of affairs. So Armstrong might be willing to accept that some states of affairs are negatively charged, since he thinks that some states of affairs are electrons, at least if we understand electrons in a certain way. However, this electron’s being negatively charged is not the state of affairs that Armstrong identifies with the electron, since it does not include all of the electron’s non-relational properties. So Armstrong’s views about thick particulars give no independent reason to think that this electron’s being negatively charged is, itself, negatively charged.
Armstrong gives other accounts of instantiation. Some, for example the one in Armstrong (1978a: 112), seem like early versions of the accounts already discussed. Others, for example those in Armstrong (1989: 96–97, 2010: 32–33), are substantially different. However, those accounts do not take instantiation to involve a partial identity between particulars and universals, so they are beyond the scope of my argument.
See Baxter (2013: 294).
See Turner (2014) for a helpful discussion of cross-count identity in another context, including an attempt to formally regiment it.
See Baxter (1988a, b). In conversation, Baxter told me that he now prefers to say existence as one is relative to a count, not that existence is relative to a count. This is because each count exhausts reality: if something exists on a count, then it exists on all counts, although how many things it exists as might vary across counts.
Underwood (2010) disagrees. He prefers taking cross-count identity to be a kind, or “dimension,” of numerical identity and dropping Baxter’s use of counts. Underwood gives an account of instantiation using multiple, primitive kinds of numerical identity. However, Underwood’s account explicitly makes instantiation asymmetric rather than nonsymmetric (see Underwood 2010: 269). He can avoid this problem by accepting higher-order particulars and introducing still further primitive kinds of numerical identity, but this would strengthen the worry that realism has too much primitive ideology.
See Baxter (2013: 293).
Baxter goes on to qualify this identification using his theory of aspects: universals are particulars insofar as the particulars are the same way, relative to a different count. Baxter takes something insofar as it is some way to be an aspect of it, where aspects of something are numerically identical to it (and each other) but can, nevertheless, qualitatively differ from it (and from each other). For Baxter’s theory of aspects, see Baxter (1999, 2013).
Baxter’s use of “partial” here seems to be in recognition of the fact that particulars usually instantiate multiple universals and universals are usually instantiated by multiple particulars. The cross-count identity is partial in virtue of the fact that the “particular and universal are not wholly identical across the count. Some aspects of each are not aspects of the other” (2001: 456).
Elsewhere, Baxter states his account of instantiation explicitly in terms of aspects. See, for example, Baxter (2001: 453, 2013: 293). For simplicity, I will talk about particulars and universals being cross-count identical rather than talk about their aspects being cross-count identical. Nothing turns on this choice; particulars and universals are cross-count identical just in case an aspect of one is cross-count identical to an aspect of the other.
For comments and discussion, thanks to Donald Baxter, Ben Caplan, David Sanson, William Taschek, and participants at “Themes from Baxter II” in Ligerz, Switzerland in October 2013. Thanks also to an anonymous referee for some very helpful feedback.
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Acknowledgments
For comments and discussion, thanks to Donald Baxter, Ben Caplan, David Sanson, William Taschek, and participants at “Themes from Baxter II” in Ligerz, Switzerland in October 2013. Thanks also to an anonymous referee for some very helpful feedback.
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Brown, S. Against instantiation as identity. Philos Stud 174, 887–900 (2017). https://doi.org/10.1007/s11098-016-0712-5
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DOI: https://doi.org/10.1007/s11098-016-0712-5