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Sorting Out the Sortals: A Fregean Argument for Essentialism

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Abstract

In his paper, “Identity Statements and Essentialism,” Loux (New Scholast 44:431–439, 1971) seeks to demonstrate sortal essentialism based on Frege’s thesis that all statements of number concerning a collection require that the members fall under the same sortal concept. I shall attempt to argue that a detailed analysis of Loux’s argument reveals it as failing to imply the type of sortal dependency thesis necessary for the justification of sortal essentialism. However, if one construes the transworld identity relation as no different from our run of the mill identity relation, then his argument can serve as the basis for a proof of a type of nontrivial essentialism, thereby showing that the possible worlds picture of modality is indeed committed to a robust essentialism.

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Notes

  1. In characterizing Non-Trivial Essentialism I am sticking pretty close to Parsons’ (1969) original formulation, subject to the caveat that the domain of possible worlds is relativized to ones where the individuals in question exist.

  2. This is a much stronger version of the sortal dependency thesis than what is usually espoused, but, as we shall explain further on in the paper, it is the strength that is requisite for a direct derivation of sortal essentialism from that thesis and the assumption that transworld identity is simply identity across worlds.

  3. See, for example, Geach (1962, 1964), Wiggins (1967, 1980, 2001), Hirsch (1982), Brody (1980), Dummett (1991) and McLeod (2001).

  4. See Dummett (1991), as well as Wiggins (1980) for excellent critiques of this view. It should be noted that they also show the logical independence of the relativity thesis and the thesis of sortal dependency.

  5. For the details of such a proof see Wiggins (1980, 2001), Chapter Two.

  6. It should be noted that both Brody (1980) and Wiggins (1980) have given arguments for sortal essentialism based on some form of the sortal dependency thesis, but these arguments assume premises that are already non-trivially essentialist, and hence would be circular in any argument for non-trivial essentialism as such. Also Mackie (1994) has given us excellent reasons for rejecting the soundness of these arguments in the first place.

  7. It should be emphasized that my claim only applies to possible worlds theories that construe transworld identity as the identity relation. Counterpart theories ala Lewis (1968) substitute transworld identity with a counterpart relation. Lewis himself admits that it is not an identity relation. He states in his article ‘Counterpart theory and Quantified Modal Logic’ that “Your counterparts resemble you closely in content and context in important respects. They resemble you more closely than do the other things in their worlds. But they are not really you.” (Lewis 112). He also indicates within the formal apparatus of his theory that “nothing is in two worlds.” This is his English translation of ∀x∀y∀z(Ixy & Ixz. ⊃ y = z), his second ‘postulate’ on page 111. It is not the project of this paper to adjudicate the essentialist commitments of such a theory.

  8. The necessity of identity is provable in S5. See Kripke (1980).

  9. All references to modal particles in this paper are to be taken in the conceptual or logical sense of necessity, unless otherwise indicated. This will also be my usage with respect to possible worlds; the domain of such worlds will include all and only conceptually or logically possible worlds.

  10. In actualist models w*only ranges over worlds where x and y exist.

  11. Here we see the importance of the assumption that trans-world identity and intra-world identity are the same relation. Without it we would not be able to apply 16 to trans-world identity statements, neither would we be entitled to infer that trans-world identity is an equivalence relation, and hence transitive.

  12. Subject, of course, to the provisos about identity detailed in footnote 7 above.

  13. I owe this way of describing the semantic situation with respect to sortals to one of the anonymous reviewers.

  14. I seriously doubt that it makes sense to count the number of propositions in Tasmania. So the number of prop-men located in Tasmania, or in any other place for that matter, would have to be reduced to the number of men in that place.

  15. This term is used in Lowe (1989, 25, 2009, 26) and in Sarnecki (2008, 151).

  16. I am indebted to one of the anonymous reviewers for raising this problem.

  17. Salmon(1996) attempts to prove the logical independence of x = y from any proposition concerning x’s or y’s possession of such and such qualities. See Catterson (2008) for a detailed critique of this proof.

  18. For more on this distinction in its modern incarnation see Wiggins (2001, 8 note 6).

  19. By principle of individuation I mean a statement of the form: for all x and y that fall under S, x = y if and only if x and y satisfy condition C, where the specification of C is relative to a determinate range of states of affairs. See Lowe (2009, 16) for a similar construal. I agree with both Lowe and Wiggins (2001, 60–61) that such a principle is a semantic/ontological one that merely determines the facts that make identity statements true for things of a particular sort. Such principles in many cases will not be susceptible to empirical verification/falsification.

  20. This principle is logically equivalent to the second conjunct in the Absolute Identity Principle mentioned in Mackie (1994, 323). See also Wiggins (2001, 67).

  21. The statue example is first adduced by Gibbard (1975) in order to prove the contingency of identity.

  22. Gibbard (1975), Lewis (1986), Olson (2001), and Wasserman (2002) are examples of monists, and Baker (1997), Fine (2003), Johnston (1992), Lowe (2002), and Wiggins (2001) are examples of pluralists.

  23. See Lowe (2002, 67–68) for a critical discussion of this option. Merricks (2001) and van Inwagen (1990) argue for a view of physical reality that excludes many physical count-nouns from expressing sortals.

  24. This in fact was the purpose behind Gibbard’s use of the thought experiment. Lewis (1986) and Noonan (1991) attempt to use the theory of temporal parts to make sense of this contingency.

  25. With the exception of the case where n = 0.

  26. This is not to say that they always provide sufficient conditions for judgments of cardinality. For doubts along these lines see Wiggins (2001, 74–76) and Lowe (2009, 14).

  27. Such an enumeration can also take place if we have either a partially recursive set or recursive set. .

  28. Of course we could deny that proper names have senses at all; but then a fortiori they cannot have identity criteria attached to them. For a more detailed discussion of the direct theory of reference see Salmon (1981) and Kripke (1980).

  29. Lowe (2009, 14) states the same point in the following manner: “…individuals are recognizable only as individuals of a sort.”

  30. See, for example, Xu (1996, 1997).

  31. See Sarnecki (2008) for a detailed discussion and defense of sortal dependency with regard to a child’s acquisition of sortal concepts.

  32. Lowe (2009, 14–15, 2007) discusses and responds to this objection.

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  1. Salve Regina University, 100 Ochre Point Ave, Newport, RI, 02840, USA

    Troy T. Catterson

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    Troy T. Catterson

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Catterson, T.T. Sorting Out the Sortals: A Fregean Argument for Essentialism. Erkenn 80, 137–157 (2015). https://doi.org/10.1007/s10670-014-9617-x

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