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Modal paradox II: essence and coherence

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Abstract

Paradoxes of nested modality, like Chisholm’s paradox, rely on S4 or something stronger as the propositional logic of metaphysical modality. Sarah-Jane Leslie’s objection to the resolution of Chisholm’s paradox by means of rejection of S4 modal logic is investigated. A modal notion of essence congenial to Leslie’s objection is clarified. An argument is presented in support of Leslie’s crucial but unsupported assertion that, on pain of inconsistency, an object’s essence is the same in every possible world (in which that object exists). A fallacy in the argument is exposed. Alternative interpretations of Leslie’s objection are provided and are found to involve equivocation between different notions of “essence.” A material artifact’s modal essence, as distinct from its quiddity essence, could have been different than it is.

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Notes

  1. This terminology differs from that of Leslie (2011). Leslie writes: “An object’s essential properties are conditions on what it is to be that object, and this set of conditions fixes just which possibilities or possible worlds the object exists in, namely just those in which it satisfies those conditions. … An object’s accidental properties are those of its properties that it can be found without at some times or at some worlds” (p. 277). Leslie’s notions appear to be at least partly modal. See note 11.

    It is more common to define a modally essential property of x to be a property such that it is metaphysically necessary that x has it if x exists. I believe this to be an error, likely due at least to some extent to the widely held myth that a thing must exist to have properties. The more common definition has two peculiar consequences. First, by this definition a property P can be a “modally essential” property of x, and x can have P “modally essentially,” even if x lacks P. For example, had the Eiffel Tower not been erected, it would not have the property of being a tower, though by this definition it would nevertheless have the property “modally essentially.” Second, on the more common definition, existence is a “modally essential” property of every possible thing, whereas existence is in fact a modally essential property of some things, e.g., the number two, but not of others, e.g., the Eiffel Tower. (It should be noted that while being a man if existent may be a modally essential property of Socrates, being a man simpliciter is not, since Socrates is not a man and does not even exist any longer.)

    Fine (1995) says that a property P of an object x is essential to x if x must have P to be what x is (p. 53). This definition conflicts with Fine’s effort to make ‘essence’ a term for quiddity essence, and is in fact better suited to the modal notion.

  2. For an overview of the nested-modality paradoxes see (chronologically listed) Chisholm (1967), Kripke (1972), at pp. 50–51; Chandler (1976), Chisholm (1976), at pp. 89–104, Quine (1976), Salmón (1981b), at pp. 229–252, Forbes (1984), Salmón (1986a), Lewis (1986), at pp. 243–248, Kripke (1987), Salmón (1989), Williamson (1990, pp. 126–143), Salmón (1993), Mackie (2006, pp. 59–69) and Robertson Ishii (2013).

  3. According to contemporary philosophical usage, a world is a total way for things (the universe) to be. Some philosophers use the phrase ‘possible world’ incorrectly for a world (in the present sense). A possible world is rather a total way things might have been, in the operative sense of ‘might have’. Accordingly, an impossible world is a total way things could not have been. The actual world is the total way things actually are, and is thereby a uniquely distinguished possible world.

  4. The formulation ignores largely irrelevant complications arising from the additional premises that ∀xh□[M(x, h) → x exists & h exists] and ∀hh′□[O(h, h′) → h exists & h′ exists].

  5. Here and elsewhere, Leslie does not adequately distinguish Tol and Ess. She says ‘what this means’ where she evidently intends ‘this entails’. The imagined entailment does not in fact exist, however, as Tol does not entail Ess. The bracketed insertions of the word ‘only’ yield Leslie’s intended instance of Ess in lieu of the corresponding cited instance of Tol. Leslie says ‘a new part’ where she should use ‘a third part’. (That third part could be the remaining original part, hence not new.) Other interpretations do not yield a viable argument.

  6. Several others have also urged plenitude-centered resolutions. See for example Kment (2014, pp. 194–197). See Robertson Ishii (2013) and Salmón (2018), at n15 for responses to Leslie’s plenitude.

  7. More precisely, this is the property expressed by ‘λx[~ ∃K□(x exists → x’s modal essence = K)]’, or more perspicuously by ‘λx[∃ww′(w is accessible to w′ & x’s modal essence in w ≠ x’s modal essence in w′)]’. Leslie contrasts the property of “a variable essence,” which she deems oxymoronic, with a “variably realizable essence,” which she defines as an “essence whose fixed fulfillment conditions can admit of varied realization from world to world” (p. 285). She says “none of these paradoxes arise if we distinguish variably realizable ‘intolerant’ essences and variable essences” (p. 286). The terminology of ‘variably realizable essence’ and ‘a variable essence’ encourages the confusion in question. To my knowledge none of the philosophers Leslie criticizes for “sliding from” the former to the latter uses Leslie’s terminology or confuses these properties.

  8. Leslie (2011) does not acknowledge that there are non-transitive-accessibility models of “variable” modal essences. Perhaps she tacitly assumes that such models violate the logic of metaphysical modality. Admittedly, there are also non-reflexive-accessibility models, and these are inadmissible in the logic of any alethic modality, since they clash with the analyticity of ‘□pp’. Likewise, there are inadmissible classical models of ‘Jones is married and Jones is a bachelor’. There is a crucial difference between the two modal cases. As regards metaphysical modality, the axioms of T are not only analytic but intuitively so. The notion of a false necessary truth is oxymoronic in the same way as the notion of a married bachelor. By contrast, the characteristic axiom of S4, ‘□p → □□p’, is not intuitively analytic; indeed, Leslie is engaged in an on-going controversy concerning its truth. Furthermore, AR is clearly coherent, and it poses a forceful case that the characteristic S4 axiom is even falsified by actual specific instances. The thesis that all instances of that axiom for metaphysical necessity are analytic, so that non-transitive accessibility models are inadmissible, carries the burden of proof and cannot be legitimately assumed, let alone assumed tacitly. Cf. Salmón (1989), pp. 28–31.

  9. Yablo (1987), Almog (1991) and Fine (1994, 1995). Fine also refers to the quiddity essence of an object x as x’s “identity” (a term better suited to x’s haecceity) and x’s “definition”.

  10. It will not do for Fine’s purposes to allow that a property that is part of an object’s quiddity essence can be a metaphysically contingent property of the object.

  11. One candidate for Troy’s quiddity essence is the property of being both Troy and a tripod, or the pair set consisting of the property of being a tripod together with Troy’s haecceity (being Troy).

    Leslie might endorse the highly dubious thesis that an object’s quiddity essence determines the object’s full modal essence, and it is possible that this thesis is part of Leslie’s rationale for P2. Numerous philosophers are committed to a weaker thesis: that the collective quiddity essence of (the plurality of) all objects determines the modal essence of each object. As Robertson Ishii observes, AR poses a very formidable challenge even to this weaker thesis. If Leslie endorses either thesis, she is not entitled simply to assume it, especially not as a tacit premise. Both the weaker thesis and the stronger thesis bear the burden of proof. AR disputes both theses, and more importantly, it presents a very forceful case against even the weaker thesis. (See note 8.)

  12. The four-world paradox compares w2, which includes Troy, with a world w2′ that is possible according to w1′ and in which Trevor instead of Troy is made from h2. David Lewis (1986, p. 245n) in effect also misidentifies w3 with w1′, for the same reason as Leslie but supported also by his highly idiosyncratic understanding of metaphysical modality (which I deem a colossal misunderstanding).

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Acknowledgements

I am heavily indebted to Teresa Robertson Ishii for discussion. I am grateful also to the editors of Philosophical Studies, especially for their recognition that philosophical criticism, guided by an aim for the truth, can have significant intellectual worth.

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Salmón, N. Modal paradox II: essence and coherence. Philos Stud 178, 3237–3250 (2021). https://doi.org/10.1007/s11098-020-01599-5

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