Abstract
Jeffrey King has recently argued: (i) that the semantic value of a sentence at a context is (or determines) a function from possible worlds to truth values, and (ii) that this undermines Jason Stanley's argument against the rigidity thesis, the claim that no rigid term has the same content as a non-rigid term. I show that King's main argument for (i) fails, and that Stanley's argument is consistent with the claim that the semantic value of a sentence at a context is (or determines) a function from worlds to truth values.
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Notes
For simplicity, I will assume for the most part that propositions can be represented as functions from possible worlds to truth values (or sets of possible worlds). King’s own view is that they are structured entities, but he claims not to appeal to that aspect of his view in the relevant paper and chapter (King 2007, p. 164). However, later in the paper we will encounter one argument which may require contents to be structured; see footnote 12.
If a theory gives extensions relative to just a context and a variable assignment, we take the semantic value of ϕ at c to be \([\!\![ \phi ]\!\!]^{c,g}\). (The double brackets “\([\!\![\,]\!\!]\)” denote the interpretation function of a semantic theory. For most of the theories we’ll discuss, they denote a four-place function that takes expression–context-index-assignment quadruples to extensions. For theories without indices, they denote the corresponding three-place function.)
Times are of type r, truth values of type t.
The semantics of an object language λ-binder can be given as follows, where ϕ is any expression: \([\!\![ \lambda x_1 \phi ]\!\!]^{c,i,g} = \lambda x.[\!\![ \phi ]\!\!]^{c,i,g^{x/1}}\) (where g x/1 is the variable assignment that maps “1” to x, but is otherwise like g).
Schlenker attributes this idea to lecture handouts prepared by Irene Heim.
A theory of this sort is described and explored in some detail in Percus (2000) (though Percus take propositions to be functions from possible situations, rather than possible worlds, to truth values).
Using a system that employs object-language λ-binders makes the move I’ve been making here seem quite natural. King doesn’t seem to employ such resources (King 2007, pp. 194–195), which may be why he overlooks or ignores this strategy for combining the view that tenses (modals) are object language quantifiers with the claim that the semantic value of a sentence is something whose truth-value varies across times (worlds).
A well-known system of this sort is developed in Kaplan (1989).
Note that a context is not just any world-time-place-individual quadruple. It must be one in which the individual in question is speaking at the time, place and world in question. Consequently, the diagonal is a partial function: it is not defined for worlds w′ in which x c is not speaking at t c at p c See Lewis (1980, p. 38) for discussion.
See King (2003, p. 14) for a discussion of the differences between Stanley’s view and the two-dimensionalist’s. I should emphasize that my remarks only concern the Stanley-inspired two-dimensionalism that King discusses. It might be that some of the other things Stanley says in his wider case against RT require something like Lewis’s picture.
Thanks to an anonymous reviewer for help in formulating this argument. I should note that the final assumption the argument makes is a (restricted) ‘reverse compositionality’ principle. That sort of principle doesn’t typically hold in intensional semantic theories of the sort we’ve been discussing. To see this, let ϕ be an open formula that cannot be satisfied at any point of evaluation; then even if τ and τ′ differ in content, the contents of ϕ(τ) at c will ϕ(τ′) at c will be the same, viz. the empty set. So the argument appears to require the idea that contents are structured. (Note that similar considerations would seem to suggest that RT itself—at least as we’ve stated it—also requires contents to be structured.)
See Stanley (1997b) for a defense of the claim that RT is a thesis about communicated content.
Of course, King would then presumably be obliged to give some explanation of why (7) and (8) seem to communicate the same information.
References
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Lewis, D. K. (1980). Index, context, and content. In S. Kanger, & S. Öhman (Eds.), Philosophy and grammar (pp. 79–100). Dordrecht: D. Reidel Publishing Company. (Reprinted from Lewis 1998, pp. 21–44, Page references to are to the 1998 reprint).
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Stanley, J. (1997b). Rigidity and content. In: R. Heck (Ed.), Language, thought, and logic, (pp. 131–156). Oxford: Oxford University Press.
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Acknowledgments
For helpful comments, thanks to Alejandro Pérez Carballo, Paolo Santorio, Seth Yalcin, and an anonymous referee for Philosophical Studies.
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Ninan, D. Propositions, semantic values, and rigidity. Philos Stud 158, 401–413 (2012). https://doi.org/10.1007/s11098-010-9677-y
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DOI: https://doi.org/10.1007/s11098-010-9677-y