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Logical truth in modal languages: reply to Nelson and Zalta

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Abstract

Does general validity or real world validity better represent the intuitive notion of logical truth for sentential modal languages with an actuality connective? In (Philosophical Studies 130:436–459, 2006) I argued in favor of general validity, and I criticized the arguments of Zalta (Journal of Philosophy 85:57–74, 1988) for real world validity. But in Nelson and Zalta (Philosophical Studies 157:153–162, 2012) Michael Nelson and Edward Zalta criticize my arguments and claim to have established the superiority of real world validity. Section 1 of the present paper introduces the problem and sets out the basic issues. In Sect. 2 I consider three of Nelson and Zalta’s arguments and find all of them deficient. In Sect. 3 I note that Nelson and Zalta direct much of their criticism at a phrase (‘true at a world from the point of view of some distinct world as actual’) I used only inessentially in Hanson (Philosophical Studies 130:436–459, 2006), and that their account of the philosophical foundations of modal semantics leaves them ill equipped to account for the plausibility of modal logics weaker than S5. Along the way I make several general suggestions for ways in which philosophical discussions of logical matters–especially, but not limited to, discussions of truth and logical truth for languages containing modal and indexical terms–might be facilitated and made more productive.

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Notes

  1. More precisely, if p is true at \( @ \) but false at some \({w\in{\mathcal{W}}}\) such that \({@{\mathcal{R}}w}\).

  2. Menzel (1990) has given a precise development of this idea.

  3. Kripke pointed this out in (1959), the paper that initiated modern model-theoretic semantics for modal logic.

  4. Both Zalta (1988) and Kaplan (in 1979, and in Almog et al. 1989) give more examples of sentences they claim are logically true but not necessary, but it will be sufficient for my argument to focus on the two cited here.

  5. I don’t think N&Z would deny that ‘actually’ is an indexical, for it is widely classified as such. (See, for example, the work of David Kaplan, who has written extensively on these matters, especially (Almog et al. 1989), pp. 489–491, 594–597.) My dispute with N&Z is not about the grammatical classification of ‘actually’, but rather about its proper role in the definition of logical truth.

  6. More precisely, general validity for formulas of the formal language under consideration is decidable in at least those cases where the underlying modal propositional logic is a standard decidable system, such as T, B, S4, S5. It is easy to show that when systems such as these are augmented with an actuality connective the resulting systems are also decidable.

  7. Kaplan also defines validity as truth at the actual world of each model. And like N&Z he applies this definition even to modal languages without indexicals. Yet unlike N&Z he treats ‘actually’ in the same way as other indexicals. His arguments for this approach depend on the distinction he draws between the character and the content of a sentence. Validity is a property of characters, while necessity is a property of contents. (See especially his “Afterthoughts” in Almog et al. 1989, pp. 489–491, 594–597.) But in (1988, p. 70), Zalta dismisses these arguments as unnecessarily complicated for the purpose of separating logical truth from necessity. What (Nelson and Zalta 2012) lacks is credible arguments for this view. A discussion of Kaplan’s arguments would take me beyond the scope of the present paper.

  8. See (Evans 1979, pp. 167–168, 181) . Evans (1979) is reprinted in Evans (1985). Page references given here are to the original. Davies and Humberstone, following Evans, use these terms in (1980); see especially pp. 3, 16, and footnote 28.

  9. See, for example, Baldwin (2001) and Stalnaker (2001).

  10. At the beginning of (2012) N&Z say they will restrict their attention to S5 and that their models therefore will not need an “accessibility relation”. But they say nothing in (2012) about the relative merits of S5 and its weaker cousins.

  11. See Salmon (1989), especially pp. 4–8. Salmon argues that T is the correct modal logic.

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  1. Department of Philosophy, University of Minnesota, 831 Walter Heller Hall, 271 19th Avenue South, Minneapolis, MN, 55455, USA

    William H. Hanson

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  1. William H. Hanson
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Correspondence to William H. Hanson.

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Hanson, W.H. Logical truth in modal languages: reply to Nelson and Zalta. Philos Stud 167, 327–339 (2014). https://doi.org/10.1007/s11098-012-0088-0

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