Actuality, Necessity, and Logical Truth

Abstract

The traditional view that all logical truths are metaphysically necessary has come under attack in recent years. The contrary claim is prominent in David Kaplan's work on demonstratives, and Edward Zalta has argued that logical truths that are not necessary appear in modal languages supplemented only with some device for making reference to the actual world (and thus independently of whether demonstratives like 'I', 'here', and 'now' are present). If this latter claim can be sustained, it strikes close to the heart of the traditional view. I begin this paper by discussing and refuting Zalta's argument in the context of a language for propositional modal logic with an actuality connective (section 1). This involves showing that his argument in favor of real world validity, his preferred explication of logical truth, is fallacious. Next (section 2) I argue for an alternative explication of logical truth called general validity. Since the rule of necessitation preserves general validity, the argument of section 2 provides a reason for affirming the traditional view. Finally (section 3) I show that the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language connective for deep necessity.

Actual Issues for Relevant Logics

“…Neither option, however, provides a plausible, attractive thing to 26. See Davies and Humberstone (1980), Zalta (1988), Humberstone (2004), Hanson (2006), Nelson and Zalta (2012), and French (2012) for discussion.…”

Characterizing Invariance

“…that is, when the content of φ determined at a context @ is true at @ only if the content of φ determined at any isomorphic context d is true at d. Failure of shallow necessity inv undermines logical truth (Hanson 2006). If a claim is not shallowly necessary, then its truth can vary from context to context, even when these contexts contain the same number of objects.…”

On What Actually Is

“…I remain agnostic about whether there are, indeed, two notions of necessity reflected in ordinary language or thought (see Hanson 2006 for a discussion). If 'actually' in natural language were a rigidifier, however, then it should have been the kind of expression that brought out this distinction-it should make available two different interpretations of a sentence according to that sentence's deep and superficial modal profiles.…”