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.
This paper presents two interpretations of the first-degree (FD) entailments of propositional logic that are based directly on the notion of inclusion of information.* It is proved in Section 2 that one of these interpretations exactly characterizes the tautological entailments of [2], while the other exactly characterizes the valid arguments of classical truth-functional logic. In Section 3, following a line of reasoning suggested in part by consideration of these interpretations, it is argued that the claim that relevance logic better captures our intuitions about entailment than classical logic is false. Section 1 presents natural-deduction formulations of both classical and relevant FD entailments that are used in subsequent proofs.
Two systems of natural deduction rulesI take -, v, and & as primitive connectives and assume that sentential letters are specified. Wffs are as usual. I let A, B, . . ., F (with or without numerical subscripts) range over wffs and let M and TV range over finite nonempty sets of wffs.Given any finite nonempty set of wffs M, an infinite set of wffs XM is defined recursively as follows:1. If A eM 9 then ,4 e X M . 2. A & B e X M iff A e X M and B e X M . 3. If A e X M or B e X M , then A v B e X M .
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