David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophical Review 78 (2):197-236 (1969)
Following Moore, I use ‘P entails Q’ as a convenient shorthand for ‘Q can be deduced logically from P’, ‘From P, Q follows logically’, ‘There is a logically valid argument with P as sole premise and Q as conclusion’, and the like.1 Apart from a minor point to be raised in Section XVI, distinctions within this cluster do not matter for present purposes. An analysis of the concept of entailment is answerable to careful, educated uses of expressions such as those. An analysis which condemned nearly everything we say about what follows from what simply would not be an analysis of the common concept of entailment. If the concept were inconsistent, some common uses of it would be condemned; but only by standards established by the others. C. I. Lewis maintained this: to say that P entails Q is to say that it is logically impossible that (P & ¬Q).2 If Quine is right, then ‘entails’ and ‘impossible’ are as suspect as all other intensional terms. So perhaps they are; but their uses are not wholly without structure, and there are wrong ways of interrelating them. Lewis’s contention is about the internal geography of the intensional area, not its relations to the surrounding conceptual territory: it is an attempted analysis of one intensional expression in terms of another. I shall argue that Lewis was right, and also - by implication - that his thesis is helpful and clarifying - that is, that it is a genuine analysis. As is well known, Lewis’s analysis implies that each impossible proposition entails every proposition. Accepting the analysis, I accept this result. For one thing, Lewis has an argument for it (I use ‘→’ to abbreviate ‘entails’): (1) P & ¬P..
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Francesco Paoli (2007). Implicational Paradoxes and the Meaning of Logical Constants. Australasian Journal of Philosophy 85 (4):553 – 579.
John Woods (2012). Semantic Penumbra: Concept Similarity in Logic. [REVIEW] Topoi 31 (1):121-134.
William H. Hanson (1989). Two Kinds of Deviance. History and Philosophy of Logic 10 (1):15-28.
Douglas N. Walton (1979). Philosophical Basis of Relatedness Logic. Philosophical Studies 36 (2):115 - 136.
B. I. Copeland (1984). Horseshoe, Hook, and Relevance. Theoria 50 (2-3):148-164.
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