The propositional logic of ordinary discourse

Abstract

The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments.

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References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
The Logic of Conditionals.Ernest Adams - 1965 - Inquiry: An Interdisciplinary Journal of Philosophy 8 (1-4):166 – 197.
A Survey of Symbolic Logic.Clarence Irving Lewis - 1918 - New York: Dover Publications.

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