Journal of Symbolic Logic

Quine's 'Limits of Decision'

William C. Purdy

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In a 1969 paper, Quine coined the term 'limits of decision'. This term evidently refers to limits on the logical vocabulary of a logic, beyond which satisfiability is no longer decidable. In the same paper. Quine showed that not only monadic formulas, but homogeneous k-adic formulas for arbitrary k lie on the decidable side of the limits of decision. But the precise location of the limits of decision has remained an open question. The present paper answers that question. It addresses the question of decidability of those sublogics of first-order logic that are defined in terms of their logical vocabularies. A complete answer is obtained, thus locating exactly Quine's limits of decision.

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J. Symbolic Logic, Volume 64, Issue 4 (1999), 1439-1466.

First available in Project Euclid: 6 July 2007

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Purdy, William C. Quine's 'Limits of Decision'. J. Symbolic Logic 64 (1999), no. 4, 1439--1466.

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