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The Tense Logic for Master Argument in Prior's Reconstruction

Tomasz Jarmużek and Andrzej Pietruszczak
Studia Logica: An International Journal for Symbolic Logic
Vol. 92, No. 1 (Jun., 2009), pp. 85-108
Published by: Springer
Stable URL: http://www.jstor.org/stable/40269052
Page Count: 24
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The Tense Logic for Master Argument in Prior's Reconstruction
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Abstract

In this paper we examine Prior's reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic $K_t 4$ plus a new axiom $(p):p \wedge Gp \supset PGp'$ . This formula was used by Prior in his original analysis of Master Argument. (P) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by (P) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction.

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