The Tense Logic for Master Argument in Prior’s Reconstruction

Studia Logica 92 (1):85 - 108 (2009)
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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 Λ G p ⊃ P G p ’. 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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Andrzej Pietruszczak
Nicolaus Copernicus University

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References found in this work

Past, Present and Future.Arthur N. Prior - 1967 - Oxford University Press.
First-Order Modal Logic.Roderic A. Girle, Melvin Fitting & Richard L. Mendelsohn - 2002 - Bulletin of Symbolic Logic 8 (3):429.
Diodoran modalities.A. N. Prior - 1955 - Philosophical Quarterly 5 (20):205-213.
First-order modal logic.Melvin Fitting, R. Mendelsohn & Roderic A. Girle - 2002 - Bulletin of Symbolic Logic 8 (3):429-430.
The master argument and branching time.Lars Gundersen - 1997 - Logic and Logical Philosophy 5:49-60.

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