Studia Logica 92 (1):85 - 108 (2009)

Andrzej Pietruszczak
Nicolaus Copernicus University
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.
Keywords Master Argument of Diodorus Cronus  time and modalities  logical structures of time  modal and tense logics
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DOI 10.1007/s11225-009-9187-0
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References found in this work BETA

First-Order Modal Logic.Roderic A. Girle, Melvin Fitting & Richard L. Mendelsohn - 2002 - Bulletin of Symbolic Logic 8 (3):429.
First-Order Modal Logic.Melvin Fitting, R. Mendelsohn & Roderic A. Girle - 2002 - Bulletin of Symbolic Logic 8 (3):429-430.
Diodoran Modalities.A. N. Prior - 1955 - Philosophical Quarterly 5 (20):205-213.
The Master Argument and Branching Time.Lars Gundersen - 1997 - Logic and Logical Philosophy 5:49-60.

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