The Tense Logic for Master Argument in Prior’s Reconstruction
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In this paper we examine Prior’s reconstruction of Master Argument  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.
KeywordsMaster Argument of Diodorus Cronus time and modalities logical structures of time modal and tense logics
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- 1.Burgess, J. P., ‘Basic tense logic’, in D. M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, vol. II, D. Reidel Publishing Company, Dordrecht, 1984, pp. 89–133.Google Scholar
- 2.Fitting M., Mendelson R.L.: First-order Modal Logic. Kluwer, Dorderecht (1998)Google Scholar
- 3.Gundersen L.: ‘The Master Argument and branching time’,. Logic and Logical Philosophy 5, 49–60 (1997)Google Scholar
- 5.Prior, A. N., Time and Modality, Oxford Univ. Press, 1957.Google Scholar
- 6.Prior, A. N., Past, Present, and Future, Oxford Univ. Press, 1967.Google Scholar
- 7.Thomason, R.H., ‘Combinations of tense and modality’, in D.M. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, vol. II, D. Reidel Publishing Company, Dordrecht, 1984, pp. 135–165.Google Scholar
- 8.Venema, Y., ‘Temporal logic’, Chapter 10, in L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell Publishers, Malden – Oxford, 2001, pp. 203–223.Google Scholar