Logic and Logical Philosophy 18 (1):33-43 (2009)

Daisuke Kachi
Saitama University
Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of the intermediate truth-value so as to reconstruct Łukasiewicz’s three-valued logic as a kind of extensional modal logic based on partial logic
Keywords Bourne  partial logic  future contingents  three-valued logic  truth-value gap  alethic modality  Łukasiewicz
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DOI 10.12775/LLP.2009.003
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Three-Valued Logic and Future Contingents.A. N. Prior - 1953 - Philosophical Quarterly 3 (13):317-326.
Many-Valued Logic.Alasdair Urquhart - 1986 - In D. Gabbay & F. Guenther (eds.), Handbook of Philosophical Logic, Vol. Iii. D. Reidel Publishing Co..
Three-Valued Logic and Future Contingents.A. N. Prior - 1954 - Journal of Symbolic Logic 19 (4):294-294.

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