De Jure and De Facto Validity in the Logic of Time and Modality

Thought: A Journal of Philosophy 2 (2):196-205 (2013)
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Abstract

What formulas are tense-logically valid depends on the structure of time, for example on whether it has a beginning. Logicians have investigated what formulas correspond to what physical hypotheses about time. Analogously, we can investigate what formulas of modal logic correspond to what metaphysical hypotheses about necessity. It is widely held that physical hypotheses about time may be contingent. If so, tense-logical validity may be contingent. In contrast, validity in modal logic is typically taken to be non-contingent, as reflected by the general acceptance of the so-called “rule of necessitation.” But as has been argued by various authors in recent years, metaphysical hypotheses may likewise be contingent. If, in particular, hypotheses about the extent of possibility are contingent, we should expect modal-logical validity to be contingent too. Let “contingentism” be the view that everything that is not ruled out by logic is possible. I shall investigate what the right system of modal logic is, if contingentism is true. Given plausible assumptions, the system contains the McKinsey principle, and is thus not even contained in S5. It also contains simple and elegant iteration principles for the contingency operator: something is contingent if and only if it is contingently contingent

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Stephan Leuenberger
University of Glasgow

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References found in this work

Mathematical Logic.W. V. Quine - 1940 - Cambridge: Harvard University Press.
The Contingency of Composition.Ross P. Cameron - 2007 - Philosophical Studies 136 (1):99-121.
The Logic of What Might Have Been.Nathan Salmon - 1989 - Philosophical Review 98 (1):3-34.

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