Actuality, Necessity, and Logical Truth |
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Authors: | William H Hanson |
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Institution: | (1) Department of Philosophy, University of Minnesota, 271 19th Ave. S. 831 Heller Hall, Minneapolis, MN 55455-0310, USA |
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Abstract: | The traditional view that all logical truths are metaphysically necessary has come under attack in recent years. The contrary
claim is prominent in David Kaplan’s work on demonstratives, and Edward Zalta has argued that logical truths that are not
necessary appear in modal languages supplemented only with some device for making reference to the actual world (and thus
independently of whether demonstratives like ‘I’, ‘here’, and ‘now’ are present). If this latter claim can be sustained, it
strikes close to the heart of the traditional view. I begin this paper by discussing and refuting Zalta’s argument in the
context of a language for propositional modal logic with an actuality connective (section 1). This involves showing that his
argument in favor of real world validity his preferred explication of logical truth, is fallacious. Next (section 2) I argue
for an alternative explication of logical truth called general validity. Since the rule of necessitation preserves general
validity, the argument of section 2 provides a reason for affirming the traditional view. Finally (section 3) I show that
the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language
connective for deep necessity.
Earlier versions of this paper were read at the universities of Graz,
Maribor, and Salzburg, and at a workshop on the philosophy of logic at the
National Autonomous University of Mexico (UNAM) in Mexico City. My
thanks to those present at these events for many helpful suggestions. Thanks
are also due to an anonymous referee for Philosophical Studies. |
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Keywords: | actuality contingent a priori deep necessity general validity logical truth necessary a posteriori real world validity superficial necessity |
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