There is no paradox of logical validity
Speaker: Roy T. Cook, University of Minnesota
Abstract: JC Beall & Julien Murzi, Lionel Shapiro and Bruno Whittle have all recently argued that one can construct a `paradox of logical validity' by supplementing Peano Arithmetic (or any theory strong enough for Godel coding and diagonalization) with a binary validity predicate that holds of (the codes of) two formulas F and G if and only if the argument with F as premise and G as conclusion is logically valid. In this paper I demonstrate that, properly understood, there is no such paradox of logical validity, since the derivations of a contradiction in all three presentations depends on the illegitimate assumption that the rules for the validity predicate are themselves logically valid. A consistency proof for the correct rules for the validity predicate is also provided. The paper concludes by examining whether the argument(s) can be reconstructed to show that other notions of validity (e.g. "analytic validity", "follows as a matter of metaphysical necessity", etc.) are, indeed, paradoxical.
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