On translating between logics

Analysis 78 (4):any001 (2018)
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Abstract

In a recent paper, Wigglesworth claims that syntactic criteria of theoretical equivalence are not appropriate for settling questions of equivalence between logical theories, since such criteria judge classical and intuitionistic logic to be equivalent; he concludes that logicians should use semantic criteria instead. However, this is an artefact of the particular syntactic criterion chosen, which is an implausible criterion of theoretical equivalence. Correspondingly, there is nothing to suggest that a more plausible syntactic criterion should not be used to settle questions of equivalence between different logical theories; such a criterion is exhibited and shown to judge classical and intuitionistic logic to be inequivalent.

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Neil Dewar
Cambridge University

References found in this work

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Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
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Glymour and Quine on Theoretical Equivalence.Thomas William Barrett & Hans Halvorson - 2016 - Journal of Philosophical Logic 45 (5):467-483.

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