“Proof Theory and Meaning: the context of deducibility,” p. 204–219 in Logic Colloquium 2007, ed. F. Delon, U. Kohlenbach, P. Maddy and F. Stephan, Cambridge University Press, 2010.
I examine Belnap’s two criteria of existence and uniqueness for evaluating putative definitions of logical concepts in inference rules, by determining how they apply in four different examples: conjunction, the universal quantifier, the indefinite choice operator and the necessity in the modal logic S5. This illustrates the ways that definitions may be evaluated relative to a background theory of consequence, and the ways that different accounts of consequence provide us with different resources for making definitions.
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I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology ¶ I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.