The Logic of Provability

Cambridge and New York: Cambridge University Press (1993)
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Abstract

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency.

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Citations of this work

The logic of justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
The Iterative Conception of Set: a (Bi-)Modal Axiomatisation.J. P. Studd - 2013 - Journal of Philosophical Logic 42 (5):1-29.
Justification logic.Sergei Artemov - forthcoming - Stanford Encyclopedia of Philosophy.
Modal Logic.James W. Garson - 2009 - Stanford Encyclopedia of Philosophy.

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