The Logic of Provability

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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 (CUP, 1979). 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 near probability and consistency. It contains the first application of quantified modal logic to formal probability, and shows the results of applying modal logic to formal provability.