Chapter

Proof Theory of Classical and Intuitionistic Logic

Jan von Plato

in The Development of Modern Logic

Published in print June 2009 | ISBN: 9780195137316
Published online September 2009 | e-ISBN: 9780199867912 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195137316.003.0033
 Proof Theory of Classical and Intuitionistic Logic

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This chapter focuses on the development of Gerhard Gentzen's structural proof theory and its connections with intuitionism. The latter is important in proof theory for several reasons. First, the methods of Hilbert's old proof theory were limited to the “finitistic” ones. These methods proved to be insufficient, and they were extended by infinitistic principles that were still intuitionistically meaningful. It is a general tendency in proof theory to try to use weak principles. A second reason for the importance of intuitionism for proof theory is that the proof-theoretical study of intuitionistic logic has become a prominent part of logic, with applications in computer science.

Keywords: Gerhard Gentzen; structural proof theory; intuitionism; Hilbert; infinitistic principles

Chapter.  8581 words.  Illustrated.

Subjects: Philosophy of Mathematics and Logic

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