Lectures on Proof Theory

William Ewald and Wilfried Sieg
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William Ewald: University of Pennsylvania, Law School
Wilfried Sieg: Carnegie Mellon University, Department of Philosophy

Chapter Chapter 3 in David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933, 2013, pp 417-653 from Springer

Abstract: Abstract The lectures in the Summer Semester of 1920 ended with consistency proofs for extremely weak fragments of arithmetic. The question, made explicit in the Introduction to Chapter 2 (see p. 296) was then this: Can these consistency proofs somehow be extended to establish the consistency of increasingly stronger and thus mathematically more interesting systems? The lectures of 1921/22 and 1922/23 give a resoundingly positive answer. However, the ‘extensions’ require a remarkable mathematical/logical and methodological breakthrough that leads to Hilbert’s proof theory and his finitist consistency programme.

Date: 2013
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DOI: 10.1007/978-3-540-69444-1_3

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