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Lectures on Proof Theory

In: David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933

Author

Listed:
  • William Ewald

    (University of Pennsylvania, Law School)

  • Wilfried Sieg

    (Carnegie Mellon University, Department of Philosophy)

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.

Suggested Citation

  • William Ewald & Wilfried Sieg, 2013. "Lectures on Proof Theory," Springer Books, in: William Ewald & Wilfried Sieg (ed.), David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933, edition 127, chapter 0, pages 417-653, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69444-1_3
    DOI: 10.1007/978-3-540-69444-1_3
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