“Clarifying the nature of the infinite”: The development of metamathematics and proof theory

Abstract

We discuss the development of metamathematics in the Hilbert school, and Hilbert’s proof-theoretic program in particular. We place this program in a broader historical and philosophical context, especially with respect to nineteenth century developments in mathematics and logic. Finally, we show how these considerations help frame our understanding of metamathematics and proof theory today.

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Jeremy Avigad
Carnegie Mellon University

Citations of this work

Hilbert's program then and now.Richard Zach - 2002 - In Dale Jacquette, Philosophy of Logic. Malden, Mass.: North Holland. pp. 411–447.
Number theory and elementary arithmetic.Jeremy Avigad - 2003 - Philosophia Mathematica 11 (3):257-284.
Necessity of Thought.Cesare Cozzo - 2014 - In Heinrich Wansing, Dag Prawitz on Proofs and Meaning. Cham, Switzerland: Springer. pp. 101-20.
Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.
Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.

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References found in this work

Was Sind und was Sollen Die Zahlen?Richard Dedekind - 1888 - Cambridge University Press.
Interpreting classical theories in constructive ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.
Recherches Sur la Th”Eorie de la D”Emonstration.J. Herbrand - 1930 - Dissertation, Universit’e de Paris

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