# Hilbert's program then and now

In Dale Jacquette (ed.),

*Philosophy of Logic*. Amsterdam: North Holland. pp. 411–447 (2007)**Abstract**

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s

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References found in this work BETA

The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program.Zach, Richard

Partial Realizations of Hilbert's Program.Simpson, Stephen G.

Hilbert's Program Revisited.Raatikainen, Panu

Hilbert’s Program.Zach, Richard

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Citations of this work BETA

Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Mulvihill, Corey Edward

On Three Arguments Against Categorical Structuralism.Pedroso, Makmiller

Proof Theory.Avigad, Jeremy

Anti-Foundational Categorical Structuralism.McDonald Darren,

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