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Hilbert's program then and now

Zach, Richard (2005) Hilbert's program then and now. [Preprint]

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    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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    Item Type: Preprint
    Additional Information: forthcoming in Dale Jacquette, ed., Handbook of the Philosophy of Logic (North-Holland, Amsterdam).
    Keywords: Hilbert's program, philosophy of mathematics, proof theory, finitism
    Subjects: General Issues > History of Philosophy of Science
    Specific Sciences > Mathematics
    Depositing User: Richard Zach
    Date Deposited: 27 Nov 2005
    Last Modified: 07 Oct 2010 11:13
    Item ID: 2547
    URI: http://philsci-archive.pitt.edu/id/eprint/2547

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