Why do we believe theorems?

Philosophia Mathematica 17 (1):84-94 (2009)

The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this?
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Reprint years 2008, 2009
DOI 10.1093/philmat/nkn030
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References found in this work BETA

Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
The Derivation-Indicator View of Mathematical Practice.Jody Azzouni - 2004 - Philosophia Mathematica 12 (2):81-106.
Some Proposals for Reviving the Philosophy of Mathematics.Reuben Hersh - 1983 - Journal of Symbolic Logic 48 (3):871-872.

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Citations of this work BETA

How to Think About Informal Proofs.Brendan Larvor - 2012 - Synthese 187 (2):715-730.

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