Confronting Ideals of Proof with the Ways of Proving of the Research Mathematician

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Studia Logica 96 (2):273-288 (2010)
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Abstract

In this paper, we discuss the prevailing view amongst philosophers and many mathematicians concerning mathematical proof. Following Cellucci, we call the prevailing view the “axiomatic conception” of proof. The conception includes the ideas that: a proof is finite, it proceeds from axioms and it is the final word on the matter of the conclusion. This received view can be traced back to Frege, Hilbert and Gentzen, amongst others, and is prevalent in both mathematical text books and logic text books

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10.1007/s11225-010-9284-0

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Norma B. Goethe
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Michele Friend
George Washington University

Citations of this work

How to think about informal proofs.Brendan Larvor - 2012 - Synthese 187 (2):715-730.
Assertion, denial and non-classical theories.Greg Restall - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli, Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 81--99.

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References found in this work

Logical Pluralism.J. C. Beall & Greg Restall - 2005 - Oxford, GB: Oxford University Press. Edited by Greg Restall.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
The collected papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam,: North-Holland Pub. Co.. Edited by M. E. Szabo.
Logical pluralism.Jc Beall & Greg Restall - 2000 - Australasian Journal of Philosophy 78 (4):475 – 493.
Models and reality.Hilary Putnam - 1983 - In Realism and reason. New York: Cambridge University Press. pp. 1-25.

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