Confronting Ideals of Proof with the Ways of Proving of the Research Mathematician |
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| Authors: | Norma B Goethe Michèle Friend |
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| Institution: | 1.School of Philosophy,National University of Cordoba,Cordoba,Argentina;2.Fellow 2009-2010, Lichtenberg-Kolleg,University of Goettingen,Goettingen,Germany;3.Department of Philosophy,George Washington University,Washington,U.S.A. |
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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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