Confronting ideals of proof with the ways of proving of the research mathematician

Studia Logica 96 (2):273-288 (2010)
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
Keywords Axiomatic proof  analytic proof  axiom  hypothesis  communication  rigor  application  context
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Jc Beall & Greg Restall (2000). Logical Pluralism. Australasian Journal of Philosophy 78 (4):475 – 493.

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