Foundations of Science 14 (1-2):9-26 (2009)
Kant discovered a philosophical problem with mathematical proof. Despite being a priori , its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathematical proofs, although conforming to the norms of contemporary (classical) logic, never were, and still aren’t, executed by mathematicians in a way that transparently reveals why these proofs—written in the vernacular to this very day—succeed in conforming to those norms.
|Keywords||Mathematical proof Reasoning Logic Meaning Natural language|
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References found in this work BETA
On What There Is.W. V. Quine - 1961 - In Tim Crane & Katalin Farkas (eds.), From a Logical Point of View. Harvard University Press. pp. 21--38.
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A Problem with the Dependence of Informal Proofs on Formal Proofs.Fenner Tanswell - 2015 - Philosophia Mathematica 23 (3):295-310.
Why the Naïve Derivation Recipe Model Cannot Explain How Mathematicians’ Proofs Secure Mathematical Knowledge.Brendan Larvor - 2016 - Philosophia Mathematica 24 (3):401-404.
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