Why do informal proofs conform to formal norms?

Foundations of Science 14 (1-2):9-26 (2009)

Authors
Jody Azzouni
Tufts University
Abstract
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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DOI 10.1007/s10699-008-9144-9
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References found in this work BETA

On What There Is.W. V. Quine - 1953 - In From a Logical Point of View. Cambridge, Mass.: Harvard University Press. pp. 1-19.
Introduction to Mathematical Logic.ALONZO CHURCH - 1956 - Princeton: Princeton University Press.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.

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Citations of this work BETA

Conceptual Engineering for Mathematical Concepts.Fenner Stanley Tanswell - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy 61 (8):881-913.

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