Axioms in Mathematical Practice

Philosophia Mathematica 21 (1):37-92 (2013)
Authors
Dirk Schlimm
McGill University
Abstract
On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at clarifying discussions in philosophy of mathematics and contributing towards a more refined view of mathematical practice.
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DOI 10.1093/philmat/nks036
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References found in this work BETA

Explanation and Scientific Understanding.Michael Friedman - 1974 - Journal of Philosophy 71 (1):5-19.
Why Do We Prove Theorems?Y. Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
The Role of Axioms in Mathematics.Kenny Easwaran - 2008 - Erkenntnis 68 (3):381-391.

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Citations of this work BETA

Philosophy as Total Axiomatics.Uriah Kriegel - 2016 - Journal of the American Philosophical Association 2 (2):272-290.

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