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

The Aim and Structure of Physical Theory.Pierre Maurice Marie Duhem - 1954 - Princeton: Princeton University Press.
The Scientific Image.C. Van Fraassen Bas - 1980 - Oxford University Press.

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Citations of this work BETA

Reliability of Mathematical Inference.Jeremy Avigad - 2020 - Synthese 198 (8):7377-7399.
Non-Deductive Methods in Mathematics.Alan Baker - 2010 - Stanford Encyclopedia of Philosophy.
Philosophy as Total Axiomatics: Serious Metaphysics, Scrutability Bases, and Aesthetic Evaluation.Uriah Kriegel - 2016 - Journal of the American Philosophical Association 2 (2):272-290.

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