Axioms in Mathematical Practice

Philosophia Mathematica 21 (1):37-92 (2013)
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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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Dirk Schlimm
McGill University

References found in this work

Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago, IL, USA: Chicago University of Chicago Press.
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, England: Oxford University Press.
Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.

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