Axioms in Mathematical Practice
Philosophia Mathematica 21 (1):37-92 (2013)
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.Author's Profile
DOI
10.1093/philmat/nks036
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Citations of this work
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Philosophy of mathematical practice: A primer for mathematics educators.Yacin Hamami & Rebecca Morris - 2020 - ZDM Mathematics Education 52:1113–1126.
Philosophy as Total Axiomatics: Serious Metaphysics, Scrutability Bases, and Aesthetic Evaluation.Uriah Kriegel - 2016 - Journal of the American Philosophical Association 2 (2):272-290.
References found in this work
Making It Explicit: Reasoning, Representing, and Discursive Commitment.Robert Brandom - 1994 - Harvard University Press.
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.
