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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| DOI | 10.1093/philmat/nks036 |
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References found in this work BETA
Making It Explicit: Reasoning, Representing, and Discursive Commitment.Robert B. Brandom - 1994 - Harvard University Press.
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2007 - Cambridge University Press.
The Aim and Structure of Physical Theory.Pierre Duhem - 1954 - Princeton: Princeton University Press.
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Citations of this work BETA
Philosophy as Total Axiomatics: Serious Metaphysics, Scrutability Bases, and Aesthetic Evaluation.Uriah Kriegel - 2016 - Journal of the American Philosophical Association 2 (2):272-290.
Extended Mathematical Cognition: External Representations with Non-Derived Content.Karina Vold & Dirk Schlimm - 2020 - Synthese 197 (9):3757-3777.
Mathematical Abstraction, Conceptual Variation and Identity.Jean-Pierre Marquis - 2014 - In Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress. London, UK: pp. 299-322.
Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
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