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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| 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.
The Classical Model of Science: A Millennia-Old Model of Scientific Rationality.Willem R. de Jong & Arianna Betti - 2010 - Synthese 174 (2):185-203.
Dedekind’s Analysis of Number: Systems and Axioms.Wilfried Sieg & Dirk Schlimm - 2005 - Synthese 147 (1):121-170.
View all 29 references / Add more references
Citations of this work BETA
Philosophy as Total Axiomatics.Uriah Kriegel - 2016 - Journal of the American Philosophical Association 2 (2):272-290.
Dedekind's Abstract Concepts: Models and Mappings.Wilfried Sieg & Dirk Schlimm - 2014 - Philosophia Mathematica:nku021.
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