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Abduction in Cognition and ActionOn Abducing the Axioms of Mathematics

Abduction in Cognition and Action: On Abducing the Axioms of Mathematics [How do we discover and justify axioms of mathematics? In view of the long history of the axiomatic method, it is rather embarrassing that we are still lacking a standard answer to this simple question. Since the axiom of choice is arguably one of the most frequently discussed famous axioms throughout the history of mathematics, Thomas Forster’s recent identification of the axiom as an inference to the best explanation (IBE) provides us with a nice point of departure. I will argue that, by separating sharply between abduction and IBE, we can give a convincing account of both the discovery and the justification of the axioms of mathematics.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Abduction in Cognition and ActionOn Abducing the Axioms of Mathematics

Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics Book Series (volume 59)
Editors: Shook, John R.; Paavola, Sami
Park, Woosuk
Springer Journals — May 30, 2021
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14 pages

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2021
ISBN
978-3-030-61772-1
Pages
161 –175
DOI
10.1007/978-3-030-61773-8_8
Publisher site
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Abstract

[How do we discover and justify axioms of mathematics? In view of the long history of the axiomatic method, it is rather embarrassing that we are still lacking a standard answer to this simple question. Since the axiom of choice is arguably one of the most frequently discussed famous axioms throughout the history of mathematics, Thomas Forster’s recent identification of the axiom as an inference to the best explanation (IBE) provides us with a nice point of departure. I will argue that, by separating sharply between abduction and IBE, we can give a convincing account of both the discovery and the justification of the axioms of mathematics.]

Published: May 30, 2021

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