On Abducing the Axioms of Mathematics

In John R. Shook & Sami Paavola (eds.), Abduction in Cognition and Action: Logical Reasoning, Scientific Inquiry, and Social Practice. Springer Verlag. pp. 161-175 (2021)
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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 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.

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Woosuk Park
Korea Advanced Institute of Science & Technology (KAIST)

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