On Abducing the Axioms of Mathematics
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.
Fields of Study & Subjects
History and Theory of Mathematics
Philosophy and History of Science
Epistemology
Ethics
and Metaphysics
Publication details
- Journal / source
- CRC Press eBooks
- Pages
- 209–224
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Book chapter