Opinionated History of Mathematics

Opinionated History of Mathematics


What makes a good axiom?

October 04, 2020

How should axioms be justified? By appeal to intuition, or sensory perception? Or are axioms legitimated merely indirectly, by their logical consequences? Plato and Aristotle disagreed, and later Newton disagreed even more. Their philosophies can be seen as rival interpretations of Euclid’s Elements.