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Opinionated History of Mathematics

What makes a good axiom?

Oct 4, 2020 · 35 min · 17.0 MB
0:00-35:21

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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. Transcript What kinds of axioms do we want in our geometry? How … Continue reading What makes a good axiom?