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Opinionated History of Mathematics
HistoriaVetenskap

What makes a good axiom?

35 min•4 oktober 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. Transcript What kinds of axioms do we want in our geometry? How … Continue reading What makes a good axiom?

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Death of Archimedes
•26 min
Torricelli’s trumpet is not counterintuitive
•57 min
Did Copernicus steal ideas from Islamic astronomers?
•1 tim 27 min
Operational Einstein: constructivist principles of special relativity
•1 tim 17 min
Review of Netz’s New History of Greek Mathematics
•52 min
The “universal grammar” of space: what geometry is innate?
•32 min
“Repugnant to the nature of a straight line”: Non-Euclidean geometry
•31 min
Rationalism 2.0: Kant’s philosophy of geometry
•30 min
Rationalism versus empiricism
•44 min
Cultural reception of geometry in early modern Europe
•34 min

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