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mathematics

The Axiomatic-Deductive Method

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Start from a tiny list of agreed-upon truths, smuggle in nothing else, and prove an entire science from there.

The axiomatic-deductive method starts with a handful of building blocks: explicit definitions, a few unproved postulates, and self-evident 'common notions.' From these alone, every later theorem follows by strict logical proof, with nothing slipped in along the way. Euclid of Alexandria (c. 300 BCE) gave the method its classic form in the Elements, drawing on earlier Greek geometry and on Aristotle's account of demonstrative science. It went on to become the template for rigorous reasoning far beyond mathematics: Spinoza, Newton, and modern logic all echo its 'from first principles' design.

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23 Greek sources

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