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## Definition

something assumed as a basis for further logical development; or the proposal of such an assumption

- Lateral truths point to the falseness of axioms and
__postulates__underlying one's existing system of getting at truth.Part 2 (29% in)

- It had long been sought in vain, he said, to demonstrate the axiom known as Euclid's fifth
__postulate__and this search was the start of the crisis.Part 3 (52% in) - Euclid's
__postulate__of parallels, which states that through a given point there's not more than one parallel line to a given straight line, we usually learn in tenth-grade geometry.Part 3 (52% in) - Finally, in the first quarter of the nineteenth century, and almost at the same time, a Hungarian and a Russian...Bolyai and Lobachevski...established irrefutably that a proof of Euclid's fifth
__postulate__is impossible.Part 3 (52% in) - They did this by reasoning that if there were any way to reduce Euclid's
__postulate__to other, surer axioms, another effect would also be noticeable: a reversal of Euclid's postulate would create logical contradictions in the geometry.Part 3 (52% in) - They did this by reasoning that if there were any way to reduce Euclid's
__postulate__to other, surer axioms, another effect would also be noticeable: a reversal of Euclid's postulate would create logical contradictions in the geometry.Part 3 (52% in) - So they reversed Euclid's
__postulate__.Part 3 (52% in) - Thus by his failure to find any contradictions he proves that the fifth
__postulate__is irreducible to simpler axioms.Part 3 (53% in) - A German named Riemann appeared with another unshakable system of geometry which throws overboard not only Euclid's
__postulate__, but also the first axiom, which states that only one straight line can pass through two points.Part 3 (53% in) - Thus it is that the
__postulates__can remain rigorously true even though the experimental laws that have determined their adoption are only approximative.Part 3 (54% in)

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*Zen and the Art of Motorcycle Maintenance*.
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