# axiom

## English

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### Pronunciation

• (US) IPA(key): /ˈæks.i.əm/
•  Audio (US) Sorry, your browser either has JavaScript disabled or does not have any supported player. You can download the clip or download a player to play the clip in your browser. (file)

### Etymology

From Middle French axiome, from Ancient Greek ἀξίωμα (aksíōma, that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle), from ἀξίοῦν (aksíoûn, to think fit or worthy, require, demand), from ἄξιος (áksios, worthy, fit, literally weighing as much as, of like value), from ἄγω (ágō, I drive).

### Noun

axiom (plural axioms); also axiomata (though, becoming less common and sometimes considered archaic)

1. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
• 1999, Bertrand Russell, Charles R. Pigden, Russell on Ethics[1]:
Can we then find axioms as self-evident as those of Arithmetic, on which we can build as on a sure foundation, which could be shaken only by a scepticism which should attack the whole fabric of our knowledge?
2. (mathematics, logic, proof theory) A fundamental assumption that serves as a basis for deduction of theorems. Examples: "Through a pair of distinct points there passes exactly one straight line", "All right angles are congruent".
• 1995, Colin McLarty, Elementary Categories, Elementary Toposes, page 13:
The axioms read as follows. For every composable pair f and g the composite $f \circ g$ goes from the domain of g to the codomain of f. For each object A the identity arrow $1_A$ goes from A to A. Composing any arrow with an identity arrow (supposing that the two are composable) gives the original arrow. And composition is associative.
3. An established principle in some artistic practice or science that is universally received.
The axioms of political economy cannot be considered absolute truths.

#### Synonyms

• (in philosophy, mathematics): axioma (now rare)