Axiom

Pronunciation

• US IPA: /ˈæks.i.É™m/

Origin

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

Full definition of axiom

Noun

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, 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 ToposesThe axioms read as follows. For every composable pair f and g the composite $f\; \backslash circ\; g$ goes from the domain of g to the codomain of f. For each object A the identity arrow $$

1. 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

Hypernyms

• (in logic) well-formed formula, wff, WFF

Hyponyms

• (in mathematics) axiom of choice
• (in mathematics) completeness axiom
• (in mathematics) parallel axiom

Holonyms

• (in logic) formal system

Derived terms

• axiomatic

Related terms

• axiomatize
• axiomatization