Other forms: axioms
An axiom is a statement you agree to accept without proof, so that reasoning has somewhere to begin. In geometry: a straight line can be drawn between any two points. Nobody proves it; everybody builds on it.
Outside mathematics, an axiom is a principle so widely accepted that people have stopped arguing about it — it is an axiom of the trade that the first offer is never the best one. The adjective is axiomatic, meaning taken as obvious. Keep an axiom apart from a theory or a hypothesis, which exist to be tested; an axiom is the ground you stand on while you test. It is also not a proverb or a wise saying: an axiom does work inside an argument, it does not decorate one. The word lives in logic, mathematics and serious writing, and it lands heavily anywhere else.
1nounaxiomA statement accepted as true without proof, used as the starting point for reasoning.
“Euclid built the whole of his geometry on five axioms.”
2nounprincipleA principle so widely accepted that people treat it as beyond question.
“It is an axiom in publishing that the cover sells the book.”
axiom is a starting principle.
English took axiom from Middle French axiome in the 1400s, which came from Latin axiōma and before that from Ancient Greek ἀξίωμα — 'that which is thought fitting', the thing a pupil is required to know before anything else can be taught. Behind it sits ἄξιος, 'worthy', and further back ἄγω, 'to weigh'. An axiom is a statement that weighs enough to be worth accepting on sight.
Proto-Indo-European
*h₂eǵ-
Ancient Greek
ἀξίωμα — that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle
Latin
axiōma — axiom; principle
Middle French
axiome
English, today
axiom
Built from
From Middle French axiome in the 15th century, from Latin axiōma (“axiom; principle”), from Ancient Greek ἀξίωμα (“that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle”), from ἀξιόω (“to think fit or worthy, to require, to demand”), from ἄξιος (“fit, worthy”) literally “weighing as much as; of like value”, from ἄγω (“to weigh (down)”).
Etymology from Wiktionary, CC BY-SA