axiom

noun

ax·​i·​om ˈak-sē-əm 

1

: a statement accepted as true as the basis for argument or inference : postulate sense 1

one of the axioms of the theory of evolution

2

: an established rule or principle or a self-evident truth

cites the axiom "no one gives what he does not have"

3

: a maxim widely accepted on its intrinsic merit

the axioms of wisdom

Did you know?

In mathematics or logic, an axiom is an unprovable rule or first principle accepted as true because it is self-evident or particularly useful. “Nothing can both be and not be at the same time and in the same respect” is an example of an axiom. The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof.

Examples of axiom in a Sentence

one of the key axioms of the theory of evolution

Recent Examples on the Web

Those who forget history, the old axiom posits, are doomed to repeat it. —Ilan Berman, Foreign Affairs, 24 Apr. 2016

Whereas neoclassical economics presented itself as a universally applicable science based on certain fundamental axioms, Dobb emphasized history, class conflict, and imperialism. —John Cassidy, The New Yorker, 2 Nov. 2024

But underneath all of these more intricate structures is that same original group idea, with its four axioms. —Leila Sloman, WIRED, 6 Oct. 2024

And these are always clearly defined by the axioms. —Manon Bischoff, Scientific American, 1 Oct. 2024

Word History

Etymology

borrowed from Middle French & Latin; Middle French axiome, borrowed from Latin axiōma "fundamental proposition," borrowed from Greek axíōma "honor, honored status, prestige, that which is reasonable (though not demonstrated to be true), self-evident principle," from axiō-, variant stem of axióō, axioûn "to consider worthy, value, consider appropriate, claim, think" (verbal derivative of áxios "valued [at a sum of money], worth, equal, of an equivalent status, worthy, suitable," of uncertain origin) + -ma, resultative noun suffix

Note: The Greek adjective áxios has conventionally been taken as originally meaning "of equal weight, counterbalancing"—hence it is seen as a derivative of an unattested noun *axis "weight" (< *ag-ti-), a derivative of ágein "to lead, carry off," also, among many other senses, "to weigh (a certain amount)," though the latter meaning is no earlier than fifth-century Attic.

First Known Use

15th century, in the meaning defined at sense 3

Phrases Containing axiom

• axiom of choice

Kids Definition

axiom

noun

ax·​i·​om ˈak-sē-əm 

: a rule or principle widely accepted as obviously true and not needing to be proved