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

Addressing reporters at the airport, Andrew Tate, who holds dual citizenship in the U.K. and United States, invoked a U.S. judicial axiom of being innocent until proven guilty. —David Catanese, Miami Herald, 27 Feb. 2025

Week 8 Winston for the win — Two more football axioms that rang true in 2024: The Ravens will find bizarre ways to lose games, and Jameis Winston will be a vehicle for metaphysical chaos. —Steven Louis Goldstein, The Athletic, 8 Jan. 2025

Since the Civil War, this axiom has been avoided only a handful of times. —Gordon G. Chang, Newsweek, 25 Jan. 2025

The hope of deriving one set of rules, or axioms, to govern all mathematical truths was fatally undermined. —Theodore McDarrah, Forbes, 14 Jan. 2025

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