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.
Example Sentences
one of the key axioms of the theory of evolution
Recent Examples on the WebLess is More or, to observe the axiom still further, Be concise. Jerry Weissman, Forbes, 3 Aug. 2022 The critical response from both sides of the debate recalled the old axiom that a compromise is sure to make everyone unhappy. Martin Fritz Huber, Outside Online, 28 June 2022 The most important axiom of California politics is that powerful interest groups like the status quo and will fight like crazy to maintain it. John Myers, Los Angeles Times, 10 June 2022 An axiom of the insurance industry is the investment of premium reserves to generate investment income. Van Carlson, Forbes, 14 Apr. 2022 There are variations in voter interest across the state, proving that old axiom that all politics is local. John Byrne, Chicago Tribune, 20 June 2022 Our other central axiom in this situation was: Show, don’t tell. Ari Rabin-havt, The New Republic, 28 Apr. 2022 An axiom that sums up the state’s wealth disparity: Vermonters either have three homes or three jobs. Hanna Krueger, BostonGlobe.com, 1 Apr. 2022 There’s a musty axiom put forward in writing classes that forging this type of connection with a reader shouldn’t be the priority, that writers should instead aim to create art that transcends personal concerns. Adam Dalva, The Atlantic, 5 June 2022 See More
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.