Definitions

from The American Heritage® Dictionary of the English Language, 5th Edition.

  • noun A self-evident or universally recognized truth; a maxim.
  • noun An established rule, principle, or law.
  • noun A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.

from The Century Dictionary.

  • noun one of those generalizations of ordinary experience which nobody doubts, and which are soon replaced by scientific formulations, which latter are also, but less properly, termed middle axioms.
  • noun A self-evident, undemonstrable, theoretical, and general proposition to which every one who apprehends its meaning must assent.
  • noun Any higher proposition, obtained by generalization and induction from the observation of individual instances; the enunciation of a general fact; an empirical law.
  • noun In logic, a proposition, whether true or false: a use of the term which originated with Zeno the Stoic.

from the GNU version of the Collaborative International Dictionary of English.

  • noun (Logic & Math.) A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, “The whole is greater than a part;” “A thing can not, at the same time, be and not be.”
  • noun An established principle in some art or science, which, though not a necessary truth, is universally received.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun philosophy A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
  • noun mathematics, logic A fundamental theorem that serves as a basis for deduction of other theorems. Examples: "Through a pair of distinct points there passes exactly one straight line", "All right angles are congruent".
  • noun An established principle in some artistic practice or science that is universally received.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • noun (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
  • noun a saying that is widely accepted on its own merits

Etymologies

from The American Heritage® Dictionary of the English Language, 4th Edition

[Middle English, from Old French axiome, from Latin axiōma, axiōmat-, from Greek, from axios, worthy; see ag- in Indo-European roots.]

from Wiktionary, Creative Commons Attribution/Share-Alike License

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").

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Examples

  • Use of the term axiom reinforces that our computational model is a mathematical, formal system and that analogue execution is a form of deduction from the axioms or assumptions explicitly programmed into the model.

    PLoS ONE Alerts: New Articles 2009

  • Although he lacks the historical context to articulate Kant's Categorical Moral Imperative, he describes a Supreme Being for whom something akin to this axiom is the ultimate measure of a man, a God who believes that one's ethical duty is to acquire and exercise wisdom, to evaluate and constantly re-evaluate one's beliefs -- including what one's ethical duty is -- by applying the utmost objectivity to one's own preconceptions and prejudices.

    THE HALLS OF PENTHEUS -- PART TWO Hal Duncan 2007

  • So if the math relates to a physics matter the "axiom" is tested.

    Critical Thinking 2007

  • It seems the operating axiom is the old "When all else fails, do what's right."

    "The Liturgy Changes Us..." 2009

  • That simple axiom is a radical critique of an age in which ideological lines are hardening and real dialogue diminishing in the public arena.

    2008 Election 2009

  • That simple axiom is a radical critique of an age in which ideological lines are hardening and real dialogue diminishing in the public arena.

    U.S. Hurt By McCain’s Campaign Of Division 2008

  • That simple axiom is a radical critique of an age in which ideological lines are hardening and real dialogue diminishing in the public arena.

    U.S. Hurt By McCain’s Campaign Of Division 2008

  • That axiom is also true in fantasy baseball, where managing a pitching staff down the stretch is often the key to winning a championship because major league teams often don't have the same agendas for their pitchers as fantasy owners do.

    Keep eye on starters' workloads heading down the stretch 2008

  • That simple axiom is a radical critique of an age in which ideological lines are hardening and real dialogue diminishing in the public arena.

    The Rev. Chuck Currie: 2008

  • No, the axiom is concerned with the morality of genocide.

    Carry-Over Thread 2007

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