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 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.
  • 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.

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").

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

  • 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

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

    Critical Thinking

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

    "The Liturgy Changes Us..."

  • 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

  • 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

  • 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

  • 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

  • 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:

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

    Carry-Over Thread

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