American Heritage® Dictionary of the English Language, Fourth Edition
- n. A self-evident or universally recognized truth; a maxim: "It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services” ( Albert Jay Nock).
- n. An established rule, principle, or law.
- n. A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.
Century Dictionary and Cyclopedia
- n. A self-evident, undemonstrable, theoretical, and general proposition to which every one who apprehends its meaning must assent. The Greek word was probably applied by Plato (though it does not occur in his dialogues in this sense) to certain first premises of mathematics; and this continues to be the ordinary use of the term. It was extended by Aristotle to similar principles supposed to underlie other branches of knowledge. The axioms or “common notions” of Euclid, as given in English translations, are twelve in number, viz.:
- n. Any higher proposition, obtained by generalization and induction from the observation of individual instances; the enunciation of a general fact; an empirical law. This use originated with Bacon, influenced probably by the employment of axiom by the Stoics to mean any proposition.
- n. In logic, a proposition, whether true or false: a use of the term which originated with Zeno the Stoic. Synonyms Maxim, Truism, etc. See
- n. 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.
- n. philosophy A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
- n. 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".
- n. An established principle in some artistic practice or science that is universally received.
GNU Webster's 1913
- n. (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.”
- n. An established principle in some art or science, which, though not a necessary truth, is universally received.
- n. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
- n. a saying that is widely accepted on its own merits
- 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"). (Wiktionary)
- Middle English, from Old French axiome, from Latin axiōma, axiōmat-, from Greek, from axios, worthy; see ag- in Indo-European roots. (American Heritage® Dictionary of the English Language, Fourth Edition)
“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.”
“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.”
“So if the math relates to a physics matter the "axiom" is tested.”
“That simple axiom is a radical critique of an age in which ideological lines are hardening and real dialogue diminishing in the public arena.”
“It seems the operating axiom is the old "When all else fails, do what's right.”
“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.”
“No, the axiom is concerned with the morality of genocide.”
“It will remain logically possible that the [pro-genocidal] axiom is objectively correct.”
“It will remain logically possible that the axiom is objectively correct.”
“To ignore such sources would be, among other things, to ignore the main axiom of historical research: Use all sources possible but treat none uncritically.”
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