axiom

American Heritage® Dictionary of the English Language, Fourth Edition

1. 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).
2. n. An established rule, principle, or law.
3. 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

1. 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.:
2. 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.
3. 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 aphorism.
4. 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.

Wiktionary

1. 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.
2. 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".
3. n. An established principle in some artistic practice or science that is universally received.

GNU Webster's 1913

1. 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.”
2. n. An established principle in some art or science, which, though not a necessary truth, is universally received.

WordNet 3.0

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