1.  axiom(n = noun.communication) maxim - a saying that is widely accepted on its own merits;
is a kind of expression, locution, saying
has particulars: aphorism, apophthegm, apothegm, gnome, moralism
Derived form adjective axiomatic₂

2.  axiom(n = noun.communication) - (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident;
is a kind of proposition
has particulars: euclid's axiom, euclid's postulate, euclidean axiom
Derived forms adjective axiomatic₁, adjective axiomatic₃, adjective axiomatical₁

1.  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.” [1913 Webster]

2.  An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy. [1913 Webster]

axiom, n.
1 an established or widely accepted principle.
2 esp. Geom. a self-evident truth.

Etymology:
F axiome or L axioma f. Gk axioma axiomat- f. axios worthy

N  maxim, aphorism, apothegm, apophthegm, dictum, saying, adage, saw, proverb, sentence, mot, motto, word, byword, moral, phylactery, protasis, axiom, theorem, scholium, truism, postulate, first principles, a priori fact, assumption (supposition), reflection, conclusion, golden rule, principle, principia, profession of faith, settled principle, accepted principle, formula, accepted fact, received truth, wise maxim, sage maxim, received maxim, admitted maxim, recognized maxim, true saying, common saying, hackneyed saying, trite saying, commonplace saying, aphoristic, proverbial, phylacteric, axiomatic, gnomic, as the saying goes, as the saying is, as they say.