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a self-evident truth that requires no proof.
a universally accepted principle or rule.
Logic, Mathematics. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
Contemporary Examples

Jakes says he believes in the axiom that the act of forgiveness is not really a gift to others as much as it is a gift to oneself.
Bishop T.D. Jakes on His New Book and Whitney Houston’s Death Allison Samuels March 9, 2012

Whether or not Hippocrates ever actually said “First, do no harm,” the axiom is central to medical ethics.
Why So Many Surgeons Are Psychos Russell Saunders December 16, 2014

Historical Examples

When either side will not collide, it is an axiom of controversy that it desires to prevent the truth from being elicited.
Essays on Life, Art and Science Samuel Butler

It is an axiom in all progress that the more we conquer the more easily we conquer.
The Conquest of Fear Basil King

“After a storm comes a calm,” says the old adage, but the reverse of this axiom holds equally good at sea.
The White Squall John Conroy Hutcheson

It’s an axiom, I think, that to heighten a nation’s wisdom you must lower its franchise.
The Stark Munro Letters J. Stark Munro

I lay it down as an axiom, that only that is criminal in the sight of God where crime is meditated.
Behind the Scenes Elizabeth Keckley

So convinced am I of the truth of this axiom, that I should not die easy if I had not told it.
Arthur O’Leary Charles James Lever

It is an axiom in conjuring that the best trick loses half its effect on repetition.
Magic Ellis Stanyon

I am able, as well as any man, to verify the truth of this axiom.
The Memoires of Casanova, Complete Jacques Casanova de Seingalt

noun
a generally accepted proposition or principle, sanctioned by experience; maxim
a universally established principle or law that is not a necessary truth: the axioms of politics
a self-evident statement
(logic, maths) a statement or formula that is stipulated to be true for the purpose of a chain of reasoning: the foundation of a formal deductive system Compare assumption (sense 4)
n.

late 15c., from Middle French axiome, from Latin axioma, from Greek axioma “authority,” literally “that which is thought worthy or fit,” from axioun “to think worthy,” from axios “worthy, worth, of like value, weighing as much,” from PIE adjective *ag-ty-o- “weighty,” from root *ag- “to drive, draw, move” (see act (n.)).

Axioms in philosophy are not axioms until they are proved upon our pulses. [Keats, letter, May 3, 1818]

axiom
(āk’sē-əm)
A principle that is accepted as true without proof. The statement “For every two points P and Q there is a unique line that contains both P and Q” is an axiom because no other information is given about points or lines, and therefore it cannot be proven. Also called postulate.
axiom [(ak-see-uhm)]

In mathematics, a statement that is unproved but accepted as a basis for other statements, usually because it seems so obvious.

Note: The term axiomatic is used generally to refer to a statement so obvious that it needs no proof.

language
A commercially available subset of the Scratchpad, symbolic mathematics system from IBM.
[“Axiom – The Scientific Computing System”, R. Jenks et al, Springer 1992].
[Relationship with AXIOM*?]
(1995-02-21)
logic
A well-formed formula which is taken to be true without proof in the construction of a theory.
Compare: lemma.
(1995-03-31)