axiom

[ ak-see-uhm ]

noun

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

axiom

/ ˈæksɪəm /

noun

1. a generally accepted proposition or principle, sanctioned by experience; maxim
2. a universally established principle or law that is not a necessary truth

   the axioms of politics

3. a self-evident statement
4. 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

axiom

/ ăk′sē-əm /

1. 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.
2. Also called postulate

axiom

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

Notes

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

Word History and Origins

Origin of axiom¹

First recorded in 1475–85; from Latin axiōma, from Greek: “something worthy,” equivalent to axiō-, variant stem of axioûn “to reckon worthy” + -ma, noun suffix

Word History and Origins

Origin of axiom¹

C15: from Latin axiōma a principle, from Greek, from axioun to consider worthy, from axios worthy

Example Sentences

With an ATP, a programmer can code in all the rules, or axioms, and then ask if a particular conjecture follows those rules.

From Quanta Magazine

Gödel’s main maneuver was to map statements about a system of axioms onto statements within the system — that is, onto statements about numbers.

From Quanta Magazine

By the first theorem, this set of axioms would then necessarily be incomplete.

From Quanta Magazine

We’ve learned that if a set of axioms is consistent, then it is incomplete.

From Quanta Magazine

It would mean that there exists a sequence of formulas built from these axioms that proves the formula that means, metamathematically, “This set of axioms is consistent.”

From Quanta Magazine

Whether or not Hippocrates ever actually said “First, do no harm,” the axiom is central to medical ethics.

From The Daily Beast

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.

From The Daily Beast

It's Tip O'Neill's famous axiom in reverse: now all politics is national.

From The Daily Beast

It is a generally accepted axiom that a public man cannot afford to be modest in these go-ahead days of "boom."

From Project Gutenberg

This truth is as old as Homer, and its proofs are as capable of demonstration as a mathematical axiom.

From Project Gutenberg

By this, OLeary understood that he was definitely adopted by virtue of the axiom of what was his was theirs.

From Project Gutenberg

That was an axiom on which was founded a vigorous war against all capillary adornments.

From Project Gutenberg

He starts with the axiom that the whole amount of attention a reader can give at any moment is limited and fixed.

From Project Gutenberg

Related Words

• adage
• aphorism
• dictum
• maxim
• precept
• proverb
• theorem