Definify.com
Webster 1913 Edition
Axiom
Ax′i-om
,Noun.
[L. ]
axioma
, Gr. [GREEK]
that which is thought worthy, that which is assumed, a basis of demonstration, a principle, fr. [GREEK]
to think worthy, fr. [GREEK]
worthy, weighing as much as; cf. [GREEK]
to lead, drive, also to weigh so much: cf F. axiome
. See Agent
, Adj.
1.
(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.
An established principle in some art or science, which, though not a necessary truth, is universally received;
as, the
. axioms
of political economy An axiom is a self-evident truth which is taken for granted as the basis of reasoning. A maxim is a guiding principle sanctioned by experience, and relating especially to the practical concerns of life. An aphorism is a short sentence pithily expressing some valuable and general truth or sentiment. An adage is a saying of long-established authority and of universal application.
Webster 1828 Edition
Axiom
AX'IOM
,Noun.
1.
A self evident truth, or a proposition whose truth is so evident at first sight, that no process of reasoning or demonstration can make it plainer; as, 'the whole is greater than a part.'2.
An established principle in some art or science; a principle received without new proof; as, 'things which are equal to the same thing, are equal to one another.'Definition 2024
Axiom
axiom
axiom
See also: Axiom
English
Noun
axiom (plural axioms); also axiomata (though, becoming less common and sometimes considered archaic)
- (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
- (mathematics, logic, proof theory) A fundamental assumption that serves as a basis for deduction of theorems. Examples: "Through a pair of distinct points there passes exactly one straight line", "All right angles are congruent".
- 1995, Colin McLarty, Elementary Categories, Elementary Toposes, page 13:
- The axioms read as follows. For every composable pair f and g the composite goes from the domain of g to the codomain of f. For each object A the identity arrow goes from A to A. Composing any arrow with an identity arrow (supposing that the two are composable) gives the original arrow. And composition is associative.
-
- An established principle in some artistic practice or science that is universally received.
- The axioms of political economy cannot be considered absolute truths.
Synonyms
- (in philosophy, mathematics): axioma (now rare)
Hypernyms
- (in logic): well-formed formula, wff, WFF
Hyponyms
- (in mathematics): axiom of choice
- (in mathematics): completeness axiom
- (in mathematics): parallel axiom
Holonyms
- (in logic): formal system
Derived terms
Related terms
See also
other terms of interest
Translations
philosophy: supposed self‐evident or necessary truth
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mathematics: fundamental assumption
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established principle in art or science
External links
- axiom in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913
- axiom in The Century Dictionary, The Century Co., New York, 1911
Czech
Noun
axiom m