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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
.
Syn. –
Axiom
,
Maxim
,
Aphorism
,
Adage
.
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.
[Gr. authority, an authoritative sentence, or that which is assumed, from worthy, and to think worthy, to esteem; Eng. to ask, that which is asked, sought or esteemed.]
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

See also: axiom

German

Noun

Axiom n ‎(genitive Axioms, plural Axiome)

  1. (mathematics, philosophy) axiom

Declension

axiom

axiom

See also: Axiom

English

Noun

axiom ‎(plural axioms); also axiomata (though, becoming less common and sometimes considered archaic)

  1. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
    • 1999, Bertrand Russell, Charles R. Pigden, Russell on Ethics:
      Can we then find axioms as self-evident as those of Arithmetic, on which we can build as on a sure foundation, which could be shaken only by a scepticism which should attack the whole fabric of our knowledge?
  2. (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.
  3. 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

Hyponyms

Holonyms

Derived terms

Related terms

See also

Translations

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

  1. axiom

Derived terms

Related terms

Swedish

Noun

axiom n

  1. axiom

Declension

Inflection of axiom 
Singular Plural
Indefinite Definite Indefinite Definite
Nominative axiom axiomet axiom axiomen
Genitive axioms axiomets axioms axiomens

Related terms

  • axiomatisk

Pronunciation

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