Forms: 6–7 axioma, axiome, 5– axiom. [a. F. axiome, ad. L. axiōma, a. Gr. ἀξίωμα that which is thought worthy or fit, that which commends itself as self-evident, f. ἀξιόειν to hold worthy, f. ἄξιος worthy.]
1. A proposition that commends itself to general acceptance; a well-established or universally conceded principle; a maxim, rule, law.
1485. Caxton, Paris & V., Prol. An axiom which in Latin expressed, hoc crede quod tibi verum esse videtur.
1579. Lyly, Euphues (Arb.), 100. The Axiomaes of Aristotle.
1604. Dekker, Honest Wh., Wks. 1873, II. 63. That’s an Axiome, a Principle.
1651. Hobbes, Govt. & Soc., i. § 2. 3. Which Axiom, though received by most, is yet certainly false.
1757. Johnson, Rambl., No. 175, ¶ 1. The axioms of wisdom which recommend the ancient sages to veneration.
1837. J. Harris, Gt. Teacher, 389. The axiom known by the name of the golden rule.
1875. H. E. Manning, Mission H. Ghost, ii. 33. It is an axiom of the human reason that God is everywhere.
† b. Specially restricted by Bacon to: An empirical law, a generalization from experience. Obs.
1626. Bacon, Sylva, § 2. Led by great Judgement, and some good Light of Axioms.
1627. Rawley, in Bacon’s Ess. (Arb.), Introd. 26. True Axiomes must be drawne from plaine Experience, and not from doubtful.
1838. Sir W. Hamilton, Logic, xxvi. II. 47. Empirical rules (Bacon would call them axioms.)
† 2. Logic. A proposition (whether true or false).
1588. Fraunce, Lawiers Log., II. i. 86 b. An axiom or proposition … hath two partes, the bande, and the partes bound.
1656. Stanley, Hist. Philos., VIII. Zeno, xx. 43. Universally negative axioms are those, which consist of an universall negative particle, and a Categorem; as, no man walketh.
1664. H. More, Myst. Iniq., Apol. 533. Otherwise no man might dispute or pronounce a false Axiome.
1742. in Bailey.
3. Logic and Math. ‘A self-evident proposition, requiring no formal demonstration to prove its truth, but received and assented to as soon as mentioned’ (Hutton).
1593. Hooker, Eccl. Pol., I. in Wks. 1666, 14 (J.). Axioms or Principles more general, are such as this, That the greater good is to be chosen before the less.
1660. R. Coke, Justice Vind., 16.
1785. Reid, Int. Powers, I. ii. Nor are they necessary truths, as mathematical axioms are.
1807. Byron, Hours Idlen., College Exam. Happy the youth in Euclid’s axioms tried.
1851. H. Spencer, Soc. Stat., II. ix. § 6. The axiom that the whole is greater than its part.
