| AXIOM (ἀξίωϋα, from ἀξιόω, to think worthy), (1) a position of worth or authority, (2) the basis of demonstration, (3) a self-evident proposition.»Philosophers give the name of axioms only to self-evident truths that are necessary, and are not limited to time and place, but must be true at all times and in all places » (Reid, Intellectual Powers, essay II. ch. XX.; Hamilton, Reid’s Works, note A, sec. 5; Stewart, Elements, pt. II. ch. I.). Aristotle applied the term to all self-evident principles, which are the grounds of all science (Anal. Post, lib. I. ch. II. 13 and ch. III. 5), things immediate, τὰ ἄμεσα, which do not admit of proof. According to him they were all subordinate to the supreme condition of all demonstration, the principle of identity and contradiction. The Stoics, under the name of axioms, included every kind of general proposition, whether of necessary or contingent truth. In this sense the term is employed by Bacon, who, not satisfied with submitting axioms to the test of experience, has distinguished several kinds of axioms, some more general than others (Novum Organum, lib. I. aphor. XIII., XVII., XIX., &c). The Cartesians, in applying the methods of geometry to philosophy have followed Aristotelian usage. |
