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.
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.
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.,
Cartesians, in applying the methods of geometry to philosophy have followed