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AXIOM (Gr. &iwµa)

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Originally appearing in Volume V03, Page 68 of the 1911 Encyclopedia Britannica.
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AXIOM (Gr. &iwµa) , a See also:general proposition or principle accepted as self-evident, either absolutely or within a particular See also:sphere of thought. Each See also:special See also:science has its own axioms (cf. the Aristotelian &pxai, " first principles"), which, however, are sometimes susceptible of See also:proof in another wider science. The See also:Greek word was probably confined by See also:Plato to mathematical axioms, but See also:Aristotle (Anal. See also:Post. i. 2) gave it also the wider significance of the ultimate principles of thought which are behind all special sciences (e.g. the principle of See also:contradiction). These are apprehended solely by the mind, which may, however, be led to them by an inductive See also:process. After Aristotle, the See also:term was used by the See also:Stoics and the school of See also:Ramus for a proposition simply, and See also:Bacon {Nov. See also:Organ. i. 7) used it of any general proposition. The word was reintroduced in See also:modern See also:philosophy probably by Rene See also:Descartes (or by his followers)who, in the See also:search for a definite self-evident principle as the basis of a new philosophy, naturally turned to the See also:familiar science of See also:mathematics. The axiom of See also:Cartesianism is, therefore, the Cogito ergo sum.

See also:

Kant still further narrowed the meaning to include only self-evident (intuitive) synthetic propositions, i.e. of space and See also:time. The nature of axiomatic certainty is See also:part of the fundamental problem of See also:logic and See also:metaphysics. Those who deny the possibility of all non-empirical knowledge naturally hold that every axiom is ultimately based on observation. For the Euclidian axioms see See also:GEOMETRY.

End of Article: AXIOM (Gr. &iwµa)

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