AXIOM (Gr. &iwµa)  , a general proposition or principle accepted as self-evident, either absolutely or within a particular sphere of thought . Each special science has its own axioms (cf. the Aristotelian &pxai, " first principles"), which, however, are sometimes susceptible of proof in another wider science . The Greek word was probably confined by Plato to mathematical axioms, but Aristotle (Anal . 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 contradiction) . These are apprehended solely by the mind, which may, however, be led to them by an inductive process . After Aristotle, the term was used by the Stoics and the school of Ramus for a proposition simply, and Bacon {Nov . Organ. i . 7) used it of any general proposition . The word was reintroduced in modern philosophy probably by Rene Descartes (or by his followers)who, in the search for a definite self-evident principle as the basis of a new philosophy, naturally turned to the familiar science of mathematics . The axiom of Cartesianism is, therefore, the Cogito ergo sum . Kant still further narrowed the meaning to include only self-evident (intuitive) synthetic propositions, i.e. of space and time .

The nature of axiomatic certainty is

part of the fundamental problem of logic and 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 GEOMETRY .