Axiom (Gr. ἀξίωμα), 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 ἀρχαί, "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 René 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.