Note:  Do not rely on this information. It is very old.


Axiom (Gk. axioo to claim), a proposition which disputants may fairly expect shall be accepted as an ultimate principle without discussion. In Aristotle's logic the term was applied to the ultimate principles common to all sciences, as, for instance, the Laws of Identity and Contradiction. Now, however, it is specially used in geometry. Some philosophers hold that belief in geometrical axioms is clue to the constitution of the mind; others that it is due to experience. In Euclid's system of geometry we have fifteen axioms assumed. Three of these are postulates, i.e. problems that experience tells us can be accomplished.