AXIOM (ἀξίωμα, from ἀξίω “I esteem, judge worthy”). - In its current sense, an a. is a general principle of immediate evidence that does not require demonstration; in particular, the first principles of mathematics. In Aristotle the meaning is somewhat narrower: an a. is an immediate universal principle common to, that is, required by, every science; for example, the principle of identity (Anal. Post., I, 2, 72 a. 16). Among the Stoics, a. becomes synonymous with a general proposition (Ἰάσοφανις of Aristotle); a meaning substantially revived by Bacone, for whom “axioms” are all general propositions (“a. generalissimi” and “a. medi”), derived from the senses and particular facts (Novum Organum, I, 19). In Kant, axioms of intuition are the synthetic a priori judgments derived from pure sensible intuition of space and time: for example, “two straight lines do not enclose a space.”
Axioms, understood in the common sense as self-evident general principles, claim, against every empiricist attempt at devaluation, an absolute noetic value, because they express both the laws of thought and the objective relations of being. Sprouting in the intellect at its first contact with experience, and therefore not to be called absolutely a priori, whether they are most universal and consequently indemonstrable, or derived from these as their particular expression, axioms remain, by virtue of their character of universality and necessity, one of the firm foundations of certainty and science.