Axiom (Ἀξίωμα, from ἀξιόω «I esteem, judge well»)

AXIOM (Ἀξίωμα, from ἀξιόω «I esteem, judge well»). - In the sense current today, an axiom is a general principle of immediate evidence that does not need to be demonstrated; in particular, the first principles of mathematics. In Aristotle the meaning is somewhat narrower: an axiom is a common immediate universal principle, that is, necessary to every science, e.g. the principle of identity (Anal. Post., I, 2, 72 a. 16). Among the Stoics, axiom becomes synonymous with general proposition (Aristotle's Ἰάσοφανις); a sense substantially taken up by Bacon, for whom "axioms" are all general propositions ("most general axioms" and "middle axioms"), derived from the senses and from particular facts (Novum Organum, I, 19). In Kant, axioms of intuition are the synthetic a priori judgments derived from the pure sensible intuition of space and time: for example, "two straight lines do not enclose a space."

Axioms, understood in the common sense as general principles evident in themselves, claim, against every empiricist attempt at devaluation, an absolute noetic value, because they are expressions at once of the laws of thought and of the objective relations of being. Sprung in the intellect at the first contact with experience, so that they cannot be called absolutely a priori, whether they be most universal, and therefore indemonstrable, or derived from these as their particular expression, axioms remain, by their character of universality and necessity, one of the firm foundations of certainty and of science.

Ugo Viglino