Axiomes & Postulats
philosophie sciences épistémologie note-mature
Définitin
Déf. axiome : « proposition évidente en soi et indémontrable ».
Définition
Déf. postulat : « proposition non axiomatique affirmée sans preuve ».
Usages :
- “évidente en soi” pour proposition générale,
- “évidente par elle-même” ou “en elle-même” pour proposition particulière,
- “auto-évidente” (anglicisme) pour proposition générale ou particulière.
One interesting question about the assumptions for Euclid’s system of geometry is the difference between the “axioms” and the “postulates.” “Axiom” is from Greek axíôma, “worthy.” An axiom is in some sense thought to be strongly self-evident. A “postulate,” on the other hand, is simply postulated, e.g. “let” this be true. There need not even be a claim to truth, just the notion that we are going to do it this way and see what happens. Euclid’s postulates, indeed, could be thought of as those assumptions that were necessary and sufficient to derive truths of geometry, of some of which we might otherwise already be intuitively persuaded. As first principles of geometry, however, both axioms and postulates, on Aristotle’s understanding, would have to be self-evident. This never seemed entirely quite right, at least for the Fifth Postulate — hence many centuries of trying to derive it as a Theorem. In the modern practice, as in Hilbert’s geometry, the first principles of any formal deductive system are “axioms,” regardless of what we think about their truth — which in many cases has been a purely conventionalistic attitude. Given Kant’s view of geometry, however, the Euclidean distinction could be restored: “axioms” would be analytic propositions, and “postulates” synthetic. Whether any of Euclid’s original axioms are analytic is a good question.
Source : https://friesian.com/space.htm