What’s the Difference Between Axioms and Postulates?

Axioms and postulates are often treated as synonyms, but in Greek logic, there’s a subtle distinction between the two:

• Axiom
  An axiom is a universal, self-evident principle that applies to all logical or deductive systems. For example, "something cannot be both true and false at the same time." It’s a foundational truth universally accepted without question.
• Postulate
  A postulate, on the other hand, is an assumption accepted without proof but specific to a particular system or context. For instance, "parallel lines never meet" is a postulate in Euclidean geometry. However, this doesn’t hold true in non-Euclidean geometries. A postulate doesn’t need to be universally valid; it only needs to work within its own framework.

In short, an axiom is more general and fundamental, while a postulate is more specific and system-dependent.