Definition:Axiom/Also known as

Definition

An axiom is also known as a postulate.

Among ancient Greek philosophers, the term axiom was used for a general truth that was common to everybody (see Euclid's "common notions"), while postulate had a specific application to the subject under discussion.

For most authors, the distinction is no longer used, and the terms are generally used interchangeably. This is the position of $\mathsf{Pr} \infty \mathsf{fWiki}$.

However, some believe there is a difference significant enough to matter:

... we shall use "postulate" instead of "axiom" hereafter, as "axiom" has a pernicious historical association of "self-evident, necessary truth", which "postulate" does not have; a postulate is an arbitrary assumption laid down by the mathematician himself and not by God Almighty.

-- 1937: Eric Temple Bell: Men of Mathematics: Chapter $\text{II}$: Modern Minds in Ancient Bodies

Sources

• 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies
• 1944: Eugene P. Northrop: Riddles in Mathematics ... (previous) ... (next): Chapter One: What is a Paradox?
• 1973: C.R.J. Clapham: Introduction to Mathematical Analysis ... (previous) ... (next): Chapter $1$: Axioms for the Real Numbers: $1$. Introduction
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): axiom
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): postulate
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): axiom
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): postulate