Definition:Axiom/Also known as
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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