- #1

- 25

- 0

## Main Question or Discussion Point

**And the definition of "axiom" is...?**

There are (broadly speaking) two basic definitions of the word "axiom".

The classical definition, with which Plato, Euclid, and Aristotle wrestled, is roughly this:

*"An axiom is a proposition for or against which no evidence can be adduced, but the truth of which, it appears intuitively impossible to deny".*

The modern definition is:

*"An axiom is a proposition which forms the starting point for a chain of deductive argument."*

An example of the former might be, "the whole is greater than the part" (vide Euclid). An example of the latter might be, "Einstein's Theory of General Relativity".

With special reference to mathematics in the 21st Century, what are the relative merits and demerits of these two definitions? Discuss.