Full Idea
The Axiom of Infinity means that there are an infinity of distinguishable individuals, which is an empirical proposition.
Gist of Idea
Infinity: there is an infinity of distinguishable individuals
Source
Frank P. Ramsey (The Foundations of Mathematics [1925], §5)
Book Reference
Ramsey,Frank: 'Philosophical Papers', ed/tr. Mellor,D.H. [CUP 1990], p.222
A Reaction
The Axiom sounds absurd, as a part of a logical system, but Ramsey ends up defending it. Logical tautologies, which seem to be obviously true, are rendered absurd if they don't refer to any objects, and some of them refer to infinities of objects.
Related Idea
Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]