more from Frank P. Ramsey

Single Idea 13430

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V]

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


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]