Single Idea 10051

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

Full Idea

There is something profoundly unsatisfactory about the axiom of infinity. It cannot be described as a truth of logic in any reasonable use of that phrase, and so the introduction of it as a primitive proposition amounts to the abandonment of logicism.

Gist of Idea

The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism


W Kneale / M Kneale (The Development of Logic [1962], XI.2)

Book Reference

Kneale,William and Martha: 'The Development of Logic' [OUP 1984], p.669

A Reaction

It seems that the axiom is essentially empirical, and it certainly makes an existential claim which seems to me (intuitively) to have nothing to do with logic at all.

Related Idea

Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]