more from Penelope Maddy

Single Idea 13021

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

Full Idea

The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics.

Gist of Idea

The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics


Penelope Maddy (Believing the Axioms I [1988], 1.5)

Book Reference

-: 'Journal of Symbolic Logic' [-], p.486

A Reaction

It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art.

Related Idea

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