Single Idea 9944

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets]

Full Idea

We seem to understand some statements about all sets (e.g. 'for every set x and every set y, there is a set z which is the union of x and y').

Gist of Idea

We understand some statements about all sets

Source

Hilary Putnam (Mathematics without Foundations [1967], p.308)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.308


A Reaction

His example is the Axiom of Choice. Presumably this is why the collection of all sets must be referred to as a 'class', since we can talk about it, but cannot define it.