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.