Full Idea
We cannot ground mathematics in any domain or theory that is more secure than mathematics itself.
Gist of Idea
There is no grounding for mathematics that is more secure than mathematics
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 4.8)
Book Reference
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.135
A Reaction
This pronouncement comes after a hundred years of hard work, notably by Gödel, so we'd better believe it. It might explain why Putnam rejects the idea that mathematics needs 'foundations'. Personally I'm prepare to found it in countable objects.