Russell's Paradox: Here's Why Math Can't Have A Set Of Everything By Andy Kiersz Nov 25, 2013, 9:32 AM PT Add us on ...

Their idea of what a set is was very loosely defined. We have an intuitive idea that a set should be a collection of things, and naive set theory basically takes this as the definition of a set.

Once Hilbert asserted that the axioms of a theory 'define' the primitive concepts of its language 'implicitly'. Thus when someone inquires about the meaning of the set-concept, the standard response ...