Full Idea
Maybe all of mathematics can be represented in set theory, but we should not think that mathematics is set theory. Functions can be represented as order pairs, but perhaps that is not what functions really are.
Gist of Idea
Set theory may represent all of mathematics, without actually being mathematics
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)
Book Reference
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.102
A Reaction
This seems to me to be the correct view of the situation. If 2 is represented as {φ,{φ}}, why is that asymmetrical? The first digit seems to be the senior and original partner, but how could the digits of 2 differ from one another?