Full Idea
One does not have to translate 'ordinary' mathematics into the Zermelo-Fraenkel system: ordinary mathematics comes embodied in that system.
Gist of Idea
We don't translate mathematics into set theory, because it comes embodied in that way
Source
John Mayberry (What Required for Foundation for Maths? [1994], p.415-1)
Book Reference
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.415
A Reaction
Mayberry seems to be a particular fan of set theory as spelling out the underlying facts of mathematics, though it has to be second-order.
Related Idea
Idea 17805 Set theory is not just another axiomatised part of mathematics [Mayberry]