Full Idea
Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects.
Gist of Idea
If mathematical theories conflict, it may just be that they have different subject matter
Source
Hartry Field (Recent Debates on the A Priori [2005], 7)
Book Reference
'Oxford Studies in Epistemology Vol. 1', ed/tr. Gendler,R/Hawthorne,J [OUP 2004], p.82
A Reaction
For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect.