Full Idea
To be able to apply any postulated abstract entities to the physical world, we need impure abstact entities, e.g. functions that map physical objects into pure abstract objects.
Gist of Idea
Abstract objects are only applicable to the world if they are impure, and connect to the physical
Source
Hartry Field (Science without Numbers [1980], 1)
Book Reference
Field,Hartry: 'Science without Number' [Blackwell 1980], p.9
A Reaction
I am a fan of 'impure metaphysics', and this pinpoints my reason very nicely.