Full Idea
The purpose of what I am calling 'eliminatory' axiomatic theories is precisely to eliminate from mathematics those peculiar ideal and abstract objects that, on the traditional view, constitute its subject matter.
Gist of Idea
'Eliminatory' axioms get rid of traditional ideal and abstract objects
Source
John Mayberry (What Required for Foundation for Maths? [1994], p.407-1)
Book Reference
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.407
A Reaction
A very interesting idea. I have a natural antipathy to 'abstract objects', because they really mess up what could otherwise be a very tidy ontology. What he describes might be better called 'ignoring' axioms. The objects may 'exist', but who cares?
Related Idea
Idea 17779 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]