Full Idea
Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects.
Gist of Idea
Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects
Source
report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6
Book Reference
-: 'Journal of Philosophy' [-], p.21
A Reaction
The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis.