Full Idea
The identification of numbers with objects works wholesale but fails utterly object by object.
Gist of Idea
Number-as-objects works wholesale, but fails utterly object by object
Source
Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)
Book Reference
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.292
A Reaction
This seems to be a glaring problem for platonists. You can stare at 1728 till you are blue in the face, but it only begins to have any properties at all once you examine its place in the system. This is unusual behaviour for an object.
Related Idea
Idea 9964 Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]