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Full Idea
The domain of the abstract can be seen as exemplifying a hierarchical structure, with differences of level reflecting the number of steps of abstraction, via appropriate equivalence relations, required for recognition at different levels.
Gist of Idea
There is a hierarchy of abstraction, based on steps taken by equivalence relations
Source
Bob Hale (Abstract Objects [1987], Ch.3.III)
Book Ref
Hale,Bob: 'Abstract Objects' [Blackwell 1987], p.61
A Reaction
I think this is right, and so does almost everyone else, since people cheerfully talk of 'somewhat' abstract and 'highly' abstract. Don't dream of a neat picture though. You might reach a level by two steps from one direction, and four from another.
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| 9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| 9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
| 9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
| 10524 | There is a hierarchy of abstraction, based on steps taken by equivalence relations [Hale] |