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Full Idea
There is a scale of abstractness that leads downwards from sets through attributes to formulas as abstract types and on to formulas as abstract tokens.
Gist of Idea
Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas
Source
JP Burgess / G Rosen (A Subject with No Object [1997], III.B.2.c)
Book Ref
Burgess,J/Rosen,G: 'A Subject with No Object' [OUP 1997], p.199
A Reaction
Presumably the 'abstract tokens' at the bottom must have some interpretation, to support the system. Presumably one can keep going upwards, through sets of sets of sets.
| 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] |