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Full Idea
For us, sets constitute the most natural example of a hierarchical structure within the abstract realm. But for Aristotle it would have been definitions, via their natural division into genus and differentia.
Gist of Idea
Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets)
Source
Kit Fine (Aristotle on Matter [1992], 1 n4)
Book Ref
-: 'Mind' [-], p.37
A Reaction
Genus and differentia are only part of the story in Aristotle, and this remarks strikes me as perceptive. It is precisely the mapping of the explanatory hierarchy which Aristotle seeks in a good definition.
| 12302 | Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K] |
| 14267 | There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K] |
| 14264 | Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K] |
| 14265 | The components of abstract definitions could play the same role as matter for physical objects [Fine,K] |
| 14266 | Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K] |
| 14268 | Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K] |