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Full Idea
Points in abstract Euclidean space are abstract objects, and yet are not objects of abstraction, since they are not introduced through a principle of abstraction of the sort envisaged by Frege.
Gist of Idea
Points in Euclidean space are abstract objects, but not introduced by abstraction
Source
Kit Fine (The Limits of Abstraction [2002], I.1)
Book Ref
Fine,Kit: 'The Limits of Abstraction' [OUP 2008], p.9
A Reaction
The point seems to be that they are not abstracted 'from' anything, but are simpy posited as basic constituents. I suggest that points are idealisations (of smallness) rather than abstractions. They are idealised 'from' substances.
| 9142 | Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert] |
| 9143 | Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert] |
| 9144 | Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert] |
| 10135 | We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K] |
| 10136 | Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K] |
| 10137 | Abstractionism can be regarded as an alternative to set theory [Fine,K] |
| 10138 | An object is the abstract of a concept with respect to a relation on concepts [Fine,K] |
| 10141 | Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K] |
| 10143 | 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K] |
| 10144 | Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K] |
| 10145 | Abstracts cannot be identified with sets [Fine,K] |