Ideas from 'The Limits of Abstraction' by Kit Fine [2002], by Theme Structure

[found in 'The Limits of Abstraction' by Fine,Kit [OUP 2008,978-0-19-953363-3]].

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2. Reason / D. Definition / 3. Types of Definition
Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Cook/Ebert]
'Creative definitions' do not presuppose the existence of the objects defined
7. Existence / A. Nature of Existence / 4. Abstract Existence
Points in Euclidean space are abstract objects, but not introduced by abstraction
Abstracts cannot be identified with sets
Postulationism says avoid abstract objects by giving procedures that produce truth
18. Thought / E. Abstraction / 1. Abstract Thought
Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Cook/Ebert]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Many different kinds of mathematical objects can be regarded as forms of abstraction
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
We can abstract from concepts (e.g. to number) and from objects (e.g. to direction)
Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Cook/Ebert]
Abstractionism can be regarded as an alternative to set theory
An object is the abstract of a concept with respect to a relation on concepts