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
9143
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Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Cook/Ebert]
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10143
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'Creative definitions' do not presuppose the existence of the objects defined
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7. Existence / A. Nature of Existence / 4. Abstract Existence
10145
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Abstracts cannot be identified with sets
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10136
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Points in Euclidean space are abstract objects, but not introduced by abstraction
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10144
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Postulationism says avoid abstract objects by giving procedures that produce truth
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18. Thought / E. Abstraction / 1. Abstract Thought
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Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Cook/Ebert]
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18. Thought / E. Abstraction / 2. Abstracta by Selection
10141
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Many different kinds of mathematical objects can be regarded as forms of abstraction
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18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10135
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We can abstract from concepts (e.g. to number) and from objects (e.g. to direction)
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9142
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Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Cook/Ebert]
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10137
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Abstractionism can be regarded as an alternative to set theory
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10138
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An object is the abstract of a concept with respect to a relation on concepts
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