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'fragments/reports', 'Philosophy of Mathematics' and 'The Limits of Abstraction'
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8 ideas
18. Thought / E. Abstraction / 1. Abstract Thought
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'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR]
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Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
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The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR]
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18. Thought / E. Abstraction / 2. Abstracta by Selection
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Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
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18. Thought / E. Abstraction / 7. Abstracta by Equivalence
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We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
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Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
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Abstractionism can be regarded as an alternative to set theory [Fine,K]
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An object is the abstract of a concept with respect to a relation on concepts [Fine,K]
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