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1
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p.791
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9141
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Abstraction theories build mathematics out of second-order equivalence principles
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Full Idea:
A theory of abstraction is any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx iff E(F,G). We ignore first-order abstraction principles such as Frege's direction abstraction.
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From:
R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1)
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A reaction:
Presumably part of the neo-logicist programme, which also uses such principles. The function § (extension operator) 'provides objects corresponding to the argument concepts'. The aim is to build mathematics, rather than the concept of a 'rabbit'.
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