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Ideas from 'Notice of Fine's 'Limits of Abstraction'' by R Cook / P Ebert [2004], by Theme Structure

[found in 'British Soc for the Philosophy of Science' (ed/tr -) [- ,]].

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18. Thought / E. Abstraction / 7. Abstracta by Equivalence
9141 Abstraction theories build mathematics out of second-order equivalence principles
                        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.
                        From: R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1)
                        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'.