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Ideas of R Cook / P Ebert, by Text

[British, fl. 2004, both at the Arch Centre at St Andrew's University.]

2004 Notice of Fine's 'Limits of Abstraction'
1 p.791 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'.