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