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Single Idea 9141

[from 'Notice of Fine's 'Limits of Abstraction'' by R Cook / P Ebert, in 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

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.

Clarification

'Second-order' principles involve predicates as well as objects

Gist of Idea

Abstraction theories build mathematics out of second-order equivalence principles

Source

R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1)

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.791


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'.