more from Kit Fine

Single Idea 10530

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle]

Full Idea

The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition.


'Predicative' definitions introduce a new predicate

Gist of Idea

Hume's Principle is either adequate for number but fails to define properly, or vice versa


Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)

Book Reference

-: 'Philosophical Studies' [-], p.312

A Reaction

I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition.