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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.
Clarification
'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
Source
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312)
Book Ref
-: '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.
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |