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Full Idea
Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth.
Clarification
Hume's Principle defines 'equinumerous' by one-to-one mapping
Gist of Idea
If Hume's Principle can define numbers, we needn't worry about its truth
Source
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310)
Book Ref
-: 'Philosophical Studies' [-], p.310
A Reaction
This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers.
| 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] |