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Full Idea
If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not.
Gist of Idea
An abstraction principle should not 'inflate', producing more abstractions than objects
Source
Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307)
Book Ref
-: 'Philosophical Studies' [-], p.307
A Reaction
I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects.
| 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] |