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Full Idea
My principle C seems unnecessary ...since it is one thing to see how many fs there are...but another to have a perfectly general method. ...One could answer whether this f-compliant is the same as that one, but there are too many ways to articulate it.
Gist of Idea
The sortal needed for identities may not always be sufficient to support counting
Source
David Wiggins (Sameness and Substance [1980], 2.8)
Book Ref
Wiggins,David: 'Sameness and Substance' [Blackwell 1980], p.73
A Reaction
His famous example is trying to count the Pope's crown, which is made of crowns. A clearer example might be a rectangular figure divided up into various overlapping rectangles. Individuation is easy, but counting is contextual.
| 17438 | Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki] |
| 17427 | Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki] |
| 17437 | Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki] |
| 17426 | A concept creating a unit must isolate and unify what falls under it [Frege] |
| 17428 | Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki] |
| 12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry] |
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| 17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
| 17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| 17434 | We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki] |