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Full Idea
Roughly, Frege's picture of counting is this. When we count something, we determine what number belongs to a given concept.
Gist of Idea
Frege says counting is determining what number belongs to a given concept
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1
Book Ref
-: 'Synthese' [-], p.405
A Reaction
If the concept were 'herd of sheep' that would need a context before there could be a fixed number. You can count until you get bored, like counting stars to get to sleep. 'Count off 20 sheep' has the number before the counting starts.
Related Idea
Idea 17429 Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki]
| 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] |