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Full Idea
Only a concept which isolates what falls under it in a definite manner, and which does not permit any arbitrary division of it into parts, can be a unit relative to finite Number.
Gist of Idea
A concept creating a unit must isolate and unify what falls under it
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54), quoted by Kathrin Koslicki - Isolation and Non-arbitrary Division 1
Book Ref
-: 'Synthese' [-], p.403
A Reaction
This is the key modern proposal for the basis of counting, by trying to get at the sort of concept which will turn something into a 'unit'. The concept must isolate and unify. Why should just one concept do that each time?
Related Ideas
Idea 17434 We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
Idea 17437 Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki]
Idea 12844 Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons]
| 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] |