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Full Idea
Non-arbitrary division concerns the internal structure of the things falling under a concept. Its point is to ensure that we cannot go on dividing these units arbitrarily and still expect to find more things of the same kind.
Gist of Idea
Non-arbitrary division means that what falls under the concept cannot be divided into more of the same
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.3
Book Ref
-: 'Synthese' [-], p.418
A Reaction
Counting something red is given as an example. This seems to define mass-terms, or stuff.
Related Ideas
Idea 17426 A concept creating a unit must isolate and unify what falls under it [Frege]
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] |