more from Gottlob Frege

Single Idea 17426

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts]

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 Reference

-: '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]