more from Gottlob Frege

Single Idea 17819

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

Given the set {Carter, Reagan} ...I still want to know How many what? Members? 2. Sets? 1. Feet of members? 4. Relatives of members? 44.

Gist of Idea

A set doesn't have a fixed number, because the elements can be seen in different ways


comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Palle Yourgrau - Sets, Aggregates and Numbers 'New Problem'

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.357

A Reaction

This is his 'new problem' for Frege. Frege want a concept to divide a pack of cards, by cards, suits or pips. You choose 'pips' and form a set, but then the pips may have a number of corners. Solution: pick your 'objects' or 'units', and stick to it.

Related Ideas

Idea 17820 If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege]

Idea 17821 You can ask all sorts of numerical questions about any one given set [Yourgrau]