Single Idea 9846

[catalogued under 18. Thought / E. Abstraction / 1. Abstract Thought]

Full Idea

The stipulation that the direction of a line a is to be the same as that of a line b just in case a is parallel to b does not determine whether the direction of a line is itself a line or something quite different.

Gist of Idea

Defining 'direction' by parallelism doesn't tell you whether direction is a line

Source

comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §60) by Michael Dummett - Frege philosophy of mathematics Ch.11

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.126


A Reaction

Nice point. Maybe not being able to say exactly what something is is either a symptom of nonsense, and simply a symptom that we are dealing with an abstract concept. If abstractions don't exist, they don't need individuation criteria.