Full Idea
Frege's discussion of 'direction' borders on incoherent. He claims that the equivalence of lines a and b and their directions being equal have the same content, which leads to the concept of direction, but we grasp the equivalence before the equality.
Gist of Idea
Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first
Source
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stephen Yablo - Carving Content at the Joints § 1
Book Reference
Yablo,Stephen: 'Things: Philosophical Papers vol. 2' [OUP 2010], p.246
A Reaction
[The Frege is in Grundlagen §64] Well said. The notion that we get the full concept of 'direction' from such paltry resources seems very weak. For a start, parallel lines exhibit two directions, not one.