Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation.

I will have to wait for my present train of thought to stop at a station before I can hop another but several recent discussions of geometry have brought this subject back to mind and I thought it might serve to drop off a few mail bags of related letters in anticipation of the next pass through this junction.

Here is a set of excerpts from Murray G. Murphey (1961), The Development of Peirce’s Philosophy, discussing Peirce’s reception of Riemann’s philosophy of geometry.

• Manifolds of Signs • (1) • (2) • (3)

Later developments of the manifold concept, looking to applications on the one hand and theory on the other, are illustrated by excerpts in the next two posts.