Single Idea 9159

[catalogued under 6. Mathematics / A. Nature of Mathematics / 2. Geometry]

Full Idea

Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of geometrical propositions seems to me to be thereby lost. Pure geometry involves spatial content, even if abstracted from physical space.

Gist of Idea

You can't simply convert geometry into algebra, as some spatial content is lost


Tyler Burge (Frege on Apriority [2000], IV)

Book Reference

'New Essays on the A Priori', ed/tr. Boghossian,P /Peacocke,C [OUP 2000], p.38

A Reaction

This supports Frege's view (against Quine) that geometry won't easily fit into the programme of logicism. I agree with Burge. You would be focusing on the syntax of geometry, and leaving out the semantics.