Single Idea 16901

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

Full Idea

Geometrical concepts appear to depend in some way on a spatial ability. Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of the propositions seems to me to be thereby lost.

Gist of Idea

The equivalent algebra model of geometry loses some essential spatial meaning

Source

Tyler Burge (Frege on Apriority (with ps) [2000], 4)

Book Reference

Burge,Tyler: 'Truth, Thought, Reason (on Frege)' [OUP 2001], p.384


A Reaction

I think this is a widely held view nowadays. Giaquinto has a book on it. A successful model of something can't replace it. Set theory can't replace arithmetic.