more from Willard Quine

Single Idea 8994

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

Full Idea

Geometry can be brought into line with logicism simply by identifying figures with arithmetical relations with which they are correlated thought analytic geometry.

Gist of Idea

If analytic geometry identifies figures with arithmetical relations, logicism can include geometry

Source

Willard Quine (Truth by Convention [1935], p.87)

Book Reference

Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.87


A Reaction

Geometry was effectively reduced to arithmetic by Descartes and Fermat, so this seems right. You wonder, though, whether something isn't missing if you treat geometry as a set of equations. There is more on the screen than what's in the software.