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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 Ref
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.
| 20296 | Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey] |
| 8998 | Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine] |
| 8999 | Logic isn't conventional, because logic is needed to infer logic from conventions [Quine] |
| 9000 | If a convention cannot be communicated until after its adoption, what is its role? [Quine] |
| 10064 | Quine quickly dismisses If-thenism [Quine, by Musgrave] |
| 8993 | If mathematics follows from definitions, then it is conventional, and part of logic [Quine] |
| 8994 | If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine] |
| 8995 | Definition by words is determinate but relative; fixing contexts could make it absolute [Quine] |
| 8996 | If if time is money then if time is not money then time is money then if if if time is not money... [Quine] |
| 8997 | There are four different possible conventional accounts of geometry [Quine] |