more on this theme | more from this thinker
Full Idea
We can construe geometry by 1) identifying it with algebra, which is then defined on the basis of logic; 2) treating it as hypothetical statements; 3) defining it contextually; or 4) making it true by fiat, without making it part of logic.
Gist of Idea
There are four different possible conventional accounts of geometry
Source
Willard Quine (Truth by Convention [1935], p.99)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.99
A Reaction
[Very compressed] I'm not sure how different 3 is from 2. These are all ways to treat geometry conventionally. You could be more traditional, and say that it is a description of actual space, but the multitude of modern geometries seems against this.
| 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] |