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 Reference
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.