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Ideas for 'Theory of Science (4 vols)', 'Letters' and 'Truth by Convention'

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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
There are four different possible conventional accounts of geometry [Quine]
     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.
     From: Willard Quine (Truth by Convention [1935], 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.