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Single Idea 8997

[from 'Truth by Convention' by Willard Quine, in 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry ]

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.