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Full Idea
If logic and mathematics being true by convention says the primitives can be conventionally described, that works for anything, and is empty; if the conventions are only for those fields, that's uninteresting; if a general practice, that is false.
Gist of Idea
Claims that logic and mathematics are conventional are either empty, uninteresting, or false
Source
Willard Quine (Truth by Convention [1935], p.102)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.102
A Reaction
This is Quine's famous denial of the traditional platonist view, and the new Wittgensteinian conventional view, preparing the ground for a more naturalistic and empirical view. I feel more sympathy with Quine than with the other two.
| 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] |