Vladimir_Nesov comments on A Sketch of an Anti-Realist Metaethics - Less Wrong

16 Post author: Jack 22 August 2011 05:32AM

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Comment author: Vladimir_Nesov 23 August 2011 09:01:07AM * 1 point [-]

Mathematical statements are sometimes (often) useful for deriving propositions about the external world, but themselves don't refer to it.

What's the distinction between the two? (Useful for deriving propositions about smth vs. referring.)

Comment author: komponisto 23 August 2011 03:24:38PM * 0 points [-]

What's the distinction between the two? (Useful for deriving propositions about smth vs. referring.)

The derived "propositions about" are distinct from the mathematical statements per se. For example:

Mathematical statement: "2+2 = 4" (nothing more than a theorem in a formal system; no inherent reference to the external world).
Statement about the world: "by the correspondence between mathematical statements and statements about the world given by the particular model we are using, the mathematical statement '2+2=4' predicts that combining two apples with two apples will yield four apples".