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”.
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”.