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”.
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”.