To spell things out further, we need to talk about semantics, which is the branch of linguistics concerned with meaning, reference, and truth—in short, with the relation between language and the world. The Fregean argument, as I shall call it, relies on the following two premises: Classical Semantics. The singular terms of the language of mathematics are supposed to refer to mathematical objects, and its first-order quantifiers, to range over such objects. Mathematical Truth. Most sentences accepted as mathematical theorems are true. We now reason as follows. Consider sentences that are
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