Truth, Negation and Other Basic Notions of Logic

Abstract

According to a story, Albert Einstein was once asked how he had come upon his strange revolutionary ideas. He replied: “By asking the questions that children are discouraged to ask.” If we want to follow Einstein’s strategy in the philosophy of logic, we are thus led to ask such questions as we ourselves discourage our own introductory logic students to ask. But what are such questions? One of them might very well be: What is the logic of our ordinary language? It is convenient to us logic teachers to pretend initially that it is the logic we are teaching, in other words, that the notation of the usual first-order logic is nothing but a streamlined version of ordinary English. In older textbooks this claim is sometimes made explicitly. If pressed, we might appeal to Chomsky (e.g. 1986) whose Ersatz logical forms alias LFs differ only inessentially from the logical forms of ordinary first-order formulas. Yet such appeals should evoke pangs of intellectual conscience, for our actual Sprachlogik differs in several disturbing ways from the received (“Frege-Russell”) first-order logic. I have shown (in Hintikka 1997) that even one of the most general notions of formal logic, the notion of scope, is not a primitive notion but one which can be applied to natural language only indirect ways. It can also be shown that the logic of natural-language conditional sentences can only be captured by going way beyond ordinary first-order logic. But even apart from such theoretical differences, there are lots of ordinary language sentences whose logic is not captured by their prima facie translations into first-order logical notation. For instance, consider the sentence