One of the late chapters of Jean-Louis Dessalles’ Why We Talk discusses how language works in argumentation, and what we can learn about language’s origins from its argumentative function. This section should be gold mine for philosophical applications, because so much of philosophy of language over the last hundred years has been based on analyzing propositions as the building blocks of arguments.
And I was sadly disappointed for traditional philosophy once again. The problem is a matter of logical rigidity, or rather the rigidity of philosophical logic. Dessalles considers, as an example of the worldly phenomenon of arguing, a conflict over whether some proposition is true. That is, one person is arguing for proposition F, the other for proposition Not-F. A fairly simple matter of marshalling evidence of one over the other. Then he introduces a very strange (for philosophy) idea. If the question of F or Not-F isn’t actually interesting to the people having an argument, the truth of F becomes irrelevant. And as far as understanding that worldly situation, F and not-F wouldn’t have a truth value. They’d be neither true nor false nor meaningless. Just indifferent.
This way of thinking doesn’t quite jive with the logic we learn in introductory philosophy classes. When we learn logic, we’re taught clearly that every statement is either true or false or nonsense, and that logic is, in its practical application, about analyzing statements about the world to understand their precise truth value: the conditions by which the statement can be true.
Alternatives to this black-and-white logical system were first seriously developed only in the late 20th century by Graham Priest. Of all the philosophers who practiced in the last hundred years, and who are still alive today, I probably stand most in awe of Priest. Priest first gained notoriety (some more philosophically conservative would say he became notorious) for developing what is called a paraconsistent logic. A symbolic logic whose rules allowed contradictory propositions (A and Not-A) to be true. It blatantly flies in the face of everything that was taken for granted, to be so obviously true that only a fool would question it. Logicians and mathematicians have worked on paraconsistent logics over the years, but Priest put the most effort into them. By demonstrating that you can build a logical system that was valid, workable, and practically valuable, that also stripped away all the intuitively basic rules of logic traditionally conceived, he opened up new possibilities for creativity in mathematical logic. These possibilities were not even considered before Priest’s popularization, were not even really thinkable by most people.
Symbolic logic isn’t my strong suit. I can teach it at the introductory level in a philosophy department if I have to, but the student evaluations won’t be the best, and all the computer science students taking the course for an easy mark will make fun of me the entire time. That’s why I stand in awe of Priest’s achievement. He introduced and popularized new directions in a field of philosophy where only one direction was ever conceived as even making sense at all.
These days, if a philosopher wants to do something absolutely weird with logic, he can just refer to Graham Priest as a precedent. Any peer reviewer who would otherwise stand up for the traditional logic of the law of non-contradiction, reductio ad absurdum, the law of the excluded middle, and modus ponens just has to drop his rage. ‘Well, if he’s appealing to Priest as a precedent, then I guess I can grant his dropping all these basic rules and inventing a bunch of different ones.’ That makes his achievement all the more impressive. Before Graham Priest became The Graham Priest, there was no Graham Priest to refer to!