In recent years, philosophers have debated the question of logical pluralism: the view that there is more than one correct logic (see my interview with Greg Restall on this very issue). The idea, roughly, is that which putative logical laws hold depends on what sorts of “cases” we take logic to be about; different kinds of cases yield different (but equally legitimate) logics. A common logical monist objection is to say that a form of argument is only a logical law if it applies in all cases. If this is true, it raises the question: what argument forms do hold in all cases? At this point in the debate, a third position becomes viable, defined by the answer: none.
Gillian Russell, a philosopher of language and logic, argues both that applying in all cases is necessary for qualifying as a logical law; and that no argument form applies in all cases. As such, she believes there are no logical laws. Much of our discussion surrounds her claim that no argument form applies to all cases. Is this really true even of the law of non-contradiction, the “law” that says that ‘A and not-A’ can never be true? Of conjunction elimination (‘A and B’ entails ‘A’)? Of identity (‘A’ entails ‘A’)? Russell runs through purported counterexamples to these laws; what’s more, she illustrates a method for conjuring counterexamples to any proposed “law”.
Consider the sentence C: “If this sentence is true, then David Ripley is a purple giraffe”. Suppose the sentence is true. Then the antecedent of the sentence (“this sentence is true”) is true. According to the inference rule modus ponens, if an if-then sentence (such as C) is true and its antecedent is true, then its consequent (“David Ripley is a purple giraffe”) must be true. It follows that if C is true, then David Ripley is a purple giraffe. But this conclusion is C: in other words, by simply supposing how things might turn out if C were true, we have proved that C, in fact, is true. So C is true, and since C’s antecedent is the claim that C is true, its antecedent is true as well. Now we can use modus ponens again to show that C’s consequent must be true. In other words, David Ripley really is a purple giraffe. QED.
This argument is Curry’s paradox. Obviously, the choice of “David Ripley is a purple giraffe” is arbitrary; a sentence of the form of “If this sentence is true, then X” can be used to prove any claim X. Now, in actual fact, David Ripley is not a purple giraffe, but a philosopher of language and logic. According to Ripley, solutions to paradoxes like Curry’s (as well as the Liar and the Sorites) fall into two broad categories: those that solve the paradoxes by messing with the meanings of important concepts (such as the meaning of “if-then”, truth, “not”, etc.) and those that solve them by changing the structural rules of inference by appeal to substructural logics.…
Chances are, if you’re reading this, you’ve heard me go on about a philosophy podcast I’m launching any moment now. Well, today’s the day. Concurrent with this post, I’m officially releasing episode one of Who Shaves the Barber? I’ll pretend you have questions and answer them:
It’s a weekly podcast – new episodes every Tuesday. Episodes will range anywhere from 40 – 90 mins (I’ll try to keep ’em short, but I’m a naturally long-winded fella). For some episodes (I’m aiming for about half-ish), I’ll interview philosophers. For the others, I’ll do my own presentation on a topic.
Oh, cool. Is there a more specific focus than just “philosophy”?
The tagline is “Exploring paradoxes, thought experiments, and other pointless problems.” That doesn’t really answer your question, but it’s kinda relevant and I wanted to share it. (By the way, I don’t really think philosophy is pointless, I just like piss off people who take it very seriously [unless they’re my guests].)
The useless but most accurate answer is that I’ll be talking about whatever topics interest me. The more useful answer is that I’m most interested in paradoxes, philosophy of logic, philosophy of language, epistemology, skepticism, ontology, and metaphilosophy. In terms of focus and style, my presentation will tend to mesh most with the “analytic” tradition (although, as the scare quotes indicate, I’m skeptical of the premise behind the “split.” But that’s a topic for another day).
I’m not super knowledgeable. How much background knowledge are you assuming?