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?
Logic is one of these things we all have intuitions about. Most of us think we know how to use it. But what actually IS it? When we say, “that’s not logical,” or, “logic dictates that x,” are we all referring to the same thing? Most of us would agree that logic is a fundamental aspect of how we reason – that, in fact, we can’t reason without it. But then, if there are disagreements about how logic works – and there are! – how can we decide which side is right without presupposing some type of logic?