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.…
A quick announcement, since I apparently do think that the tree makes a sound.
I’ve been hosting Who Shaves the Barber? as a weekly podcast for nearly a year now (I just released Episode 50 today). It’s been a lovely and fruitful experiment. Alas, you can only do a weekly in-depth podcast for so long while still having a full-time job and attacking other ambitious projects. So I’m officially calling the end of the weekly release. I’m still releasing episodes, but not on any regular schedule.
There are two episodes I expect to release in August that I’m super excited about. One is with David Ripley about Curry’s paradox. I’ve wanted to do a primer on Curry since the inception of the podcast, but it has always seemed daunting since it is something of a technical paradox (though fairly broad and fundamental issues lie at its heart). So I’m super stoked to talk to Dave Ripley himself about it.
The other is with a good friend of mine, Kazi Reza. This will be unlike any other interview in that I don’t expect it to focus on any one topic. Rather, I’ll be trying out how a casual, mostly undirected philosophical conversation works as a Barber episode. This may be excellent, it may not work at all – we’ll find out shortly. I also hope during that interview to talk about some of the new projects that have me stepping away from the podcast.
An old problem: I say, “Santa Claus is fat”. I am saying something true about Santa Claus. But (content warning) Santa Claus doesn’t exist. So what is it that I am correctly saying is fat? And what – if not its ostensive subject – makes the sentence true?
This problem is at the center of ontology. The most influential approach in the 20th century was offered by W. V. O. Quine, who argued that we’re committedto the existence of any object that we must quantify over in order to state the truths of physics in first-order logic. At first, this seems rather arbitrary. Why first-order logic? What makes quantifiers so special? Why physics? And what does what we’re “committed to” tell us about what actually exists? For roughly the first half of this interview, philosopher Jody Azzouni unpacks the thinking behind Quine’s famous criterion. In the second half, he expounds his own view: he rejects Quine’s criterion, and so sees no problem with referring to that which doesn’t exist. This leaves Azzouni open to embrace a radical nominalism, in which almost none of the objects we typically think of as existing really do. This is because, as Azzouni explains, “ontological borders” are projected. There is nothing “out there” that separates one object from another. The fact that our language is built around distinct objects tells us plenty about our psychology, but nothing about the world itself, which comes with “features” but not individual objects.…