What is a Paradox? (part 2)

My rough-and-ready suggestion before was that a paradox is a puzzle of some kind. But what kind? Not all puzzles are paradoxes, after all. There is nothing particularly paradoxical about standard jigsaw puzzle. Even those frustrating little metal puzzles aren't paradoxical — even if we can't figure out how to solve them. One might suggest that a paradox is a linguistic puzzle something that has to be stated in words — a "riddle", perhaps. This apparently rules out M.C. Escher drawings as paradoxes, but let that go for the moment. It still seems too permissive a definition. Crossword puzzles are linguistic puzzles; but again, even if they can be frustrating (especially on Sundays), they do not seem especially paradoxical.

We might cross the puzzle suggestion with the surprising suggestion from before and say that a paradox is a surprising puzzle or riddle. This raises an interesting connection and a further question: can paradoxes be simply questions? This would run against the grain in philosophy of understanding paradoxes as sets of propositions with a certain character. But consider Zen Koans. The OED defines them as "A paradox put to a student to stimulate his mind." As I understand Koans (and I'm a bit out of my depth here), they are often presented as questions. The most famous is, of course, "What is the sound of one hand clapping?" On the other hand, you might have heard demonstrations of the straightforwardness of this puzzle. For example, there's this guy:



Perhaps he's not ready to have his mind stimulated. . . . Perhaps the question isn't too deep after all. Here's another one: "Could there be a barber who shaves all and only those who do not shave themselves?"

Draft Syllabus

If anyone wants to check out a draft of the syllabus for 222, it can be found here. Don't hesitate to let me know if you have any questions.

What is a Paradox?

Like many questions in philosophy, this one is deceptively difficult. In fact, it will be one of the subjects of the course. But let me start the wheels of analysis turning (if slowly!) before we all get together. Here's a try at a definition: it's something surprising whose surprise we have trouble shaking. Take the "Twin Paradox", of for example. Al and Beth are twins. Beth wins a contest when they're 20 and gets a ride in a spaceship travelling at speeds approaching the speed of light. She's gone a long time, according to Al. She comes back when Al's 40 having aged only a few years. So twins can be different ages. That is certainly surprising, but apparently true — at least, according to Special Relativity.

However, what is surprising probably depends on one's context. People used to speak of the "Copernican Paradox": the fact that the spinning Earth hurtles around the sun (rather than vice versa) and we don't much notice. But even if I can work up a certain degree of wonder at the thought of Earthly motion, it seems wrong to call it a surprising fact. So on this definition, apparently, things are only paradoxes for particular people (or in particular ages, relative to certain bodies of knowledge). Perhaps the "Twin Paradox" will one day go the way of the "Copernican Paradox" and dissolve into familiarity. . . .

One might reject the definition on these grounds or accept it as a result. I'm not sure what stance is appropriate. In any case, it's probably too broad. Natural wonders — the Grand Canyon, for example — can seem permanently surprising too. But surely they're not paradoxes!

More tries later. . . .

Philosophy from Puzzlement

PHIL 222: Analytic Philosophy will be taught in the Fall 2013 term on Tuesdays and Thursdays from 2:30–3:52 PM. It will be focused on the theme of paradoxes. For those curious about the course thinking of taking it, here's a little background intended to help you decide whether the course would be of interest.

What is Analytic Philosophy? There are different ways of glossing it, but I think of Analytic Philosophy as a methodological tradition in philosophy. While some historical philosophical movements are united by the specific conclusions they reach on certain questions, Analytic Philosophy began with the general thought that the best way to answer philosophical problems involves a careful attention to language — that the main role of philosophy should be to analyze our concepts, putting some of the newly devised logical methods to work clarifying classic philosophical problems. The movement diversified as it grew up, but retained a certain "analytical spirit" that prized careful argumentation and clear writing. It is arguably the dominant (non-historical) approach to philosophy in the Anglo-English world. If you've taken Metaphysics, Theory of Knowledge, Philosophy of Language, Philosophy of Mind, or Philosophy of Science, chances are good that you've already been exposed to Analytic Philosophy.

Can a picture be a paradox?

What's a paradox? This is itself an interesting philosophical question, but to a close enough approximation, a paradox is a puzzle — perhaps a puzzle that has a solution, perhaps not. It turns out that a lot of philosophical theories are motivated by paradoxes. Zeno's most famous paradox, for example, takes the following form: to go from point A to point B, one has to go halfway between those points first (call that point C). Then one must go halfway between C and B, and then halfway between those points, and so on. But since there are infinitely many "halfways", between any two points and we cannot do infinitely many things in a finite stretch of time, motion is impossible.

Of course, we know that motion is possible, so something must have gone haywire in the above argument. But what? The trouble is that all of the premises look pretty plausible and the reasoning seems above reproach (i.e., the argument seems sound). Notice that figuring out what to say about this paradox will likely have consequences for our views of space, time, motion, infinity, and so on. That is, grappling with the paradox is one way of coming to a better understanding of these things.

Zeno's paradox is ancient. Interest in it spans thousands of years. The same is true of many of the paradoxes that we'll survey in the course. Paradoxes are unsolved problems. That's one of the things that makes contemplating them so exciting: we can not only learn something about the history of philosophy by studying them, we can hold out some hope of adding to it.

So what's with the ': Paradoxes' suffix? 

"Analytic philosophy accreted into existence as pearls accrete from irritating grains of sand. This makes analytic philosophy dependent on a supply of irritants. Artificial pearls can be cultivated by slipping paradoxes into otherwise contented oysters."  

— Roy Sorensen, interview in 3AM Magazine

One way of learning about the history of Analytic Philosophy proceeds like any other history of philosophy course: we read, in order, the most significant contributions to the field and try to understand its discursive unity — what the main topics and positions were, how certain contributions influenced others, what the conversation was like, and so on. The next incarnation of PHIL 222 is will take a more thematic approach, examining the history of Analytic Philosophy by examining how philosophers have responded to paradoxes.

In the coming weeks, I'll be adding more to this course blog (including a syllabus by summer). Subscribe to the RSS feed if you wish to stay abreast of the developments. In the meanwhile, you might check out the book we'll be using, Sainsbury's Paradoxes. As far as nitty-gritty registration info goes, here's the Bucknell Course Guide. The official pre-requisite is PHIL 100, though having some logic would also be good (I'd consider it an alternative pre-requisite). But a willingness to have your brain twisted into an MC Escher-esque pretzel is a must. Free free to send me an email or come talk to me if you're unsure about taking the course. See you next term!