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. . . .