Plato and a Platypus Walk Into a Bar

by Thomas Cathcart

  When it comes to holding two mutually exclusive ideas simultaneously, Zeno of Elea was a real cutup. Have you heard his story about the race between Achilles and the tortoise? Naturally, Achilles can run faster than the tortoise, so the tortoise is given a big head start. At the gun—or as they said in the fifth century B.C., at the javelin—Achilles’s first goal is to get to the point where the tortoise started. Of course, by then the tortoise has moved a little way. So now Achilles has to get to that spot. By the time he gets there, the tortoise has moved again. No matter how many times Achilles reaches the tortoise’s prior location, even if he does it an infinite number of times, Achilles will never catch up with the tortoise, although he’ll get awfully close. All the tortoise needs to do to win the race is to not to stop.

  Okay, so Zeno isn’t Leno, but he’s not bad for a fifth-century B.C. philosopher. And, like the classic stand-up comedians of yore, Zeno can say, “I’ve got a million of ’em.” Well, actually, only four. Another was his racetrack paradox. In order to get to the end of the racetrack, a runner must first complete an infinite number of journeys. He must run to the midpoint; then he must run to the midpoint of the remaining distance; then to the midpoint of the still remaining distance, etc., etc. Theoretically speaking, because he has to get to midpoints an infinite number of times, he can never get to the end of the track. But of course he does. Even Zeno can see that.

  Here’s an old comedy routine that seems to come straight out of Zeno:

  Salesman: Ma’am, this vacuum cleaner will cut your work in half.”

  Customer: “Terrific! Give me two of them.”

  There’s a weird thing about this joke. The racetrack paradox runs counter to common sense, and even if we can’t figure out what’s wrong with it, we’re confident that something is. In the vacuum cleaner joke though, Zeno’s reasoning is not paradoxical at all. If the woman’s goal is to get the work done in no time at all, no number of time-saving vacuum cleaners (and people to run them concurrently with her) is going to do it. Running two vacuums will only cut the rug-cleaning time by three quarters; running three, by five sixths; and so on, as the number of vacuum cleaners goes on to infinity.

  LOGICAL AND SEMANTIC PARADOXES

  The mother of all the logical and semantic paradoxes was Russell’s paradox, named for its author, twentieth-century English philosopher Bertrand Russell. It goes like this: “Is the set of all sets that are not members of themselves a member of itself?” This one is a real screamer—that is, if you happen to have an advanced degree in mathematics. But hang on. Fortunately, two other twentieth-century logicians named Grelling and Nelson came along with a more accessible version of Russell’s paradox. It’s a semantic paradox that operates on the concept of words that refer to themselves.

  Here goes: There are two kinds of words, those that refer to themselves (autological) and those that don’t (heterological). Some examples of autological words are “short” (which is a short word), “polysyllabic” (which has several syllables), and our favorite, “seventeen-lettered” (which has seventeen letters). Examples of heterological words are “knock-kneed” (a word that has no knees, touching or otherwise) and “monosyllabic” (a word that has more than one syllable). The question is: Is the word “heterological” autological or heterological? If it’s autological, then it’s heterological. If it’s heterological, then it’s autological. Ha! Ha!

  Still not laughing? Well, here’s another case where translating a philosophical concept into a funny story makes it clearer:

  There is a town in which the sole barber—a man, by the way—shaves all the townsmen, and only those townsmen, who do not shave themselves. Does the barber shave himself?

  If he does, he doesn’t. If he doesn’t, he does.

  Now that’s Russell’s paradox for the party set.

  We don’t often visit women’s restrooms, so we can’t be sure what goes on in there, but we do know that male readers will be familiar with the paradoxes often scribbled on the walls of men’s room stalls, especially in college communities. They are logical/semantic paradoxes along the lines of Russell’s and Grelling-Nelson’s, but snappier. Remember these? Remember where you were sitting at the time?

  True or false: “This sentence is false.”

  Or,

  If a man tries to fail and succeeds, which did he do?

  Just for fun, inscribe, “Is the word ‘heterological’ autological or heterological?” over the urinal next time you drop by. It’s a classy thing to do.

  DIMITRI: Cute. But what does any of this have to do with answering the Big Questions?

  TASSO: Well, let’s say you visit the Oracle at Delphi and ask him, “What’s it all about, Delphi?” And he answers, “Life is a picnic; all picnics are fun: therefore, life is fun.” Logic gives you something to chat about.

  {III}

  Epistemology:

  The Theory of Knowledge

  How do you know that you know the stuff you think you

  know? Take away the option of answering, “I just do!” and

  what’s left is epistemology.

  DIMITRI: I’m feeling good now, Tasso. I’ve got logic down cold, so the rest should be a picnic in the Acropolis.

  TASSO: What Acropolis?

  DIMITRI: That one! Right over there! Maybe you ought to ease off on the ouzo, pal.

  TASSO: But is that the Acropolis or just something that you believe is the Acropolis? How do you know it’s real? For that matter, how do you know anything is real?

  DIMITRI: Next round’s on me.

  REASON VS. REVELATION

  So how do we know anything at all, if in fact we do know anything at all?

  During the Middle Ages this question boiled down to whether divine revelation trumps reason as a source of human knowledge or vice versa.

  A man stumbles into a deep well and plummets a hundred feet before grasping a spindly root, stopping his fall. His grip grows weaker and weaker, and in his desperation he cries out, “Is there anybody up there?”

  He looks up, and all he can see is a circle of sky. Suddenly, the clouds part and a beam of bright light shines down on him. A deep voice thunders, “I, the Lord, am here. Let go of the root, and I will save you.”

  The man thinks for a moment and then yells, “Is there anybody else up there?”

  Hanging by a root has a tendency to tip the scales toward reason.

  In the seventeenth century, René Descartes opted for reason over a divine source of knowledge. This came to be known as putting Descartes before the source.

  Descartes probably wishes he’d never said, “Cogito ergo sum” (“I think, therefore I am”), because it’s all anybody ever remembers about him—that and the fact that he said it while sitting inside a bread oven. As if that weren’t bad enough, his “cogito” is constantly misinterpreted to mean that Descartes believed thinking is an essential characteristic of being human. Well, actually, he did believe that, but that has nothing whatsoever to do with cogito ergo sum. Descartes arrived at the cogito through an experiment in radical doubt to discover if there was anything he could be certain of; that is, anything that he could not doubt away. He started out by doubting the existence of the external world. That was easy enough. Perhaps he was dreaming or hallucinating. Then he tried doubting his own existence. But doubt as he would, he kept coming up against the fact that there was a doubter. Must be himself! He could not doubt his own doubting. He could have saved himself a lot of misinterpretation if only he had said, “Dubito ergo sum.”

  Every American criminal-trial judge asks the jury to mimic Descartes’s process of looking for certainty by testing the assertion of the defendant’s guilt against a standard almost as high as Descartes’s. The question for the jury is not identical to Descartes’s; the judge does not ask whether the defendant’s guilt is open to any doubt, but only whether it is open to reasonable doubt. But even this lower standard demands that the jury carry out a similar—and nearly as radical—mental experiment as Descart
es did.

  A defendant was on trial for murder. There was strong evidence indicating his guilt, but there was no corpse. In his closing statement, the defense attorney resorted to a trick. “Ladies and gentlemen of the jury,” he said. “I have a surprise for you all—within one minute, the person presumed dead will walk into this courtroom.”

  He looked toward the courtroom door. The jurors, stunned, all looked eagerly. A minute passed. Nothing happened. Finally the lawyer said, “Actually, I made up the business about the dead man walking in. But you all looked at the door with anticipation. I therefore put it to you that there is reasonable doubt in this case as to whether anyone was killed, and I must insist that you return a verdict of ‘not guilty.’”

  The jury retired to deliberate. A few minutes later, they returned and pronounced a verdict of “guilty.”

  “But how could you do that?” bellowed the lawyer. “You must have had some doubt. I saw all of you stare at the door.”

  The jury foreman replied, “Oh, we looked, but your client didn’t.”

  EMPIRICISM

  According to the eighteenth-century Irish empiricist Bishop George Berkeley, “Esse est percipi” (“To be is to be perceived”), which is to say that the so-called objective world is all in the mind. Berkeley argued that our only knowledge of this world is what comes to us through our senses. (Philosophers call this information “sense data.”) Beyond these sense data, Berkeley said, you cannot infer anything else, such as the existence of substances out there sending out vibes that stimulate our senses. But the good bishop did go on to infer that sense data has to come from somewhere, so that somewhere must be God. Basically, Berkeley’s idea is that God is up there tapping out sense data on a cosmic Web site to which we are all tuned in 24/7. (And we always thought God only worked 24/6!)

  The story goes that Berkeley’s contemporary, Dr. Samuel Johnson, upon being told of the “Esse est percipi” theory, kicked a hitching post, exclaiming, “Thus do I refute Bishop Berkeley!”

  To Berkeley, it would have sounded like a gag. That kick and the sore toe that followed from it only proved that God was busy at his task of sending coordinated sense data Dr. Johnson’s way: first, the sensation of foot motion stopping, followed immediately by the sensation of pain.

  Things get more complicated when the source of our sense data is another human being:

  A man is worried that his wife is losing her hearing, so he consults a doctor. The doctor suggests that he try a simple at-home test on her: Stand behind her and ask her a question, first from twenty feet away, next from ten feet, and finally right behind her.

  So the man goes home and sees his wife in the kitchen facing the stove. He says from the door, “What’s for dinner tonight?”

  No answer.

  Ten feet behind her, he repeats, “What’s for dinner tonight?”

  Still no answer.

  Finally, right behind her he says, “What’s for dinner tonight?”

  And his wife turns around and says, “For the third time—chicken!”

  Now, what this couple has is a serious sense-data interpretation problem.

  SCIENTIFIC METHOD

  Today it seems like a no-brainer that all knowledge of the external world comes through our senses. But it was not always so. Many philosophers in bygone eras thought that there were some innate ideas in our minds that were there a priori—or prior to experience. Some thought our ideas of God were innate; others claimed that our idea of causality was innate too.

  Even today, when someone says, “Everything happens for a reason,” or “I believe in reincarnation,” he is making a statement that cannot be either confirmed or disconfirmed by experience. But most of us accept that the best evidence for the truth of a statement about the external world is sensory experience, and in that sense we are all empiricists. That is, unless we are the King of Poland, the exception that proves the rule:

  The King of Poland and a retinue of dukes and earls went out for a royal elk hunt. Just as they approached the woods, a serf came running out from behind a tree, waving his arms excitedly and yelling, “I am not an elk!”

  The king took aim and shot the serf through the heart, killing him instantly.

  “Good sire,” a duke said, “why did you do that? He said he was not an elk.”

  “Dear me,” the king replied. “I thought he said he was an elk.”

  All right, now let’s compare the king with a hot-shot scientist.

  A scientist and his wife are out for a drive in the country. The wife says, “Oh, look! Those sheep have been shorn.”

  “Yes,” says the scientist. “On this side.”

  At first blush we might think that the wife is only expressing a commonsense view, while the scientist is taking a more cautious, more scientific view, in that he refuses to go beyond the evidence of his senses. But we would be wrong. It is actually the wife who has formulated what most scientists would consider the more scientific hypothesis. The “experience” of empiricists is not restricted to direct sensory experience. Scientists use their prior experiences to calculate probabilities and to infer more general statements. What the wife is in effect saying is, “What I see are sheep that are shorn, at least on this side. From prior experience I know that farmers do not generally shear sheep only on one side and that, even if this farmer did, the probability of the sheep arranging themselves on the hillside so that only their shorn sides face the road is infinitesimal. Therefore, I feel confident saying, ‘Those sheep have been completely shorn.’”

  We assume that the scientist in the joke is some sort of overeducated egghead. More typically, we assume that a person who cannot extrapolate from his prior experience is simply a dingbat, or, as they say in India, a Sardar.

  A New Delhi policeman is interrogating three Sardars who are training to become detectives. To test their skills in recognizing a suspect, he shows the first Sardar a picture for five seconds and then hides it. “This is your suspect. How would you recognize him?”

  The Sardar answers, “That’s easy, we’ll catch him fast because he only has one eye!”

  The policeman says, “Sardar! That’s because the picture I showed you is his profile.”

  Then the policeman flashes the picture for five seconds at the second Sardar and asks him, “This is your suspect. How would you recognize him?”

  The second Sardar smiles and says, “Ha! He’d be too easy to catch because he only has one ear!”

  The policeman angrily responds, “What’s the matter with you two? Of course only one eye and one ear are showing, because it’s a picture of his profile! Is that the best answer you can come up with?”

  Extremely frustrated at this point, he shows the picture to the third Sardar and in a very testy voice asks, “This is your suspect. How would you recognize him?”

  The Sardar looks at the picture intently for a moment and says, “The suspect wears contact lenses.” The policeman is caught off guard because he really doesn’t know whether the suspect wears contact lenses. “Well, that’s an interesting answer,” he says. “Wait here for a few minutes while I check his file and I’ll get back to you on that.”

  He leaves the room, goes to his office, checks the suspect’s file in his computer, and comes back smiling. “Wow! I can’t believe it. It’s true! The suspect does in fact wear contact lenses. Good work! How were you able to make such an astute observation?”

  “That’s easy,” the Sardar replied. “He can’t wear regular glasses because he only has one eye and one ear.”

  The triumph of empiricism in Western epistemology is reflected in the fact that we automatically assume it to be the method of verification everyone uses:

  Three women are in a locker room dressing to play racquetball when a man runs through wearing nothing but a bag over his head. The first woman looks at his wiener and says, “Well, it’s not my husband.” The second woman says, “No, it isn’t.” The third says, “He’s not even a member of this club.”

  Sti
ll, despite the triumph of empiricism and science, many people continue to interpret some unusual events as miraculous rather than the result of natural causes. David Hume, the skeptical British empiricist, said that the only rational basis for believing that something is a miracle is that all alternative explanations are even more improbable. Say a man insists he has a potted palm that sings arias from Aida. Which is more improbable: that the potted palm has violated the laws of nature, or that the man is crazy, or fibbing or high on mushrooms? Hume’s response: “Puh-leez!” (We’re paraphrasing here.) Since the odds of the man having been deceived or having stretched the truth are always somewhat greater than the odds of a violation of the laws of nature, Hume could foresee no circumstance in which it would be rational to conclude that a miracle had happened. Add to this the generally known fact that potted palms prefer Puccini to Verdi.

  Interestingly, in the following story, Bill, an apparent student of Hume, puts a presumed miracle to the test, but in the end is driven to the conclusion that the alternative explanation is even more unlikely:

  One day Bill complained to his friend that his elbow really hurt. His friend suggested that he visit a swami who lived in a nearby cave. “Simply leave a sample of urine outside his cave, and he will meditate on it, miraculously diagnose your problem, and tell you what you can do about it. It only costs ten dollars.”

  Bill figured he had little to lose, so he filled a jar with urine and left it outside the cave with a ten-dollar bill. The next day when he came back, there was a note waiting for him that said, “You have tennis elbow. Soak your arm in warm water. Avoid heavy lifting. It will be better in two weeks.”