Logic
Without logic, reason is useless. With it, you can win
arguments and alienate multitudes.
DIMITRI: There are so many competing philosophies. How can I be sure anything's true?
TASSO: Who says anything is true?
DIMITRI: There you go again. Why do you always answer a question with another question?
TASSO: You got a problem with that?
DIMITRI: I don't even know why I asked, because some things just are true. Like two plus two equals four. That's true, end of story.
TASSO: But how can you be sure?
DIMITRI: Because I am one smart Athenian.
TASSO: That's another question. But the reason you can be sure two plus two equals four is because it follows the irrefutable laws of logic.
THE LAW OF NONCONTRADICTION
Tasso's right.
Let's start off with a classic joke that draws on Aristotelian logic.
A rabbi is holding court in his village. Schmuel stands up and pleads his case, saying, "Rabbi, Itzak runs his sheep across my land every day and it is ruining my crops. It's my land. It's not fair."
The rabbi says, "You're right!"
But then Itzak stands up and says, "But Rabbi, going across his land is the only way my sheep can drink water from the pond. Without it, they'll die. For centuries, every shepherd has had the right of way on the land surrounding the pond, so I should too."
And the rabbi says, "You're right!"
The cleaning lady, who has overheard all this, says to the rabbi, "But, Rabbi, they can't both be right!"
And the rabbi replies, "You're right!"
The cleaning lady has informed the rabbi that he has violated Aristotle's Law of Noncontradiction, which for a rabbi isn't quite as bad as violating the law against coveting your neighbor's maidservant, but it's close. The Law of Noncontradiction says that nothing can both be so and not be so at the same time.
ILLOGICAL REASONING
Illogical reasoning is the bane of philosophers, but heaven knows, it can be useful. That's probably why it's so prevalent.
An Irishman walks into a Dublin bar, orders three pints of Guinness, and drinks them down, taking a sip from one, then a sip from the next, until they're gone. He then orders three more. The bartender says, "You know, they'd be less likely to go flat if you bought them one at a time."
The man says, "Yeah, I know, but I have two brothers, one in the States, one in Australia. When we all went our separate ways, we promised each other that we'd all drink this way in memory of the days when we drank together. Each of these is for one of my brothers and the third is for me."
The bartender is touched, and says, "What a great custom!"
The Irishman becomes a regular in the bar and always orders the same way.
One day he comes in and orders two pints. The other regulars notice, and a silence falls over the bar. When he comes to the bar for his second round, the bartender says, "Please accept my condolences, pal."
The Irishman says, "Oh, no, everyone's fine. I just joined the Mormon Church, and I had to quit drinking."
In other words, self-serving logic can get you served.
INDUCTIVE LOGIC
Inductive logic reasons from particular instances to general theories and is the method used to confirm scientific theories. If you observe enough apples falling from trees, you will conclude that apples always fall down, instead of up or sideways. You might then form a more general hypothesis that includes other falling bodies, like pears. Thus is the progress of science.
In the annals of literature, no character is as renowned for his powers of "deduction" as the intrepid Sherlock Holmes, but the way Holmes operates is not generally by using deductive logic at all. He really uses inductive logic. First, he carefully observes the situation, then he generalizes from his prior experience, using analogy and probability, as he does in the following story:
Holmes and Watson are on a camping trip. In the middle of the night Holmes wakes up and gives Dr. Watson a nudge. "Watson," he says, "look up in the sky and tell me what you see."
"I see millions of stars, Holmes," says Watson.
"And what do you conclude from that, Watson?"
Watson thinks for a moment. "Well," he says, "astronomically, it tells me that there are millions of galaxies and potentially billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is approximately a quarter past three. Meteorologically, I suspect that we will have a beautiful day tomorrow. Theologically, I see that God is all-powerful, and we are small and insignificant. Uh, what does it tell you, Holmes?"
"Watson, you idiot! Someone has stolen our tent!"
We don't know exactly how Holmes arrived at his conclusion, but perhaps it was something like this:
1. I went to sleep in a tent, but now I can see the stars.
2. My intuitive working hypothesis, based on analogies to similar experiences I have had in the past, is that someone has stolen our tent.
3. In testing that hypothesis, let's rule out alternative hypotheses:
a. Perhaps the tent is still here, but someone is projecting a picture of stars on the roof of the tent. This is unlikely, based on my past experience of human behavior and the equipment that experience tells me would have to be present in the tent and obviously isn't.
b. Perhaps the tent blew away. This is unlikely, as my past experiences lead me to conclude that that amount of wind would have awakened me, though perhaps not Watson.
c. Etc., etc., etc.
4. No, I think my original hypothesis is probably correct. Someone has stolen our tent.
Induction. All these years we've been calling Holmes's skill by the wrong term.
FALSIFIABILITY
Patient: Last night I dreamt I had Jennifer Lopez and Angelina Jolie in bed, and the three of us made love all night.
Shrink: Obviously, you have a deep-seated desire to sleep with your mother.
Patient: What?! Neither of those women looks remotely like my mother.
Shrink: Aha! A reaction formation! You're obviously repressing your real desires.
The above is not a joke-it is actually the way some Freudians reason. And the problem with their reasoning is that there is no conceivable set of actual circumstances that would disprove their Oedipal theory. In his critique of inductive logic, twentieth-century philosopher Karl Popper argued that in order for a theory to hold water, there must be some possible circumstances that could demonstrate it to be false. In the above pseudo joke, there are no such circumstances that the Freudian therapist will admit as evidence.
And here's a real joke that hits Popper's point even more pointedly:
Two men are making breakfast. As one is buttering the toast, he says, "Did you ever notice that if you drop a piece of toast, it always lands butter side down?"
The second guy says, "No, I bet it just seems that way because it's so unpleasant to clean up the mess when it lands butter side down. I bet it lands butter side up just as often."
The first guy says, "Oh, yeah? Watch this." He drops the toast to the floor, where it lands butter side up.
The second guy says, "See, I told you."
The first guy says, "Oh, I see what happened. I buttered the wrong side!"
For this guy, no amount of evidence will falsify his theory.
DEDUCTIVE LOGIC
Deductive logic reasons from the general to the particular. The bare-bones deductive argument is the syllogism "All men are mortal; Socrates is a man; therefore, Socrates is a mortal." It's amazing how often people screw this up and argue something like, "All men are mortal; Socrates is mortal; therefore, Socrates is a man," which doesn't logically follow. That would be like saying, "All men are mortal; my kid's hamster is mortal; therefore, my kid's hamster is a man."
Another way to screw up a deductive argument is by arguing from a false premise.
An old cowboy goes into a bar and orders a drink. As he sits there sipping his whiskey, a young lady sits down next to him. She turns to the cowboy and asks him, "Are you a real cowboy?"
He replies, "Well, I've spent my whole life on the ranch, herding horses, mending fences, and branding cattle, so I guess I am."
She says, "I'm a lesbian. I spend my whole day thinking about women. As soon as I get up in the morning, I think about women. When I shower or watch TV, everything seems to make me think of women."
A little while later, a couple sits down next to the old cowboy and asks him, "Are you a real cowboy?"
He replies, "I always thought I was, but I just found out I'm a lesbian."
Perhaps it would be fun to analyze exactly where the cowboy went wrong. Perhaps not. But we're going to do it anyhow.
In his first answer to the question of whether he is a real cowboy, he reasoned,
1. If someone spends all his time doing cowboy-type things, he is a real cowboy.
2. I spend all my time doing those cowboy-type things.
3. Therefore, I am a real cowboy.
The woman reasoned,
1. If a woman spends all her time thinking about women, she is a lesbian.
2. I am a woman.
3. I spend all my time thinking about women.
4. Therefore, I am a lesbian.
When the cowboy then reasons to the same conclusion, he assumes a premise that in his case is false: namely, (2) I am a woman.
Okay, we never promised you that philosophy is the same as jokes.
THE INDUCTIVE ARGUMENT FROM ANALOGY
There's nothing like an argument from analogy. Well, maybe a duck. One use of the argument from analogy is found in response to the question of what or who created the universe. Some have argued that because the universe is like a clock, there must be a Clockmaker. As the eighteenth-century British empiricist David Hume pointed out, this is a slippery argument, because there is nothing that is really perfectly analogous to the universe as a whole, unless it's another universe, so we shouldn't try to pass off anything that is just a part of this universe. Why a clock anyhow? Hume asks. Why not say the universe is analogous to a kangaroo? After all, both are organically interconnected systems. But the kangaroo analogy would lead to a very different conclusion about the origin of the universe: namely, that it was born of another universe after that universe had sex with a third universe. A fundamental problem with arguments from analogy is the assumption that, because some aspects of A are similar to B, other aspects of A are similar to B. It ain't necessarily so.
Recently, the clockwork argument has staged a comeback as the "theory" of Intelligent Design, which proposes that the supercomplexity of stuff in nature (think snowflakes, eyeballs, quarks) proves that there must be a superintelligent designer. When the Dover, Pennsylvania, Board of Education was challenged for including Intelligent Design as an "alternate theory" to evolution in their school curriculum, the presiding judge, John Jones III, ruled, in effect, that they should go back to school. In his often wittily written opinion, Jones could not restrain himself from poking fun at some of the defense's so-called expert witnesses, like one professor who admitted that the argument from analogy was flawed, but "it still works in science-fiction movies." Next witness, puh-leez!
Another problem with arguments from analogy is that you get totally different analogies from different points of view.
Three engineering students are discussing what sort of God must have designed the human body. The first says, "God must be a mechanical engineer. Look at all the joints."
The second says, "I think God must be an electrical engineer. The nervous system has thousands of electrical connections."
The third says, "Actually, God is a civil engineer. Who else would run a toxic waste pipeline through a recreational area?"
Ultimately arguments from analogy are not very satisfying. They don't provide the kind of certainty we would like when it comes to basic beliefs like the existence of God. There is nothing worse than a philosopher's bad analogy, except perhaps a high-schooler's. Witness the results of the "Worst Analogies Ever Written in a High School Essay" contest, run by The Washington Post:
? "Long separated by cruel fate, the star-crossed lovers raced across the grassy field toward each other like two freight trains, one having left Cleveland at 6:36 p.m. traveling at 55 m.p.h., the other from Topeka at 7:47 p.m. at a speed of 35 m.p.h."
? "John and Mary had never met. They were like two hummingbirds who had also never met."
? "The little boat gently drifted across the pond exactly the way a bowling ball wouldn't."
? From the attic came an unearthly howl. The whole scene had an eerie, surreal quality, like when you're on vacation in another city and Jeopardy comes on at 7 p.m. instead of 7:30.
THE "POST HOC ERGO PROPTER HOC" FALLACY
First, a word about the social usage of this term: In some circles, when uttered with a straight face, this phrase can help you get lucky at a party. Interestingly, it has the exact opposite effect when uttered in English: "After this, therefore because of this." Go figure.
The phrase describes the error of assuming that because one thing follows another, that thing was caused by the other. For obvious reasons, this false logic is popular in sociopolitical discourse, such as "Most people hooked on heroin started with marijuana." True, but even more started with milk.
Post hoc makes life more entertaining in some cultures: "The sun rises when the rooster crows, so the rooster's crowing must make the sun rise." Thanks, rooster! Or take our colleague:
Every morning, she steps out onto her front stoop and exclaims, "Let this house be safe from tigers!" Then she goes back inside.
Finally, we said to her, "What's that all about? There isn't a tiger within a thousand miles of here."
And she said, "See? It works!"
Post hoc jokes have multiplied in direct proportion to human delusions.
An older Jewish gentleman marries a younger lady, and they are very much in love. However, no matter what the husband does sexually, the woman never reaches orgasm. Since a Jewish wife is entitled to sexual pleasure, they decide to ask the rabbi. The rabbi listens to their story, strokes his beard, and makes the following suggestion:
"Hire a strapping young man. While the two of you are making love, have the young man wave a towel over you. That will help the wife fantasize and should bring on an orgasm."
They go home and follow the rabbi's advice. They hire a handsome young man and he waves a towel over them as they make love. It doesn't help, and she is still unsatisfied.
Perplexed, they go back to the rabbi. "Okay," says the rabbi to the husband, "let's try it reversed. Have the young man make love to your wife and you wave the towel over them." Once again, they follow the rabbi's advice.
The young man gets into bed with the wife, and the husband waves the towel. The young man gets to work with great enthusiasm and the wife soon has an enormous, room-shaking, screaming orgasm.
The husband smiles, looks at the young man and says to him triumphantly, "Schmuck, that's the way you wave a towel!"
Okay, one last post hoc joke. Promise.
An octogenarian man in a nursing home comes up to an elderly lady wearing hot pink capri pants and says, "Today's my birthday!"
"Wonderful," she replies. "I bet I can tell you exactly how old you are."
"Really? How?"
The lady says, "Easy. Drop your pants."
The man drops his pants.
"Okay," she says, "now drop your shorts."
The man does her bidding. She fondles him a moment and says, "You're eighty-four!"
He says, "How did you know that?"
And she says, "You told me yesterday."
The old man has fallen for the oldest trick in the book, post hoc ergo propter hoc, or after she copped a feel, therefore because she copped a feel… It's that propter part that gets you every time.
In general, we're deceived by post hoc ergo propter hoc because we fail to notice that there's another cause at work.
A New York boy is being led through the swamps of Louisiana by his cousin. "Is it true that an alligator won't attack you if you carry a flashlight?" asks the city boy.
His cousin replies, "Depends on how fast you carry the flashlight."
The city boy saw the flashlight as a propter when it was only a prop.
MONTE CARLO FALLACY
Gamblers will recognize the Monte Carlo Fallacy. Some may be surprised to hear it's a fallacy. They may be treating it as the Monte Carlo Strategy. Actually, croupiers depend upon that.
We know that a roulette wheel that has half red positions and half black positions has a 50 percent chance of stopping on red. If we turn the wheel a large number of times-say 1,000-and the wheel isn't rigged or otherwise faulty, on average it should stop on red 500 times. So, if we turn the wheel six times and it stops on black all six times, we are tempted to think that the odds are in our favor if we play red on the seventh turn. Red is "due," right? Wrong. The wheel has exactly the same 50 percent chance of stopping on red on the seventh turn as it had on every other turn, and this would be true no matter how many blacks had come up in a row.
Here's some sage advice based on the Monte Carlo Fallacy:
If you are getting on a commercial airliner, for safety's sake, take a bomb with you… because the overwhelming odds are there won't be two guys on the same plane with a bomb.
CIRCULAR ARGUMENT
A circular argument is an argument in which the evidence for a proposition contains the proposition itself. Often a circular argument can be a joke all by itself, with no adornment necessary.
It was autumn, and the Indians on the reservation asked their new chief if it was going to be a cold winter. Raised in the ways of the modern world, the chief had never been taught the old secrets and had no way of knowing whether the winter would be cold or mild. To be on the safe side, he advised the tribe to collect wood and be prepared for a cold winter. A few days later, as a practical afterthought, he called the National Weather Service and asked whether they were forecasting a cold winter. The meteorologist replied that, indeed, he thought the winter would be quite cold. The chief advised the tribe to stock even more wood.
A couple of weeks later, the chief checked in again with the Weather Service. "Does it still look like a cold winter?" asked the chief.
"It sure does," replied the meteorologist. "It looks like a very cold winter." The chief advised the tribe to gather up every scrap of wood they could find.
A couple of weeks later, the chief called the Weather Service again and asked how the winter was looking at that point. The meteorologist said, "We're now forecasting that it will be one of the coldest winters on record!"
"Really?" said the chief. "How can you be so sure?"
The meteorologist replied, "The Indians are collecting wood like crazy!"
The chief's evidence for the need to stock more wood turns out to be that he was stocking more wood. Fortunately, he was using a circular saw.
ARGUMENT FROM RESPECT FOR AUTHORITY
(ARGUMENTUM AD VERECUNDIAM) FALLACY
The argument from respect for authority is one of our boss's favorite arguments. Citing an authority to support your argument is not a logical fallacy in and of itself; expert opinion is legitimate evidence alongside other evidence. What is fallacious is using respect for authority as the sole confirmation of your position, despite convincing evidence to the contrary.
Ted meets his friend Al and exclaims, "Al! I heard you died!"
"Hardly," says Al, laughing. "As you can see, I'm very much alive."
"Impossible," says Ted. "The man who told me is much more reliable than you."
What is always at play in arguments from authority is whom one accepts as a legitimate authority.
A man walks into a pet store and asks to see the parrots. The store owner shows him two beautiful ones out on the floor. "This one is $5,000 and the other is $10,000," he says.
"Wow!" says the man. "What does the $5,000 one do?"
"This parrot can sing every aria Mozart wrote," says the store owner.
"And the other?"
"He sings Wagner's entire Ring cycle. There's another parrot out back for $30,000."
"Holy moley! What does he do?"
"Nothing that I've heard, but the other two call him 'Maestro.'"
According to our authorities, some authorities have better credentials than others; the problem arises when the other side doesn't accept those credentials.
Four rabbis used to argue theology together, and three were always in accord against the fourth. One day, the odd rabbi out, after losing three to one again, decided to appeal to a higher authority.
"O, God!" he cried. "I know in my heart that I am right and they are wrong! Please give me a sign to prove it to them!"
It was a beautiful, sunny day. As soon as the rabbi finished his prayer, a storm cloud moved across the sky above the four rabbis. It rumbled once and dissolved. "A sign from God! See, I'm right, I knew it!" But the other three disagreed, pointing out that storm clouds often form on hot days.
So the rabbi prayed again. "O, God, I need a bigger sign to show that I am right and they are wrong. So please, God, a bigger sign!" This time four storm clouds appeared, rushed toward each other to form one big cloud, and a bolt of lightning slammed into a tree on a nearby hill.
"I told you I was right!" cried the rabbi, but his friends insisted that nothing had happened that could not be explained by natural causes.
The rabbi was getting ready to ask for a very, very big sign, but just as he said, "O, God…," the sky turned pitch-black, the earth shook, and a deep, booming voice intoned, "HEEEEEEEE'S RIIIIIIIGHT!"
The rabbi put his hands on his hips, turned to the other three, and said, "Well?"
"So," shrugged one of the other rabbis, "now it's three to two."
ZENO'S PARADOX
A paradox is a seemingly sound piece of reasoning based on seemingly true assumptions that leads to a contradiction or another obviously false conclusion. In slightly different words, this could be the definition of a joke-at least, most of the jokes in this book. There's something absurd about true stuff that leads ever so logically to false stuff; and absurd is funny. Holding two mutually contradicting ideas in our heads at the same time makes us giddy. But most significantly, you can tell a tricky paradox at a party and get a good laugh.
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.
Epistemology: