<s> I T H I N K , T H E R E F O R E I L AU G H
This page intentionally left blank
I T H I N K , T H E R E F O R E I L AU G HThe Flip Side of Philosophy
J O H N A L L E N PA U L O S
C O L U M B I A
C
U N I V E R S I T Y
N E W
YO R K
P R E S S
Columbia University PressPublishers Since 1893New YorkChichester, West SussexCopyright © 2000 John Allen PaulosAll rights reservedLibrary of Congress Cataloging-in-Publication DataPaulos, John Allen.I think, therefore I laugh : the flip side of philosophy / John AllenPaulos. — [2nd ed.]p. cm.Includes bibliographical references (p.167) and index.ISBN 0–231–11914–3. — ISBN 0–231–11915–1 (pbk.)1. Logic. 2. Philosophy Humor. I. Title.BC71.P38 2000190.’207—dc2199–34799
∞Casebound editions of Columbia University Press books are printed on permanent and durable acid-free paper.Printed in the United States of Americap 10 9 8 7 6 5 4 3 2 1
For my wife, Sheila
This page intentionally left blank
CONTENTSP R E FAC E TO T H E S E C O N D E D I T I O N
ix
chapter oneT WO U N L I K E LY PA I R S O F M E N
1
IntroductionWittgenstein and CarrollGroucho Meets Russellchapter twoLOGIC
Either-OrYou Bet Your LifeSillygismsThe Titl of This Section Contains Three ErorsRussell’s Dr. Goldberg and Dr. RubinLanguage and Metalanguage: Do You Get It?Meaning, Reference, and Dora Black’sFirst HusbandAnalytic vs. Synthetic, Boole vs. Boyle, andMathematics vs. CookeryMiscellany
248
13142023303540485258
VIII
CONTENTS
chapter threeSCIENCE
Induction, Causality, and Hume’s EggsThe Tortoise Came First?Of Birds and Strange ColorsTruths, Half-Truths, and StatisticsDuhem, Poincaré, and the Poconos-Catskill DietReductionism, Fallibilism, and OpportunismRandomness and the Berry TaskDeterminism and Smart ComputersBell’s Inequality and WeirdnessOn Assumptionschapter fourPEOPLE
Context, Complexity, and Artificial IntelligenceWhy Did He Just Now Touch His Head?Arrow, Prisoners, and Compromise
63647176838995102110114124
131132139150
A F T E RWO R D
161
BIBLIOGRAPHY
167
INDEX
173
P R E FA C E TO T H ESECOND EDITIONI Think, Therefore I Laugh is the second of my six books, and ithas been out of print for a while. When ColumbiaUniversity Press asked me if I would be interested in reissuing it and writing a new preface, I immediately agreed. Withan author’s myopic vanity, perhaps, I have always liked thislittle book, inspired, as it was, by Wittgenstein’s quip that abook on philosophy might consist entirely of jokes. Sincethe book went out of print rather quickly, I’ve used it as asmall quarry, and readers of my subsequent books may recognize bits and pieces of it in them. Moreover, many of thebook’s concerns are similar to those of my later books: misunderstandings of mathematics and science and of the relation between them, pseudoscience and its appeal, the usesand misuses of probability and statistics, humor and “higher-order” endeavors, the interplay between narrative andnumbers.Although my Ph.D. is in mathematics, specificallymathematical logic, I’ve always had an interest in analyticphilosophy and its puzzles. It seemed to me when I wrote IThink, Therefore I Laugh, and it still seems, that the borderbetween such philosophical abstractions and the concernsof everyday life is well worth exploring. The payoff to this
X
P R E FA C E
exploration is of a largely intellectual sort. Recall one definition of a philosopher: he is the one who attends a conference on crime sentencing guidelines and delivers a paperon the meaning of “time” and the logical dilemma faced byimprisoned accomplices. Since social, economic, and topical issues are not the focus of this book (as they have beenin a couple of my later works), there is no compellingtemptation to update it. Aside from eliminating a numberof infelicities and a few minor mistakes, I have not changedanything.If I were to do the book over, I would choose a slightlydifferent set of philosophical problems and a different setof jokes and parables and would develop them at a moreleisurely pace. The presentation here is a bit relentless—something, something else, and then some other thing.Nevertheless, I reiterate and stand by the book’s guidinginsight: conceptual humor and analytic philosophy resonate at a very deep level. Did you hear what George Carlinand Groucho Marx said to Robert Nozick and BertrandRussell? . . .
I T H I N K , T H E R E F O R E I L AU G H
This page intentionally left blank
chapter one
T W O U N L I K E LY PA I R S O F M E N
IntroductionLudwig Wittgenstein, the Austrian philosopher, onceremarked that “a serious and good philosophical work couldbe written that would consist entirely of jokes”(Wittgenstein). If one understands the relevant philosophical point, one gets the joke. This has always seemed to meto be a wise remark, and this book is written in part toexemplify it. The book will contain a number of jokes aswell as stories, parables, puzzles, and anecdotes, all of whichin one way or another will relate to various philosophicalproblems. These stories and anecdotes will be linked bysome (minimal) exposition and will be loosely integrated bytopic. I hope they convey something of the flavor and substance of modern philosophy and dispel the feeling amongsome that philosophy is some sort of guide to life, a branchof theology or mathematics, or merely a matter of beingstoical in the face of adversity.One obvious criticism of an endeavor such as this is thatfor the philosophical points to be comprehensible, thejokes, examples, and metaphors relating to them must beplaced in a relevant context and must be made part of atightly reasoned argument. This is often true, of course,but for most of them the context and argument are at leastpartly implicit in the stories themselves. Consider, forexample, the story of monkeys randomly typing on a typewriter and King Lear resulting. Even with no context or argu-
T W O U N L I K E LY PA I R S O F M E N
3
ment, the isolated story is thought-provoking, no matterthat the “wrong” thoughts are often provoked. Similarremarks can be made about other classic stories—the soundof a tree falling in an uninhabited forest, Laplace’s deterministic image of the universe as something like a giant andinexorable clock, or Plato’s metaphor of the cave and thevague reflections of reality it allows. Often what one retainsfrom a philosophical discussion are just such stories, vividmetaphors, examples, and counterexamples. The samething holds for philosophical jokes.Finally, even without much supporting context or argument, these stories and jokes are such that any fuller discussion or theory must accommodate and account for them.They provide part of the raw material that any reasonablephilosophical theory must make sense of and thus should bepart of the intellectual gear of all curious human beings.
Wittgenstein and CarrollLet me consider a couple of unlikely pairs of men: the first,Wittgenstein and Lewis Carroll; the second, BertrandRussell and Groucho Marx. The first pair I also comparedin my previous book, Mathematics and Humor, from which thissubsection is taken. However, in this book, among muchelse, I expand a bit on the comparison, as well as on a fewother points made in Mathematics and Humor.George Pitcher in “Wittgenstein, Nonsense, and LewisCarroll” has written of some very striking similaritiesbetween the philosophical writings of Wittgenstein and thework of Carroll (Charles Lutwidge Dodson). Both menwere concerned with nonsense, logical confusion, and language puzzles—although, as Pitcher notes, Wittgenstein wastortured by these things, whereas Carroll was, or at leastappeared to be, delighted by them. (The relation betweenthe two men is similar in this latter respect to that betweenSoren Kierkegaard and Woody Allen: same concerns, different approaches.) Pitcher cites many passages in Alice’sAdventures in Wonderland and Through the Looking Glass as illustrating the type of joke Wittgenstein probably had in mindwhen he made the comment on philosophical jokes mentioned earlier.The following excerpts are representative of the manyin Lewis Carroll that concern topics that Wittgenstein alsoconsidered in his writings:
T W O U N L I K E LY PA I R S O F M E N
5
1. She [Alice] ate a little bit, and said anxiously to herself,“Which way? Which way?” holding her hand on the top ofher head to feel which way it was growing, and she was quitesurprised to find that she remained the same size. (Alice inWonderland)2. “That is not said right,” said the Caterpillar. “Not quiteright, I’m afraid,” said Alice timidly; “some of the wordshave got altered.”“It is wrong from beginning to end,” said theCaterpillar decidedly, and there was silence for some minutes. (Alice in Wonderland)3. “Then you should say what you mean,” the March Harewent on.“I do,” Alice hastily replied; “at least—at least I meanwhat I say—that’s the same thing, you know.”“Not the same thing a bit!” said the Hatter. “Why, youmight just as well say that ‘I see what I eat’ is the same thingas ‘I eat what I see’!” (Alice in Wonderland)4. “Would you—be good enough,” Alice panted out, afterrunning a little further, “to stop a minute just to get one’sbreath again?”“I’m good enough,” the King said, “only I’m not strongenough. You see, a minute goes by so fearfully quick. Youmight as well try to stop a Bandersnatch!” (Through the LookingGlass)
6
T W O U N L I K E LY PA I R S O F M E N
5. “It’s very good jam,” said the Queen.“Well, I don’t want any to-day, at any rate.”“You couldn’t have it if you did want it,” the Queen said.“The rule is jam to-morrow and jam yesterday—but neverjam to-day.”“It must come sometimes to ‘jam to-day,”’ Alice objected.“No, it can’t,” said the Queen. “It’s jam every other day;today isn’t any other day, you know.”“I don’t understand you,” said Alice. “It’s dreadfullyconfusing.” (Through the Looking Glass)What do these examples have in common? They allbetray some confusion about the logic of certain notions.One does not lay one’s hand on top of one’s head to see ifone is growing taller or shorter (unless only one’s neck isgrowing). One cannot recite a poem incorrectly “frombeginning to end,” since then one cannot be said to be evenreciting that poem. (Wittgenstein was very concerned withcriteria for establishing identity and similarity.) In the thirdquotation the Mad Hatter is presupposing the total independence of meaning and saying—an assumption that,Wittgenstein shows, leads to much misunderstanding. Thenext passage confuses the grammar of the word “minute”with that of a word like “train”; and the last illustrates thatthe word “to-day,” despite some similarities, does notfunction as a date. Both these latter points were also discussed by Wittgenstein.
T W O U N L I K E LY PA I R S O F M E N
7
Wittgenstein explains that “when words in our ordinarylanguage have prima facie analogous grammars we areinclined to try to interpret them analogously; i.e., we try tomake the analogy hold throughout.” In this way we “misunderstand . . . the grammar of our expressions and, like thefly in the fly bottle, sometimes need to be shown our wayclear” (Wittgenstein). As I have mentioned, these linguisticmisunderstandings can be sources of delight or of torture,depending on one’s personality, mood, or intentions.Wittgenstein, for example, was tormented by the fact that aperson does not talk about having a pain in his shoe, eventhough he may have a pain in his foot and his foot is in hisshoe. Carroll, had he thought of it, probably would havewritten of shoes so full of pain that they had to be hospitalized.
Groucho Meets RussellJust as Wittgenstein and Lewis Carroll shared some of thesame preoccupations with language and nonsense, soBertrand Russell and Groucho Marx were both concernedwith the notion of self-reference. Furthermore, Russell’stheoretical skepticism contrasts with Groucho’s streetwisebrand as do Russell’s aristocratic anarchist tendencies withGroucho’s more visceral anarchist feelings. I try to illustratethese points in the following dialogue between the two.Some of the topics mentioned in the dialogue will be discussed more fully in later chapters.
Groucho Marx and Bertrand Russell: What would thegreat comedian and the famous mathematician-philosopher, both in their own ways fascinated by the enigmas ofself-reference, have said to each other had they met?Assume for the sake of absurdity that they are stuck together on the thirteenth metalevel of a building deep in theheart of Madhattan.groucho: This certainly is an arresting development. Howare your sillygisms going to get us out of this predicament, Lord Russell? (Under his breath: Speaking to a Lordup here gives me the shakes. I think I’m in for somehigher education.)
T W O U N L I K E LY PA I R S O F M E N
9
russell: There appears to be some problem with the electrical power. It has happened several times before andeach time everything turned out quite all right. If scientific induction is any guide to the future, we shan’t havelong to wait.groucho: Induction, schminduction, not to mentionhorsefeathers.russell: You have a good point there, Mr. Marx. As DavidHume showed two hundred years ago, the only warrantfor the use of the inductive principle of inference is theinductive principle itself, a clearly circular affair and notreally very reassuring.groucho: Circular affairs are never reassuring. Did I evertell you about my brother, sister-in-law, and GeorgeFenniman?russell: I don’t believe you have, though I suspect you maynot be referring to the same sort of circle.groucho: You’re right, Lordie. I was talking more about atriangle, and not a cute triangle either. An obtuse,obscene one.russell: Well, Mr. Marx, I know something about the latter as well. There was, you may recall, a considerablebrouhaha made about my appointment to a chair at theCity College of New York around 1940. They objectedto my views on sex and free love.groucho: And for that they wanted to give you the chair?russell: The authorities, bowing to intense pressure, withdrew their offer and I did not join the faculty.groucho: Well, don’t worry about it. I certainly wouldn’t
10
T W O U N L I K E LY PA I R S O F M E N
want to join any organization that would be willing tohave me as a member.russell: That’s a paradox.groucho: Yeah, Goldberg and Rubin, a pair o’ docs up inthe Bronx.russell: I meant my sets paradox.groucho: Oh, your sex pair o’ docs. Masters and Johnson,no doubt. It’s odd a great philosopher like you havingproblems like that.russell: I was alluding to the set M of all sets that do notcontain themselves as members. If M is a member ofitself, it shouldn’t be. If M isn’t a member of itself, itshould be.groucho: Things are hard all over. Enough of this sleazytalk though. (Stops and listens.) Hey, they’re tapping a message on the girders. Some sort of a code, Bertie.russell: (Giggles) Perhaps, Mr. Marx, we should term thegirder code a Godel code in honor of the eminentAustrian logician Kurt Godel.groucho: Whatever. Be the first contestant to guess thesecret code and win $100.russell: I shall try to translate it. (He listens intently to the tapping.) It says “This message is . . . This message is . . .”groucho: Hurry and unlox the Godels, Bertie boy, and stst-stop with the st-st-stuttering. The whole elevator shaftis beginning to shake. Get me out of this ridiculous column.russell: The tapping is causing the girders to resonate.“This message is . . .
T W O U N L I K E LY PA I R S O F M E N
11
A LOUD EXPLOSION.THE ELEVATOR OSCILLATES SPASMODICALLYUP AND DOWN.russell: “. . . is false. This message is false.” The statementas well as this elevator is ungrounded. If the message istrue, then by what it says it must be false. On the otherhand if it’s false, then what it says must be true. I’mafraid that the message has violated the logic barrier.groucho: Don’t be afraid of that. I’ve been doing it all mylife. It makes for some ups and downs and vice versa, butas my brother Harpo never tired of not saying: Why aduck?
This page intentionally left blank
chapter two
LOGIC
Either—OrThere are no more basic principles of logic than the law ofnoncontradiction and the law of the excluded middle, andhence there is no better place to start the study of logic thanwith them. The law of noncontradiction states: “It is not thecase that A and not A”—or, as Aristotle phrases it: “The sameattribute cannot at the same time belong and not belong tothe same subject and in the same respect.” The law of theexcluded middle states: “Either A or not A”—or, to state aspecific instance of the law: “Either Wittgenstein was a redhead or he was not.” (Symbolically, using ⬃ for “not,”  for“and,” for “or,” and parentheses ( ) to indicate that thestatement within them is to be taken as a whole, the law ofthe excluded middle can be expressed as A ⬃A and the lawof noncontradiction as ⬃(A ⬃A).)Even such basic principles as these can cause problems,however, if they’re used uncritically. Consider, for example, the law of the excluded middle. Below are three uses ofthe principle: one, unexceptionable and vaguely humorous; the second, puzzling and distinctly misleading; and thethird, straightforward except to a minority.The first is a story due to Leo Rosten (1968) that tellsof a famous rabbi-logician who was so wise that he couldanalyze any situation no matter how complex. His studentswondered, though, if his reasoning power could withstanda bout of drinking—so these respectful yet curious students

LOGIC
15
induced him during a feast to drink enough wine to makehim quite tipsy. When he fell asleep, they carried him to thecemetery and laid him on the ground behind a tombstone.They then hid themselves and awaited his analysis of the situation.When he awoke they were most impressed by hisTalmudic use of the law of the excluded middle: “Either I’malive or I’m not. If I’m living, then what am I doing here?And if I’m dead, then why do I want to go to the bathroom?”The second instance deals with future events. If it’s truenow that I shall do a certain thing next Tuesday, let’s say falloff a horse, then no matter how I resist doing so, no matterwhat precautions I take, when Tuesday comes, I shall fall offa horse. On the other hand, if it’s false now that nextTuesday I shall fall off a horse, then no matter what effortsI make to do so, no matter how recklessly I ride, I shall notfall off a horse that day. Yet that the prediction is either trueor false is a necessary truth—the law of the excluded middle.It seems to follow that what shall happen next Tuesday isalready fixed, that in fact not just one event next Tuesdaybut the entire future is somehow decided, logically preordained.The problem with the above is not the law of theexcluded middle, but the meaning, or rather meaninglessness, of statements of the form “It is true now that somespecified event will happen.”Interestingly, a small minority of mathematicians denythat the law of the excluded middle is a law of logic. Theyobject to statements such as “Either there is a string of eight
16
LOGIC
consecutive 5s somewhere in the decimal expansion of π orthere is not.” Since there is lacking both a constructiveproof of the existence of this string of 5s and a constructiveproof of its nonexistence, the intuitionists and constructivists do not count the above third and most common useof the law of the excluded middle as being valid. For them,truth is a matter of constructive provability.For quite different reasons, some quantum physicistsalso reject the applicability of the law of the excluded middle in some contexts. In fact ever since J. Lukasiewicz, aninfluential Polish logician of the 1920s, initiated the formalstudy of three-valued logics—true, false, undetermined(indeterminate, intermediate)—it has been an object ofpersistent, though limited, interest. In more benightedtimes, classical logicians who accepted the law of the excluded middle sometimes mocked those who did not with thefollowing: “Did you hear the one about the Polish logician?He thought there were three truth values.”The moral of these stories is simply that even such abasic principle of logic can be misapplied, can be controversial. Logic is the most important theoretical tool we possess but, as with all tools, one must know how and when touse it. We want to avoid the sad fate of that proverbial tribeof Indians who, being experts on the theoretical propertiesof arrows (vectors), simultaneously fired arrows northwardand westward whenever they spotted a bear to the northwest,or two arrows northward and one eastward when they spotted a bear north-northeast of them.
LOGIC
17
“If I had a horse, I’d horsewhip you!”—Groucho Marx
Conditional statements can be tricky, even straightforwardones like the following.*: “If George is hungry, then Martha is hungry.” It’sclear, I hope, that if * is true and George is hungry, thenMartha is also hungry. It’s equally clear that if George ishungry and Martha is not, then * is false. What if Martha ishungry and it’s unknown whether or not George is? Inalmost all mathematical (and many logical) contexts, theconvention is that in this case * is true. What if George isnot hungry and it’s unknown whether or not Martha is?Again, the convention most useful in mathematics and logicis that * is true.To summarize: In mathematical, logical, and manyeveryday contexts any sentence having the form “If P, thenQ” or “P implies Q ,” or, symbolically, “P → Q ,” is (1) truewhenever Q is true whether P is true or not, (2) true whenever P is false whether Q is true or not, and (3) false onlywhen P is true and Q is false.
The following two stories are relevant and illustrative:Bertrand Russell was discussing conditional statementsof the above type and maintaining that a false statement
18
LOGIC
implies anything and everything. A skeptical philosopherquestioned him, “You mean that if 2 + 2 = 5, then you arethe Pope?” Russell answered affirmatively and supplied thefollowing amusing “proof”:“If we’re assuming 2 + 2 = 5, then certainly you’ll agreethat subtracting 2 from each side of the equation gives us 2= 3. Transposing, we have 3 = 2, and subtracting 1 from eachside of the equation gives us 2 = 1. Thus since the Pope andI are two people and 2 = 1, then the Pope and I are one.Hence I’m the Pope.”
logician: So you see, class, anything follows from a falsestatement.student: I’m afraid I’m lost.logician: It’s really quite simple. Are you sure you don’tunderstand?student: All I’m sure of is that if I understood that stuff,then I’d be a monkey’s uncle.logician: You’re right there. (Laughs)student: Why are you laughing?logician: You wouldn’t understand.student: Anyway, doc, if you’re interested, we’re having aparty tonight.logician: And if I’m not interested?student: What?logician: Thanks anyway, but I’m busy.
LOGIC
19
Nonmathematical contexts in which the foregoinganalysis of if-then statements does not hold are not hard tofind. Two statements that are false despite the falsity of theirif-clauses are:(1) If one were to place that nail in that glass of water,it would dissolve.(2) If Harpo Marx had spoken in any of the Marxbrothers’ movies, World War II would have beenaverted.The truth of such so-called subjunctive and counterfactual conditional statements does not, as in the case ofmathematical conditional statements “If P, then Q,” dependonly on the truth or falsity of P and Q. Rather, it dependson the lawlike relationship that may or may not existbetween P and Q.Still, there are many uses of the mathematical conditional outside of logic and mathematics. If someone says “Ifit’s raining, I’m going to punch you, and if it’s not raining,I’m going to punch you,” you can be sure that that personis using the mathematical conditional and that he intends topunch you.
Yo u B e t Yo u r L i f eImagine a very rich superscientist who claims to have thepower to predict with great accuracy which of two alternatives a person will choose. Imagine further that this scientist, let’s call him Dr. Who, sets up a booth at a big World’sFair somewhere in the Midwest to demonstrate his abilities.Dr. Who explains that he tests people by using two boxes:box A is transparent and contains $1,000, whereas box B isopaque and contains either nothing or $1,000,000. Dr.Who tells each person that he or she can choose to take thecontents of box B alone, or the contents of both box A andbox B. However—and this is important—if, before the person chooses, Dr. Who believes that he or she will take thecontents of both boxes, he leaves box B empty. On the otherhand, if, before the person chooses, Dr. Who believes thathe or she will take only the contents of box B, he places$1,000,000 in box B. Witnesses can verify afterwardwhether or not the $1,000,000 was placed in box B.George and Martha are at the World’s Fair and see forthemselves that when a person chooses to take the contentsof both boxes, 95 percent of the time box B is empty and theperson gets to keep only the $1,000 in box A. They alsonote that when a person chooses to take the contents of boxB alone, 95 percent of the time it contains $1,000,000,making the person an instant millionaire.Now it’s Martha’s turn. Dr. Who examines her careful-
LOGIC
21
ly, prepares the boxes, places them in front of her, and goeson to George. Impressed by these demonstrations, Marthachooses the contents of box B alone, hoping that Dr. Whoaccurately assessed her state of mind.Next it’s George’s turn. Dr. Who examines him carefully, prepares the boxes, places them in front of him, andgoes on to the next person. George reasons that since Dr.Who has already gone, and since the $1,000,000 either hasor hasn’t been placed in box B already, he may as wellchoose the contents of both boxes, thereby insuring himselfat least $1,000 and possibly $1,001,000.Finally it’s your turn. Dr. Who has already examinedyou. What choice will you make? (Selling your right to makethe choice to someone else for $500,000 is cheating.) Thereaction to this paradox, due to the physicist WilliamNewcombe and made well-known by the philosopherRobert Nozick, is intimately connected with one’s attitudetoward free will, determinism, and money.
Another, better-known story of choice and “higherpowers” is due to Blaise Pascal, whose argument for becoming a Christian takes the form of a wager. If, according toPascal (1966), one elects to believe in Christian doctrine,then if this doctrine is false, one loses nothing—whereas ifit’s true, one gains everlasting life in heaven. On the otherhand, if one elects not to believe in Christian doctrine,then if this doctrine is false, one loses nothing—whereas if
22
LOGIC
it’s true, one suffers unrelenting punishment in hell. Onlyif one already believes in Christian doctrine, as Pascal did,does this argument have any persuasive power. The argument, of course, has nothing to do with Christianity, andcould be used by any other religion (or cult) to rationalizeother already-existing beliefs.
Everyone would agree that “A is false,” “B is false,” “C isfalse,” and “One of A, B, or C is true” are, taken together,an inconsistent set of statements. Yet consider a lottery having 1,000,000 entrants, including you: you don’t believeticket 1 will win, nor ticket 2, nor ticket 3, . . . nor ticket1,000,000; still, you do believe that some ticket will win.A similar tale can be told about your attitude towardwhat you read in the newspaper. Unless you have first-handknowledge of a story, you tend to believe each individualitem you read in the paper; still, you also believe that some(many) of the items are false. An understanding of thisseeming inconsistency is what prompts celebrities to suesensationalist tabloids.
Get your tickets for the million-dollar lottery righthere. Ten cents apiece, three for a quarter, five for a dollar.Step right up and win a million dollars—a dollar a year fora million years.
SillygismsPeople underestimate the extent to which play enters intoany serious intellectual endeavor. Doing something for thewhat-if fun of it frees one from the shackles of goal-directed plodding and sometimes leads to otherwise unlikely newinsights. (And if it doesn’t, so what?) This tradition ofintellectual play is very old. Even Plato was not above constructing silly “arguments” for his protagonists. A wellknown example in the dialogue Euthydemus is the exchangebetween Dionysodorus and Ctessipus:dionysodorus: You say you have a dog?ctessipus: Yes, a villain of one.dionysodorus: And he has puppies.ctessipus: Yes, and they are very like himself.dionysodorus: And the dog is the father of them.ctessipus: Yes, I certainly saw him and the mother of thepuppies come together.dionysodorus: And