le: I can’t stomach the sight of him. He’s plastic,phony, and insensitive. Just hearing his voice makes myflesh crawl.
george: Sure is hot today, about 80° I’d say.waldo: Yeah, got down to 40° last night. It’s twice as hotnow.
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On the subject of hot summer days, there was a midwestern state legislator who opposed the adoption of daylight savings time because the increased daylight would morequickly fade curtains and fabrics.
That balance and moderation, a sense of perspective,and the harmonious integration of disparate elements arevalued is evidenced by the laughter occasioned by theirabsence. Exaggeration and distortion, in particular, oftenlead to humor. The following is an old story due to GeorgeBernard Shaw. It seems more appropriate with Groucho,however:groucho (to woman seated next to him at an elegant dinner party):Would you sleep with me for ten million dollars?woman (giggling): Oh, Groucho, of course I would.groucho: How about doing it for fifteen dollars?woman (indignant): Why, what do you think I am?groucho: That’s already been established. Now we’re justhaggling about the price.
Politics is the art of balance and compromise. Considerthe fact that the two most important ideals—liberty andequality—are, in their purest form, incompatible: completeliberty results in inequality, while enforced equality resultsin loss of liberty. Liberty and equality must thus be bal-
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anced, refined, made conditional. The differences betweenthe political right and the political left can be simplisticallydescribed as a difference between prepositions, betweenfreedom to (speak, move about, buy and sell, etc.) and freedom from (hunger, joblessness, etc.). The following pair ofstories point up a couple of these differences:George and Waldo come upon a couple of apples, onelarge, the other small. George, being quicker, grabs thelarger apple and gobbles it up, while Waldo just manages toget hold of the smaller one.waldo: “That’s not polite, George. If I’d reached herefirst, I would have left the larger apple for you.”george: “Then what are you complaining about? You gotwhat you wanted.”George, Martha, Waldo, and Myrtle come upon a loafof bread. They decide to divide it evenly, and use the following procedure: George cuts off what he considers to bea quarter of the loaf. If Martha thinks the piece is a quarterof the loaf or less, she doesn’t touch it; if she thinks it’s bigger than a quarter of the loaf, she cuts off a sliver to make itexactly a quarter. Waldo then either leaves the piece alone ortrims it further if he thinks it’s still bigger than a quarter ofthe loaf. Finally, Myrtle has the same option: trim it if it’stoo big, or leave it alone if it’s not. The last person to touchthe slice keeps it. This finished, there are three peopleremaining who must divide the rest of the cake evenly. Thesame procedure is followed: the first person cuts off what he
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considers to be a third of the remaining loaf, and so on. Inthis way everyone is satisfied that he or she has received aquarter of the loaf.
The following story is due to Raymond Smullyan(1980):george: Mmm, chocolate cake. I’m going to eat all of it.martha: I want dessert, too. We should split it 50-50.george: I want all of it.martha: No, we have to split it evenly. Let’s ask Myrtle todecide. She’s always fair.myrtle: You should compromise: three-fourths forGeorge, and one-fourth for you, Martha.Mort Sahl remarked that in the 1980 election manypeople did not vote for Ronald Reagan so much as theyvoted against Jimmy Carter. He continued, “If Reagan hadbeen unopposed, he would’ve lost.”
People have individual preferences out of which, sincethese preferences often differ, group preferences must befashioned. This is obviously a difficult practical problem. Itis a more difficult theoretical problem, in a certain senseeven an impossible one.Consider first a voting paradox due to the eighteenthcentury French philosopher Condorcet. Three candidates—
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George, Martha, and Waldo—are running for governor ofWisconowa. A third of the electorate prefers George toMartha to Waldo; another third of the electorate prefersMartha to Waldo to George; and the remaining thirdprefers Waldo to George to Martha. There is nothing especially unusual about this unless we consider what happens intwo-person races given the above preferences. George canboast that two-thirds of the electorate prefers him toMartha. Waldo responds that two-thirds of the electorateprefers him to George. Finally, Martha counters by notingthat two-thirds of the electorate prefers her to Waldo.If the societal preferences in this example are determined by majority vote, we have an irrational societalordering of preferences—that is, “society” prefers Georgeover Martha, Martha over Waldo, and Waldo over George.Thus even if the preferences of all the individual voters aretransitive (transitivity holds if, whenever a voter prefers x toy and y to z, he or she prefers x to z), the societal preferencesdetermined by majority vote are not necessarily transitive(rational).A general theorem can be proved showing that all “reasonable” voting systems (or equivalently, economic marketsystems) are subject to such irrationalities; but before discussing this, it should be pointed out that individuals arenot immune to Condorcet’s paradox.The mathematician Paul Halmos has proposed the following variation of the paradox that applies to individuals:Imagine a woman trying to decide which of three cars tobuy: Car G, Car M, or Car W. She, being a methodical sort,
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had three criteria (of equal weight) for making this decision: looks, affordability, and performance. Car G lookedbetter than Car M, which looked better than Car W. On theother hand, Car M was more affordable than Car W, whichin turn was more affordable than Car G. Finally, Car W performed better than Car G, which performed better thanCar M. Since the woman placed equal weight on each ofthese criteria, she was in a quandary. She clearly preferredCar G to Car M (G outscored M on two criteria). She alsopreferred Car M to Car W (for the same reason). Yet shepreferred Car W to Car G.Though the same problem of nontransitivity holds forindividuals, it seems somehow more tractable. In the caseabove you just have to induce the woman to declare one ofthe criteria more important than the others. This is easierthan convincing one-third of an electorate to change itsmind.The economist Kenneth J. Arrow proved (1951) aninteresting generalization of Condorcet’s paradox. Heshowed that there is no way to derive societal or group preferences from individual preferences that can be guaranteedto satisfy the following four minimal conditions: The societal preferences (1) must be transitive (if society prefers x toy and y to z, then it must prefer x to z); (2) must satisfy thePareto principle (if alternative x is preferred to alternative yby everyone in the society, then society must prefer x to y);(3) must satisfy the independence of irrelevant alternatives(the societal preference depends only on the orderings ofthe individuals with respect to alternatives in that environ-
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ment); and (4) must not be susceptible to dictatorship(there is no individual whose preferences automaticallydetermine all of society’s preferences).
communist: “Man’s inhumanity to man,” that is what capitalism is all about.george: Yes, in communism it is the other way around.Bumper sticker: GOD SAID IT, I BELIEVE IT, ANDTHAT SETTLE’S IT. (The apostrophe is most informative.)
There was once a scorpion who wanted to cross a river.Spotting a turtle on a rock, the scorpion asked if he wouldtake him across the river. In return he would show the turtle where he could find some very succulent vegetation.The turtle responded, “How can I be sure you won’tsting my neck?”“Don’t be silly,” the scorpion replied. “If I did that,we’d both drown.”The turtle was convinced, and they began swimmingtoward the vegetation the scorpion had told him about.When they had nearly reached the far side of the river, however, the scorpion stung him in the neck after all.Struggling to make it to the river bank, the turtle gasped,
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“Why, why did you do this to me?”Hopping off the dying turtle’s back, the scorpionexplained, “I thought you might dive under the water todrown me.”
The Prisoners’ Dilemma is another old puzzle withsocietal implications. Imagine two prisoners Waldo andGeorge against whom there is little real evidence. Althoughthese prisoners have committed a crime, they can expect little punishment (say one year in prison) if they both remainsilent. If George confesses to their crime, however, andWaldo remains silent, George will be released while Waldocan expect a five-year sentence. Conversely, if Waldo talksand George remains silent, Waldo will be released whileGeorge can expect a five-year sentence. Thus each man hasa choice of confessing or not. If they both confess, each getsa three-year term; if they’re both silent, each gets a oneyear term; if A confesses and B is silent, A gets off and B getsfive years.The punchline, so to speak, is that the optimum courseof action, remaining silent, is in general not the course thatGeorge and Waldo are likely to follow: they’re both likely toconfess so as to avoid being a patsy for the other. This situation is, of course, not limited to prisoners. Spouses in amarriage, businessmen in a competitive market, andnational governments in an arms race can all fall subject tosuch prisoners’ dilemmas. Adam Smith’s invisible hand
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ensuring that individual pursuits will necessarily ensuregroup well-being is at times quite arthritic.
Results like Arrow’s paradox and the Prisoners’Dilemma, the well-known problems of quantification andmeasurement in the social sciences (6.28 on the pleasurescale, 2.89 on the pain scale, let’s do it), and the inherentriskiness of all explanation, especially intentional explanation, should, but probably won’t, make for cautious skepticism in predicting ourselves, society, and the future. LewisCarroll’s Cheshire Cat reminds us of the single mostimportant, yet unpredictable, determinant of that future:“Would you tell me please, which way I ought to go fromhere,” asked Alice.“That depends a good deal on where you want to getto,” said the Cat.
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When I was young, I forgot to laugh. Later when I opened myeyes and saw reality I began to laugh and haven’t stoppedsince.—Soren Kierkegaard
Wittgenstein once remarked that he looked forward to theday when philosophy was no longer a subject in its own rightbut rather infused all other subjects. Philosophy is (orshould be), in this view, an adverb: one does linguisticsphilosophically, one studies science philosophically, oneinvestigates political issues philosophically. Humor or playhas something of the same character. It’s awkward forhumor itself to be the focus of an activity. The announcement “We will now tell jokes and be humorous” sounds distinctly totalitarian. Humor too is adverbial and qualifiesone’s approach to other activities: one answers questionshumorously, analyzes a situation humorously, writes orspeaks humorously.Of course, “quickly,” “painfully,” and “odoriferously”are also adverbs, but I hope I’ve managed to indicate that“philosophically” and “humorously,” at least in their bestmanifestations, share more than adverbial status. Bothrequire a free intelligence in a relatively open society, andboth evince a keen concern for language and its (mis)interpretation, as well as a skeptical tendency toward debunking.The incongruity that lies at the heart of most jokes is analogous to the conundrum that lies at the heart of mostphilosophical problems. Likewise, the aggressive tone present in many jokes and the social control that the jokes tendto foster are analogous to the argumentative nature of manyphilosophical papers and the intellectual dominance that
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the papers are meant to establish. It should be noted,though, that this aggressive tone and argumentative natureare clearly circumscribed and presuppose an independentintelligence in others.Finally, both humor and philosophy are quintessentially human, requiring as they do the characteristically humanability to transcend one’s self and one’s situation. The discrepancy between our hopes or pretensions and reality is,try though we sometimes do, impossible not to see. Tworesponses to the starkness of this discrepancy are throughphilosophy and humor. I think, therefore I laugh.
Our heroes—Ludwig Wittgenstein, Bertrand Russell,Lewis Carroll, and Groucho Marx—are discussing the question “What is philosophy?” Let us join them for the end oftheir discussion and ours.wittgenstein: I repeat, the question is not well posed.There are a whole family of uses for the term “philosophy.” Still, my primary aim has been to clarify, to showhow to pass from a piece of disguised nonsense to something that is obvious nonsense. Misunderstandings, asI’ve always insisted, must be cured if we are to be free ofthem.groucho: Is that anything like curing hams?russell: Asking the question indicates, I think, that youknow quite well what Mr. Wittgenstein is talking about.groucho: Easy on the self-reference shtick, Bertie. We’re
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not in the elevator anymore. I understand Ludwig’spoint, but most of this other philosophical stuff you guysdream up seems so nit-picking and technical. Whatabout the big questions: the meaning of life, the death ofGod, the residuals on my television reruns?russell: Better some real progress on the meaning of confirmation and probability, on the nature of logic andscientific law, on reductionism, artificial intelligence,and intentional explanation, for example, than a lot ofempty blather on the so-called big questions. The bigquestions, at least the ones that make sense, will always bethere. They’re sometimes clarified by the answers to thesmaller questions, sometimes not. When they’re not,though, listening to woolly-headed pontificatorsexpound on them doesn’t help either. A courageousacknowledgment of ignorance is much preferable.groucho: Calm down, Bertie. Without those woollyheaded pontificators we might both be unemployed or,worse yet, lawyers. Maybe what I’m trying to get at—or becured of, as Ludwig might say—is what difference does itall make? What difference will the answers to thesesmaller questions, or anything else for that matter, makein fifty thousand years? Even my reruns won’t be onthen, and there’ll be no more copies of PrincipiaMathematica, Ludwig’s Philosophical Investigations, or even Alicein Wonderland.lewis carroll (overcoming his shyness, stammers):Maybe n-n-nothing we do now will make a difference infifty thousand years, but if that is so, then it would seem
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that nothing that will be the case in fifty thousand yearsmakes a difference now, either. In particular, it doesn’tmake a difference now that in fifty thousand years whatwe do now won’t make a difference.groucho: You can bet your walrus that I’m not going totangle with you about time. The time has passed, in fact,to talk of many things. Enough. If you fellas will excuseme, I’m going to be leaving in a minute. If you persistwith this talk, though, I might leave in a huff, or maybeeven in a minute and a huff. In any case, since youhaven’t asked, I’m going over to make love with our oldfriend Martha. Fortunately her husband George is outlooking for grue emeralds with Waldo.Groucho slouches off, leaving the three philosopherswondering.
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INDEX
Alice in Wonderland (Carroll), 5Another Way of Laughter (Farzad),91–93Arrow’s paradox, 157–158Artificial intelligence, 109,132–138Astronomy, 48, 56–57Augustine, Saint, 71Averages, 150. See alsoCompromiseBaseball, 59–61, 84–85, 139,144Bateson, Gregory, 33Bavelas, A., 127Behavioral cues for joketelling, 33Behaviorism, 96–97Belief vs. knowledge, 80–82Bell, J. S., 120Bell’s inequality, 114–120Benchley, Robert, 36Bentham, Jeremy, 150–151Bergson, Henri, 142Berry paradox, 106–108Biology, 98, 127Birthday coincidence, 86–87Cantor, Greg, 125Carlin, George, 94Carroll, Lewis, 4–7, 41–44,52–53, 163–165
Causal explanations, 140–145Causality, 67–75, 114–120Chaitin, Gregory, 103,108–109Complexity, 103–108,132–138Compromise, 150–160Computer science, 140–141;artificial intelligence,109, 132–138; and complexity, 103–104, 108,132–138; and determinism, 111; hardware-software distinction, 137;Turing test, 133, 136Condercet, Marquis de, 155Condercet’s paradox, 156–158Conditional statements,17–19, 31, 81–82Dating, 51, 68–69Dawkins, Richard, 98Decision paradoxes, 20–21,111–112Dennett, Daniel, 140Descartes, René, 137Determinism, 15, 20–21,110–113Disraeli, Benjamin, 83Dog stories, 23, 24, 126Double-blind situations, 33Dretske, Fred, 81Duhem, Pierre, 89
INDEX
Einstein, Albert, 55, 113, 118Epimenides, 30, 38EPR experiment, 118–119, 121Euclid, 49Euthydemus (Plato), 23Eves, Howard, 128, 146Farzad, Masud, 91–93First-cause arguments, 71,73–74Frege, Gottlob, 48–49Freudianism, 100, 140Fry, W. F., 33Gardner, Martin, 87Gettier, Edmund L., 80God: gambling habits of, 113;proofs of existence of, 31,71–72Gödel’s theorem, 44–45,108–110Goodman, Nelson, 67, 76Goodman’s projectibilityparadox, 76–78Grice, H. P., 143Group preferences, paradoxesof, 155–158Halmos, Paul, 156Hegel, G. W. F., 57Hempel, Carl, 78–79, 98Hempel’s “raven” paradox,78–79
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Hidden variables, 118–119Historicism, 100Hume, David, 9, 52, 64–67Inductive reasoning, 9, 64–67Intensional explanations, 130,137–149Kant, Immanuel, 52, 56, 67,130Knowledge vs. justified truebelief, 80–82Kolmogorov, A. N., 103Kripke, Saul, 38–39, 74Language: conventions in,91–94; meaning, reference, names, anddescription, 48–51; nonsense and logical confusion, 4–7; object language distinguished frommetalanguage, 40–47;Russell’s theory of types,37–38, 40; and syllogisms, 23–30; use-mention distinction, 46–47Law of the excluded middle,14–16Law of noncontradiction, 14Leibniz, Gottfried, 52Leper boxing, 28Liar paradox, 30, 38
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Logic, 14–62; analytic vs. synthetic truth, 52–57; conditional statements,17–19, 31, 81–82; Gödel’stheorem, 44–45,108–110; inductive principle, 9, 64–67; law ofthe excluded middle,14–16; law of noncontradiction, 14; meaning,reference, names, anddescription, 48–51; miscellaneous jokes, 58–62;object language distinguished from metalanguage, 40–47; and selfreference, 30–34; syllogisms, 23–30; three-valued logics, 16Lotteries, 22Lukasiewicz, J., 16MacKay, D. M., 112Marx, Groucho, 8–11, 36, 41,153, 163–165Marx, Hy, 130Marxism, 100Mathematics, 54–56,102–109. See also StatisticsMedicine, 69, 126Mermin, David, 116, 119, 121Metaphysics, 110Mind-body problem, 137
Minsky, Marvin, 135Miracles, 73Morgenbesser, Sidney, 37Moser, David, 37Newcombe, William, 21Newcombe’s paradox, 20–21News media, 22, 85–86, 146Nonsense language, 4–7Nozick, Robert, 21, 73–74,