“My father,” for example, when uttered by merefers to my father, whereas when uttered by Waldo, it refersto Waldo’s father (surprise). Similarly, words like “you” or“I,” “yesterday” or “tomorrow,” “here” or “there” refer todifferent entities depending on when, where, and by whomthey’re uttered.
A man and an acquaintance of his are walking down astreet one afternoon. The man spots his wife and his mistress talking in a café and amusedly remarks, “Imagine amistress spending the morning with her lover and then having a friendly chat with his wife that afternoon.” Theacquaintance, a pale, shocked look on his face, responds“How did you find out?”
Two clergymen were discussing the present sad state ofsexual morality. “I didn’t sleep with my wife before we weremarried,” one clergyman stated self-righteously. “Didyou?”“I’m not sure,” said the other. “What was her maidenname?”
Analytic vs. Synthetic,Boole vs. Boyle, andMathematics vs. CookeryAn analytic truth is one that is true in virtue of the meanings of the words it contains, and a synthetic truth is onethat is true in virtue of the way the world is. (“If George issmelly and bald, then he’s bald,” vs. “If George is smelly,then he’s bald.” “Bachelors are unmarried men,” vs.“Bachelors are lascivious men.” “UFOs are flying objectsthat have not been identified,” vs. “UFOs contain littlegreen men.”) This distinction is a sprucing up of ImmanuelKant’s original one, which in turn derives from similar distinctions due to David Hume and Gottfried Leibniz. Somephilosophers, in particular the American W. V. O. Quine,have argued that the distinction is not hard and clear, butrather one of degree or convenience. It is still, even if notabsolute and immutable, a useful distinction.When Molière’s pompous doctor announces that thesleeping potion is effective because of its dormitive virtue,he is making an empty, analytic statement, not a factual,synthetic one. The same thing can be said about the WhiteKnight in Through the Looking Glass when he describes to Alicethe song he wants to sing:“It’s long,” said the Knight, “but it’s very, verybeautiful. Everybody that hears me sing it—either itbrings tears to their eyes, or else—”
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“Or else what?” said Alice, for the Knight hadmade a sudden pause.“Or else it doesn’t, you know.”Likewise, “A well-told joke will not be funny unless it’swell-told,” despite the appearance that it’s saying somethingsubstantial, is simply an analytic truth. It is equivalent to “Ifa well-told joke is funny, it is well-told.”Conversely, synthetic truths are sometimes mistakenfor statements that are analytically true or analytically false.Examples are “The second-place Chicago White Sox tookthe field wearing white sox,” or the perennial “The HolyRoman Empire was not holy, Roman, or imperial.” Someof the pronouncements on space and time in Einstein’stheory of relativity are also seen now to be synthetic truthsand not, as they appeared and still appear to many people,analytic falsehoods.Even more common are exchanges like the following,in which prejudices are preserved by making them, throughredefinition, analytically true:george: Scotsmen don’t buy jewelry.martha: But MacGregor just bought fourteen diamondnecklaces.george: MacGregor is not a true Scotsman, then.Capitalists (neurotics, Jews, Englishmen, Greeks, blacks,etc.) don’t do such and such. But so and so did do such andsuch. Well then, he’s not a real capitalist (neurotic, Jew,Englishman, Greek, black, etc.).It can be said that the difference between analytic truthsand synthetic truths is the difference between an “o” and a
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“y,” between Boole’s laws of logic and Boyle’s laws of gases.It is roughly the difference between the formal sciences(mathematics, logic, and linguistics) and the empirical sciences (physics, psychology, and cooking).
Bertrand Russell once wrote:Pure mathematics consists entirely of such asservations as that, if such and such a proposition is trueof anything, then such and such another propositionis true of that thing. It is essential not to discusswhether the first proposition is really true, and notto mention what the anything is of which it is supposed to be true. . . . If our hypothesis is aboutanything and not about some one or more particularthings, then our deductions constitute mathematics.Thus mathematics may be defined as the subject inwhich we never know what we are talking about, norwhether what we are saying is true.(Russell)Though the ubiquity of people who do not know whatthey’re talking about nor whether what they’re saying is truemay suggest that mathematical talent is widespread, thequote does give a succinct summary of the formal approachto mathematics. Certain axioms, expressed in a formal language, are laid down; precise rules of inference are formulated; and theorems are derived from the axioms by meansof the rules of inference. What anything means is (or canbe) ignored. In this respect, mathematics can be compared
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to the game of chess—the axioms to the initial positions, therules of inference to the rules governing the allowablemoves, and theorems to subsequent positions of the pieces.Mathematical truths, in particular Euclidean geometrictruths, were thought to be (using Immanuel Kant’s terms)synthetic a priori—that is, they were considered to be truebecause of the way the world is, yet independent of experience. The development of consistent non-Euclideangeometries by Bolyai, Lobachevsky, and Gauss led to therealization, implicit in Russell’s quote, that points, lines,and other primitive geometric terms and relations could betaken to be anything at all that satisfied the formal axioms containing these terms and relations, and that geometrical theorems were simply any formal statements that followed fromthe axioms by means of the rules of inference.Not until (if ever) the terms are given a particularempirical meaning do the notions of truth or falsity becomeappropriate. As the French mathematician Poincaré oncewrote, “What are we to think of the question: Is Euclideangeometry true? It has no meaning. . . . One geometry cannot be more true than another; it can only be more convenient” (Poincaré 1913). This is because mathematics chasesnot truth (a metalevel notion) but formal consequences(provability, an object-level notion), not “Is this true of theworld?” but “Does this follow from that?” Einstein phrasedit: “As far as the properties of mathematics refer to reality,they are not certain: and as far as they are certain, they donot refer to reality” (Einstein). Mathematical truths, by andlarge, are certain because they are analytic; physical truthsare not certain because they are synthetic.
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George goes to the You-Bet-Your-Life computer dating service to register his requirements (axioms). He wantssomeone who is white, not very talkative, comfortable infur, yet disdainful of city life. The computer sends him apolar bear.Immanuel Kant goes to the Lobachevsky LumberCompany to order a flat board with which to cover his desk.Feeling mischievous, he asks for a surface that satisfies the(first four) axioms of Euclidean plane geometry. The lumber company gives him a saddle-shaped piece of wood.
That synthetic scientific laws and facts cannot be determined a priori now seems a commonplace. That this wasnot always the case is illustrated by the following excerptfrom Francesco Sizi wherein he “argues” that, contrary towhat his contemporary Galileo had seen through his telescope, Jupiter could have no satellites:There are seven windows in the head, two nostrils,two ears, two eyes and a mouth; so in the heavensthere are two favorable stars, two unpropitious, twoluminaries, and Mercury alone undecided and indifferent. From which and many other similar phenomena of nature such as the seven metals, etc.,which it were tedious to enumerate, we gather that
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the number of planets is necessarily seven. . . .Moreover, the satellites are invisible to the naked eyeand therefore can have no influence on the earthand therefore would be useless and therefore do notexist.The German philosopher Hegel, just before the discovery of the asteroid Ceres, also chastised astronomers fornot paying more attention to philosophy—a science thatwould, according to Herr Hegel, have shown them thatthere could not possibly be more than seven planets.
MiscellanyI’d like to close this chapter with a short collection of logical jokes and stories. The first “joke” consists merely ofpairs of phrases, each element of the pair sharing the samegrammar yet having a different logic (in a broad, informalsense of “logic”):“Waldo likes to move his rooks out early,” vs. “TheMATE-IAC II computer likes to move its rooks out early.”“Going on to infinity,” vs. “going on to Paris.”“Honesty compels me,” vs. “The IRS compels me.”“The present Czar of Russia is obese,” vs. “The presentpresident of the United States is obese.”“Being a baseball player,” vs. “being a baseball.”“An alleged murderer,” vs. “a vicious murderer.”“Have you stopped beating your husband?” vs. “Haveyou voted for Megalomeeti yet?”“If only Pat had a different job,” vs. “If only Pat had adifferent sex.”“Before the world began,” vs. “before the Phillies gamebegan.”“Studying for a physics test,” vs. “studying for a urinetest.”Modern analytic philosophy has sometimes been calledlinguistic therapy, and philosophers like Wittgenstein, Ryle,
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and Austin have devoted much effort and analysis to curingsome of the “linguistic diseases” lurking all over, in particular in phrases such as the above.
t.v. sportscaster: Folks, we’re running out of time so I’llhave to hurry with the baseball scores. 4 to 2, 6 to 3, 8 to5, and in a real cliff-hanger, 2 to 1.
t.v. football commentator: These teams really came toplay today.
peasant: Is kebab with an “a” or an “o”?sufi master: With meat.
10-year-old: Pete and Repeat were walking down thestreet. Pete fell down. Who was left?7-year-old: Repeat.10-year-old: Pete and Repeat were walking down thestreet. Pete fell down. Who was left?
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martha: George, in this game cheating is allowed.
A wife laughs at her distraught husband who has aloaded revolver at his temple. “Don’t laugh,” he tells her.“You’re next.”
Title of Book: 20 Ways to Regain Your Virginity
There was once a very brilliant horse who masteredarithmetic, algebra, plane geometry, and trigonometry.When presented with problems in analytic geometry, however, the horse would kick, neigh, and struggle desperately.One just couldn’t put Descartes before the horse.
What’s a question that contains the word “cantaloupe”for no apparent reason?
costello: Who’s on first?abbot: Yeah. Who is on first, Johnson’s on second.costello: Who’s on first?
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abbot: Right, Who is. Johnson’s on second and Walters isup to bat.costello: But who is on first?
waiter: Would you like white wine or red wine with yourdinner?george: It doesn’t matter. I’m color blind.
Speaking of liquids, the following is an old conundrum: A tablespoon of water is removed from an 8-oz. glassof water, placed in an 8-oz. glass of wine, and the resultingmixture stirred. A tablespoon of the mixture is thenremoved, placed in the water glass, and stirred. Is theremore wine in the water or more water in the wine?
If you’re sick of such logical niceties, the last story mayplease you. Bertrand Russell, in satirizing the empty precision of some philosophers, told of a man who comes to afork in the road. He asks a philosopher who happens to beloitering there, “Which way to the town of Dresher?” Thephilosopher responds, “Which one of these two roadshere?”“Yes, yes.”
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“It’s the town of Dresher you’re looking for?”“Yes, yes.”“You want to follow one of these two roads here to thetown of Dresher?”Growing impatient, the man repeats, “Yes, which roadleads to Dresher?”“I don’t know.”The philosopher was not a very good one. He shouldhave asked the man if he was sure that one and only one ofthe two roads really did lead to Dresher, before telling himthat he didn’t know which. A more significant and disturbing revelation of ignorance begins the next chapter.
chapter three
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Induction, Causality,and Hume’s Eggswoman: Doctor, doctor. You must help me. My husbandthinks he’s a chicken.doctor: That’s terrible. How long has he thought this way?woman: As long as I can remember.doctor: Then why didn’t you see me sooner?woman: I would have, but we needed the eggs.If the doctor were to answer that he too needed theeggs, we would have something analogous to the problem ofinduction:woman: Professor, professor. You must help me. My husband uses an inductive argument to justify the use ofinductive arguments.professor hume: That’s terrible. How long has he actedthis way?woman: As long as I can remember.hume: Then why didn’t you see me sooner?woman: I would have, but we needed (the conclusions of)the inductive arguments.hume: I’m afraid I need them too.Let me summarize what is usually referred to as Hume’straditional problem of induction or, as Russell once calledit, “the scandal of philosophy.’’ We, every day of our lives,confidently use inductive arguments (arguments whose
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conclusions go beyond, contain more information than,the premises). Why are we so confident that these arguments usually yield true conclusions from true premises?There certainly is no deductive argument that since the sunhas risen regularly in the past, it will probably rise tomorrow, or that since stones that have been dropped have alwaysfallen in the past, they will probably fall when dropped inthe future. It seems that the only argument for the continuation of these regularities is an inductive one: since theseregularities have obtained in the past, they will probablycontinue into the future. But to try to justify the use ofinductive arguments by an inductive argument is clearly circular and begs the question. To put the matter a littlecrudely, the answer to the question “Why will the future belike the past in certain relevant respects?’’ is nothing moresatisfying than “It will be because past futures have been likepast pasts in certain relevant respects.’’ This is helpful onlyif the future will be like the past—which is the point at issue.There have been many attempts to clean up “the scandal of philosophy.’’ One way out is just to accept a nonempirical principle of the uniformity (over time) of nature.The problem with this “solution’’ is that it also begs thequestion; it is equivalent to what is to be established. It hasthe advantage, as Russell said in a different context, of“theft over honest toil.’’ Another attempted way out is tonote that some inductive arguments are of higher orderthan others, and to try to make use of this hierarchy (ofinductive arguments, meta-inductive arguments, metametainductive arguments, and so on) to somehow justify
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induction. This does not quite work—or rather it works toowell, and “justifies’’ a lot of weird practices.Charles Saunders Peirce and Hans Reichenbach haveadvanced a different pragmatic justification of induction,which amounts roughly to this: “Maybe induction does notwork, but if anything does, induction will. Maybe there isno order in the universe, but if there is any (on any level),induction will eventually find it (on the next-highestlevel).’’ There is some merit to this approach, but there isalso a problem with the word “eventually.’’ Finally, therehas been an attempt to dissolve the problem by showing thatfollowing our commonsense inductive rules is what is meantby rationality, and therefore no further justification iscalled for.I wrote in the introduction that philosophy is not aguide to life, a branch of theology or mathematics, ormerely a matter of being stoical in the face of adversity.Whatever the resolution of Hume’s traditional problem ofinduction, it beautifully exemplifies the nature of philosophical inquiry. Once Hume enunciated his insight intoinduction (and causality, which we will treat later), itbecame impossible for anyone to think about induction inthe same way again. No new facts or theorems or prescriptions were offered, just a sometimes scary realization thatinduction is not what it appears to be in our uncritical dailylife, where our focus is usually on the eggs we need.
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A Humerous induction:martha: On all my birthdays up to now I’ve been less thantwenty-five years old. So by induction, on all my birthdays I’ll be less than twenty-five years old.
Hume’s analysis of the notion of causality is similarlyunsettling. According to Hume, when we say “A causes B’’we mean nothing more than that A and B are constantlyconjoined, that in every instance we’ve examined, the eventA has been followed by the event B. Since it’s quite easy toimagine A not being followed by B, the connection betweenA and B cannot be a necessary or logical one. Causes andeffects are discoverable by experience and not by a priorireasoning. Many people—including, of course, Kant—believe this.Still, there are problems with this view of cause andeffect. Consider, for example, scientific laws. Are theymerely concise summaries of past “constant conjunctions’’of A’s and B’s, descriptive restatements of A’s being followedby B’s? What makes it hard to maintain this view is, asNelson Goodman has noted, that scientific laws, unlikeaccidental generalizations, seem to support counterfactualconditionals. (A counterfactual conditional is a statementof the form “If A were the case, then B would be the case,’’when in fact A is not the case.)Thus the scientific law “All objects with a specific density greater than that of water sink when placed in water’’
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supports the counterfactual conditional “If this nail hadbeen placed in the water, it would have sunk.’’ The accidental generalization “All the students in George’s Math 5class are functionally illiterate’’ does not, however, supportthe counterfactual conditional “If Martha were placed inGeorge’s Math 5 class, she would be functionally illiterate.’’Similarly, the accidental generalization “All bodies of purearsenic have a mass of less than one ton’’ does not supportcounterfactual statements like “Two bodies of pure arsenicwhose combined masses are more than one ton cannot befused to form one body,’’ or “If two such bodies were fused,the mass of the resulting body would still be less than oneton.’’The ontological status of scientfic laws is thus not quiteclear. They seem to be more than just summaries of constant conjunctions, since they support counterfactuals, yetthey are certainly less than necessary or logical truths.
There is a story by Leo Rosten (1968) that is marginally relevant:An insensitive oaf (a bulvon) was about to go out on ablind date and asked his Lothario of a friend for someadvice. The friend responded, “I’ll tell you a secret. Jewishgirls love three topics of conversation: food, family, andphilosophy. That’s all you need to remember. To ask abouta girl’s tastes in food is to make her feel important. To ask
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about her family shows that your intentions are honorable.And to discuss philosophy with her shows you respect herintelligence.’’The bulvon was pleased. “Food, family, philosophy!’’He met the girl and blurted, “Hello. Do you like noodles?’’“Why, no’’ said the startled girl.“Do you have a brother?’’“No.’’The bulvon hesitated for just a moment: “Well, if youhad a brother, would he like noodles?’’
Medical people and biologists sometimes use “cause’’ ina bizarre way. They reason that if x cures y, then lack of xmust cause y. If dopamine, for example, lessens the tremorsof Parkinson’s disease, then lack of dopamine must cause it.If an antagonist of dopamine reduces the symptoms ofschizophrenia, then an excess of it must cause schizophrenia. One is less likely to make this mistake when the situation is more mundane. Few people believe that since aspirincures headaches, it must be the case that lack of aspirin inthe bloodstream causes them.Similar things can be said about some uses of “cause’’ inthe social sciences.
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Two Australian aborigines were brought to this countryand saw for the first time a waterskier winding and cavorting his way around a lake. “Why is the boat going so fast?’’asked one of the aborigines. The second answered,“Because it is being chased by a madman on a string.’’
Th e To r toi s e Ca me F i r s t ?In clarifying the structure of the first-cause argument forthe existence of (a) God, Bertrand Russell cites the Hindumyth that the world rests on an elephant and the elephantrests on a tortoise. When asked about the tortoise, theHindu replies, “Let’s change the subject.’’But let’s not change the subject. Assuming some reasonable understanding of the word “cause,’’ either everythinghas a cause or something does not. If everything has a cause,God does too. If there is something that does not have acause, it may as well be the physical world as God or a tortoise.The cogency of this reply to the first-cause argument isindicated by Saint Augustine’s reaction to a version of it.When he was asked what God was doing before He made theworld, he answered, “He was creating a hell for people whoask questions like that.’’The natural-law argument for the existence of God hasa similar structure and is thus open to a similar reply. Theargument posits God as the lawgiver, the author of orderand law in the natural world. Whatever power the argumenthas is greatly diminished by asking why God created the particular natural laws that He did. If He did it whimsically, forno reason at all, there is then something that is not subjectto natural law; the chain of natural law is broken. On theother hand, if He had reasons for issuing the particular laws
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that He did, then God himself is subject to law and there isnot much point in introducing Him as an intermediary inthe first place.
There is a statistical “law of nature’’ that says that if youthrow a pair of dice, you will get a two (one on each die)only about once in thirty-six throws. Many laws of natureare, of course, of this sort. Though they indicate an orderor lawfulness on one level, this order or lawfulness existsonly because of disorder or randomness on a lower level.Compare the second law of thermodynamics, which statesthat in any closed system, entropy (disorder, roughly), beingmore probable, is continually increasing. (Living things—little islands of order that replicate themselves, and fromwhich more complex configurations can evolve—are notclosed systems, and thus do not constitute a counterexample to the second law of thermodynamics. They eat, arewarmed by the sun, etc.)It is in fact hard, if not impossible, to imagine a completely random universe. It seems that in any universe therewould necessarily be, on some level, some kind of order orlawfulness, even if only of a very Pickwickian sort. Even in avery messy universe one could describe the mess (assumingone were around, which is not likely) or enunciate somehigher-order prediction to the effect that no lower-orderpredictions seem to work.
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Why is it not termed a miracle when a freak gust of windtopples a single flowerpot from a tenth-story window andthe flowerpot falls onto the head of a person walking on thesidewalk below, or when a faith healer ministers to a blindman who then becomes lame?
Constants of different sorts: Planck’s constant, 55 mphspeed limit, 3 ft. in a yard, π.Laws of different sorts: Conservation of mass-energy,parking ordinance, Thou shalt not kill, Boyle’s laws ofgases.
One reasonable reaction to the refutation of the firstcause and natural-law arguments is to try to make sense ofthe first cause not only causing the second cause(s) but alsocausing itself—or, analogously, the most general law notonly explaining the next most general law(s) but alsoexplaining itself. Robert Nozick, in Philosophical Explanations,considers one such self-subsumptive principle, P, of thefollowing type : Any lawlike statement having characteristicC is true. Principle P is used to explain why other, less general laws hold true: they hold true because they have characteristic C. What, however, explains why P holds true? Theanswer is that P, since it also has characteristic C, explainswhy it itself holds true. In short, P, if true, explains itself.
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Even Nozick acknowledges that this “appears quiteweird—a feat of legerdemain’’ (1981). Still, there are not, ashe notes, many alternatives. The chain of causes (laws) iseither finite or infinite. If it is finite, the most basic cause(most general law) either is a brute, arbitrary fact or is selfsubsuming.Self-subsuming principles need not be any deeper orof any higher order than what they explain. They could perhaps be handled by a variant of Kripke’s theory of truth, inwhich statements attain their level naturally rather thanbeing preassigned a fixed level, and in which self-referential statements sometimes receive truth values. (Perhapseven the oscillation associated with certain paradoxicalstatements—if they’re true, they’re false, which makes themtrue, which makes them false, etc.—could be given a physical meaning consistent with the notion of self-subsumption.)Nozick writes also of certain yogic mystical exercises thathelp to bring about the experiential analogue of self-subsumption. He theorizes that “one of the acts the (male)yogis perform, during their experiences of being identicalwith infinitude, is auto-fellatio, wherein they have anintense and ecstatic experience of self-generation, of theuniverse and themselves turned back upon itself in a selfcreation’’ (1981).All this, of course, is contrary to Marxist theory. AsMarx (Groucho) himself might have observed, “FirstRussell defines mathematics as the subject where we neverknow what we’re talking about nor whether what we’re say-
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ing is true, and now this Nozick joker says that the mostbasic laws of the universe have something to do with yogisplaying with themselves; and yet they call me a comedian.’’Pascal once said, “To poke fun at philosophy is to be aphilosopher’’ (1966). Although this is not quite true—poking fun being a necessary but not a sufficient condition forbeing a philosopher—it and Groucho’s imagined reactionto Russell and Nozick do suggest a deep resonance betweenhumor and philosophy. Ideally, both activities require—infact, presuppose—a free intelligence stepping back fromroles, rules, and rote, in order to respond to the world withhonesty and courage. Ideally.
Of Birds and Strange ColorsHume’s traditional problem of induction aside (consider itsolved, resolved, dissolved, or just ignored), there remainsthe problem of exactly which regularities in nature are projectable into the future. All samples of water so far examined (under normal atmospheric pressure) have beenfound to have a freezing point of 32°F; it thus seems reasonable to project this regular connection between being awater sample and having a freezing point of 32°F into thefuture. It is also true that all major economic depressionshave occurred at the same time as large sunspots; yet in thiscase, it does not seem reasonable to project this regularconnection between economic depressions and sunspotsinto the future.Nelson Goodman has shown (1965) that the questionof which regularities are projectable into the future is moreproblematical than these two examples indicate. Goodman’sprojectability paradox can be explained by considering thestrange electrical terms “condulator’’ and “insuductor.’’ Adate in the future is selected, say January 1, 2010.Something is termed a condulator if it is a conductor andthe time is before 2010, or if it is an insulator and the timeis after January 1, 2010. Something is an insuductor, on theother hand, if it’s an insulator and the time is before 2010,or if it’s a conductor and the time is after January 1, 2010.Now let’s consider the properties of copper wire. All sam-
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ples of copper wire tested up to now (1984) have been conductors; we therefore feel we have good evidence that allcopper wires are conductors of electricity. But, Goodmanpoints out, all copper wires so far tested are also condulators: it seems as though we have just as good a body of evidence for the proposition that all copper wires are condulators (and hence insulators beginning in 2010).Of course, a natural objection to these electrical terms“condulator’’ and “insuductor’’ is that they are defined interms of the year 2010. But what if there really were a people who developed a language or scientific theory of whichcondulator/insuductor was a part? They could make thesame charge against us. “Conductor,’’ they could maintain,is an odd term, being defined as condulator before 2010and insuductor afterward. “Insulator’’ is just as strange,being insuductor before 2010 and condulator from thenon.More generally, it is not just these isolated terms butthe languages, theories, and worldviews of which they’re apart that structure the world and its observers in incommensurable ways, and thus lead to very different expectations about the future. One could, for example, rig up twoelectric chairs, one with copper wiring and the other withasbestos wiring, and have the leading scientists from eachside sit in the chair of their choice on January 1, 2010.Goodman’s original example concerned the odd colorterms “grue’’ and “bleen’’ and is usually referred to as thegrue-bleen paradox. An object is grue if green before 2010,say, or blue afterward. Bleen is defined similarly, and it’s
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stressed that whatever evidence we have for all emeraldsbeing green is also evidence for all emeralds being grue.Grue-bleeners, however, can point out that it is really“blue’’ and “green’’ that are the strange color terms, the latter being grue before 2010 or bleen afterward, and the former being bleen before 2010 or grue afterward. Of course,an indefinite number of such puzzles can be generated—republicrats and democans (2010 could be a cataclysmicyear)—but how to get around them is not completely clear.
Another intriguing paradox is due to Carl Hempel(1965). His “raven’’ paradox, so called because it is usuallyillustrated with ravens, can be easily stated. Suppose we wantto confirm the statement “All ravens are black.’’ We go out,look for ravens, and check to see if they are black. We believethat if we observe enough instances of black ravens, we willhave confirmed (not necessarily conclusively verified