THREE WAYS OF GETTING IT WRONG: INDUCTION IN WONDERLAND B rendan S hea Alice encounters three curious inductive problems in her struggles to understand and navigate Wonderland. The fi rst arises when she attempts to predict what will happen in Wonderland based on what she has experienced outside Wonderland. In many cases, this proves diffi cult - she fails to predict that babies might turn into pigs or that a grin could survive without a cat. Alice ' s second problem involves her efforts to fi gure out the basic nature of Wonderland. So, for example, it is diffi cult for Alice to see how she could prove that her experiences were the result of her dreaming and not something else. The fi nal problem is manifested by Alice ' s attempts to understand what the various residents of Wonderland mean when they speak to her. In Wonderland, " mock turtles " are real creatures and people go places with a " porpoise " (and not a purpose). All three of c07.indd 93 11/23/09 8:55:30 AM 94 B R E N DA N S H E A these problems concern Alice ' s attempts to infer information about unobserved events or objects from those she has observed. In philosophical terms, they all involve induction . Induction, it turns out, is hugely important to our daily lives. Induction allows us to fi gure out which foods nourish and which poison; induction guides our conviction of criminals and pardoning of the innocent; induction is the basis of all scientifi c knowledge. Induction also provides our sole basis for understanding language . But the problem with induction, as Alice learns, is that one always risks being wrong. In Wonderland, many of Alice ' s inductively supported beliefs turn out suddenly to be false, and she is forced to start from scratch. Her successes and failures in doing so offer a window into the working of inductive reasoning, and should therefore be of real interest to us. How to Avoid Poison and Red Hot Pokers Induction is a type of reasoning that stands in explicit contrast to deduction . In order to reason deductively from known facts to a conclusion, one must show that it is impossible for the conclusion to be false on the assumption that the original facts are as we thought. Lewis Carroll offers the following example of a deductive argument in his Symbolic Logic : " All cats understand French; some chickens are cats " therefore, " Some chickens understand French. " 1 The conclusion is, of course, false. However, if one assumes that the fi rst two statements are true, there is no way the third statement could be false. In using deduction, one never really goes beyond what one knows - one merely restates it in new (and sometimes interesting) ways. In contrast to deductive reasoning, inductive reasoning attempts to go beyond what is already known. An inductive argument attempts to supply probable reasons for its conclusion. There are no guarantees. So, for example, were Alice to reason from No rabbits have ever spoken to me before today to the c07.indd 94 11/23/09 8:55:30 AM T H R E E WAYS O F G E T T I N G I T W R O N G 95 conclusion that No rabbits will speak to me today , she would be reasoning inductively. This is because, as Alice discovers, it is possible for the fi rst statement to be true and the second false. Most, if not all, of our everyday beliefs about the world have been arrived at by inductive reasoning. Alice provides a few good examples of inductively supported beliefs when she considers drinking the bottle labeled drink me : It was all very well to say, " Drink me, " but the wise little Alice was not going to do that in a hurry. " No, I ' ll look fi rst, " she said, " and see whether it ' s marked ' poison ' or not " ; for she had read several nice stories about children who got burnt, and eaten up by wild beasts, and other unpleasant things, all because they would not remember the simple rules their friends had taught them: such as, that a red hot poker will burn you if you hold it too long; and that, if you cut your fi nger very deeply it usually bleeds; and she had never forgotten that, if you drink much from a bottle marked " poison" , it is almost certain to disagree with you, sooner or later. 2 All of the rules Alice cites are good (if simple) ones. Nevertheless, we have only inductive reasoning to support them. For instance, the reason we think that fi res will burn us in the future is because we know that they have burned us in the past. The same holds true any time we believe something on the authority of some reliable teacher, parent, or book. In fact, nearly all of our basic beliefs about history, science, and other people have been arrived at by inductive reasoning. Why Predicting the Future Is a Problem One common type of inductive reasoning involves our attempts to predict what we will experience in the future based on what has happened in the past. For example, most of us believe that rabbits will not begin talking, nor will babies suddenly become pigs. But suppose that somebody (we ' ll pretend it is Humpty c07.indd 95 11/23/09 8:55:31 AM 96 B R E N DA N S H E A Dumpty) disagrees with us about these beliefs. Humpty claims that at 6:00 a.m. tomorrow the world we know will suddenly turn into Wonderland. Animals will talk, playing cards will hold trials, and people will change size dramatically when they eat certain foods. What, if anything, could we say to convince Humpty that he is wrong? In his famous book An Enquiry Concerning Human Understanding , David Hume (1711 – 1776) argues that there is nothing we could say to rationally persuade someone like Humpty that he is wrong. Hume ' s argument proceeds as follows. First, he divides knowledge into two categories: that pertaining to relations of ideas and that pertaining to matters of fact . 3 Hume thinks that knowledge of the former category is possible, but it pertains only to truths we can fi gure by refl ecting on the nature of our own ideas. For example, Hume thinks we can know that all triangles have three sides and that all bachelors are unmarried, but this knowledge doesn ' t depend on the existence of any triangles or bachelors. Even if every male in the world were married, for example, it would remain true that if there were a bachelor, he would be unmarried. This is guaranteed by our idea of bachelorhood. Hume might be quite happy with Humpty ' s observation that we are the " master " of our words. 4 According to Humpty ' s story, we can fi gure out whether " All triangles have three sides " is true or false simply by considering what we mean by words like " triangle. " In addition to our knowledge of relations of ideas, Hume grants that we can have knowledge about the matters of fact we have already observed . For example, we know that we have not up until now observed rabbits talking or playing cards holding trials. Hume ' s problem of prediction concerns the possibility of knowing about unobserved matters of fact. Humpty ' s challenge is just a more specifi c version of this problem. We have not yet observed what will happen at 6:00 a.m. tomorrow; Humpty challenges us to justify our belief that the world will not suddenly change into Wonderland. c07.indd 96 11/23/09 8:55:31 AM T H R E E WAYS O F G E T T I N G I T W R O N G 97 The diffi culty of Hume ' s problem becomes apparent when we consider how we might do this. When we defend claims about relations of ideas, we can appeal to what we can or cannot imagine as our test. So, for instance, it is impossible to imagine a non three sided triangle or a female bachelor. Therefore, triangles must be three sided, and bachelors must be male. But Humpty ' s claim that the world will become Wonderland isn ' t impossible to imagine; in fact, we visualize Wonderland whenever we read Carroll ' s work. As Hume notes, we can imagine any matter of fact being different: " That the sun will not rise tomorrow is no less intelligible a proposition, and implies no more contradiction, than the affi rmation, that it will rise . " 5 Nor can we defend our prediction as we do our beliefs about matters of fact we have already observed. Our beliefs about observed matters of fact are based on what we have seen, smelled, touched, and tasted. We can ' t sense the future in this way. According to Hume, the only reason we don ' t think that the world will radically change tomorrow is that it hasn ' t ever changed in this way before . In fact, Hume thinks all of our beliefs about unobserved matters rest on one key assumption - that the future will resemble the past . The problem is that this assumption is itself a belief about an unobserved matter of fact. Moreover, it is precisely what Humpty was asking us to defend. He agrees that up until today, the world has never radically changed. He just thinks that starting tomorrow, it will. And it seems we have no rational way of convincing him he is wrong. Hume ' s conclusion is not that we have no basis for making predictions, but rather that our ability to do so successfully is quite independent of our deductive reasoning ability. Alice, for instance, shows little evidence of being an expert on deductive logic. However, she uses inductive reasoning with great success. In learning how to change her size by the consumption of various foods and drinks, for example, Alice is using c07.indd 97 11/23/09 8:55:31 AM 98 B R E N DA N S H E A inductive reasoning in order to make successful predictions. Her use of evidence about past events to predict and control the future course of nature is prototypical of scientifi c reasoning, and gives some idea of just how important prediction is to our everyday lives. Humpty Dumpty, who by contrast seems fairly competent at deductive logic, provides a good example of a poor inductive reasoner. When Alice fi rst encounters Humpty, he is singing a song about how all the King ' s men won ' t be able to put him back together again. When queried by Alice, however, Humpty seems oblivious to the obvious predictive relevance of such a song, and refuses to move from his precarious perch. Humpty, despite his argumentative acumen, seems destined for a poor end. Whose Dream Is This, Anyway? From now on, let ' s suppose we ' ve solved Hume ' s problem, and have managed to become perfect predictors. That is, let ' s suppose we ' re perfect at predicting what will happen to us in the future - what we will see, touch, taste, and smell for the rest of our lives. We now come to a new problem: What about our beliefs about things we can ' t sense in this way? Are they justifi ed? Consider Alice ' s dilemma at the end of Through the Looking Glass , when she is trying to determine whether her experiences were the result of her dream or whether they were the result of the Red King ' s dream. It seems obvious to us, of course, that it must have been Alice ' s dream. The problem for Alice, however, is to explain to a skeptic (like Tweedledee) why she is justifi ed in believing that it is her dream. Alice ' s problem is a special case of what the philosopher W. V. Quine (1908 – 2000) calls the problem of underdetermination of theory by evidence. 6 Here a person ' s theory is simply the collection of all of her beliefs about the world. Alice ' s theory, for instance, includes such beliefs as London is located in c07.indd 98 11/23/09 8:55:31 AM T H R E E WAYS O F G E T T I N G I T W R O N G 99 England and I am not a character in the Red King ' s dream . By contrast, Tweedledee ' s competing theory includes the belief that Alice is a character in the Red King ' s dream . Someone ' s evidence , in Quine ' s sense, consists of everything that she can sense. Alice ' s evidence, for example, includes her memory of seeing the Red King sleeping and her memory of apparently " waking up. " The problem, says Quine, is that no matter how much evidence we gather, there will always be multiple incompatible theories that can explain all of it. Consider Alice ' s experience of waking up. This might seem to rule out Tweedledee ' s theory. After all, if Alice woke up, it must have been her dream, right? Tweedledee has an easy response, however. The reason that it seems to Alice that she is real and has woken up is because this is exactly what the Red King is dreaming. Tweedledee makes just this point when refuting Alice ' s claim that her tears show her reality: " I hope you don ' t suppose those are real tears. " 7 In fact, it turns out there is no possible piece of evidence that Tweedledee cannot accommodate by making suitable changes elsewhere in his theory. On the basis of such considerations, Quine concludes that nearly any statement can be reconciled with any piece of evidence: " Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. " 8 No amount of evidence gathering, it appears, will allow Alice to prove Tweedledee wrong. The relevance of underdetermination to everyday life becomes apparent when we note that Tweedledee ' s style of argument can be applied to challenge any belief we have about things that can ' t be directly sensed. And we have lots of those beliefs. Many scientifi c theories, for example, posit the existence of things too small or strange to be directly sensed: quarks, gamma rays, electrons, and gravitational forces. Scientists, using inductive reasoning, believe that these things exist because their existence explains the types of things we can examine with our senses. The problem of underdetermination c07.indd 99 11/23/09 8:55:32 AM 100 B R E N DA N S H E A states that there will always be some other theory (incompatible with ours) that could also explain this evidence. It is not just scientists who believe in things they can ' t see. Alice, for example, believes that drinking the potion caused her to shrink and not the rest of the world to grow. However, there is nothing she could sense that would allow her to determine which process is actually happening. Alice, like the rest of us, also believes in object permanence . She believes that the Duchess she encounters at the Queen ' s party is the same Duchess she saw earlier. But this isn ' t the only theory that could explain Alice ' s experience. One might alternatively think that the world is being destroyed and instantaneously created anew each second. We don ' t remember any such destructions, of course, but that is only because we were created so as to have (false) memories of a continuous experience. According to this theory, Alice is in fact seeing a different Duchess than the one she remembers meeting. Once again, there is nothing Alice could ever do to discover whether such a theory was true or false. Like Hume, Quine does not intend for his problem to induce skepticism about the value and legitimacy of scientifi c inquiry or our ordinary ways of doing things. Instead, he is merely pointing out that successful inductive reasoning requires more than (1) deductive reasoning or (2) making successful predictions. Quine goes on to suggest three criteria by which we decide which theories we adopt. 9 First, we need to make sure our theory doesn ' t contain false claims about our sensory experiences. Thus, Alice shouldn ' t adopt the theory that she ' s never had a Wonderland experience. Second, we should adopt theories that are as simple as possible. It ' s simpler, all things considered, to believe that there was only one Duchess instead of two. Finally, when we add new beliefs to our theory, we ought to change as few of our old beliefs as possible. If Alice were to believe that she were a character in the Red King ' s dream, for instance, she would have to change c07.indd 100 11/23/09 8:55:32 AM T H R E E WAYS O F G E T T I N G I T W R O N G 101 nearly every other belief she had (all of which presumed that she was real). The belief that the land beyond the looking glass was her own dream, in comparison, fi ts quite well with the rest of Alice ' s beliefs. In the end, of course, there is no way of ensuring that one ' s theory is correct, just as there is no system for making perfect predictions. It might simply turn out that Alice and Tweedledee, even after comparing evidence, are both justifi ed in their respective beliefs, despite these beliefs contradicting each other. The correct response to this, according to Quine, is simply to note that one must continue to believe in the truth of some theory; without it, one couldn ' t get around in the world. Alice ' s solution of recognizing the problem and simply going about her life is thus perfectly fi ne. There ' s No Meaning in It, After All Before considering the fi nal problem, let ' s pretend that we ' ve solved the fi rst two. We ' re perfect at predicting what will happen to us, and we ' ve come up with a complete, true theory of how the physical world works. The last problem of induction asks us to use this knowledge to determine what various people mean by their words. This is a source of constant frustration to Alice, who has to deal with such nonsensical characters as the Mad Hatter, the Queen of Hearts, and Humpty Dumpty. Almost every character in Wonderland and beyond the looking glass misuses or equivocates on some key English word or phrase, and Alice is tasked with using her inductive reasoning skills to fi gure out what is meant in English by such Wonderland words as " Time, " " whiting, " and so on. Quine takes up the problem of determining what people mean by their words in a book called Word and Object . In order to simplify matters, he supposes that a hypothetical translator fi nds himself (like Alice) alone in an environment in which it is unclear what various people mean by their words. c07.indd 101 11/23/09 8:55:33 AM 102 B R E N DA N S H E A The translator has no dictionary and no access to bilinguals who speak both English and the native language (which I ' ll call Wonderese). After a careful consideration of the process by which this translation might proceed, Quine concludes that there will always be multiple incompatible ways to translate Wonderese words into English; that is, it is indeterminate what people mean by their words. To see how he arrives at this strange conclusion, it will help to consider Alice ' s struggles in a little more detail. The fi rst step in any translation is to establish which native sounds mean yes and no . Alice herself notes the reason for this when she fails in her attempt to translate her kittens ' sounds into English: It is a very inconvenient habit of kittens (Alice had once made the remark) that, whatever you say to them, they always purr. " If they would only purr for ' yes ' and mew for ' no ' , or any rule of that sort, " she had said, " so that one could keep up a conversation! But how can you talk with a person if they always say the same thing? " 10 Once we have fi gured out which native sounds mean yes and no , we can ask the natives questions to determine what they mean by various other sounds. It is through this process that Alice discovers that " whiting " is the stuff used to polish shoes beneath the ocean and that " Time " is somebody that the Mad Hatter knows. The problem arises, Quine observes, when one realizes that there will always be multiple English translations that can explain the answers Wonderland residents give to Alice ' s questions. So suppose that Alice is trying to fi gure out whether the Wonderese speakers mean the same thing she does by " rabbit. " She fi rst points to the White Rabbit and asks a group of them, " Rabbit " ? They respond affi rmatively. In order to be extra careful, Alice points to the White Rabbit and his rabbit relatives at various times and places, and under all sorts of c07.indd 102 11/23/09 8:55:33 AM T H R E E WAYS O F G E T T I N G I T W R O N G 103 conditions. The Wonderland inhabitants continue to agree. However, Alice cannot establish that the Wonderese word " rabbit " means the same thing as the English word until she rules out the possibility that the Wonderland inhabitants are referring to something that is co located with rabbits. Some things that are co located with the White Rabbit, for example, are all of his various parts (arms, legs, and so on). Perhaps the Wonderese word " rabbit " refers only to some essential part of a rabbit (the heart, for example) when this part is attached to the rest of the rabbit. It is in this spirit that Quine writes, " Point to a rabbit and you have pointed to a stage of a rabbit, to an integral part of a rabbit, to the rabbit fusion, and to where rabbithood is manifested. " 11 The problem becomes even worse when one is trying to fi gure out the meanings of abstract words such as " intelligence, " " courage, " or " acceleration. " The things these words refer to are quite diffi cult (nay, impossible) to point to. The Dormouse ' s question, " Did you ever see such a thing as a drawing of a muchness! " 12 might strike us as quite silly, but it presents a signifi cant problem for Quine ' s translator. In the case of an expression such as " much of a muchness, " there might be quite a number of sayings in other languages that could serve as adequate translations. No doubt there are some limits on the translations we can adopt. In particular, we shouldn ' t adopt translations that get the natives ' patterns of assent and dissent wrong. For example, Alice has good reasons not to translate the Wonderese " rabbit " as meaning mouse . The problem is: once we satisfy this minimal constraint, we have no grounds for convincing someone who has a different translation that she ought to adopt ours instead. Suppose that the Red Queen were to visit Wonderland with Alice. She would presumably try to come up with a translation that made the connections to her own language as simple (Looking Glass ish) and straightforward as possible, while Alice would try to do the same with English. Still, even after c07.indd 103 11/23/09 8:55:33 AM 104 B R E N DA N S H E A all the facts not related to meaning are settled, the translations might not agree. In the real world, there are a variety of factors that keep us from disagreeing about translations of particular languages. It is very diffi cult, after all, to inductively reason our way to a translation based solely on our observations of native speakers. It is much easier to rely on dictionaries or textbooks, many of which are based on decades of careful research by linguists. In Wonderland, by contrast, this indeterminacy presents a much more obstinate and obvious problem. Wonderland residents repeatedly misunderstand both Alice and one another in strange (and sometimes malicious) ways. When Alice objects that the note in the Knave ' s trial means nothing, the King exclaims, " If there ' s no meaning in it that saves a world of trouble, you know, as we needn ' t try to fi nd any, " 13 before launching into his own biased translation. Humpty Dumpty seems to have much the same philosophy when he offers Alice a translation of " Jabberwocky. " Not surprisingly, Alice ' s actions again suggest to us the best path to follow. In most cases, she strives to translate people ' s words in the way she would want her own words understood. If it seems crazy to Alice that people would mean a certain thing by a particular word, she usually assumes that they don ' t mean that until their actions prove her wrong. Her attempts to provide translations are thus based on her sense of charity . Alice presumes that other people agree with her on the types of things that she takes to be true. This assumption cannot be established by perfect prediction, nor by scientifi c investigation, but must be assumed as a starting point for translation. Wonderland and the Real World At the end of her adventures, Alice wakes up and returns to a world more similar to our own. It would be a mistake, however, to suppose that Alice need leave behind all she has learned c07.indd 104 11/23/09 8:55:33 AM T H R E E WAYS O F G E T T I N G I T W R O N G 105 about Wonderland, or that her experiences have nothing to teach us. Wonderland presents us with a weird sort of parallel Earth where our expectations fail us and we must fi gure out everything anew. In doing so, we come to see the importance of inductive reasoning for surviving our daily lives, for uncovering the nature of the world around us, and for understanding one another. These are projects that we, like Alice, cannot help but care about. As readers, we can look to Alice for a model of what it takes to be a good inductive reasoner. Alice, unlike the strange creatures she encounters, learns to control her size, and does not fall prey to the fatalistic belief that she lives only in the dream of another. In contrast to the jurors in the Knave ' s trial, Alice realizes how preposterous the interpretation of the note really is. And she does all of this in the face of repeated challenges to her justifi cation for reasoning as she does. In the end, Alice serves as a good reminder that not all reasoning is pointless or silly, and that a good reasoner is much more than an expert in the verbal gymnastics practiced by the residents of both Wonderland and our own world. NOTES 1. Lewis Carroll, Symbolic Logic (London: Macmillan, 1896), 64. 2. Lewis Carroll, The Annotated Alice: Alice ' s Adventures in Wonderland and Through the Looking-Glass , ed. Martin Gardner (Bungay, UK: Penguin Books, 1965), 31. Subsequent references to the Alice stories are from this text. 3. David Hume, An Enquiry Concerning Human Understanding , 2nd edition, ed. Eric Steinberg (Indianapolis: Hackett Publishing Company, 1993), 14. 4. Carroll, The Annotated Alice , 269. 5. Hume, Enquiry , 15. 6. Quine discusses this problem in his book Word and Object (Cambridge, MA: MIT Press, 1960) and his famous paper " Two Dogmas of Empiricism, " in From a Logical Point of View (Cambridge, MA: Harvard University Press, 1980), 20 – 47. c07.indd 105 11/23/09 8:55:34 AM 106 B R E N DA N S H E A 7. Carroll, The Annotated Alice , 239. 8. Quine, " Two Dogmas of Empiricism, " 43. 9. Quine, Word and Object , 19 – 22. 10. Carroll, The Annotated Alice , 341. 11. Quine, Word and Object , 52 – 53. 12. Carroll, The Annotated Alice , 103. 13. Ibid., 159. c07.indd 106 11/23/09 8:55:34 AM