17. INDUCTION AND THE BOUNDARY OF SCIENCE Today we will look more closely at one of the fundamental issues in the philosophy of science: the reliability of inductive knowledge. But before doing so, I will direct your attention to a question not obviously related to the philosophy of science, which I want you to think about during the next few lectures. The question, a paraphrase of a statement which Kierkegaard (1813- 1855) quoted from Lessing (1729-1781) in his Concluding Unscientific Postscript (p.97), is: If God had all truth in his right hand and the lifelong search for truth in his left, which hand would you choose? In a later lecture, about the time I think you will have forgotten to reflect on this difficult question, I will make some suggestions as to how I believe we should respond. Do you recall our discussion in Lecture 9 of the analytic and synthetic methods of argument? At that point we contrasted deduction, the method which begins with two or more premises and draws a necessary conclusion from them, with induction, the method which begins by gathering the evidence from observations and generalizes from these to form a probable conclusion. Many scientists, from the beginnings of science down to the present day, have assumed their task requires careful observation more than rigorous argumentation, so that the proper way of doing science is to proceed by the path of induction. The problem this raises is that scientists nearly always view their task as a search for facts, and they normally assume that once a "fact" is demonstrated, it is known for certain to be true; yet, as we saw in Lecture 9, induction on its own cannot provide us with such certain knowledge, since it always depends to some extent on guesswork. Solving this problem is of the utmost importance for the philosophy of science, because it appears to call into question one of our most basic beliefs about scientific knowledge: that scientific facts are reliable and trustworthy, because scientists have proved that they must be true. For most scientists who have thought philosophically about what they are doing, the solution to the "problem of induction" has been to assume the phenomena they observe are somehow bound together by some kind of necessary connection. This would mean that the necessity of scientific facts comes not from the logical structure of the scientific method, but from some law within the phenomena themselves. And the most basic scientific law, governing all other more specific laws about how phenomena interact, is that any effect we observe in the world is necessarily determined by some preceding cause. The important thing to understand about this solution is that this use of the law of necessary causation is a philosophical assumption, not one based on any scientific proof. Indeed, we could call it the "myth", upon which most of modern science is constructed. In this century there have been some scientists, mostly physicists, who claim to reject this myth, on the grounds that on the subatomic level events "just happen": the path of an electron, for example, is believed to be entirely random, and thus unpredictable at any given point of time, so that only the "probability" of any given path can be known beforehand. Other scientists, however, believe that such an explanation, even as a way of accounting for the mysterious movements of subatomic particles, is merely a confession that the physicists have come to the end of their science. Indeed, it is as if they had "bumped their heads" on the outer boundary of science itself. If physicists really have reached the boundary of the physical world, then the assumption that subatomic events are uncaused is just as mythical as the more traditional assumption that all events have a cause. In either case scientists ought to recognize that the debate over which assumption serves as a better myth upon which to build a science is primarily a philosophical debate, not one that can be answered merely through scientific observation. Accordingly, I would like to introduce to you today two ways philosophers have dealt with the issue of the necessary connection which is so often believed to give inductive knowledge its reliability. One comes from the skeptical doubts raised by David Hume, and the other comes from the attempts of Immanuel Kant to give an adequate reply to Hume's skepticism. David Hume (1711-1776) was a Scottish philosopher who thoroughly defended a philosophical method called "skepticism". Skeptics call into question the reliability of our knowledge (in science, morality, aesthetics, or any other area where some people claim to have knowledge), usually by demonstrating that the foundations for that knowledge are either insufficient or nonexistent. Hume called into question many kinds of knowledge, and defended his skeptical alternatives with many persuasive arguments. At the basis of all his arguments is the assumption that truth can be reached in only two legitimate ways: through mathematical reasoning (i.e., deduction, producing what Kant would call "analytic a priori" knowledge), and through empirical observation (i.e., induction, producing "synthetic a posteriori" knowledge). Hume used this assumption, sometimes called "Hume's fork", to locate and discard any and all claims to knowledge that do not depend on one of these two methods. Thus, his book, An Enquiry Concerning Human Understanding (1748), concludes with the following paragraph: When we run over libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume--of divinity or school metaphysics, for instance--let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames, for it can contain nothing but sophistry and illusion. When it comes to scientific knowledge, Hume used this "fork" not to deny the validity of all science whatsoever, but to argue that it is wrong to think of such knowledge as giving us access to any necessary truth. For he believed it is impossible to use induction to reach necessity. The reason is that he could find no grounds for believing in a hidden law of necessary connection. We cannot observe such a law; and we cannot prove it by deductive reasoning. So it must not be true! He expressed this argument earlier in his Enquiry in a variety of ways. For example, when discussing the possibility that the human will might give us access to such a law, he reasoned (p.69, my italics): Why has the will an influence over the tongue and fingers, not over the heart and liver? This question would never embarrass us, were we conscious of a power in the former case, not in the latter. We should then perceive, independent of experience, why the authority of will over the organs of the body is circumscribed within such particular limits. Being in that case fully acquainted with the power or force ... we should also know, why its influence reaches precisely to such boundaries, and no farther. Here Hume recognized that the search for necessary connection is a search for a boundary, outside of ordinary experience, which would give us consciousness of why things are connected the way they are. But he went on to reject such a possibility, on the following grounds: But consciousness never deceives. Consequently, neither in the one case nor in the other are we ever conscious of any power. We learn the influence of our will from experience alone. And experience only teaches us, how one event constantly follows another; without instructing us in the secret connection, which binds them together, and renders them inseparable. Hume's argument here is that, in order to understand the reasons why the human will works the way it does, we would have to be conscious of some power underlying and determining our experience. But we are in fact conscious of nothing but our own experiences, which never give us any glimpse of such a hidden power. Moreover, this conclusion can be generalized to apply to all our experiences (p.79): .. upon the whole, there appears not, throughout all nature, any one instance of [necessary] connection which is conceivable by us. All events seem entirely loose and separate. One event follows another; but we never can observe any tie between them. They seem conjoined; but never connected. And as we can have no idea of anything which never appeared to our outward sense or inward sentiment, the necessary conclusion seems to be that we have no idea of connection or power at all, and that these words are absolutely without any meaning, when employed either in philosophical reasonings or common life. If the idea of necessary connection is indeed "without any meaning", then this poses seemingly insurmountable problems for the view that the inductive method is sufficient for establishing scientific facts. This way of undermining the foundation of what was previously assumed to constitute knowledge is typical of the skeptical method in philosophy. Hume's skepticism concerning the common feeling that there is a necessary connection between cause and effect implicitly raises two challenges, one directed more to scientists, and the other, more to philosophers. If Hume is right, his ideas challenge scientists to choose between two alternatives: either find a scientific method which is more suitable than induction, or else give up the notion that science can ever achieve the goal of certainty. That this choice is implied by Hume's skepticism should be clear enough, especially if we revise Figure 9.2b by taking Hume's arguments into consideration, as follows: [Figure 17.1: The Uncertainty of Inductive Knowledge] Of course, it is usually philosophers of science, rather than scientists, who have responded to this challenge. One response has been to suggest Hume was right in rejecting the certainty of inductive knowledge, but to claim that, in fact, the method followed by scientists is not primarily inductive but deductive. Karl Popper, for example, argued that scientists actually begin not with a bare observation, but with an hypothesis, which functions like the premise of a deduction. The scientist assumes this hypothesis, and then tests it by trying to "falsify" it through various experiments. Induction on its own would never enable scientists to reach factual conclusions; but deduction and induction together are able to do so. Another response has been simply to agree with Hume, so that scientists need not view their task as a search for certainty. For instance, Paul Feyerabend has argued that, rather than searching for the one perfect scientific theory, philosophers and scientists should encourage a proliferation of theories: the more different scientific theories there are, the better--even if they seem to be opposed to each other. There are also many other ways in which philosophers have attempted to legitimize science; but they are beyond the scope of this course. The more strictly philosophical challenge arising out of Hume's skepticism is to find a way of defending induction in one of two ways: either by appealing to some principle other than necessary connection, or by attacking Hume's arguments more directly, and demonstrating that the idea of necessary connection is meaningful after all. Hume himself actually pursued something like the former alternative. He recognized that some explanation must be given for our feeling of expectation that things will happen in the future the way they have happened in the past. Accordingly, he argued that the feeling we have that the "gap" between the evidence and the conclusion in an inductive argument is actually a result of nothing but "custom" or "habit" (p.80): But there is nothing in a number of instances, different from every single instance, which is supposed to be exactly similar; except only, that after a repetition of similar instances, the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe that it will exist. This connection, therefore, which we feel in the mind, this customary transition of the imagination from one object to its usual attendant, is the sentiment or impression from which we form the idea of power or necessary connection. Nothing farther is the case. Contemplate the subject on all sides; you will never find any other origin of that idea. In other words, when we get used to experiencing objects in a certain way, we imagine that this way is necessary, and so we expect to continue experiencing them in the same way. We expect, and even feel "certain" that the sun will rise in the east tomorrow, even though there is no factual basis whatsoever for real certainty, but only for a judgment of probability, based on the habits we have developed out of our past experiences. We might defend Hume's answer to his own challenge by noting that, in fact, some people do not expect the sun to rise in the east! For instance, on the north and south poles there are certain times of year when the sun never rises or never sets. Indeed, I was actually born in a small town in northwest Alaska in the early morning of a long summer's day. My father has told me that he walked home from the hospital at 2am that morning, watching the sun set in the north. A few hours later it rose again, a bit to the east, but still mainly in the north. So the example I've been using about the sun rising in the east also illustrates how what seems to be a reasonable conclusion ("The sun always rises in the east") can actually turn out to be based on our habit of viewing the world from the limited perspective of our own past experiences. Only when we are surprised by discovering an unexpected exception do we realize the influence of our habits on what we believe to be true. Kant, however, was radically dissatisfied with Hume's way of accounting for our feeling that phenomena are connected with each other in a necessary way. He therefore took the second way of responding to this challenge. Kant agreed with Hume about the importance of regarding necessary connection as a boundary between what science can and cannot know; but he rejected Hume's claim that all knowledge must be either mathematical or observational. There is, according to Kant, a third type of knowledge, called "transcendental", which is synthetic and yet also a priori--i.e., it is expressed by a proposition which is necessarily true, yet its necessity is not derived merely from logic (see Lecture 9). And this, it turns out, is the distinctively philosophical type of knowledge. Anyone who accepts Hume's fork in its strictest sense will find that it eventually excludes philosophy itself from the realm of worthwhile knowledge! But when we recognize that Hume's fork functions as the mythical foundation for his system, we will be free to replace it by some alternative, more appropriate myth, such as Kant's "Copernican" myth, that the mind imposes certain synthetic a priori conditions onto any object in the very process of coming to know that object. Kant responded to Hume's skepticism in a number of different ways; but for our purposes, his most important response comes in his theory of the "principles of pure understanding", which, he argued, exist in the mind, and yet determine the character of our experience to be the way it is. One of the principles Kant defended in this way is precisely the one Hume had rejected as a mere feeling, based on our habitual way of interpreting our past experiences: the idea of necessary connection. Kant defended this principle in a section of his Critique of Pure Reason entitled the "Second Analogy", calling it the "principle of succession in time, in accordance with the law of causality" (p.218). This principle states: "All alterations take place in conformity with the law of the connection of cause and effect." He provided a complex set of interconnected arguments in defense of this principle--far too complex for us to examine here. However, we can get a general idea of how he argued by taking one paragraph out of context and examining it in a bit more detail. Kant and Hume both agreed that we have experience, but they disagreed over what our subjective experience implies about the objective world. Whereas Hume argued that our subjective experience is merely a "bundle of perceptions", which implies little or nothing about objective reality, Kant argued that "we must derive the subjective succession of apprehension from the objective succession of appearances", otherwise it would be impossible to explain why we perceive, or "apprehend", a series of events in a given order, or a group of objects as distinct from each other (p.221). In other words, our subjective experience is only possible on the assumption that it is "bound down" to some objective reality. With this in mind, Kant constructed the following argument: If, then, we experience that something happens, we in so doing always presuppose that something precedes it, on which it follows according to a rule. Otherwise I should not say of the object that it follows. For mere succession in my apprehension [as in Hume's theory of "habit"], if there be no rule determining the succession in relation to something that precedes, does not justify me in assuming any succession in the object. I render my subjective synthesis of apprehension objective only by reference to a rule, in accordance with which the appearances in their succession, that is, as they happen, are determined by the preceding state. The experience of an event [i.e., of anything as happening] is itself possible only on this assumption. (p.223) If Kant's argument is correct, then the principle that there is a necessary connection between cause and effect must be true, even though we cannot use either observation or mathematical reasoning to prove it. This type of argument has come to be known as a "transcendental argument". The general form of such an argument is: In order for experience to happen, p must be true. I, at least, have experience. Therefore, p must be true. Hume would not deny the second premise; so his only rebuttal would be to question the first premise. Is there really anything that must be true in order for our experience to be possible at all? If so, then those truths, taken together, would define the boundary line between what we can and cannot know. Would it be possible, for example, to imagine a kind of experience in which we do not presuppose that our experiences are in some way determined by something that happened at some time in the past? Kant believed that in such a case we would not be justified in claiming to have any experience. "Experience" here refers to an awareness of "subjective succession" in our perceptions; and if there were not also some "objective succession", then there would simply be no basis upon which our subjective succession could be apprehended. In other words, an appeal to "habit" is irrelevant, since without an objective succession on which to base our so-called habits, we could not even be conscious of our own experience. Some of you are probably rather confused at this point. This is not surprising, for the arguments we have been considering are among the most difficult ever proposed by philosophers. Professional philosophers who study Hume and Kant all their life still debate over how to interpret their views, and which one gives a better description of the way the world really is. So we cannot hope to settle the question once and for all in an introductory course! Nevertheless, I would like to help clarify what each of these positions involves, and perhaps at the same time, help you to make up your mind about which one is closer to the truth, by performing a little "thought-experiment". Imagine it is 5pm right now, and you are finished with all your classes for the day. Let's assume you live in Shatin, as I do; so you walk up the road to the nearest bus stop and wait there for the next bus. After only a few minutes, the bus you normally ride drives up. It is full of people; but the driver, a friendly man who you remember seeing before, stops to let you on. Even though the only place for you to stand is an awkward space right next to the driver, you love philosophy so much that you immediately pull out the book you are currently reading from the lists of "Recommended Readings", and begin to read. The traffic is not too bad, so after only a minute or two the bus enters Lion Rock Tunnel, on its way to Shatin. You hardly notice this, though, since you are so engrossed in your philosophizing. Then, all of a sudden, you feel the bus stopping. At first, you just continue reading, since you know the bus often stops as it's passing through the tunnel. But after a few minutes, you begin to wonder why the bus isn't moving. So you pull your eyes away from your book to see if you can tell what is causing the hold up. To your surprise, there are no vehicles in front of the bus; and the bus driver is still sitting in the same position he was in before, with his hands on the steering wheel and his feet on the pedals, just as if he were still driving! What would you do in such a case? I would guess that, given a long enough delay, you would eventually ask the bus driver to explain why he had stopped the bus. Now let's imagine he answers you by saying "I didn't stop the bus" (or the equivalent expression in Cantonese). You would probably respond by saying "Well, then, you better call for help, because the bus must be having some engine trouble." But the driver replies: "No, the engine is working just fine. Listen." And sure enough, you then hear the rumble of the bus engine, which sounds the same as it normally does when it is driving through the tunnel at a normal speed. I think you would be a bit perplexed; but after a while, especially if you were going to be late for dinner, you would again raise some kind of question, such as: "Well, if you didn't stop the bus, who did? God? Or a ghost?" If the driver then answered "No, of course not. How many times do I have to tell you, nobody stopped the bus", then most of us, I think would say, or at least think, something like: "Look, either someone stopped the bus intentionally, or there is some engine trouble, because buses just don't stop for no reason at all!" I wonder how would you respond if the bus driver replied to this claim by retorting: "Ha! You just feel that way because of the habit you have developed over your years of living in Hong Kong, of thinking that buses don't stop in smelly tunnels for no reason. In fact, they can and do sometimes stop for no reason; it's just that this is the first time you have experienced an exception to your habitual expectations." If the driver then turned away and resumed his driving position, as if nothing at all were unusual, I suspect that most of us would try to get out of that bus as fast as you could! Why? Because we would all assume this driver is either playing a very inappropriate (possibly dangerous) joke on his passengers, or else he is crazy! We all (even physicists who believe there is no cause behind the movements of subatomic particles) normally assume that whatever we see and experience in our everyday life is caused by something. Even miracles are caused events, since they are events believed to be caused by God. Likewise, people living in primitive tribes naturally assume that whatever happens is caused to happen, perhaps by some spirit or god. If we didn't make some kind of causal assumption, we would simply be unable to function in any human society. If Kant's view is right, we would not even be able to be aware of our own subjective experiences. But it is important to understand that Kant's principle is transcendental, whereas Hume's "habit" is empirical. That means the two views are not necessarily incompatible, provided we reject the narrow presupposition of Hume's fork. Hume is actually right when he says there is no way to observe or calculate our way to an understanding of necessary connection. Kant's argument is intended to show that his mistake was to ignore the transcendental boundary line between these two, because that is the true home of necessary connection, and so also the best justification scientists can appeal to in defending their use of the inductive method. Even if you are not convinced by Kant's arguments, or by the foregoing thought-experiment, to believe that the principle of causality, or necessary connection, is a transcendental condition for the possibility of experience, I hope you will agree by now that a view like Hume's would, on its own, undermine the possibility of science. There could be no objective facts if everything depended on our own subjective habits. I think most of you probably agree that habit alone is simply not good enough. There is something absolute about our idea of the necessary connection between cause and effect, something which seems almost beyond question! (Incidentally, the fact that Hume disagrees with this, does not prove that the idea is "relative"; Hume's theory could be incorrect!) However, if we accept Kant's argument, and regard everything that happens as determined by something that happened prior to it, a new problem arises: How can we explain the feeling we human beings have that we are free? If everything in the world is determined, does this mean we must discard our belief in human freedom? In this way the philosophy of science impinges directly upon one of the central questions of the branch of applied philosophy we will climb in the next lecture, the branch of moral philosophy. There we will find to what extent our search for wisdom can lead us to accept both the determinism of science and the freedom of moral action. QUESTIONS FOR FURTHER THOUGHT 1. Are there any subjective facts? 2. Is Popper's "falsifiability principle" itself falsifiable? 3. What is a habit? 4. Could we ever have knowledge of an uncaused event? RECOMMENDED READINGS 1. David Hume, An Enquiry Concerning Human Understanding (Chicago: Henry Regnery, 1956), Section VII, "On the Idea of Necessary Connection", pp.62-85. 2. Immanuel Kant, Critique of Pure Reason, tr. Norman Kemp Smith (London: Macmillan, 1929), "Second Analogy", pp.218-233. 3. Karl Popper, The Logic of Scientific Discovery (London: Hutchinson, 1972). 4. Paul Feyerabend, Against Method: Outline of an anarchistic theory of knowledge (London: Verso, 1978).