To the non-philosopher, these problems raised by these examples may seem rather contrived. It is tempting simply to say “I know valid inductive support when I see it” and, I think, one would fare quite adequately. But, the philosophers want to define precisely both how one would “know it” and how one would “see it.”
Some observations
In short, while we might support efforts better to understand and to systematize how we make valid inductive inferences, non-philosophers may have trouble taking too seriously Hume’s circularity argument with respect to justification for induction. Lipton stated the issue as follows: “In short, induction will work because it has worked. This seems the only justification our inductive ways could ever have or require. Hume’s disturbing observation was that this justification appears circular, no better than trying to convince someone that you are honest by saying that you are.” Inference to the Best Explanation, p.10. But, is that really a fair analogy? Is it not a more apt comparison to look at someone trying to convince another that he is honest and will continue to be so by pointing to a track record of honest behavior?
As discussed below, Sir Karl Popper criticized the notion that successful predictions prove the correctness of a theory. He allowed that success constituted corroboration (a kind of confirmation), but he recognized that there could be an abundance of rather trivial corroborations that should give rise to little confidence in the theory and that, more importantly, no amount of corroboration could ever conclusively establish that the theory was an accurate reflection of reality. Thus, he asserted that the real essence of the scientific method was (or should be) the seeking of refutation of theories (disconfirmation) through falsification. Then, it is the success of a theory relative to its competitors in that process of attempted refutation that constitutes a basis for belief in the theory. One consequence of this reformulation of the process of scientific inquiry was believed by Popper to be the elimination of the “problem” of induction by the elimination of inductive inference in the process of testing theories. Popper, The Logic of Scientific Inquiry (1959), pp.27–34.
Here the questions become how to test or assess theories and how to choose among them. Thus, we are simply back to the discussion of theories and how they can be tested that we were discussing above. The problem of induction is the problem of scientific inquiry and understanding.
Hume argued that simple induction was the only way in which man interpreted and understood the world. I am suggesting a somewhat different view. I can assume that early man’s efforts to comprehend the world and survive were based upon simple induction—the observation of apparent patterns and the conclusion that they were likely to be repeated. That conclusion is reasonable when choice or action is required. For example, take the mouse that twice discovers food in a particular place. Next time the mouse is hungry should it go back to that place or try someplace new? Is it not “rational” to try first the place of previous success? Of course, if that place is not productive, then the mouse presumably would try elsewhere, perhaps at random.
But, mankind has been functioning in a much more complicated fashion for millennia. Apparent patterns are observed. Efforts to construct theories of cause and effect are made. Those theories then are tested and, thereafter, eventually revised or replaced. Certainly, scientists today do not simply look for patterns and then make inferences; although, that is undoubtedly part of what they do. I suspect that many discoveries are the result of manipulating existing theories and playing with new ones, or simply indulging guesses and imaginative speculation.
Inductive reasoning undoubtedly has and does play a role in the generation of discoveries, but it cannot be the basis of scientific understanding. It is a tool for making educated guesses—sometimes for pragmatic reasons (like in the search for food), sometimes for intellectual ones (like in the formulation of new theories or revision of old ones). Its record of success in this process is a justification for its continued use. The inference being made is simply that the apparent regularities are potentially fruitful areas for exploration and theorizing.
Prediction versus Explanation
At this point, it seems appropriate to address explicitly one debate in the philosophy of science—that is, whether science can, or should try to, do more than predict consequences. One view that held considerable influence during the first half of the twentieth century is called the predictivist thesis: that the purpose of science is to enable accurate predictions and that, in fact, science cannot (or need not) actually achieve more than that. The test of an explanatory theory, therefore, is its success at prediction, at forecasting. This view need not be limited to actual predictions of future, yet to happen, events; it can accommodate theories that are able to generate results that have already been observed or, if not observed, have already occurred. Of course, in such cases, care must be taken that the theory has not simply been retrofitted to the observations that have already been made—it must have some reach beyond the data used to construct the theory.
In 1960, Stephen Toulmin attacked the “predictivist thesis,” a philosophical approach that he claims he once shared. Foresight and Understanding, pp.22–3. He asserted: “Forecasting…is a craft or technology, an application of science rather than the kernel of science itself. If a technique of forecasting is successful, that is only one more fact, which scientists must try to explain, and may succeed in explaining… . [A] novel and successful theory may lead to no increase in our forecasting skill; while, alternatively, a successful forecasting-technique may remain for centuries without any scientific basis. In the first case, the scientific theory will not be necessarily any the worse; and, in the second, the forecasting-technique will not necessarily become scientific … .” Id., p.36. He explained how historically several theories that have been rejected were capable of more precise predictions than the theories that superseded them, such as Babylonian astronomy and Kepler’s laws of planetary motion, the tables of the times and heights of tides. Id., pp.27–34.
Now these methods of forecasting were the result essentially of the compilation of data reflecting apparent patterns or regularities in the phenomena under examination combined with the assumption that the patterns would repeat themselves, which they have. The techniques are mechanical (or, as Toulmin characterized them, merely “arithmetical”); they do not otherwise explain the successes or the failures of the forecasts. Id., pp.28, 29. “The Babylonians acquired great forecasting-power, but they conspicuously lacked understanding. … [Newton gave us] a number of general notions and principles which make sense of the observed regularities, and in terms of which they all hang together.” Id., pp.30, 33. (As discussed later, however, one might question the extent to which Newton’s theories actually gave us explanations; but, there clearly is a rather profound sense in which Newton’s theories were an improvement.) Toulmin describes the aims of science as lying “in the field of intellectual creation.” Id., p.38.
My discussion has been in terms of prediction and explanation, words that I think are more modest than foresight and understanding. Toulmin’s concepts seem to include greater grasps of the causal relationships involved. Thus, while prediction includes mechanical techniques that generate accurate forecasts, forecasting suggests (at least to me) some element of vision or appreciation of the factors at work in the relationships and, often, a sense of the likely outcome prior to the complication of a precise computation. Similarly, understanding suggests an appreciation of the relationships that is deeper than mere explanation. So, I shall stick with my more humble words.16
Some scientists do take an interest in these issues, at least when writing for the general public. For example, contemporary physicist David Deutsch recently set out an attack on the philosophical view that “denies that what I have been calling ‘explanation’ can exist at all.” He claims that “during the twentieth century, most philosophers, and many scientists, took the view that science is incapable of discovering anything about reality. Starting from empiricism, they drew the conclusion … that science cannot validly do more than predict the outcome of observations, and that it should never purport to describe the reality that brings those outcomes about.”