problem of induction. First stated by Hume this problem concerns the logical basis of inferences from observed matters of fact to unobserved matters of fact. Although discussion often focuses upon predictions of future events (e.g., a solar eclipse), the question applies also to inferences to past facts (e.g., the extinction of dinosaurs) and to present occurrences beyond the range of direct observation (e.g., the motions of planets during daylight hours). Long before Hume the ancient Skeptics had recognized that such inferences cannot be made with certainty; they realized there can be no demonstrative (deductive) inference, say, from the past and present to the future. Hume, however, posed a more profound difficulty: Are we justified in placing any degree of confidence in the conclusions of such inferences? His question is whether there is any type of non-demonstrative or inductive inference in which we can be justified in placing any confidence at all.
According to Hume, our inferences from the observed to the unobserved are based on regularities found in nature. We believe, e.g., that the earth, sun, and moon move in regular patterns (according to Newtonian mechanics), and on that basis astronomers predict solar and lunar eclipses. Hume notes, however, that all of our evidence for such uniformities consists of past and present experience; in applying these uniformities to the future behavior of these bodies we are making an inference from the observed to the unobserved. This point holds in general. Whenever we make inferences from the observed to the unobserved we rely on the uniformity of nature. The basis for our belief that nature is reasonably uniform is our experience of such uniformity in the past. If we infer that nature will continue to be uniform in the future, we are making an inference from the observed to the unobserved – precisely the kind of inference for which we are seeking a justification. We are thus caught up in a circular argument. Since, as Hume emphasized, much of our reasoning from the observed to the unobserved is based on causal relations, he analyzed causality to ascertain whether it could furnish a necessary connection between distinct events that could serve as a basis for such inferences. His conclusion was negative. We cannot establish any such connection a priori, for it is impossible to deduce the nature of an effect from its cause – e.g., we cannot deduce from the appearance of falling snow that it will cause a sensation of cold rather than heat. Likewise, we cannot deduce the nature of a cause from its effect – e.g., looking at a diamond, we cannot deduce that it was produced by great heat and pressure. All such knowledge is based on past experience. If we infer that future snow will feel cold or that future diamonds will be produced by great heat and pressure, we are again making inferences from the observed to the unobserved. Furthermore, if we carefully observe cases in which we believe a cause–effect relation holds, we cannot perceive any necessary connection between cause and effect, or any power in the cause that brings about the effect. We observe only that an event of one type (e.g., drinking water) occurs prior to and contiguously with an event of another type (quenching thirst). Moreover, we notice that events of the two types have exhibited a constant conjunction; i.e., whenever an event of the first type has occurred in the past it has been followed by one of the second type. We cannot discover any necessary connection or causal power a posteriori; we can only establish priority, contiguity, and constant conjunction up to the present. If we infer that this constant conjunction will persist in future cases, we are making another inference from observed to unobserved cases. To use causality as a basis for justifying inference from the observed to the unobserved would again invovle a circular argument.
Hume concludes skeptically that there can be no rational or logical justification of inferences from the observed to the unobserved – i.e., inductive or non-demonstrative inference. Such inferences are based on custom and habit. Nature has endowed us with a proclivity to extrapolate from past cases to future cases of a similar kind. Having observed that events of one type have been regularly followed by events of another type, we experience, upon encountering a case of the first type, a psychological expectation that one of the second type will follow. Such an expectation does not constitute a rational justification.
Although Hume posed his problem in terms of homely examples, the issues he raises go to the heart of even the most sophisticated empirical sciences, for all of them involve inference from observed phenomena to unobserved facts. Although complex theories are often employed, Hume’s problem still applies. Its force is by no means confined to induction by simple enumeration.
Philosophers have responded to the problem of induction in many different ways. Kant invoked synthetic a priori principles. Many twentieth-century philosophers have treated it as a pseudo-problem, based on linguistic confusion, that requires dissolution rather than solution. Carnap maintained that inductive intuition is indispensable. Reichenbach offered a pragmatic vindication. Goodman has recommended replacing Hume’s ‘old riddle’ with a new riddle of induction that he has posed. Popper, taking Hume’s skeptical arguments as conclusive, advocates deductivism. He argues that induction is unjustifiable and dispensable. None of the many suggestions is widely accepted as correct.
See also CAUSATION, GRUE PARADOX, HUME , SKEPTICISM , UNIFORMITY OF NATUR. W.C.S.