David Hume
The original identification of the problem of induction has traditionally been attributed to David Hume. See, e.g., Ian Hacking, The Emergence of Probability (1975), p.176. Hume’s A Treatise on Human Nature was published in 1739. A more focused (or, at least, more concise) statement of the arguments relevant here was set out in An Enquiry concerning Human Understanding, published in 1748 (originally entitled Philosophical Essays concerning Human Understanding). While Hume may have been the first person to have explicitly identified the problem of induction, Hume himself did not present induction as raising a philosophical problem. For him it was just a fact—one which he used to justify a philosophy of “skepticism.” Hume set the stage for his argument as follows: “Man is a reasonable being; and as such, receives from science his proper food and nourishment: But so narrow are the bounds of human understanding, that little satisfaction can be hoped for in this particular, either from the extent or security of his acquisitions.” Hume, An Enquiry concerning Human Understanding and Other Writings (2007) (edited by Stephen Buckle), p.6.11 He furthered stressed the inherent limits on man’s ability to know and understand the real world. Then, he presented the following thought: “It may, therefore, be subject worthy of curiosity, to inquire what is the nature of the evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory.” Id., p.29.
Hume effectively rejected the applicability of deduction to the external world.12 He expressly distinguished between “relations of ideas” and “matters of fact”, the former including mathematics and logic, subject to intuition and deductive reasoning with the consequent necessity of the conclusions (because contrary conclusions would be logically contradictory and, therefore, inconceivable). In contrast, “[m]atters of fact…are not ascertained in the same manner [through intuition and deductive reasoning]; nor is our evidence of their truth, however great, of a like nature… . The contrary of every matter of fact is still possible; because it never implies a [logical] contradiction… . Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind.” Id., pp.28–29; see also, id., p.36.
Hume argued that everything that man knew was a result of sensory perceptions combined with the search for patterns or “associations” of events and facts. The most important (or only) such association for matters of fact was “cause and effect.” Id., pp.20–21. (“All reasonings concerning matters of fact seem to be founded on the relation of cause and effect. By means of that relation alone we can go beyond the evidence of our memory and senses.” Id., p.29).
In other words, man continually scans the available sensory inputs and attempts to identify relationships of cause and effect. Such activity was essential to man’s survival, but was also the heart of scientific knowledge. Hume believed that induction was inherent and essential—there is no alternative available. He recognized the circularity involved in efforts to justify inductive reasoning. (“It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future, since all these arguments are founded on the supposition of that resemblance.” Id., p.38.)
Hume also highlighted the distinction between practical conduct and philosophical inquiry. “My practice, you say, refutes my doubts. But you mistake the purport of my question. As an agent, I am quite satisfied in the point; but as a philosopher, who has some share of curiosity, I will not say skepticism, I want to learn the foundation of this inference.”13 Subsequent philosophical inquiries have focused on the alleged logical shortcomings of induction or solving the “problem” of induction.
Probabilities
There is something more to say about the alleged problem of induction. It is obvious that the fact two events happen in sequence once does not mean that they will or are even likely to do so again. Even the fact that the two events happen in sequence twice (or one hundred times) does not guarantee that they will do so again. Even if there has never been a recorded instance in which A was not followed by B, one cannot say that it is inevitable that the next time A occurs, B will follow. We might say that we can at least assert that it is likely. Philosophers supposedly have shown that the characterization of induction as a matter of probability does not solve the “problem.”14 But, regardless, I do not think that our understanding of induction is simply probabilistic.
More repeated observations of a pattern can give rise to a belief that it is possible (or more probable) that there is a causal relationship between them. But, what gives rise to a reasonable and justifiable belief that B will follow A is a theory of the relationship between them that explains why B will occur when A has occurred.15 This element is, again, the concept of causation and the belief in the necessity of causal relationships. Man’s apparently inherent belief in the existence of causation was discussed above. The nature of the causal relationship is set out in the theory. The theory explains why the observed pattern is expected to repeat itself. That theory will also often identify factors that could cause the pattern not to be repeated in a given instance.
Commonly, a theory will contain (explicitly or implicitly) the ceteris paribus condition, saying that if A occurs then B will necessarily follow if, but only if, all relevant things remain the same. The use of “an unspecifiable ceteris paribus (all else being equal) clause” is a technique used in efforts to “connect” deductive models to the real world. Peter Lipton, Inference to the Best Explanation (Routledge, 2004) (Second Edition), p.64. But, one would hope that the real life variations in the initial conditions that can be identified when the predictions do not materialize will make sense in terms of the relationship being presented by the theory. If so, then the theory provides a basis for understanding the events that occur, including the failure of a predicted B to follow A.
We can illustrate these issues with some simple examples.
Bells, beer and ravens
Suppose that over three years as an undergraduate, one observed that whenever the bells of St. John’s College chapel rang, the bells of Trinity College chapel rang almost immediately thereafter. Inductively, one might infer (correctly) that there was a relationship between the two events. However, one might also (incorrectly) infer that the ringing of the John’s bells “caused” the ringing of the Trinity bells. In fact, presumably, the cause of the regular occurrence was that both bells were set to chime on the hour but the Trinity clock was slightly slower than the John’s clock. The causal relationship is thereby described by a more complex and extended theory.
The example that I recall being used in my statistics class 45 years ago was the close negative correlation between infant mortality and beer consumption (or, perhaps, it was a positive correlation between life expectancy and beer consumption). The misleading inference that could be drawn was a result of the selection of the data used. It reflected experiences across several countries in different stages of economic development. What was apparently behind the results was that economic development caused increased per capita beer consumption and also caused greater life expectancies (or lower infant mortality). There was no causal relationship between the two variables that were being correlated, only correlations of each with something else. But, those other correlations may well have reflected causal relationships.
Finally, there are many examples of empirical observations that would satisfy the description of “successful predictions” that could not meaningfully be considered as confirmation of the theory. One example is the “raven problem.” The proposition that “all ravens are black” logically entails the proposition that “All non-black objects are not ravens.” Yet, the observation of an object of a color other than black that is not a raven (e.g.,