THE PROBLEM OF INDUCTION

Rationality in drawing inferences means that the conclusion of an argument must follow from the premises and must not go beyond them; it must be true if the premises are true. The rational force of an argument may then be measured by the extent to which the evidence in it entails the conclusion.

In these nonformal, inductive inferences the evidence does not entail the conclusion but lends it some sort of support or cor­roboration. Accordingly, the rationality and logical entailment in inductive arguments are a matter of degree and thus do not fit the neat paradigms of formal validity. The conclusion is not en­tailed by the available evidence but is more or less corroborated by it.^[218] Here, there is no demonstrative confirmation unless it can be established beyond any doubt that the total body of evidence needed to prove a generalizing statement has indeed been pro­vided. In such a case there is no problem, for when total evidence becomes available there is no question concerning the certainty of the conclusion if the particulars of the evidence which led to it are true. Instead, the real problem lies in the absence of total evidence, in drawing ampliative inferences by going from the ob­served to the unobserved with the inevitable result of reaching an uncertain conclusion.

This rudimentary conception of induction represents to a vary­ing degree an essential assumption in the logic of Aristotle, of medieval Muslim logicians, as well as of modern Western philo­sophers.^[219] Among the latter, David Hume restated the traditional problem of induction in terms of inferences from past experience to similar future events. If such events establish themselves in a law-like manner as being connected to current or past experiences, then what had applied to a particular case in the past must also apply to it in the future. Clearly, this argument presupposes a necessary causal connection between distinct events which neither Hume nor his posterity could establish.^[220] In the absence of such INDUCTIVE CORROBORATION, PROBABILITY, AND CERTAINTY 5 causal connection, Hume resorted to the next guiding principle in extending our present knowledge of things to yet unobserved instances, namely, the principle of the “uniformity of nature,” which affirms that what held good in the past will hold good in the future.⁴ But should this principle be grounded in an assump­tion that cannot be logically justified, then we have no good rea­son to trust any inference of this kind. Hume therefore concluded that inductive inferences cannot yield conclusive assurances but are at best highly probable.⁵ To rephrase this argument and to eliminate the concern with future events—which is of no interest to us here—Hume’s proposition comes down to the question of whether or not we are able to reach, on the basis of incomplete but highly corroborative evidence, a conclusion or a generalization which can be deemed conclusive. The answer, of course, is that we are not. Corroboration strengthens a generalization but does not render it certain; it enhances its credibility to the extent of the corroborative evidence.

While multiple pieces of corroborative evidence cannot estab­lish the certainty of a proposition, it takes only a single nega­tive instance to falsify that proposition. Like Greek and modern Western philosophers, medieval Muslim logicians acknowledged the validity of this principle. The oft-quoted and long-lived ex­ample of the crocodile was frequently introduced to illustrate this point. An investigation into the eating habits of animals, such as humans, horses, rabbits, birds, and so on, leads to the conclu­sion that “All animals move their lower jaw when they chew.” This statement, however, is falsified when we examine crocodiles, which move their upper jaw, and which we failed to investigate before we formed our conclusion.⁶ This example teaches that whatever the level of corroboration may be, there will always

⁴ Frederick L. Will, “Will the Future be Like the Past?” in Logic and Language, ed. Anthony Flew (New York: Doubleday, 1965), p. 248 ff.

⁵For a lucid analysis of Hume's ideas on this issue see A. J. Ayer, Probability and Evidence, pp. 3-26; idem, The Central Questions of Philosophy (Middlesex: Penguin, 1976), p. 137ff., 174ff.; For a statement and critique of the same see Goodman, Fact, Fiction, chapter 3, especially p. 63 ff., 81 ff.

⁶ Abu Hamid al-GhazalT, Maqasid al-faldsifah, ed. Sulayman Dunya (Cairo: Dar al-Ma‘arif, 1961), p. 89; Taqi al-DTn Ibn Taymiyah, Jahd at-qarihah fi tajrid al-nasihah (being an abridgement by SuyutT of At-Radd ‘ala al-mantiqiyin), ed. ‘A1T Sami al-Nashshar (Cairo: Matba‘at al-'Sa‘adah, 1947), p. 296 ff.

exist the possibility of falsifying the conclusion because of counter evidence. This problem of induction, whether in its basic Aris­totelian and medieval Muslim form or in its highly articulated reformulation by Hume, Mill, Carnap, Keynes, and others, can­not be solved except in terms of probabilistic, nondemonstrative logic.⁷