Secular Responses to the Problem of Induction

James N. Anderson


The so-called ‘problem of induction’ has proved to be one of the enduring problems of epistemology. Since it was first raised by David Hume in the 18th century, numerous philosophers have grappled with the challenge laid before them by Hume, resulting in some ingenious attempts to solve (or dissolve) the problem.

The basic problem can be summarised as follows. Suppose that we observe a large number of objects with characteristic A, noting that all of them also possess characteristic B. It is natural for us to conclude that, in all probability, all objects with A also possess B — including those objects with A that have yet to be observed (or cannot be observed). The question posed by Hume is: What rational justification is there for making this inference? More generally, what reason do we have to believe that our conclusions about observed instances may be extended (even with probability) to include unobserved instances? The same basic question is most frequently framed in temporal terms: What reason do we have to think that we can draw reliable conclusions about future (unobserved) instances on the basis of past (observed) instances?

Hume’s conclusion was that, regrettably, we have no good reason to think that such inductive inferences are justified. The problem of induction, then, is the problem of answering Hume by giving good reasons for thinking that the ‘inductive principle’ (i.e., the principle that future unobserved instances will resemble past observed instances) is true. The need for such an answer is immeasurable, since the majority of scientific research is based on inductive reasoning — not to mention most of our everyday inferences about what to expect in the world.

In this paper, I will summarise the most significant attempts to solve the problem of induction from a secular perspective; that is, without introducing such ‘religious’ themes as divine design or revelation. I will also briefly explain why each of these attempts is unsuccessful.

The Naïve Inductive Response to the Problem

Before considering more sophisticated responses to the problem, it will be instructive to consider the popular reply to Hume’s question. When asked, “What reason do we have for supposing that the inductive principle is true?”, the majority of people who have not reflected carefully on the issue will say something like, “Because it has been proved to be true in the past.”

The reasoning of such a reply may be spelled out in more detail as follows. Whenever we have observed instances in the past, and have drawn conclusions about (at that time) future unobserved instances, our conclusions invariably turn out later to be confirmed via direct observation (i.e., once we get round to observing those formerly unobserved instances). Since it has always been the case that unobserved instances have been found to resemble observed instances, we can confidently conclude that (at least probably) all unobserved instances will resemble observed instances.

The trouble with this answer, as Hume was at pains to point out, is that it begs the question. The reply itself takes the form of an inductive argument — reasoning about the future on the basis of the past — and thus must presuppose the very thing it aims to establish: the inductive principle. It is therefore guilty of fallacious circular reasoning. As Hume succinctly puts it:1

To say [the inference that the future will be like the past] is experimental [i.e., based on experience], is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. 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.

Sophisticated Inductive Responses: Will and Black

Despite Hume’s arguments, and the concurrence of thinkers as distinguished as Bertrand Russell,2 some philosophers have argued that the inductive principle can be supported inductively, i.e., that past experience can serve as evidence for its truth.

Frederick L. Will, for example, argues that the problem as posed contains a concealed equivocation on the word ‘future’.3 He advises that when speaking of ‘future instances’ we should distinguish between ‘future-1’, which qualifies specific events and things that are currently future but will eventually become past, and ‘future-2’, which describes in the abstract that portion of the space-time universe which is always “beyond the line of the moving present”. (It is the second of these senses that we have in mind when we playfully argue that “tomorrow never comes”.) Having made this distinction, Will argues that Hume and Russell must be employing ‘future-2’ when they say that we cannot know that the future will resemble the past, for we are in fact continually confirming that ‘future-1’ instances resemble past instances (i.e., whenever a ‘future-1’ instance finally becomes a present observed instance). Yet ‘future-2’ instances are by definition unobservable — and we ought not to be in the least concerned about that trivial truth.

The problem with Will’s response is that it misses the point. ‘Future-1’ instances cannot be evidence for anything until they are finally observed. But the real issue is this: How can we know prior to observing it that any particular ‘future-1’ instance will resemble past instances? Moreover, the problem can be rephrased without reference to relative temporal terms such as ‘future’: For any time t, what reason do we have for thinking at t that instances at any time t+ (where t+ > t) resemble instances at any time t (where tt)? Will has provided no answer.

Other philosophers, such as Max Black, have argued that Hume’s charge of circular reasoning can be dismissed once we note that the inductive justification of ordinary inductive inferences is actually a second-level inductive argument concerning first-level inductive arguments.4 The induction applied at the second level (to arguments) is distinct from that applied at the first level (to objects in the world), thus no objectionable circularity is involved. Furthermore, second-level induction can be justified via a third-level inductive argument (applied to second-level arguments), and so forth as required.

This response to the problem, while creative, is entirely unsatisfactory. As BonJour notes, not only does it lead to an infinite regress (in which the actual justification of the first-level induction is indefinitely deferred), but it also misses the point.5 The fundamental question raised by Hume, and repeated by Russell, is whether the premise of an inductive argument ever warrants its conclusion, regardless of the subject matter of the argument. Thus, Black’s response plainly fails to evade the charge of begging the question.

Popper’s ‘Solution’

In his book Objective Knowledge, Karl Popper writes, “I may be mistaken; but I think that I have solved a major philosophical problem: the problem of induction.”6 Popper is indeed mistaken — at least, he is if we take him to be referring here to the problem as set out above. It transpires that Popper actually concedes Hume’s position on the problem.7 The solution he offers pertains to a different problem, one that asks whether past experience can ever justify attributing a truth value (i.e., either ‘true’ or ‘false’) to a scientific theory. Popper argues, rightly, that a scientific theory (involving predictions about future instances) can indeed be shown to be false by present or past observations. Yet Popper’s arguments here provide no reason for thinking that scientific theories can be shown to be true (or probably true) by present or past observations. Indeed, Popper believes that no such reason can be given — and thus he supplies no comfort to the scientist who has been left wondering, after Hume, whether she can ever conclude that her empirically based theories are likely to be true.

Pragmatic Justification: Reichenbach and Salmon

A novel response to Hume’s problem has been offered by Hans Reichenbach, and has been defended more recently by Wesley Salmon.8 Reichenbach acknowledges the seriousness of the problem, rejects deductive and inductive attempts to prove the inductive principle, and offers instead a ‘pragmatic’ justification for induction. In essence, he argues that it is more prudent to ‘bet’ on inductive reasoning than on any alternative method of reasoning from experience. His reasoning runs along the following lines. If we opt to use induction, then we have at least some chance of success (i.e., if it turns out that the inductive principle is true); however, if we opt to use some alternative method, then we have no chance of success (i.e., regardless of whether the inductive principle is true); therefore, we are justified in choosing induction.

Numerous criticisms can be levelled at Reichenbach’s answer to the problem.9 The fatal weakness with a pragmatic justification of induction, however, is just that it is a pragmatic justification and not an epistemic justification. That is, while it may motivate us to employ a certain strategy (to reason inductively), it gives us no indication of the actual likelihood of its success (i.e., whether the inductive principle is true). In this respect, it suffers from the same ailment as Pascal’s Wager (which may offer motivation for believing in God, but leaves us none the wiser as to whether He actually exists). A true solution to the problem of induction requires an epistemic justification — a reason for believing that induction is reliable — yet Reichenbach’s solution, for all its ingenuity, offers no such thing.

The Ordinary Language Response: Strawson

While many philosophers, such as Reichenbach, concede that the problem of induction is indeed a real problem and acknowledge that the demand for a justification of induction is legitimate and important, other philosophers have argued that demanding a justification for induction is improper — or worse, incoherent. P. F. Strawson is just one such philosopher.10

Strawson characterises the inductive skeptic as doubting whether relying on inductive procedures is “reasonable” (i.e., epistemically justified). In response, Strawson argues that our very understanding and use of the word “reasonable” includes the idea of conformance with inductive standards (in the present context). So, for example, when we say that a scientific theory about a natural law is “reasonable”, we are saying (at least) that it draws general conclusions based on an appropriate number of observed instances. Thus, the statement “induction is reasonable” is an analytic truth, and the inductive skeptic is confused in the same way as the man who asks, “Is the law legal?”

However, BonJour notes that there is something amiss with Strawson’s response to the problem of induction, since in the same passage he also concedes that the statement “induction will continue to be successful” is contingently true (if true at all), and in doing so gives credence to the concerns of the inductive skeptic. This shows that the skeptic can always rephrase his doubts to avoid Strawson’s ‘immune’ terms such as “reasonable” and “justified”.

Even if Strawson is correct that our everyday usage of the word “reasonable” includes the idea of conformance to inductive standards, the inadequacy of citing this fact as a response to the problem of induction can be clearly seen by comparing it to analogous scenarios. For example, suppose there were a community for whom wishful thinking was considered a respectable and reasonable way of coming to conclusions about the future. For that community, with its own peculiar linguistic usage, the statement “wishful thinking is reasonable” would be analytically true; but nonetheless we would be entirely within our rights to question their reliance on such dubious epistemic methods. In the same way, Strawson’s claim that “induction is reasonable” cannot be meaningfully denied is perfectly compatible with the skeptical conclusions of Hume.

An A Priori Justification: BonJour

It should be evident from the foregoing discussion that no satisfactory answer to the problem of induction has been given by any responses based on a posteriori or linguistic factors. Laurence BonJour suggests that only an a priori justification for induction offers any hope of a solution.11 BonJour responds persuasively to those who would object to an a priori justification in principle, before sketching a scheme by which such a justification might be formulated.

While BonJour concedes that his treatment is far from complete, and frankly notes some of the problems remaining for his case, it will be informative to mention one particular difficulty that it faces. Crucial to BonJour’s scheme is the idea that an objective regularity in the universe (of the sort presupposed by inductive inference) can be justified a priori by taking it to offer the best explanation of standard inductive evidence (i.e., of those orderly observed instances employed in the premise of an inductive argument). However, he recognises that this claim “depends on the tenability of a non-Humean, metaphysically robust conception of objective regularity (or objective necessary connection).”12 That is to say, it presupposes a universe in which there are real and constant (or near-constant) causal relations between the objects within it.

While BonJour acknowledges the difficulties of “explicating … such a conception”, he does not consider them to be “insurmountable”. However, he gives no indication as to how one might even begin to provide an a priori justification for such a significant metaphysical perspective. It should be noted that this is no small matter. On the contrary, it was arguably Hume’s doubts about whether we could know of any “metaphysically robust objective regularity” that fuelled his inductive skepticism in the first place. The justification of our belief in the kind of universe that makes inductive inference possible is the very crux of the problem of induction. While I sympathise with BonJour’s insistence on seeking an a priori justification, I must conclude that his proposed route of ascent takes us at best only a fraction of the way up the mountainside.


On the basis of this survey, it is evident that there presently exists no satisfactory solution to the problem of induction from a secular perspective. Moreover, certain types of approach — the a posteriori, the pragmatic, the linguistic — suffer from fatal inadequacies. Only an a priori solution seems feasible, yet even BonJour’s treatment leaves at least one of the biggest gaps unbridged. It seems clear that any successful solution must depend, at some point, on universal a priori knowledge of the very constitution of the universe. Yet (to borrow from the Psalmist) we cannot help but despair that “such knowledge is too wonderful for me, too lofty for me to attain”.

Of course, a Person for whom universal a priori knowledge of the very constitution of the universe is attainable (and perhaps even essential) would be an invaluable ally in such an epistemological predicament — especially so if that Person were inclined toward revelation of Himself and His universe. But how high a price are philosophers prepared to pay in order to banish the epistemological terrorism of inductive skepticism?


  1. Hume (1748), IV. ii. 32.
  2. Russell (1967).
  3. Frederick L. Wills, ‘Will the Future Be Like the Past?’, in Flew (1953), pp. 32-50.
  4. Max Black, ‘Self-Supporting Inductive Arguments’, in Swinburne (1974), pp. 127-34. Cf. Black, Problems of Analysis (New York: Ithaca, 1954), chapter 11.
  5. Bonjour (1998), pp. 200-3.
  6. Popper (1979), p. 1.
  7. Ibid., p. 7.
  8. Wesley Salmon, ‘The Pragmatic Justification of Induction’, in Swinburne (1974), pp. 85-97.
  9. See BonJour (1998), pp. 192-6.
  10. See Strawson (1952), pp. 256-63. A. J. Ayer and Paul Edwards have attacked the problem along similar lines to Strawson.
  11. BonJour (1998), pp. 187-216.
  12. Ibid., pp. 214-5.