Although the “problem of induction” dates back at least as far as Pyrrhonism in the West, and the Carvaka school of thought in the East, David Hume later popularized it in the 18th century. Long before that, in the 2nd century, the Pyrrhonian skeptic Sextus Empiricus first questioned the validity of inductive reasoning, positing that a universal rule could not be established from an incomplete set of particular instances:
When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite.
Sextus Empiricus also wrote that:
Those who claim for themselves to judge the truth are bound to possess a criterion of truth. This criterion, then, either is without a judge’s approval or has been approved. But if it is without approval, whence comes it that it is truthworthy? For no matter of dispute is to be trusted without judging. And, if it has been approved, that which approves it, in turn, either has been approved or has not been approved, and so on ad infinitum.
David Hume drew on the logic of that latter argument to formulate his own kind of skeptical approach to epistemic philosophy. Then, in 1739, the modern source of what has become known as the “problem of induction” was published in Book 1, part iii, section 6 of A Treatise of Human Nature by David Hume. As such, his name has been attached to the concept ever since then. So, then just what is “Hume’s Dilemma”? Well, according to the Stanford Encyclopedia of Philosophy, in the 2018 entry for “The Problem of Induction” by Leah Henderson:
We generally think that the observations we make are able to justify some expectations or predictions about observations we have not yet made, as well as general claims that go beyond the observed. For example, the observation that bread of a certain appearance has thus far been nourishing seems to justify the expectation that the next similar piece of bread I eat will also be nourishing, as well as the claim that bread of this sort is generally nourishing. Such inferences from the observed to the unobserved, or to general laws, are known as “inductive inferences”.
The problem of induction arises because any given inductive statement can only be deductively shown if one assumes that nature is uniform, and the only way to show that nature is uniform is by using induction. Thus, induction cannot be justified deductively, and that’s a big problem, philosophically speaking. In other words, the problem of induction is the question of whether or not inductive reasoning can lead to knowledge as it is understood in the classic philosophical sense, specifically highlighting the apparent lack of justification for (1) generalizations and (2) presuppositions.
- Generalizing about the properties of a class of objects based on some number of observations of particular instances of that class.
- Presupposing that a sequence of events in the future will occur as it always has in the past.
Ultimately, the problem calls into question all of the empirical claims made in everyday life, as well as the scientific method. So, simply put, to what extent does the past predict the future? The philosopher C. D. Broad put it this way, “induction is the glory of science and the scandal of philosophy.” What assurances do we have that the laws of physics will hold as they have always been observed? Hume called this the “uniformity of nature”, and he was incredibly skeptical of the overall assumption, in general. First of all, it is never certain, regardless of the number of observations, that the Sun will rise tomorrow. In fact, Hume would even argue that we cannot even claim that it is probable since this still requires the assumption that the past predicts the future. Second, the observations themselves do not establish the validity of inductive reasoning, except inductively. Bertrand Russell famously described this in The Problems of Philosophy:
Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.
Consider a turkey, fed every morning without fail, who following the laws of induction concludes that this will surely continue, but then his throat is abruptly cut on Thanksgiving Day. In this way, philosophers like Hume and Russell ask us on what grounds we come to our beliefs about the unobserved on the basis of inductive inferences. In essence, Hume presents an argument in the form of a dilemma which appears to rule out the possibility of any reasoning from the premises to the conclusion of all inductive inferences. He said that there are two possible types of arguments, “demonstrative” and “probable”, but that neither will serve. This is because a demonstrative argument produces the wrong kind of conclusion, and a probable argument would be circular. Thus, the premise would lead to the conclusion which would lead to the premise.
The challenge, as Hume saw it, is to understand the “foundation” of the inference. In other words, the “logic” or “process of argument” that it is based upon. The problem of meeting this challenge, while evading Hume’s argument against the possibility of doing so, is “the problem of induction”. The way David Hume understood the world to work, reasoning alone cannot establish the grounds of causation. For Hume, establishing the link between causes and effects relies not on reasoning alone, but on the observation of “constant conjunction” throughout one’s experiences. In A Treatise of Human Nature, Hume wrote:
…there can be no demonstrative arguments to prove, that those instances, of which we have had no experience, resemble those, of which we have had experience.
In other words, we cannot apply a conclusion about a particular set of observations to a more general set of observations. So, while deductive logic allows one to arrive at a conclusion with certainty, inductive logic can only provide a conclusion that is probably true. According to the literal standards of logic, deductive reasoning arrives at certain conclusions while inductive reasoning arrives at probable conclusions. Furthermore, Hume’s treatment of induction helps to establish the grounds for probability, just as he wrote in A Treatise of Human Nature:
…probability is founded on the presumption of a resemblance betwixt those objects, of which we have had experience, and those, of which we have had none.
To quote Leah Henderson again:
Hume’s argument is one of the most famous in philosophy. A number of philosophers have attempted solutions to the problem, but a significant number have embraced his conclusion that it is insoluble. There is also a wide spectrum of opinion on the significance of the problem. Some have argued that Hume’s argument does not establish any far-reaching skeptical conclusion, either because it was never intended to, or because the argument is in some way misformulated. Yet many have regarded it as one of the most profound philosophical challenges imaginable since it seems to call into question the justification of one of the most fundamental ways in which we form knowledge.
As if that wasn’t bad enough, Bertrand Russell even expressed the view that if David Hume’s problem cannot be solved, then “there is no intellectual difference between sanity and insanity”. Now, that’s a really big claim to make, but is it valid? Fortunately, although it is true that deduction reveals certainties and induction only reveals probabilities, there is no reason to think that likelihoods are not useful. Hume was right, but it’s not the big deal that Russell made it out to be. Donald Williams explained why this is in the book The Ground of Induction. Then, David Stove came up with an argument for induction based on statistical syllogism, which he presented in the Rationality of Induction. He argued that it is a statistical truth that the great majority of the possible subsets of a specified size are similar to the larger population to which they belong. So, for example, the majority of the subsets which contain 1,000 people which can be formed from the human population are similar to the population itself. Moreover, this applies no matter how large the human population is, as long as it’s not infinite. Consequently, Stove argued that if you find yourself with such a subset then the chances are that this subset is one of the ones that are similar to the population, and so you are justified in concluding that it is likely that this subset reasonably represents the overall population. The bottom line is that as long as you have no reason to think that your sample is an unrepresentative one, then you are justified in thinking that it probably is, just not for certain. Sure, it’s possible that the Sun might not come up tomorrow, but I highly doubt it, and that’s the whole point. So, although Hume is right in theory, it doesn’t actually matter in practice.