One of Hume’s most renowned insights in An Enquiry Concerning Human Understanding is the problem of induction, in which he argues that inductive reasoning cannot be justified. In this paper I will analyze Hume’s problem of induction and its possible solutions.
To understand the problem of induction, we must understand Hume’s fork. There are two kinds of judgements – relations of ideas and matters of facts (Enquiry 4.1). Relations of ideas are a form of intuitive or demonstrative knowledge. Intuitive knowledge is gained from inspection of ideas. Demonstrative knowledge is gained from reasoning from ideas and is only possible for long chains of mathematics. Relations of ideas are known a priori, thus we ascertain them through thought alone. Truths about relations of ideas are the only ones whose falsehood implies a contradiction – our minds cannot imagine them being otherwise. An example is “bachelors are unmarried” or “5+5=10” (4.1-4.2). Matters of fact are facts about what exists or how things are arranged in the universe. They are discerned through experience via probable reasoning. They are based on the assumption that the future will resemble the past; however, they are not known with certainty. An example is “the sun will rise tomorrow.” I have ascertained this knowledge through experience. Via probable reasoning, I assume that the future will resemble the past, so I conclude that the sun will rise tomorrow; however, I can conceive of a situation in which the sun does not rise (4.2).
Hume argues that we must learn about the world through the relation of cause and effect, (4.4), and we learn about cause and effect from experience (4.6). For example, how do I know that if I drop a baseball from mid-air, it will fall to the floor? This knowledge cannot be a priori since I can deny that the baseball will fall without contradiction. I must gain this knowledge from experience. I have observed that when I previously dropped baseballs, they fell to the ground. Therefore, I infer that if I let go of this baseball, it will do the same. This is induction – inference from the observed to the unobserved by means of resemblance.
Hume then argues that the foundation of our conclusions from experience is not argument or reasoning (4.16). Any argument to justify induction would have to be demonstrative or probable. This is where Hume faces a dilemma. We cannot use a demonstrative argument to justify induction because we can conceive of the course of nature changing (4.18). For example, imagine that on Monday I see a raven, and it is black. On Tuesday I see a raven, and it is black. I see a raven every day for 100 days, and every time, it is black. Through induction, I conclude that all ravens are black. Yet, I can conceive of a case in which I see a raven and it is white. But demonstrative reasoning only applies for relations of ideas, those which we cannot conceive of being otherwise. Therefore, we cannot use a demonstrative argument to justify induction (4.18).
Hume then moves on to determine whether a probable argument can be used to justify reasoning from experience. Hume considers the connecting principle called the uniformity of nature principle, which states that the future will resemble the past. Consider the following argument:
1. I prick my finger, and it bleeds.
2. I prick my finger, and it bleeds.
3. …
4. The world is uniform.
5. If I prick my finger, it will bleed.
If the world is uniform, then the future will resemble the past, so if I prick my finger, it will bleed. But I have only determined that the world is uniform because my experience of the world has repeatedly shown it to be uniform. I do not know if this is actually true. Therefore, any argument to justify reasoning from experience with experience is circular. Hume concludes that neither demonstrative nor probable reasoning can justify induction. The problem of induction is to find a way to avoid this conclusion (4.19).
Hume presents a skeptical solution in which he does not reject his previously skeptical argument. He argues that the practice of forming beliefs on the basis of experience still cannot be justified by reason. This is unavoidable, and Hume concedes that it can make us doubt ourselves. Yet, he does not think that we should stop reasoning on the basis of experience. Skeptical doubts cannot affect our ordinary lives (5.5).
Hume then argues that if our belief in induction is not due to reason, it must be due to some other principle of equal weight and authority – “custom” or “habit.” If we see similar objects or events constantly conjoined, then our mind starts to expect this regularity in the future (5.12). Hume defines belief as an idea that is more vivid or lively than imagination. When our mind associates two ideas, the impression of one gives more liveliness to the idea of the other. Therefore, when I perceive the cause this gives me a more forceful idea of the effect (5.14).
While Hume’s skeptical solution is insightful, it does not solve the problem of induction. Other philosophers have attempted to respond to the problem of induction, but no arguments prove successful. One response is that there exists another type of reasoning that can justify induction by producing a demonstrative argument that the conclusion of an inductive inference is highly probable, even if it is not certain. One type of reasoning is probabilistic reasoning. The more we notice a uniformity, the higher the probability it will continue. Therefore, the more often that we associate two things, the higher the probability that they will appear together next time (Mackie, The Cement of the Universe Ch. 1). For example, if I see one 1 million cats that all have tails, the probability that the next cat I see will have a tail is much higher than if I only see 1 cat with a tail. The more evidence we gather, the closer the probability will get to 1. The problem with this response is that the number of observed cases will always be finite, so there is no way to prove that probability will reach close to 1; therefore, it is very hard to give a justification for induction along these lines. Another type of reasoning is inference to the best explanation. IBE says that we should infer that the hypothesis which provides the best explanation of the evidence is probably true. One could argue that the course of nature has been stable so far, and there must be a reason for this. The course of nature could change, but it should not do so without a reason. Therefore, based on IBE, our inductive inferences are likely to be right (Armstrong 1983; BonJour 1998; Foster 2004). Yet again, this reasoning is still circular. Laws have been exceptionless up until now. We have no reason to believe that this will continue. Both probabilistic reasoning and IBE raise questions of how they can be justified. This creates further circular arguments, which only complicates Hume’s problem.
Another reply is Peter Strawson’s solution. He argues that deduction is something you know by logic alone. Hume is trying to justify induction by making inductive inferences deductively valid, and this does not make sense. Induction just is a rational way to proportion one’s beliefs to the evidence; therefore, it does not need further justification (Strawson Introduction to Logical Theory Ch.9.) Hume might not deny this response, but this response still seems unsatisfying since, as Hume notes, when we recognize that there is no justification for induction, we feel doubt (Enquiry 5.5).
One final response is the pragmatic justification for induction. Reichenbach’s argument is as follows. Hume is correct in saying that we cannot prove the conclusion of an inductive inference to be true. But, it appears that induction is the best guide to action that we have. Therefore, we are pragmatically justified in using induction (Reichenbach Experience and Prediction 349). For example, a man is dying of a fatal illness. A doctor says that he does not know whether an operation will save him, but it is his best chance of survival. We do not know if the operation will save him, but since it is his best option, he is pragmatically justified in getting the operation (349). Reichenbach argues that the world is either ordered or not. If it is not ordered, then no method will work. If it is ordered, then induction will work. Therefore, we are justified in using induction (475). While Reichenbach’s response is insightful, there is still one problem. Even if induction is the best principle that we have available to us, this does not prove that it is a good one. This seems unsatisfying as well.
Hume’s problem of induction shows that we cannot justify induction with reasoning. Several philosophers have tried to answer Hume’s problem, but no responses have succeeded.