David Hume is credited with raising what is known as the problem of induction. As Hume noted, the contrary of any matter of fact is logically possible. To illustrate, it is not a contradiction to claim that although the earth is now rotating around the sun, it will not be doing so tomorrow. This is in contrast with the truths of reason—it is a contradiction to deny them. For example, to deny that a triangle has three sides is to assert that a three-sided figure does not have three sides.
In considering our reasoning about matters of fact, Hume notes that we try to justify our beliefs by appealing to other beliefs about causal laws. That is, people tend to think that there is a causal order set in the laws of nature that ensure a consistent universe. For Hume, an empiricist, this process is based on experience. As he sees it, people observe similarities between events and then form the expectation that the same things will occur in unobserved cases (such as those occurring in the future). While anyone who is not a fool or mad has faith in causality based on their experience, Hume contends that the reasoning from the observed cases to the unobserved cases is unwarranted. The gist of his argument focuses on the idea that the future will be like the past, which is essential to engaging in inductive reasoning about the future. After all, this reasoning is that because X happened in situation Y in the past, X will happen in situation Y in the future. Going back to the earth example, people think the earth will be revolving around the sun tomorrow because it has done so in the past. The challenge is showing that the past to future reasoning is warranted. Hume claims that this cannot be done.
As Hume argued, the argument that because X has happened in the past, X will happen in the future is not a sound deductive argument. This is because it could be true that X has happened in the past, while the conclusion could be false. A sound deductive argument must, of course, be valid (such that if all the premises are true, then the conclusion must be true) and have all true premises.
If one attempts to justify inductive logic by using an inductive argument, this would be begging the question—to justify induction by induction inductive logic would already need to be justified. As such, neither a deductive nor inductive argument can justify induction, thus the problem of induction. In practical terms, the problem is that since an inductive argument always involves a leap from what has been observed to what has not been observed, even if all the premises are true and the reasoning is strong, the conclusion could be false.
Like some other philosophical problems, the problem of induction initially seems silly and trivial. It seems silly because, as Hume noted, only a fool or a mad person would deny faith in induction. For example, someone who insisted that while fire heats today it might cool tomorrow would be regarded as a lunatic. It seems trivial because, like the problem of the external world, it seems to have no real-world implications. However, it is neither silly nor trivial.
The easy way to argue for this is to point out that the problem of induction has serious practical consequences that impact the real world. Inductive reasoning is used throughout all aspects of life, including matters of considerable importance and to fail to consider the problem of induction can range from the merely embarrassing to the disastrous. For example, most of the inductive generalizations (surveys and polls) predicted that Clinton would win in 2016. While many were shocked when these polls got it wrong, this was merely one more example of the problem of induction: no matter how careful the evidence is gathered and how skilfully the argument is crafted, the conclusion can always be false. As another example, a person might be confident that they will safely arrive at their destination and end up dying in a plane crash—after all, that inference is also inductive. More broadly, the problem infects all inductive reasoning ranging from simple analogies to massive controlled experiments. As such, it is only be fools and lunatics who do not worry about the problem of induction and consider that no matter how careful they are in their reasoning, they could still get things wrong.
At this point, it might be claimed that although this practical aspect of the problem of induction is a meaningful problem, the philosophical variation is still trivial and silly. To be more specific, the notion that our faith in basic aspects of reality is unfounded is a silly idea. For example, to say that while gravity, fire and electromagnetism work in certain ways now, they might not work the same tomorrow would be absurd. Gravity will always work as it does, fire will always burn and so on. Even those who accept inductive arguments can always fail tend to have faith in a consistent and reliable reality. However, as Hume argued, this faith is unwarranted.
As noted above, the idea that induction can fail in everyday cases seems quite reasonable. For example, it is clearly not absurd to consider that while a friend has always been dependable in picking you up from the airport, they might not be able to get you this time. As another example, it is not silly to think that while you have never been allergic to something in the past, you might become allergic to it. In such cases, our faith is not absolute, so we accept that we could be in error. But, in the case of things like fire and gravity, our faith tends to be absolute—a seemingly faithful spouse might betray, but fire will always burn. But, of course, our faith reflects our feelings and not reality—we simply feel strongly, rather than know, that fire will always burn and so on for the other matters of our faith in the workings of the world. If we set aside our faith and consider the matter in terms of inductive reasoning, then we would realize that our confidence that the workings of the future will be like those of the past is not well founded—we could be quite wrong, though we certainly feel otherwise. After all, the same inductive logic that is used for brand buying (“my previous Asics shoes were good, so this pair I plan to buy will also be good”) is also used for predicting that future fire will be like past fire. The main difference thus cannot be in the logic; it lies in how we feel. Because of this, what is needed is not another logical argument about the problem, but a way to sway intuitions. This is a common approach in the case of the big and weird philosophical problems, such as the problem of the external world.
The problem of the external world, which was most famously developed by Descartes in his Meditations, is the problem of proving that the world I think I am experiencing is really real for real. Like most philosophy professors, I found it challenging to motivate students to see the problem as a real problem—after all, thinking that the world is not real seems like insanity. Then the Matrix hit the big screen and motivating the problem became very easy. Fortunately, shows like Black Mirror and Legion have continued to provide fresh examples for the current crop of students. Unfortunately, there has yet to be a big movie or show that includes the problem of induction as a central theme. However, I can avail myself of a fairly popular medium, that of video games.
Imagine, if you will, that you are a character in a video game like Destiny 2, World of Warcraft or Warframe. From your perspective, the world has clear rules and most things work in the same way. At least until they do not—after all, a game world is under the control of the programmers and they can change the reality at will. Think of what the inhabitants of such game worlds would think if they were aware and could remember what had come before. For example, the developers of Destiny 2 accidentally released a bugged weapon, the Prometheus Lens, into the game. Because of the bug, the weapon could kill a character in player versus player battles almost instantly—making it insanely overpowered and broken. Bungie then patched the weapon (“nerfing” it, in gamer slang) so that it would perform properly. From the standpoint of the game world inhabitants, the weapon suddenly and inexplicably went from a fiery engine of instant death to an average gun. Game worlds can also experience far more radical alterations: entire sections of mechanics can change with a patch or update. Players, of course, know that the changes are made in the code by programmers. But, from the perspective of the hypothetical game world inhabitants, reality suddenly changes without any warning or explanation.
Now imagine that we live in a world subject to the alterations of a creator or coders—we could suddenly find that our game has been patched or updated and that there are radical differences between yesterday and today. To say that we have not seen such changes in the past would miss the point—after all, the last patch or update could have been long before our time or perhaps it will be the first update or patch. We have no way of knowing whether this is impossible or not—which is, of course, the problem of induction.