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.
Such is the nature of science – as I learned it, anyway. Observation comes first, then prediction, then control. All of this tempered by the acceptance that everything might be different tomorrow.
The missing ingredient to your examples is that in science, anyway, the assumptions are made within a set of stable unchanged variables. Fire, for example, could very easily burn today but not tomorrow if somehow tomorrow’s environment were to be oxygen-deprived.
The prediction that Clinton would win in 2016 was really nothing more than wishful thinking – right-leaning pollsters predicted a Trump victory. From a scientific point of view, there are simply too many uncontrolled variables to make any kind of reasonable inductive prediction in that situation.
Then again, there’s also the argument that says that “doing the same thing over and over and expecting a different result is the definition of insanity”. Maybe that’s true for politicians, but back in the old days when I sold life insurance and mutual funds, doing the same thing every day was the mantra – make 100 phone calls, send out 1000 direct mail pieces, etc., etc.
In some of my classes, we spend a fair amount of time discussing what’s really real in terms of image making. When a student wants to create an image that is “Photorealistic”, I will point out that “Photorealism” is not “Realism-realism”, as it is either restricted by or enhanced by technology. Modern cameras, for example, cannot capture as broad a “dynamic range” as the human eye
“Dynamic range is the ability to simultaneously expose correctly for dark and light areas. You can walk into a room with sun streaming in through the windows and see the whole thing – but a photograph would either overexpose the windows or underexpose the interior. There have been some pretty good developments in High Dynamic Range photography – but the interesting phenomenon there is that when it was first introduced, viewers thought it looked somehow “wrong”. It looks more like what you see with your eyes, but not like what you understand a photograph to look like.
But, just to be ornery, I’ll then ask them what’s more real – what you capture in a photograph, or what you see with your own eyes …? Despite the technical limitations/enhancements of photography, I would argue that photographs are more quantifiably real – after all, every pixel contains a hard set of three numbers representing values in RGB – it can be reproduced exactly the same an infinite amount of times. On the other hand, how can I possibly know that what you call “Red” is the same as what I perceive?
So the question becomes, “What’s more real? Photorealism, or “realism-realism”? At least photorealism is quantifiable, the other is probably a completely undefinable concept. I don’t think we can truly say what “real” is except to say that it does exist in some form. We poor humans can only slog around and deal with what we see, no matter how wrong that might be.
In CG and image-making, “realism” is relative. For example, if I am making CGI props or environments for a film, I must absolutely adapt my understanding of realism to the language or context of the film. Standing alone, either the film or the CG elements can look perfectly real – but when composited together if they don’t use the same language of light and color and focus – and even the color space and chemistry of the film, something will be off and the illusion of realism will fall apart. Today’s render-engines are mostly physically based – meaning that the reflective and refractive qualities, the light absorption and sub-surface scatter of physical materials are calculable and can be represented with an extremely high degree of accuracy – and made even more physically correct by applying similar physical calculations to light – incident energy, reflective energy, wave energy, secondary & tertiary diffuse bounces …
Ironically, traditional cinematographers work very hard to overcome “realism” and go to great lengths to stylize their work for aesthetic and narrative purposes – but all that is completely transparent to the average viewer who wants to be taken in by the fantasy, and suspend his disbelief completely.
But – I digress.
Ah, but the problem of induction raises the possibility that there are no such variables.
If there are no variables, then there cannot be any causality. Everything is random. Consider, for example, if I hold a ball up above the ground and let it go. Suppose I do this ten times in a row, and every single time it falls to the ground. I can (correctly) predict that if I let it go an eleventh time it would behave in the same way – and a twelfth, thirteenth, and so on.
There’s an outside force acting here – “gravity”, which has predictable and calculable qualities. Gravity is based on the mass of the attracting object – the lower the mass, the lower the attraction – so we can accurately predict that gravitational force is less on the moon, for example, and does not exist at all in space.
On the other hand, if we were to flip a coin ten times, and for each of those ten times it came up “heads” – we would be incorrect in predicting that “heads” would be the result of the next flip. Many who are familiar with odds and statistics would say that this prediction is incorrect. Some would say that the odds would be greater that the next flip would be “tails”, but they, too, would be wrong.
Enter the “law of large numbers”, which is kind of a post facto explanation of the chances of heads or tails. There is no explanation for this other than empirical data – but that data suggests that given enough flips, the incidence of “heads” vs. “tails” would be 50/50. This does not mean that every other flip will be heads or tails, or that if you get ten “heads” in a row it will be followed by ten “tails” – nor does it suggest that the more “heads” in a row you flip, the odds of getting a “tails” on the next flip would increase. Every flip carries the same 50/50 odds.
Of course, that’s all just based on current empirical data – “reverse engineered” in a way, to explain away natural phenomena that we don’t understand. Maybe there are invisible aliens controlling the outcomes just to confound us.
If a scientist were to drop a ball for the 10,000th time and suddenly it did not fall, that scientist would immediately begin looking for variables that have changed. Maybe like this..
In this case, it wasn’t a steel ball, it was a magnet – and it wasn’t just any old space, it was a tube of copper – but the “law of gravity” was turned upside down. Science considers this, explores the changed variables, and alters the hypotheses.
But what about the coin flip? The law of large numbers tells us that eventually, the incidence of heads and tails will even out – but it cannot say if this will happen after 20 flips, 200 flips, 2,000 flips, or 200 trillion flips.
If we apply that as a principle, I suppose that causality really is an illusion – and we live in a completely random world. Perhaps a steel ball will drop 50% of the time, and rise the other 50% – we just haven’t dropped enough balls to see it even out yet.
Of course, if you take mass (as in the mass of the Earth) out of the equation, that throws off the entire equation.
I note that quantum mechanics has a probabilistic interpretation of reality.
Schrodinger’s cat could not be reached for comment.