Modal Realism Undermines Induction

The sad demise of an elegant theory

If someone were to say “there could have never been life on earth,” it’s unclear exactly what makes that true. They’re not making a claim about what might be true at some point in the future—they are, after all, making a claim about the past. And they’re not making a claim about the physical world; they are making a claim about the way that physical world could have been, not the way it is. The statements “there are no married bachelors,” and “there can’t be married bachelors,” say exactly the same things about the physical world—namely, that no matter how hard you look, whenever you find a bachelor, they won’t be married—but they are nonetheless completely different statements, both different in what they imply about the world and what they mean.

So what is this talk about possibility? What makes statements about what could be true? Well, David Lewis, in his famous book On The Plurality of Worlds provides a totally bizarre, yet very thought-provoking account. He claims that statements about what is possible and necessary are about concretely existing, real worlds. So he thinks that there actually is a world—one that exists, comprised of atoms and so on—in which there is an earth without insects, in which the Bentham’s Bulldog Substack is written by Derek Parfit, and more! And there are so, so many more possibilities—the space of concretely existing worlds is, according to Lewis, so vast as to be incomprehensible.

Lewis thinks that this can explain a lot of things. We can account for the meanings of terms about possibility and necessity in the following way: things are possible if they’re true in some of the concretely existing worlds, they are necessary if they’re true in all of them. Lewis also develops an account of causation based on reference to nearby possible worlds, as well as properties, modality, closeness, and content.

It’s a very elegant theory. It nicely explains why there’s something rather than nothing—because there can be. It allows all of reality to be encapsulated by the following four words: what can be is. It’s a little bit like utilitarianism in that it aims to capture all of modality with this single, parsimonious theory, appealing to only one existent entity, just like utilitarianism does with morality. So I find myself dispositionally attracted to modal realism—it is, as Lewis says, a paradise for philosophers.

But unfortunately, I think that it is rather implausible. There are various worries—some based on other plausible assumptions about modality, others based on epistemic concerns. But I think the biggest, the one which is really the nail in the coffin of modal realism, is that it undermines induction.

Suppose you currently have some belief, say, that the Cubs are going to win the world series. But you find out that the universe is filled with alternative earths, exactly like ours up until this point, and throughout those earths, of all the people who are exactly like you up until this point and have the same evidence of you, who bet that the Cubs will win, 99.9999999999999% of them are wrong. That would seem to undermine your justification for believing that the Cubs will, in fact, win.

If you find out that almost every time that people form a belief based on some piece of evidence, they are wrong, that would seem to undermine the justification for believing things based on the evidence. If your counterparts have exactly the same evidence and mental states as you do, and are almost always wrong in holding a belief, then you’re not justified in holding that belief.

Why think this? Well, it just seems intuitively obvious to me. Additionally, for some evidence to be convincing, it must make its conclusion likely. But in this case, the evidence does not make its conclusion likely—we know that nearly every time people have that evidence, the conclusion is false. Thus, the evidence is unconvincing.

But modal realism holds that the situation for induction is exactly like it is for the cubs in the hypothetical scenario. There are people exactly like me up until this point—and for an infinite number of them, induction fails one second later. Induction, for those that don’t know, is the idea that the future will be like the past, that the fundamental laws of the universe won’t spontaneously break down one second from now, that the sun will rise tomorrow.

But for every possible world in which induction works, there are innumerable ones in which it does not. In modal space, there are enormous numbers of people exactly like me up until this point, who one second from now turn into a bowling ball or a cantaloupe or who will get teleported to a random spot in the universe or whose room turns to cheese. Lots of things have to not happen for induction not to collapse, while many things can collapse induction—for every world exactly like ours, there’s one where induction collapses because the Indian Ocean is turned into a black hole spontaneously.

Lewis, in his On The Plurality of Worlds, argues that this problem is not unique to modal realism. After all, all plausible views entail that nearly all possible worlds contain induction collapsing—that’s just what the problem of induction is. So why does making them concrete make a difference?

The reason it makes a difference, however, is that concrete worlds mean that there really are actually existing people exactly like me up until this point for whom induction will collapse in one second. For every world where induction doesn’t collapse, there are infinity where induction does collapse. If they are just abstract objects, then the fact that modal space is mostly non-inductive is no threat. Modal entities, as I conceive of them, have a lot in common with mathematical facts, moral facts, epistemic facts, and logical facts. But it would be absurd to say that, because there are infinity numbers, it’s a miracle that I’m not a number. Numbers, like merely possible entities, are a very different type of entity from what I am, and the percent of modal space that is non-inductive is flatly irrelevant to whether I should expect induction to fail later.

We can avoid the problem of induction entirely by just taking as brute that simpler worlds are more likely to be actual. This seems reasonably likely—if, prior to observing any of reality, one was guessing about what reality would be like, I think they would assign some decent probability to something like modal realism being true, some decent probability to nothing existing, and some decent probability to the world being simpler. But simpler worlds mostly have induction work—one needs to add an extra law to turn me into a cantaloupe.

So I think that if we think of possible worlds as abstract entities, the way we might think of mathematical objects, modal objects, or moral facts, there is not a significant problem of induction. But if the possible worlds have actual, flesh and blood human beings, whose experiences are exactly like mine up until this point, then I have no reason to expect I’m in the world where induction doesn’t collapse and they’re in the world where induction does collapse. Nearly everyone in existence who bets on induction, on modal realism, would lose the bet.

Can’t the modal realist say the same thing? Can’t they also presuppose that the actual world is more likely to be simple? No, because according to the modal realist, actual is indexical. What they mean by actual is “the spatiotemporally connected universe in which I live.” Thus, actual is a phrase like “my house,” it is relative to the observer. I live in my house, but when you say “I live in my house,” that’s true even though it’s talking about your house, not my house.

Nearly everyone who thinks that the actual world is one where induction would work will turn out to be wrong. Nearly all of them live in worlds where the actual world is one in which induction fails. Thus, this would be analogous to, after hearing that nearly all people in the universe whose conscious experiences up till this point have been the same as yours are actually brains in vats, claiming that these people aren’t analogous to you, because you live in your house (or, as you prefer to call it, the actual house). This would not be convincing.

A friend of mine who is a modal realist, in response to this, suggests that the modal realist is in the same boat as the person who believes in possible worlds being abstract. We both agree that nearly all possible people, and nearly all real people (for the possible people are in some sense real) are deceived. But, as was argued before, there’s a big difference between a real person with a heart, lungs, and blood, versus a merely possible person, and we have no reason to suggest that what would be actual is just a random possible world. As I said before, it seems intuitive—and think that it would even in the absence of sense data—that the actual world would be likely to be simple. Even absent that brute intuitiveness, we can still get a high probability of successful induction by applying the correct version of the indifference principle.

One could object that, just as I’m brutely positing that the world is simpler than most possible worlds, the modal realist could posit that they’re in a world where induction works. But these are different types of posits—one is totally arbitrary, unlike the other. Suppose that for induction to work, I need to win the lottery 100,000 times each day. That situation is actually better than the situation is for the modal realist, but even putting that aside, it would not be rational to just assume that you’ll keep winning the lottery. There’s a big difference between intuitions about what actually exists and intuitions that one will keep getting lucky—be in the narrow slice of people who exist who don’t live in worlds where induction fails.

One could object by suggesting treating induction as a Moorean fact—one accepts that induction exists because it’s more plausible than any argument against it. Thus, consequently, one accepts that they’re in the narrow slice of worlds where induction doesn't fail.

But this is clearly cheating. Sure, you get to invoke Moorean facts, but you don’t get to affirm Moorean facts while affirming a view of reality on which the Moorean facts require repeated miracles. You can think that pain is bad even in the face of debunking arguments, but you can’t think that while simultaneously thinking that, for pain to be bad, there must be exactly 10^244 atoms. You get to invoke the Moorean facts, but only when you don’t add in features of the world that make the existence of the Moorean facts require miracles.

But even if we allow you to cheat philosophy Moore than should be allowed, another problem surfaces. Nearly all possible worlds that have induction work up until this point have very complicated laws. Complicated laws have various things that are the case, each of which could not be the case. For each world with each of the infinite possible laws, there is one without the law, so each world should be expected to have half of the infinite laws. Thus, the vast majority of modal space has lots of laws that do random, chaotic things. So even if we treat induction as a Moorean fact, we sure as heck don’t get to treat there not being lots of laws as a Moorean fact. So we should expect there to be enormous numbers of laws, but we only see a few that have been efficacious up until this point. Thus, modal realism is almost certainly false.

This is the sad fate of modal realism. An elegant, beautiful theory, facing a tragic, slow demise at the hands of the induction challenge. If you’re looking for parsimonious, elegant, beautiful theories that explain all of some word that starts with mo and ends with ality, utilitarianism is the only game in town.