I’m teaching Philosophy of Science this semester. It’s a fun class. I just had occasion to discuss the philosophy of Sir Karl Popper, who was among the most influential philosophers of science of the last century (and therefore of all time). He had an enormous influence on our intellectual culture, especially on scientists, and he is the reason why you hear complaints about “unfalsifiability” from time to time (accusations that religion is “unfalsifiable”, etc.).

If you’re a philosopher of science, you probably don’t take Popper’s philosophy seriously. But if you’re an ordinary person, or a libertarian, or especially a scientist, there is a pretty good chance that you think you agree with Karl Popper.

So, as a public service, I am here to explain to you that no, you probably do not agree with Popper at all — unless you are completely out of your mind.

What He Said

You probably associate Popper with these ideas: It’s impossible to verify a theory, with any number of observations. Yet a single observation can refute a theory. Also, science is mainly about trying to refute theories. The way science proceeds is that you start with a hypothesis, deduce some observational predictions, and then see whether those predictions are correct. You start with the ones that you think are most likely to be wrong, because you’re trying to falsify the theory. Theories that can’t in principle be falsified are bad. Theories that could have been falsified but have survived lots of attempts to falsify them are good.

I wrote that vaguely enough that it’s kind of what Popper said. And you might basically agree with the above, without being insane. But the above paragraph is vague and ambiguous, and it leaves out the insane basics of Popper’s philosophy. If you know a little bit about him, there is a good chance that you completely missed the insane part.

The insane part starts with “deductivism”: the view that the only legitimate kind of reasoning is deduction. Induction is completely worthless; probabilistic reasoning is worthless.

If you know a little about Popper, you probably think he said that we can never be absolutely certain of a scientific theory. No, that’s not his point (nor was it Hume’s point). His point is that there is not the slightest reason to think that any scientific theory is true, or close to true, or likely to be true, or anything else at all in this neighborhood that a normal person might want to say.

Thus, there is no reason whatsoever to believe the Theory of Evolution. Other ways of saying this: we have no evidence for, no support for the Theory of Evolution. There’s no reason to think it’s any more likely that we evolved by natural selection than that God created us in 4004 B.C. The Theory of Evolution is just a completely arbitrary guess.

(This is not something special about Evolution, of course; he’d say that about every scientific theory.)

This is not a minor or peripheral part of his philosophy. This is the core of his philosophy. His starting point is deductivism, which very quickly implies radical skepticism. The deductivism is the reason for all the emphasis on falsification: he decided that since one can’t deduce the truth of a theory from observations, the goal of science must not be to identify truths. But, since we can deduce the falsity of a theory from observations, the goal of science must be to refute theories.

As I say, most people don’t realize that this is Popper’s view — even though he makes it totally clear and explicit. I think there are two reasons why people don’t realize this: (a) the view is so wildly absurd that when you read it, you can’t believe that it means what it says; (b) Popper’s emotional attitude about science is unmistakably positive, and he clearly doesn’t like the things that he calls “unscientific”. So one would assume that his philosophy must give us a basis for saying that scientific theories are more likely to be correct than unscientific ones. But then one would be wrong.

Now, in case you still can’t believe that Popper holds the irrational views I just ascribed to him, here are some quotations:

“We must regard all laws and theories as guesses.” (Objective Knowledge, 9)

“There are no such things as good positive reasons.” (The Philosophy of Karl Popper, 1043)

“Belief, of course, is never rational: it is rational to suspend belief.” (PKP, 69)

“I never assume that by force of ‘verified’ conclusions, theories can be established as ‘true’, or even as merely ‘probable’.” (Logic of Scientific Discovery, 10)

“[O]f two hypotheses, the one that is logically stronger, or more informative, or better testable, and thus the one which can be better corroborated, is always less probable — on any given evidence — than the other.” (LSD, 374)

“[I]n an infinite universe […] the probability of any (non-tautological) universal law will be zero.” (LSD, 375; emphasis in original)

About the last quotation, note that many scientific theories contain universal laws (e.g., the law of gravity). So, Popper is not just denying that we can be certain of these theories, and not just denying that they are likely to be true; he claims that they are absolutely certain to be false.

In the penultimate quotation, note the “on any given evidence” clause: When you get done testing your scientific theory, and it survives all tests, you can’t say that it’s likely to be correct; it’s less likely to be correct, even after you’ve gathered all the evidence, than some unfalsifiable, unscientific theory.

All of this is the sort of view that you would expect from the most extreme science-hater. The weird thing about Popper is that he inexplicably combines this stuff with a strong positive evaluation of science. We have no reason to believe in science, and pseudoscience is more likely to be correct, and in fact the paradigmatic scientific theories are definitely wrong . . . but hey, isn’t science great? Okay, now let’s get on with the wonderful science stuff!

I can’t explain this combination of attitudes. I don’t think Popper ever attempted to explain it himself.

By the way, the core idea — deductivism, and inductive skepticism — seems to be surprisingly popular among philosophers. It’s ridiculous. It’s like if a major position within geology were that there are no rocks.

How He’s Wrong

I’m only talking about objections that I like here, so I’ll ignore objections based on Thomas Kuhn.

The Duhem-Quine Thesis

This is something widely accepted in philosophy of science: a typical scientific theory doesn’t entail any observational predictions by itself. You at least need some auxiliary assumptions.

Ex.: Newton’s Theory of Gravity, together with Newton’s Laws of Motion, are sometimes said to entail predictions about the orbits of the planets (in particular, to predict Kepler’s laws). But that’s false. Newton’s second law only gives the acceleration of a body as a function of the total force acting on it. The Law of Gravity doesn’t tell you the total force on anything; nor is “total force” observable. So there are no observational predictions from this set of laws, even when combined with all our observations.

Of course, the laws and the observations make certain patterns of motion more plausible or likely than others. If the planets moved in squares around the night sky, it would be very implausible to explain that using Newton’s laws + the hypothesis of some unknown, unobservable forces. But that is completely irrelevant for Popper. Again, for Popper, the only thing that counts as scientific reasoning is deducing the falsity of a theory from observations. You’re not allowed to appeal to any probabilistic judgments to support a theory.

Probabilistic Theories

Another counter-example: Quantum Mechanics. It’s a scientific theory if anything is. But it is clearly unfalsifiable, because all of its observational predictions are probabilistic. It enables one to calculate the probabilities of different possible observed results, but a probabilistic claim (as long as the probability isn’t 0 or 1) can never be falsified — i.e., you can’t logically deduce the falsity of the probability claim from observations. And again, that’s the only thing you’re allowed to appeal to. So, on Popper’s view, quantum mechanics must be unscientific.

Evolution

But QM is weird. So let’s think about some perfectly ordinary, paradigmatic examples of scientific theories. Real scientific theories, by the way, are not normally of the form “All A’s are B” (as in philosophers’ examples).

Here’s one: the Theory of Evolution. Humans and other living things evolved by natural selection from simpler organisms, over a long period of time. Here’s an example of the evidence for this: some of the larger constrictor snakes have degenerate hind limbs underneath the skin. This can be explained, in the theory of evolution, by the hypothesis that they evolved from lizards. On the rival theory (Creationism), there’s no obvious explanation.

This isn’t a matter of deduction. The Theory of Evolution does not entail that the larger constrictors would have subcutaneous degenerate hind limbs. It merely gives a reasonable explanation of the phenomenon, which the rival theory doesn’t (but creationism doesn’t entail that there wouldn’t be such degenerate hind limbs; it merely fails to explain why there would).

The Dinosaur Extinction

Here’s another theory: the dinosaurs were driven extinct by a large asteroid impact. And here’s some evidence: there is an enormous crater at the edge of the Yucatan Peninsula in Mexico (the Chicxulub Crater), partly underwater. The crater has been dated to about the time of the Cretaceous–Paleogene extinction event. That’s evidence that an asteroid impact caused the mass extinction.

Again, that’s not deductive. The asteroid-impact theory of the extinction does not entail that we would find a crater. (It’s logically possible that the crater would have been filled in, or that the asteroid hit a mountain and didn’t leave a visible crater, or that the crater was somewhere we haven’t looked, etc.) It merely makes it much more likely that we would find a crater.

So, Popper’s philosophy entails that the Theory of Evolution and the asteroid-impact theory are unscientific, besides that we have no evidence at all for either of them.

The Obvious

Of course, the obvious problem is that it’s absurd to say that we don’t have any reason to think any scientific theory is true. We have excellent reasons, for example, to think that humans evolved by natural selection. There is not any serious doubt about that in biology, and that is not something that we should be arguing about. And in fact, I’m not going to argue about it, because I just don’t think that’s serious.

The Correct Theory

What is the correct view of scientific reasoning? Basically, the Bayesian view: it’s probabilistic reasoning.

Take the example of the degenerate hind limbs again: that is evidence for the theory of evolution because it’s more likely that we would see stuff like that if organisms evolved by natural selection, than it is if they were all created by God in 4004 B.C. (or, in general, if they did not evolve). In standard probability theory, that entails that Evolution is rendered more probable by our seeing things like the degenerate hind limbs.

Why Care About Falsifiability?

There really is something important about falsifiability. Intuitively, there is something bad about unfalsifiable theories, and we have Popper to thank for drawing attention to this.

Unfortunately, almost no one seems to have any idea why falsifiability matters, and Popper did not help with that situation, because his theory is incapable of accepting the correct explanation.

The correct explanation is a probabilistic/Bayesian account. In the Bayesian view, a hypothesis is supported when P(h|e) > P(h) (the probability of hypothesis h given evidence e is greater than the initial probability of h). It is a trivial theorem that, for any e, P(h|e) > P(h) iff P(h|~e) < P(h). In other words: e would be evidence for h if and only if the falsity of e would be evidence against h.

That means that if nothing counts as evidence against h, then nothing counts as evidence for h either. But if there’s no evidence for h, then one typically shouldn’t believe it. This is why you shouldn’t believe unfalsifiable theories. By contrast, falsifiable theories are supportable: when one tries and fails to falsify them, their probability goes up.

The point is more general than a point about Popperian falsifiability. Let’s say a theory is “falsifiable” iff one could deduce its falsity from some possible observations, and a theory is “testable” iff there are some observations that would lower the probability of the theory. Then the general point to make is that one can have evidence for a theory iff the theory is testable (it needn’t also be falsifiable), and good scientific theories should be testable.

Popper couldn’t say this, because he was obsessed with deduction, and this is a point about probabilistic reasoning, not deduction. Popper didn’t eschew all talk of probabilities; he just insisted on the most perverse probability judgments (e.g., that scientific theories are less likely to be correct than unscientific ones, even after they survive stringent tests). Which would make one wonder why anyone should prefer scientific theories. Obviously, the correct view is that scientific theories, after surviving tests, become more probable.