“This is my defense of Popper's Critical Rationalism, which I recently posted on the London Libertarian blog. I haven't figured out how to do italics and other layout things on Facebook, so what follows does not quite capture all the nuances of the original.
“I see that one of the items listed in my References has been picked up by Facebook as a separate attachment. Well, that's okay, and it's worth reading.
Are Critical Rationalists Completely Out of Their Minds?
Michael Huemer has published a brief and blistering attack on the thinking of Karl Popper. He proclaims that Popper’s ideas are “insane.” He maintains that if you actually agree with Popper, “you are completely out of your mind,” which implies that Popper himself was completely out of his mind.
Huemer titles his piece, posted on his blog, “You Don’t Agree with Karl Popper.” The point of this title is that, in Huemer’s opinion, a lot of people (he mentions libertarians, many of whom admire Popper’s ideas) think they agree with Popper, only because they don’t fully understand what Popper is saying. If they did understand it, as Huemer does, they would find they wouldn’t agree with it at all, unless they were completely out of their minds.
Huemer gives a summary of some of the ideas people attribute to Popper, and which he is willing to concede they can accept without being completely out of their minds. He then goes on to impute to Popper additional views which he considers to be seriously wrong, and which people can’t accept without being completely out of their minds.
Here’s his summary of the first set of views, the ones Huemer acknowledges that sane people, in his judgment, can readily accept:
“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.”
Is this, as far as it goes, a correct statement of Popper’s views? It’s not wildly off, but there are some things which are not strictly accurate.
Most obviously, Popper did not hold that theories that can’t in principle be falsified are necessarily “bad,” merely that they don’t belong to empirical science. He held, for example, that metaphysical theories, such as whether or not the universe is deterministic, can’t be empirically falsified and are therefore not scientific, thought they can be, and should be, seriously argued about. Popper wrote an entire book arguing against determinism and for indeterminism (The Open Universe), an issue which he insists does not belong to science. In his view there is no empirical test which could conceivably falsify determinism or indeterminism, and so this is an issue which belongs to metaphysics.
Another example is realism. Are trees, mountains, and stars things which exist independently of our awareness, or are they products of our minds and senses? Popper argues strongly for realism (Realism and the Aim of Science, 80–158). At the same time, he maintains that there is no way of empirically testing realism. So, this is not a scientific question but a metaphysical one. It can’t be tackled by empirical research but only by philosophical argument.
Popper holds that with some metaphysical theories, it may be possible to reframe them so that they become falsifiable. This may then lead to an advance in scientific knowledge. For example, the atomic theories of some of the ancient Greeks were not falsifiable. They were therefore, in Popper’s terminology, metaphysical rather than scientific, though this does not imply that they were not meaningful, important, or interesting. Nor does it imply that they were not objectively true or false.
John Dalton’s theory of the atom published in 1807 made numerous claims about atoms which could be tested by experiment: we could attempt to falsify them. Thus theories about atoms moved from metaphysics into science. Popper does not think this can happen to all metaphysical theories; he does not seek or expect the elimination of metaphysics. His view is that metaphysics will never be disposed of, and some metaphysics will always be required, even for and by science.
There are some non-falsifiable theories that may present themselves as scientific, so in that sense we might say that they’re “bad,” that’s to say, not really what they claim to be. Examples include some of the propositions of psychoanalysis, such as the theory that all dreams represent fulfillment of wishes (Realism and the Aim of Science, 163–174), or that all infants undergo an Oedipal phase of wanting to kill their fathers so that they can have sex with their mothers (Edelstein et al., Therapy Breakthrough, 255–266).
Another possibility is that something might look superficially like a scientific theory, but on examination might turn out to be tautologous, and therefore not empirically refutable. And, Popper points out, truly scientific theories can always be turned into tautologies by interpreting them in such a way that they are immune to empirical refutation. Thus, ‘All swans are white’ becomes a tautology if we add that anything not white cannot be a swan.
That “science is mainly about trying to refute theories” is a bit misleading as a statement of Popper’s logic of science. Popper holds that science is about trying to find good and better explanations of the world, which involves comparing and evaluating theories according to several criteria, one of which is whether they agree with observations.
When Huemer says, “You start with the ones that you think are most likely to be wrong”, I’m not sure what he means. You might perhaps be inclined to start with the theories that have the widest acceptance, since then you will make the most progress by showing them to be false. More generally, I suppose, you’re most likely to start with theories which you find unsatisfactory. You may criticize a scientific theory in ways other than empirical testing, for example by arguing that the theory does not address a problem it was claimed to address, has hidden ambiguities or inconsistencies, or has components that can be eliminated without loss of empirical content (Realism and the Aim of Science, 55–56).
Having looked at the elements of Popper which Huemer thinks we can accept without being completely out of our minds, let’s now turn to those which he considers so terribly mistaken that agreeing with them is tantamount to insanity.
Huemer does not seriously attempt to give an outline of what he takes to be Popper’s philosophy and then explain what he thinks is wrong with it. Instead, he identifies specific assertions he attributes to Popper, and he appears to think that these assertions are so outrageous, ridiculous, and self-evidently “insane,” that it’s enough to cite them and pull faces at them to convince his readers that Popper is completely out of his mind. Because of this procedure of Huemer’s, I will list each of the distressing propositions Huemer imputes to Popper and try to say something helpful about each of them.
These assertions are a mixed bag, some of them are roughly the same as each other or overlap somewhat. Some of them accurately reproduce Popper’s thinking; others don’t. I list them here in the order Huemer gives them, without any attempt to sort them, rank them, or make sense of them. Double quotation marks indicate that Huemer is directly quoting Popper; single quotation marks indicates that Huemer is reporting in his own words what he takes to be Popper’s position. No quotation marks indicates this is my paraphrase of something Huemer attributes to Popper.
I identify seventeen of these statements, which all express contentions Huemer attributes to Popper, and all of which allegedly constitute evidence that Popper is completely out of his mind.
1. ‘. . . the only legitimate kind of reasoning is deduction. Induction is completely worthless. . . . His [Popper’s] 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’.
2. ‘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’.
3. ‘. . . the goal of science must be to refute theories’.
4. “We must regard all laws and theories as guesses.”
5. “There are no such things as good positive reasons.”
6. “Belief, of course, is never rational: it is rational to suspend belief.”
7. “I never assume that by force of ‘verified’ conclusions, theories can be established as ‘true’, or even as merely ‘probable’.”
8. “Of 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.”
9. “In an infinite universe . . . the probability of any (non-tautological) universal law will be zero.”
10. ‘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’.
11. ‘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’.
12. ‘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. . . .’
13. ‘. . . 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’.
14. The existence of vestigial legs in the bodies of some snakes is evidence for evolution, and this ‘isn’t a matter of deduction’.
15. ‘. . . 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’.
16. ‘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’.
17. ‘. . . scientific theories are less likely to be correct than unscientific ones, even after they survive stringent tests’.
By my count, nine of these seventeen propositions are false—in these nine cases Huemer attributes a view to Popper which Popper most definitely does not hold. A couple of the propositions are a bit indeterminate, so only six of the seventeen are definitely correct. In those six cases where Huemer gives Popper’s view correctly, I will generally defend what Popper says. The one case where I don’t defend what Popper himself says, or at least the way he expresses it, is #6.
I will comment specifically on each of Huemer’s seventeen allegedly Popperian positions, but before I do that, I will now give a very brief account of that part of Popper’s philosophy which Huemer judges to be insane and which, in Huemer’s view, you cannot accept unless you are completely out of your mind.
Critical Rationalism in a Nutshell
Before Popper, it was generally accepted by philosophers that science, as well as ordinary common-sense knowledge, relied upon a procedure known as induction. Induction is supposedly the way we get from the particular to the general, from the individual to the universal, from a limited number of observations to a universal law. For example, it is held that objects near the Earth will fall toward the Earth with an acceleration of 9.8 meters/second/second. Certain conditions have to be imposed. The object must be in a vacuum, otherwise the atmosphere will make a difference to the acceleration because of air resistance. But these conditions don’t matter for our discussion here. We assume an acceleration of 9.8 m/s/s, then make an added calculation to allow for air resistance. Several additional and very minute adjustments have to be made for good accuracy. The point is that apart from changes in these stated conditions, the acceleration is always the same.
The question is: what entitles us to say that because we have observed a number of instances of falling bodies which conform to an acceleration of 9.8 m/s/s, the same will be true of all falling bodies near the Earth, for example, a thousand miles away from where we have made our observations, or a thousand years in the past or the future?
In 1739, David Hume pointed out that there is no logical operation which enables us to make this leap: to say that what we have observed of a certain finite range of instances will apply to other instances which we have not observed. We observe today in Edinburgh that sodium chloride dissolves in water whereas iron filings do not dissolve in water. There is no logically sound way to infer from today’s findings that next week in Edinburgh, or today in London, we will not find that sodium chloride does not dissolve in water whereas iron filings do. Nor does the fact that things have behaved a certain way in the past, or in our neighborhood, even make it more probable that they will behave the same way in the future, or in a distant location—not an eentsy weentsy bit more probable. These are elementary logical points. They hold equally for the Aristotelian logic with which Hume was acquainted and for the modern logic developed by Peano, Frege, and Russell at the end of the nineteenth century. Consequently, there can be no valid method of induction.
Both science and everyday common sense require that we do form conclusions about what happens invariably, in all times and places. Therefore Hume’s insight looks as if it must undermine both science and everyday common sense—as long as we cling to the notion of induction, the assumption that we can logically derive statements with a boundless range from a limited set of observations.
As a result of this discovery of Hume’s, the philosophy known as empiricism was put in question. Empiricism holds that we get knowledge of the world only through the evidence of our senses, through observation, and through logical deductions from our observations, but since logic does not permit us to extend our conclusions beyond a list of our past observations, much of our knowledge (which is of a general or law-like character) can never be logically obtained by following empiricism.
Philosophers have attempted to tackle this problem in a number of ways, but nothing has shaken Hume’s finding that, according to logic, valid induction is impossible and therefore gaining knowledge of the world by a purely empiricist approach is impossible.
Skipping over the history of the many failed attempts to find a reasonable basis for induction, which have always necessarily tended to move in the direction of saying that we know some things prior to any experience, we can now explain Popper’s radically different approach.
Popper accepts Hume’s conclusion that, in our search for general laws, we cannot support these laws by induction. The fact that some regularity has been observed on all occasions, around here and up to now, cannot logically offer any support for the proposition that the same regularity will continue to be observed in other places or other times. So, Popper entirely agrees with Hume’s rejection of the possibility of valid induction.
Unlike Hume, who considered that we do use induction, even though it is logically indefensible, Popper goes on to say that we never do use induction; if we think we have arrived at a conclusion by induction, we are victims of a kind of optical illusion, whereby we falsely reconstruct the actual steps of our reasoning (Realism and the Aim of Science, 35). Consequently, Huemer’s #1, that ‘Induction is completely worthless’, is a little misleading. Rather, in Popper’s view, induction does not exist; there is no such thing as induction. It would be odd to say, ‘Levitation is completely worthless’.
Against Hume, Popper says that we do not have to conclude that we cannot gain knowledge of the world and extend and improve our knowledge. We can do this by the method of conjecture and refutation. First, we come up with a conjecture (a surmise, guess, or hypothesis) about some apparent regularity in the world. Then we test that conjecture by comparing it with subsequent experience. Sometimes we find that our conjecture is contradicted by an experience or observation, and then we may decide to abandon that conjecture and replace it with a second conjecture. If we find that experience contradicts our first conjecture while not contradicting our second conjecture, we may conclude that our first conjecture has to be scrapped, while our second conjecture can survive being scrapped, at least for the moment.
So, returning to the question of what entitles us to say that objects always fall to Earth with an acceleration of 9.8 m/s/s, the answer is that we cannot soundly deduce this conclusion from our observations, but that since no observation has been found to contradict this guess, we have decided to stick with it. Obviously, this does not mean that it is true or likely to be true, though, as far as we can tell, given our present stock of knowledge, including all our past observations, it might be true. (However, in this case we have found a better theory, in which 9.8 m/s/s occurs as a special case: a general theory of gravitational attraction between two bodies, which enables us to say that the acceleration will be different on other planets and moons.)
Unlike induction, which must always be logically unsound, conjecture and refutation is logically impeccable. It would not be logically impeccable if we were to claim of our first guess that we have proved it from observation or experience, or even if we were to claim that it had a probability greater than zero. We have not proved it, in the sense of logically deriving it from observations, nor have we shown it to be more probable because it is consistent with all observations so far. As the controversy over ‘grue’ should have reminded us, an infinite number of false theories are always entirely consistent with all observations so far.
We can remain logically correct if we simply say that we have made a guess at the truth, that our guess might be true, and that we’re going to stick with it for the time being. That’s what we can say about our first theory, then about a second theory which might replace our first theory, then about a third theory which replaces our second theory, and so on indefinitely. We stick to each guess up to a point, and abandon it when it apparently becomes incompatible with experience or observation. We then move on to a new guess, and the same process repeats itself, possibly without end.
Having come up with a guess, we at first stick to that guess, since we have nothing better. Our minds are pre-programmed by millions of years of evolution to search for patterns and generalities in the incoming flood of experiences. Now, in practice it may be that we become emotionally committed to our guess—we may believe in our guess—and we have in fact evolved to be prone to believe stuff (perhaps because it was advantageous to the survival of humans to stick to their guesses quite tenaciously, or perhaps because there is something in the very nature of consciousness that induces us to believe). But from a logical point of view, belief is extraneous, redundant, and immaterial. Logic is not psychology. Scientific method has nothing to do with belief, just as the proof or disproof of a mathematical theorem has nothing to do with belief.
As we move from one guess to another, our currently accepted guesses tend to get better—better in the sense of seeming to us, given the totality of our knowledge, to be more promising stabs at the truth. When we replace theory A with theory B because we have refuted theory A by finding a counter-example to it, we can conclude that theory A is false, whereas theory B might be true but is not necessarily true. We prefer theory B to theory A because theory B has not yet been refuted, while theory A has been refuted. If someone proposes theory C, we can look for some way in which the predictions of B and C are different, and then perform the ‘crucial experiment’ which will tell us which of the two predictions comes true. We can never demonstrate the truth of our theory, but we can demonstrate that one theory is better than another because it tests out better, and we may be able to say that the theory we have provisionally accepted is the best we have been able to come up with so far. We therefore prefer it to any of its known rivals, even though we have no guarantee, and can never have any guarantee, that it is true.
Conjecture and Refutation in the Crib
Popper’s process of conjecture and refutation, or trial and error, is the method used by human babies, as they learn about the world. The research of Alison Gopnik and her associates, which has been able to reconstruct by very strict attention to human baby behavior, what babies believe, even in the first few weeks of life outside the womb, shows that babies adopt a theory about the world, revise or replace it when it clashes with their subsequent experience, and do this sequentially and progressively, getting gradually closer to what we regard as the common-sense knowledge of grown-ups—which will then be further revised and in large part discarded by those grown-ups who pursue an education in science.
By the way, it seems that Gopnik did not know about Popper and did not realize how well her research fit the Popper conception. She refers to a baby’s first guess as “induction.” Since reading Gopnik, and being impressed by her congruence with Popper, I have found that other psychologists have argued along somewhat similar lines, notably Robert Siegler.
It was reading and pondering Gopnik’s exciting results (The Scientist in the Crib) which prompted me to understand that, not only is the critical rationalist theory of conjecture and refutation the correct account, but all other accounts are absurd and preposterous. There is no other way in which conscious animals could conceivably have developed a culture involving progressive accumulation of knowledge, except the Popperian system of conjecture and refutation. But even if I were to be wrong about that, it would remain true that conjecture and refutation is in fact the only method by which knowledge does accumulate.
Over many years of thinking and talking about Popper, I have noticed some common misinterpretations which tend to lead people astray. Here I will just point out one of these: the assumption that Popper’s philosophical account of the logic of science offers a recipe for doing science. According to Popper, there can be no recipe for doing science successfully, any more than there can be a recipe for creating a great work of art. The logic of science is not a cookbook for doing science, any more than a textbook of logic is a handbook for winning debates.
In particular, we ought to keep clear the distinction between the purely logical and the practical applications of falsification. Whereas no accumulation of observing white swans and only white swans can substantiate or even make slightly probable the universal statement that all swans are white, a single observation of a black swan automatically and necessarily refutes the statement that all swans are white. That is a simple truth of logic. But in the actual practice of science, it may be that a theory continues to gain acceptance despite the existence of a falsifying observation (Schilpp, 1021, 1035).
A particular observation may be dismissed after failure to reproduce it. But even a reproducible falsifying observation may be acknowledged without abandoning the theory it contradicts. This will be recognized as a troubling anomaly, something that ought to be resolved somehow, but scientists will not always feel that they ought to immediately make the problem go away by abandoning the theory. Our preferred theory may have such merits that we’re prepared to put on hold the problem that some observation conflicts with it—that, in simple terms, it appears to have been refuted.
Another qualification to the simplest model of conjecture and refutation is that certain methodological conventions must be adhered to if science is to work at all, the best-known of these being that, wherever possible, an experiment or observation should be reproducible by many different researchers on many different occasions. A different convention or set of conventions is required to cope with the fact that measurement is never perfectly precise, so we need practical rules to determine what degree of approximation of a result will agree or disagree with a prediction. And, as I will explain shortly, another convention is required to enable us to treat some predictions of probabilities as falsifiable.
Huemer’s Seventeen Propositions
One thing which will immediately strike anyone who has read Popper and then looks at Huemer’s seventeen propositions is that Huemer sometimes attributes to Popper views which Popper very definitely rejects or which contradict things Popper explicitly and frequently states. Nine of Huemer’s seventeen propositions are false accounts of Popper’s thinking: they are never stated by Popper and directly contradict what Popper repeatedly and emphatically asserts.
Huemer might reply that this just shows that Popper contradicts himself. But I’m not sure that would really harmonize with the tone of Huemer’s polemic. The impression he gives is that Popper takes an unambiguous and consistent position which Huemer says is crazy. He doesn’t convey the impression that he thinks Popper occasionally makes crazy remarks which are at odds with the main body of his less crazy philosophy.
In any event, it can be shown that these points where Popper’s statements contradict Huemer’s account of Popper’s thinking cohere quite naturally with the rest of Popper’s theory of science. They are not isolated departures from Popper’s general account.
I will now comment on Huemer’s seventeen points, moving from examples where Huemer incorrectly attributes some position to Popper to examples where Huemer reproduces Popper’s view accurately and where I will defend what Popper says.
Huemer’s #1 (that science has nothing to do with truth) is contradicted by Popper’s numerous statements that science is trying to get at the truth. There are hundreds of these statements; you can hardly read a few pages of Popper without tripping over them. For example Popper writes (combatting instrumentalism, the view that scientific theories are merely tools for prediction rather than claims about objective reality): “in the search for knowledge, we are out to find true theories, or at least theories which are nearer than others to the truth—which correspond better to the facts” (Conjectures and Refutations, 226).
Huemer’s #3 (the assertion that the goal of science is to refute theories) contradicts Popper’s assertion that the aim of science is “to find satisfactory explanations,” which means explanations “in terms of testable and falsifiable universal laws and initial conditions” (Realism and the Aim of Science, 132–35). Popper sees the growth of knowledge, the progress of science, as the overthrow of currently accepted theories by better theories, which occurs by criticizing existing theories and offering competing alternative theories, which may turn out to be preferable.
Popper adds that it is reasonable, sensible, and sound policy to prefer the best theories we have, and we keep trying to improve our theories by a process of critical discussion and debate. In the realm of empirical science, refuting a theory empirically by showing that it contradicts observations is one, but not the only, important means to that end. We never arrive at a point where we can demonstrate that we have the truth, though we can hope to make progress towards the truth. Thus, in Popper’s account, we can say that Einstein’s relativity theory is better than Newton’s theory of gravitation. Newton’s theory was, in Popper’s words, “a splendid approximation” (The Open Universe, 47), yet it was supplanted by Einstein’s theory, also a splendid approximation, which has advantages over Newton’s theory. Newton is a good approximation to Einstein in a range of circumstances, but not in all circumstances. Observation corroborates Einstein better than it does Newton, because many singular observations contradict Newton without contradicting Einstein.
In his #4, Huemer gives Popper’s claim that all theories and laws are guesses, as one of Popper’s self-evidently insane statements. Huemer does not explain why he supposes this is insane or what else theories and laws might be. The craziness is not self-evident to everyone. Consider the following quotation from a talk by the outstanding physicist Richard Feynman:
“Now I’m going to discuss how we would look for a new law. In general, we look for a new law by the following process. First, we guess it [audience laughter]. No, don’t laugh, that’s the truth. Then we compute the consequences of the guess, to see what, if this is right, if this law we guess is right, to see what it would imply and then we compare the computation results to nature or we say compare to experiment or experience, compare it directly with observations to see if it works. If it disagrees with experiment, it’s wrong. In that simple statement is the key to science.” [Feynman 2020. Ungrammatical expressions in the original.]
Another of the Popperian contentions which Huemer apparently takes to be self-evidently insane is his #5, that there are no such things as good positive reasons. (The context makes clear that Popper is talking about good positive reasons for accepting a theory.) Again, Huemer does not explain why he disagrees, or what he thinks might be a good positive reason. Maybe he’s thinking of examples where a piece of evidence clearly supports a particular theory. What Popper would say is that, in such a case, the piece of evidence is incompatible with rival theories. It is therefore, despite what we may at first suppose, a negative reason; it supports a theory insofar as it contradicts that theory’s competitors.
Huemer’s #10 and #12 both have Popper claiming that scientific theories “are absolutely certain to be false.” This is a serious misreading of Popper. Popper contradicts this proposition over and over again. Popper consistently maintains the view, advanced by the ancient philosopher Xenophanes, that we might very well arrive at a true theory, but we could never be in a position to demonstrate conclusively (or to ‘know’) that it was true (Realism and the Aim of Science, 33; Conjectures and Refutations, 114–16, 151–53).
It seems to be a difficulty for some readers of Popper that he combines the objectivity of truth with fallibilism. Popper thinks (and I agree) that the truth or falsity of a theory is absolute and objective, while our being able to determine its truth or falsity can be very difficult, and in many cases impossible—especially when we’re looking at general, law-like theories, which are the most fertile and useful. We should not confuse truth with guaranteed truth.
Huemer does not quote Popper as asserting anything like #10 or #12, and he doesn’t try to show that #10 or #12 can be inferred from anything Popper says. Why then does Huemer make the totally ludicrous claim that Popper asserts that our best scientific theories are “absolutely certain to be false”? It appears that Huemer simply assumes that a true theory cannot have zero probability. Since Popper says that theories have zero probability (Huemer’s #9), Huemer thinks he must be saying that those theories are false. If Huemer supposed that a theory with zero probability must be false, then he would think that his #10 and #12 followed from his #9. Huemer’s supposition here is no doubt the supposition of many people. But it is incorrect, where infinity is involved (Cthaeh 2017; 3blue1brown 2020).
An impossible event necessarily has the probability of zero, but the converse is false. Any event has zero probability where the sample space is infinite. What applies to events applies to propositions specifying events, and so Popper has not made a leap in extending this conclusion of probability theory from events to theories.
If you possess a lottery ticket, one of a thousand tickets, your probability of winning (stipulating that precisely one ticket has the winning number) is one in a thousand; if your ticket is one of a million tickets, your probability of winning is one in a million, and so on. If your ticket is one of an infinity of tickets, your probability of winning is zero. This does not mean you cannot win, because, after all, you do have a ticket, one ticket must win, and your ticket is equally as likely as any of the other tickets to be the winner.
Since critical rationalism does not require that its adherents don’t have beliefs—it just says that belief is a subjective psychological quality immaterial to the logic of science—a critical rationalist may very well believe that a theory is true, while acknowledging that it has zero probability. (But what if the universe isn’t infinite? Well, it’s still quite big.) As I inspect the contents of my own mind, I find that I do believe in conservation of momentum. So I believe, simultaneously, that conservation of momentum is true and that the probability of its being true is zero. But, remember, these are just my beliefs, which, like your beliefs, or anyone else’s beliefs, always count for nothing.
By the way, if we adopt the metaphysical principle that nature is strictly governed by universal laws which can be grasped by humans, we may (with a few more steps) hope to be able to avoid the ‘zero probability’ conclusion, but we don’t know a way to demonstrate the truth of any such metaphysical principle. We can’t validly deduce from observations that we don’t live in a universe bereft of universal laws, or bereft of any that we could possibly discover. I’m guessing, though, that a lot of people do tacitly hold to some such metaphysical principle, which may help to explain why they seem to find it intuitively obvious that a well-corroborated theory like relativity or quantum electrodynamics must have a greater than zero probability of being true.
But can’t we reasonably say that the current theories of scientific cosmology are more probably true (or closer to the truth) than, say, a literal reading of the first chapter of Genesis? Of course we can! But we should clarify what is meant by such a claim.
Popper points out that we often use words like ‘probable’ and ‘likely’ in ways that are not defined in terms of the calculus of probabilities—the branch of mathematics which we learn when we study probability theory. Confusion can arise when we start supposing that a use of the term ‘probable’ which owes nothing to the calculus of probabilities is an application of the calculus of probabilities (Realism and the Aim of Science, 282–83). We sometimes use ‘probable’ or ‘likely’ as a synonym for ‘rationally preferable’ or ‘promising as a candidate for truth’. We cannot meaningfully say that the probability that Genesis is correct is one number, and the probability that the Big Bang happened is a different and presumably somewhat higher number. That would be a strange thing to try to do, since we judge that the Genesis theory has been refuted.
But what about when one theory replaces another, as Einstein replaced Newton? Can’t we compare the probability of Newton’s being right with the probability of Einstein’s being right? Well, although Popper himself took a dim view of arguments from the history of science, I can point out that this is just not what happens. There was a crucial experiment (precession of the perihelion of Mercury) which corroborated Einstein and falsified Newton. Other crucial observations have been consistent with Einstein and not with Newton. So, most scientists, some more quickly than others, came around to the view that Newton was false and Einstein possibly true. No one, in 1916, thought about the probability of Newton or Einstein being correct; they thought about making observations to determine which one was correct (or closer to being correct).
Huemer apparently presents #8 (that more informative theories are always less probable than less informative theories) as one of the things you can only accept if you are insane or completely out of your mind. And yet this statement by Popper is not really controversial. The point Popper is making is that theories with more content are to be preferred to theories with less content, and the theories with more content must be less probable than the theories with less content.
For example, the theory that all persons named Huemer are color-blind is more probable than the theory that all persons named Huemer are color-blind and left-handed, which is in turn more probable than the theory that all persons named Huemer are color-blind, left-handed, and bald. The theory that all cyclists in Chicago have antibodies for SARSCov2 is more probable than the theory that all cyclists in the Midwest have antibodies for SARSCov2, which is in turn more probable than the theory that all cyclists in the US have antibodies for SARSCov2. These are elementary applications of a fundamental truth of probability theory.
The more informational or empirical content a theory has, the more it claims, the more improbable it is. We want theories that claim as much as possible, and the more they claim, the less probable they must be. A theory with more content prohibits more; it is bolder; it takes more risks. If we find we can adopt it, it is more useful because it yields more information. It follows that we look for theories that are as improbable as possible, since these, caeteris paribus, must be the best theories.
There is therefore a special sense in which scientific theories may often be less probable than pseudoscientific theories. If the pseudoscientific theories are vacuous, impossible to pin down, compatible with an unlimited range of observations, then the pseudoscientific theories will be more probable; in fact their probability of being true will be 1. They don’t commit themselves to anything in the world because they are vague and waffly. They say so little that it is impossible to find counter-examples, and therefore impossible to disprove them.
Astrology is an example. Not counting the serious statistical work of Michel Gauquelin (‘neo-astrology’), the problem with traditional astrology is that it’s compatible with an indefinite range of imaginable observations; we can’t think of any conceivable observation which could refute it. The same is true of Freudian or Jungian analysis. ‘Pseudoscientific’ systems, like traditional astrology, Freudianism, and Jungianism, are generally characterized by including centrally important theories which are compatible with any conceivable observable events; they therefore have a maximally high probability of being unrefuted by observations. It’s characteristic of genuinely scientific theories that they imply that many conceivable observable events will never, in fact, be observed, and therefore these theories could easily be refuted by observing one of these events.
Aside from that kind of example, due to a difference in content, I don’t see that Popper’s theory implies that a scientific theory must always be less probable than a pseudoscientific theory, as Huemer seems to be suggesting in his #11, and #17. Is it always true that a pseudoscientific theory is more probable than a scientific theory? That’s an interesting question which might be worth pursuing, but, as far as I can recall, Popper has made no claim anent it. On quick reflection, it’s not obvious to me that, say, Velikovsky’s theory, normally considered pseudoscience, is more probable, because more vacuous, than standard cosmology.
According to Huemer, Popper holds that “The Theory of Evolution is just a completely arbitrary guess.” This is an astounding misreading. In Popper’s view, all theories are guesses but these guesses are rarely arbitrary. In science, they are usually attempts to solve problems. Perhaps the main problem Darwin attempted to solve was ‘How can we account for the diversity of life forms, along with the varying degrees of similarity of some of them?’ And there are various related problems, such as ‘How can we account for the fact that different geological strata bear the fossils of different life forms?’
Guesses arise as solutions to problems, and different guesses compete with each other. Guesses which are better at solving problems tend to win out in competition with less successful guesses. So guesses which survive are far from arbitrary, though they always remain guesses.
According to Huemer’s #15, Popper holds that evolution and the asteroid-impact theory of the extinction of dinosaurs are “unscientific.” Popper didn’t write about the asteroid-impact theory, but he wrote quite a bit about Darwin’s theory and accepted it as a momentous achievement. (And he often pointed out that the growth of human knowledge—conjecture and refutation—is a form of natural selection, in which theories compete and die.)
These two theories, evolution and asteroid-impact, do have the peculiarity, however, that they are each accounts of a unique chain of events that happened just once—the evolution of life on Earth and (a subset of that) the extinction of the dinosaurs. These are theories which do not take the form of universal laws. They do require the application of a number of universal laws, from physics, chemistry, and biology. Much of what Popper says about some scientific theories would not apply in these cases, since they do not possess a law-like logical structure, and Popper tends to be focused on theories which do possess a law-like logical structure.
Huemer asserts that “Real scientific theories . . . are not normally of the form ‘All A’s are B’ (as in philosophers’ examples).” This perhaps carries the innuendo that philosophers are making some sort of mistake by giving so much attention to theories of the form ‘All A’s are B’ (or ‘All swans are white’). But all scientific theories having the form of laws (or putative laws) do indeed take the form ‘All A’s are B’. All other theories, such as a theory, or story, of what happened at a particular time and place, involve applications of these law-like or universal theories. Philosophers are not slipping up when they give so much attention to theories of the form ‘All A’s are B’.
Nonetheless, theories of what happened historically, such as the theory of evolution, are still subject to conjecture and refutation. We can compare the theory of what happened with observations. The creationist theory in its most popular form can be refuted by many observations, including the existence of datable fossils gradually changing over billions of years.
In both the general account of evolution and the asteroid extinction theory, the theory in question has competed with alternative theories. The best-known alternative to evolution is special creation. Given evolution, the best-known alternative to natural selection is the Lamarckian theory involving the inheritance of acquired characteristics. In both these examples, we decide by refutation. Special creation, especially special creation less than ten thousand years ago, has been falsified. As an explanation for complex adaptations, inheritance of acquired characteristics has been falsified.
Alternatives to the asteroid extinction theory still have some following among the relevant scientific specialists: continental movement, volcanic activity, climate change, and competition from mammals are among the contenders. Here we don’t look at probabilities, but at the possibility of refuting one or more of the competing theories. (We accept there was an asteroid impact at approximately the right time, because of the evidence of worldwide iridium deposits, but that doesn’t prove that the impact was the cause of the extinction.)
Theories about a unique historical succession of events have the quality that in these theories the ‘problem of induction’ does not arise. Since these theories take numerous universal laws for granted, and try to establish what happened in some specific instance, they don’t make any attempt to proceed from the particular to the general, from the singular to the universal. They may make use of probability, but the use of probability is purely deductive. Probability is involved, but it is not involved in the process of arriving at a universal law. These theories are—like the theories of Sherlock Holmes in solving crimes—all a matter of observation and deduction, with no place for induction.
Huemer gives the observation that some snakes have vestigial legs as evidence in favor of Darwinian evolution and against creationism. As a somewhat facetious aside, let me point out that the most popular form of creationism derives from the first few chapters of Genesis, where we are indeed informed that snakes originally had limbs (as well as being highly intelligent and fluent in Hebrew), which they lost after a snake persuaded Eve to eat the forbidden fruit (Genesis 3). So a fundamentalist Jew or fundamentalist Christian might not be fazed by the vestigial legs in some snakes.
A better example would be the feet on some fossilized whales. Creationists scoffed at the evolution story that whales descended from land-dwelling animals and ridiculed the claim that whales had ever possessed feet. After many decades of arguments about evolution, fossil whales with feet were dug up in Egypt, one of many examples where new observations have strikingly corroborated—in a highly ‘improbable’ way—Darwin’s theory.
Huemer seems to reason like this. Snakes’ vestigial legs are not required by the theory of evolution; the absence of vestigial legs would not contradict evolution nor would it contradict the specific example of an evolutionary pathway, that snakes are descended from animals with limbs. Therefore, no refutation is involved in the finding that snakes have vestigial legs, nor would it be involved in the opposite finding.
There are numerous potential falsifiers to the prevailing account of evolution—to take the most popular example, if a fossil of a rabbit were to be found in pre-Cambrian strata. But Huemer’s point is that the vestigial legs on snakes do help to support the theory that evolution occurred, and that snakes are descended from animals with limbs, simply because this is the kind of thing you might expect to find if evolution were true, even though such a finding is not required. Hence, we have here a case of the strengthening of a theory because of something that increases the probability of the theory’s being correct.
All this seems quite persuasive, but I don’t accept that it contradicts Popper’s account because we are not dealing here with the attempt to arrive at a universal law. ‘Probability’ here has no inductive implication. I might add that we’re not compelled to approach even this matter in anything like the Bayesian manner. We can simply say that the vestigial legs in fossil whales constitutes an observation that has to be explained; a theory which offers a good explanation has an advantage; a theory which predicted precisely this would be even better (the theory did not predict that fossils of whales with vestigial feet would be found but it did assert that there were once whales with feet; finding precisely that kind of fossil is a good corroboration for that very prediction).
To avoid a possible misunderstanding, I should mention something that Huemer does not raise: that Popper at one time explicitly stated that the Darwinian theory was not a scientific theory, but a “metaphysical research programme” (Schilpp, 133–143) because, he argued, it was not falsifiable. In taking this position he did not dispute the fact that it might very well be a true account of evolution, nor did he dispute that it had a productive role to play in guiding scientific research. Nor did he dispute that many narrower components of the evolutionary story would be falsifiable (no rabbits in the pre-Cambrian). Later Popper reversed himself on this issue, and accepted Darwinism as falsifiable and therefore scientific (Radnitzky and Bartley, 143–47).
Deduction and Probability
Huemer reports Popper as holding that “Induction is completely worthless; probabilistic reasoning is worthless” (Huemer’s #1). Most of what we might want to call ‘probabilistic reasoning’ is not inductive. From the fact that a coin has a one-half chance of landing heads, plus the fact that a die has a one-sixth chance of landing 4, it follows that the chance of the coin landing heads and the die landing 4 is one-twelfth. This is presumably a case of probabilistic reasoning, yet there is nothing inductive about it. It is purely deductive—with the multiplication law for the joint probability of independent events as a premiss. And then, we can take the whole of inferential statistics: there’s no attempt at induction here. I assume that Huemer might call statistics probabilistic reasoning, yet it’s all purely deductive.
Huemer gives quantum theory as an area where the predictions are probabilities, and he says that probabilities cannot be falsified, which is true. Therefore, the implication seems to be, quantum theory is not scientific by Popper’s definition. He then says that quantum theory is “weird” so he will not rely on it as a counter-example to Popperian falsifiability, and goes on to his examples of evolution and the asteroid extinction theory.
Yet, as well as its predictions of probabilities, quantum theory makes some predictions which are not probabilities and are extremely precise. In fact, famously, the most extraordinarily precise prediction in the entire history of science, the anomalous magnetic moment of the electron, is made by quantum electrodynamics. So, in addition to its predictions of probabilities, quantum theory also makes amazingly precise non-probabilistic predictions, and quantum theory would therefore still qualify as scientific.
However, long before quantum theory, physics relied heavily on predictions of probabilities, notably in statistical mechanics—and there is surely nothing less weird than statistical mechanics. And even in quantum theory, we don’t want to say that the predictions of probabilities, taken by themselves, are always unscientific.
From the beginning, Popper confronted the obvious problem for the falsifiability criterion that predictions of probability cannot be refuted. He pointed out that physicists themselves have never seen this as a practical problem, and have routinely viewed their statistically-based theories as refutable. Popper’s theoretical solution to this problem is essentially along the lines developed by practical scientists: we adopt a methodological convention which requires us to disregard extremely low probabilities. (The solution is more precise and elegant than I can unpack here; see The Logic of Scientific Discovery, 190–97).
The Irrelevance of Belief
Huemer’s #2 and #6 refer to beliefs (#2 to what someone “thinks” is true). Popper has no great interest in the philosophy of belief, and the methodology of science does not need to say anything about beliefs. Science is not about beliefs. We should bear in mind that neither Newton nor Einstein believed their theories to be true—Newton because he could not accept action at a distance, and Einstein because he felt general relativity was not complete and would eventually be supplanted by a better theory, a unified field theory.
Although neither Newton nor Einstein believed their theories to be true, they did believe their theories were objectively superior to their predecessors. Any account of scientific discovery has to make room for the fact that we can prefer one theory to another, we can even say that one theory is objectively better than another, without believing the preferred or better theory to be true.
Belief is a subjective feeling of conviction that something is true. It is a fact about human psychology that people have a need, or at least a strong tendency, to believe. But we make no appeal to belief when we try to explain scientific methodology.
We might hit upon a theory which is actually true though we would not be able to demonstrate its truth, since any putative universal law might turn out to have exceptions and thus to be false. For critical rationalists, science is not about subjective feelings but about what can be demonstrated logically, to explain events in the world, in light of the observational evidence.
As a Bayesian, Huemer must be a pure subjectivist, who must suppose that science is all about beliefs, and this no doubt helps to explain why he finds the Popperian theory so hard to fathom. A Gestalt switch is needed to abandon the paradigm of subjective knowledge and embrace the paradigm of objective knowledge.
Now of course, scientists often do believe their theories, and scientific debates often display passionate commitment to beliefs, just as much as religious or political debates. Popper’s aim, however, in most of his writing, is not to give a history of science, accounting for all the aspects of science, including the psychological ones, as they actually played out, but to reconstruct the ‘logic’ of scientific research. Similarly, the theory of probability tells us nothing about the emotional states of gamblers, and the subject known as logic ignores what happens psychologically when people make conflicting assertions in debate. If you look at a textbook on decision theory, you will probably not find an index entry for ‘agony’.
Belief as a motivating force is generally ignored in the great majority of Popper’s discussion of the logic of empirical science, though it is a perfectly legitimate field of study, no doubt belonging mainly to psychology.
Popper sometimes mentions that he believes such and such a theory to be true (Realism and the Aim of Science, 72, 75), but when he does this, his belief is not offered as a reason to accept that theory, and is not logically compelled by the evidence supporting that belief. Such remarks by Popper are informal and illustrative. They do incidentally refute Huemer’s assertions that Popper considered all scientific theories to be false. Popper also volunteers that he believes certain metaphysical propositions, for example realism and indeterminism, but also such metaphysical theories as “There exists at least one true law of nature,” a metaphysical, and therefore non-scientific, claim which can never be empirically tested, but which Popper argues for on philosophical lines (Realism and the Aim of Science, 79).
This brings me to Popper’s statement, Huemer’s #6, that “belief is never rational.” I think I understand what Popper was driving at here, and to that extent I agree with it, but I would never word it that way. For that matter, if we take it with pedantic literalness and ignore context, it is flatly contradicted by what Popper says elsewhere (“But this belief, I assert, is rational.” Realism and the Aim of Science, 57).
Popper’s central position is that science is not about belief at all. The relation between a theory and the observational evidence is not a matter of belief, nor is the relation between a theory and other theories. So the ‘rationality’ of science owes nothing to belief—and belief is therefore non-rational in the sense that it is a psychological phenomenon which intrudes into science from somewhere other than ‘scientific rationality’. But in most cases, when people accept that a theory is a good theory, they tend to believe that theory, and that tendency to believe, while not probative in any way, and irrelevant to the validity of scientific reasoning, is usually heavily influenced by what the believer perceives to be the available evidence. As a matter of fact, I agree with Ray Scott Percival (The Myth of the Closed Mind) that all belief is rational, but that’s a revelation for which I guess most of the world, including Michael Huemer, is not yet quite ready.
I think I have said enough to show that Michael Huemer has misunderstood and mischaracterized Karl Popper. You do not need to be completely out of your mind to agree with Popper and me—though I don’t deny that it might help.
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