# Must Science be Falsifiable?

There's a common notion floating around, due to Karl Popper, that scientific theories are characterized by the fact that they are falsifiable.  The idea is that it is never possible to verify a scientific theory (i.e. the sun always comes up) because one day it might not happen.  But it is possible that the sun might not come up some day, and then the theory is falsified.  It must then be rejected, and replaced with something more complicated.

Now, let me confess right away that I have not gotten this idea by reading any of Popper's writings.  It is an idea which has been popularized in the scientific community.  You see, everyone knows what Popper said without having read any of it ourselves.  It could be that if I actually read Popper's books, my idea of what he said would be falsified.  So let me confine myself in this post to discussing Popperism as commonly understood.

If a theory is unfalsifiable (that is, if no experiment you could possibly perform would rule it out, then according to Popperism it is not a scientific theory.  Among those who subscribe to Scientism, this is usually assumed to be A BAD THING™.  (The way some people talk, if a theory is unfalsifiable, that means it is false!)

People often characterize bogus pseudoscientific ideas as unfalsifiable, because of the tendency of people who believe in them not to subject them to rigorous scrutiny.  But this is clearly an oversimplification.  True, there is such a thing as mystical Woo-Woo from which no definable predictions can be made, either because the ideas are not precise enough or because they don't relate to any actually observable phenomena.  But many psuedoscientific ideas, such as homeopathy, reflexology, or astrology, can be tested experimentally, it's just that the people who believe in them don't like the results when people do!)  I've heard people refer to Young Earth Creationism (YEC) as unfalsifiable.  I think their reasoning must be the following:

1. YEC is unscientific and wrong.

2. I've been taught that when ideas are unscientific, the reason is because they are unfalsifiable.

3. Therefore, YEC is unfalsifiable.

In fact, though, the real problem with YEC is that it IS falsifiable, and in fact has been falsified many time over. If the universe were created about 6,000 years ago and we have to get all of the layers of fossils and rock from a single planet-wide Flood about 4,500 years ago, then there are a gazillion problems with observation.  It contradicts the results of almost every branch of science which tells us anything about the past.  (Adding bizarre extra ideas, like God created the earth with fossils in it in order to trick us into believing in evolution, may make YEC unfalsifiable, but it might be better to characterize this as pigheaded refusal to accept reasonable falsification.)

[Fun fact: if you interpret all of the genealogies in Genesis as being literal, with no gaps—which of course I don't—then it follows that when Abraham was born, all of his patrilineal ancestors were still alive, back to the tenth generation (Noah)!  (This is using the Masoretic Hebrew text that omits Cainan, who is included in the Septuagint Genesis and Luke.)]

All right, digression over.

Clearly there is something right about the idea that theories ought to be falsifiable, yet not confirmable with certainty.  Major scientific theories usually deal with generalities: they make predictions for a large (perhaps infinite) number of different situations.  Normally, it is not possible to verify them in all respects, because even if it works well in many cases, it could always be an approximation to something else.

On the other hand, I think there are some scientific ideas which are verifiable but not falsifiable.  Here's an example:

Ring Hypothesis: Somewhere in this universe or another, there exists a planet with a ring around it.

I submit to you that: 1) our observation of Saturn verifies the Ring Hypothesis, 2) when scientists verify a proposition by looking through a scientific instrument, that counts as Science, and 3) no possible observation could have falsified the Ring Hypothesis.  (Even restricting to the Milky Way, eliminating planets with rings would be a tall order, impossible with current technology.)  Therefore, there are scientific propositions which are verifiable but not falsifiable.

On the other hand, even if an experiment "falsifies" a theory, it could be that the experiment rather than the theory is wrong. As Einstein once said "Never accept an experiment until it is confirmed by theory".  This witticism may seem to turn science on its head, but nevertheless it has a bit of truth to it.  A while back, there was an experimental observation which seemed to suggest that neutrinos travel faster than light.  Soon there were many papers on the arxiv trying to explain the anomaly.  But it turned out, not surprisingly, that there was an error in the measuring devices.  Usually, when a well-tested theory is in conflict with an experiment, and the anomaly has no particularly good theoretical explanation, it is the experiment which is wrong.  Not always, but usually.

What this means is that we need a more flexible set of ideas in order to discuss falsification and verification.  In particular, we ought to accept that falsification and verification can come in degrees—observations can make an idea more or less probable, without reducing the probability to exactly 0 or 1.  The accumulation of enough experimental data against a theory should make you reject it, but it may be able to withstand one or two anomalous measurements.

The quick answer is that one ought to use Bayes' Theorem instead.  This is a general rule for updating beliefs, taking into account both our prior expectations and observation.  This goes not just for Science, but also for everything else.  The only thing that makes Science special is that, due to a number of special circumstances, the process of testing through observation is particularly easy to do.

Even though falsification is not the best way to think about Science, it still works pretty well in many cases.  In a later post, I hope to explain the connection between Bayes' Theorem and falsification.  Usually we should expect good theories of the universe to be falsifiable, but in certain situations they don't have to be.  Bayes' Theorem can be used to understand both the general rule, and why there are exceptions.

I am a postdoctoral researcher studying quantum gravity and black hole thermodynamics at the Institute for Advanced Study in Princeton. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my first postdoc at UC Santa Barbara.
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### 12 Responses to Must Science be Falsifiable?

1. Luke says:

I think your views on Popper (that's *Sir* Karl Popper btw ;0p) are in broad alignment with the views of most current philosophers of science - that he gets something right when he talks about falsification as being central to science, but there's also something that's not quite right about it too. People generally agree that it's an improvement over the confirmation account of what makes science, um, science. But ultimately, as you point out, it falls victim to the same problems that confirmation faces...e.g., that there are cases where it's impossible to falsify a reasonable theory/hypothesis (*in practice* if not *in principle*), that you can always come up with post hoc explanations, that you can always question the reliability of the measuring equipment, and so on. Your take that confirmation and falsification come in degrees is quite aligned with Lakatos' insight: Scientific theories rest on a network of beliefs and assumptions, some of which are more core to the theory than others; such that, if there is an anomalous observation, the outermost, "auxiliary" assumptions are the first to go (e.g., the assumptions that the measuring devices are functioning properly, and other things of that nature). The auxiliary assumptions act as a protective belt surrounding the core assumptions (e.g., that energy is conserved, every action has an equal & opposite reaction, and things of that nature). These core assumptions only get challenged, shifted, and abandoned in very rare occasions, as Kuhn would say, at periods of scientific revolutions (Copernicus, Einstein, that kind of stuff). Ultimately, I like to think of falsifiability in terms of Kuhn's account - as one of the many aesthetics that factor into theory appraisal, but not always the most important one for any given scientist or any given theory appraisal (though sometimes very important). Speaking of which, I'm not ready to jump on the Bayesian bandwagon (Bayeswagon?) just yet. It strikes me as unfalsifiable! Not unlike the Drake equation, its virtue is that it's a useful tool for organizing thoughts and assumptions. You're going to have to convince me of anything further! ;0p

2. mpc755 says:

The whole notion of “falsifiability” is meaningless in mainstream physics.

The particle does not always travel through a single slit in a double slit experiment.

How do you falsify the above statement? You place detectors at the entrances, throughout or at the exits to the slits.

When you do this the particle is always detected entering, traveling through and exiting a single slit.

The notion the particle does not travel through a single slit is refuted by the evidence. It’s been falsified.

So, what does mainstream physics do? They ignore the physical evidence which refutes the notion the particle does not travel through a single slit and state that something else occurs when you don’t detect the particle.

What is that something else? Well, now mainstream physics can make up all sorts of stuff about a multiverse or many worlds or whatever nonsense it wants because you can’t falsify made up nonsense.

The notion the particle does not travel through a single slit is falsified by the physical evidence.

However, mainstream physics is so screwed up it can’t understand something as simple as the particle always being detected entering, traveling through and exiting a single slit in a double slit experiment is evidence the particle always travels through a single slit. It is the associated physical wave in the aether which passes through both.

3. Aron Wall says:

Luke,

It's nice to know that some contemporary philsophers of science are saying some fairly sensible things. Thanks for the input. Even though I am an American and don't believe in such things, I apologize to SIR Popper for forgetting his title of nobility. I wish that I could call him SAINT Popper (Acts 26:29), a far better thing, but at least in his earthly life it appears from a cursury internet search that he did not know the Savior.

Kuhn (another great whom I haven't read, but expect to disagree with when I do) always seemed to me to be unnecessarily disrespectful to his elders when he appropriated Planck's dictum:

a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.

The idea you attribute to Kuhn about theories being protected by auxilliary assumptions which (at first) we are more willing to discard seems entirely sensible. However, I note that we didn't actually need to change any of our ideas about how equipment works in general to save ourselves from faster than light neutrinos. We only needed to change our view that the equipment in the OPERA experiment was properly calibrated. (Indeed, now that it is fixed and is giving sensible results, presumably we all go back to believing that it is probably properly calibrated.)

I also want to observe that this is not quite the same thing I was saying when I said falsification and verification come in degrees. I was talking about my Bayesian degree of confidence in a particular proposition/i>. But of course, in general there are multiple propositions running around, and when we update our credences according to Bayes' Law, this will generally require us to start by doubting the principles which seemed least certain to us.

Regarding your doubts of Bayesian epistemology: I don't think that it has to be falsifiable. Bayesianism purports to say how an idealized rational agent should adjust their beliefs based on evidence. In principle, the way you would support this is by thinking about lots of different possible situations (real or counterfactual) and ask whether it gives a sensible prescription in all of these situations. Then you compare to other epsitemologies and see which is better. Since the situations don't have to be actual, I think this is in principle a purely a priori inquiry. I think that means it doesn't have to be falsifiable, any more than 2+2=4 is falsifiable. But I also think it works great when applied in practice (just like arithmetic is a highly practical art).

Anyway, there are various Dutch book arguments which say that if you have to accept or decline bets on various propositions at various odds, and if we define your probability credences based on which bets you take, then EITHER your credences can be represented as following Bayesian rules, OR you might accept a set of bets which is guarenteed to lose you money. To me this is as close to a "proof" as one is likely to get in philosophy.

4. Aron Wall says:

Welcome to my blog, mpc755.

The interpretation of quantum mechanics is a notoriously tricky subject. There are a number of different interpretations. People who hold different interpretations all agree on how to calculate probabilities in real experimental setups. Hence there is no experimental way to distinguish between them. Instead, we have to use some combination of logical consistency and theoretical elegance to determine which is the best. Really, it's a question in metaphysics, not physics.

All metaphysical theories involve postulating some sort of additional stucture, not directly observed, in order to make better sense of what we do see. Your Bohm-like "physical wave in the aether" is just as much an example of this as Copenhagen or the Many Worlds Interpretation. There's nothing wrong with this in principle, the question is just which type of postulates seem most reasonable. (Personally I think that MWI is logically inconsistent in its treatment of probability theory, but obviously other people disagree.)

However, the rules for calculating probabilities for different events happening are plenty falsifiable. You just do an experiment and see if the frequencies of outcomes agree with the predicted probabilities, within the relevant error bars. If you can agree with the rules for doing this, then we mainstream physics will be happy to have you.

Anyway, it seems rather cynical for you to condemn my entire profession based on this one issue, which even mainstram physicists would agree is controversial. Just because pop-science books and intro-level courses use certain heuristic concepts to try to explain QM to people, doesn't necessarily mean that they are Articles of Faith which you have to accept to be a physicist.

I don't know enough about your "physical aether waves" interpretation to say whether it agrees with experiment, but if it does, great! We can add it to the long list of alternative interpretations of QM people have come up with. On the other hand, if it doesn't agree with experiment, or if we can't understand what it is saying, then there might be a problem.

The main issue with postulating a "physical wave in the aether" to guide the particles, comes in situations where there are 2 or more particles running around. In situations like that, the guide "wave" needs to be a function, not living in the three space coordinates, but rather in the space of all possible configurations of the particles. But once you say that, it is obviously no longer a conventional wave of a usual sort. It's a really weird and counterintuitive type of wave. But if you're comfortable with that metaphysics, great! All of the choices on the table involve assuming something really bizarre is going on.

5. g says:

Aron, would you like to be more specific about the inconsistency you find in MWI's treatment of probability theory?

6. Aron Wall says:

g,
At some point, I should devote a blog post to this subject. But before that, I'll need to explain QM some. So as not to drive you mad with curiosity before then, here's a very brief explanation:

If all branches of the wavefunction truly exist as separate "worlds", that seems to me logically equivalent to saying that everything that can happen, happens with probability one. But that's in flat contradiction with the Born rule, which says that some events have a greater probability of occuring than others. I don't even know what it would mean to say that all physical possibilities exist, but that some of them exist more than others. Existence is not something that comes in quantitative degrees!

7. g says:

OK, thanks.

I don't see that there's a contradiction here. MWI says (kinda) that everything happens-somewhere-in-the-multiverse with probability 1, but it doesn't say that everything happens-on-this-particular-occasion with probability 1, and it's the latter that would contradict the Born rule (or everyday probability theory). (Compare a very-large-universe theory that has a universe large enough and random enough that there are almost certainly vast numbers of "versions" of us (with our present surroundings and history) in it. Maybe even an infinite universe, with infinitely many copies of us. Then, e.g., when you roll a die, "with probability 1" there's some version of you somewhere that rolls a 6. But there's no contradiction between that and the fact that (with the usual idealizing assumptions) the probability that you roll a 6 on this occasion is 1/6 rather than 1.)

I agree there's something of a puzzle about how wavefunction amplitudes produce probabilities. But one can make an argument along the following lines (there's a famous paper by Wallace that goes into more detail, though his language is a bit different from mine; I think it's expanding on some ideas of Deutsch, and from what he says about Deutsch it seems possible that Deutsch's approach is more like mine below).

Assume (this, if anywhere, is where something gets smuggled in) that sufficiently small wavefunction changes (measured in the "obvious" norm) correspond to small changes in probabilities in some sense, and in particular that if you decompose the wavefunction into orthogonal bits one of which has a tiny norm then the probability associated with the latter is very small. (That's shorthand for a statement about limits.) Then I'm pretty sure you can show that histories in which frequencies diverge badly from the ones you get from the Born rule have very small measure and hence (in the limit) tiny probability. In other words, if you're willing to assume that tiny measure => tiny probability, then that suffices to show that "the Born rule almost always holds approximately in the long run".

Wallace's paper takes a slightly different approach, making not a substantive assumption about probabilities (infinitesimal measure => infinitesimal probability) but a normative assumption about preferences (agents' preferences should be continuous functions of the wavefunction), and deducing (with a bunch of other very reasonable axioms) that rational agents should act as if they predict outcomes in accordance with the Born rule.

8. g says:

(I should maybe stress a bit more that "tiny measure => tiny probability" is a consequence of "probability is a continuous function of the wavefunction", which may be a more plausible axiom. I should also add that I am not a quantum physicist, or any other sort of physicist, and any amount of what I've written may be wrong, though I'm pretty sure the basic ideas are OK.)

9. Aron Wall says:

g,

I'm familar with attempts to smuggle in the Born rule, and they seem rather unconvincing to me. The elegance of MWI is popularly supposed to be that all need is the wavefunction---no need for any additional rules like collapse. But in fact, as you point out, you do need some auxilliary assumptions, in all the rules that you point out. And in particular, the assumption that "sufficient tiny norm events never happen" seems rather contrary to the premise that "all possible events happen".

It seems to me, that once you've specified everything that IS (and saying either 1) "every possibile outcome happens" or 2) the wavefunction $\Psi$ is all that exists seem to me to be such specifications), there is no more room for additional arbitrary assumptions. You've already said everything there is to be said about the universe. That would make MWI incoherent.

(Compare a very-large-universe theory that has a universe large enough and random enough that there are almost certainly vast numbers of "versions" of us (with our present surroundings and history) in it. Maybe even an infinite universe, with infinitely many copies of us. Then, e.g., when you roll a die, "with probability 1" there's some version of you somewhere that rolls a 6. But there's no contradiction between that and the fact that (with the usual idealizing assumptions) the probability that you roll a 6 on this occasion is 1/6 rather than 1.)

Actually, about such situations I would be inclined, hesitantly, to say that it is also meaningless what you roll (and therefore that we know we don't live in such a universe). When you roll a die, there are infinitely many versions of you which get a 6, and infinitely many versions where the die explodes and you die, and infinitely many versions of you where green monkeys pop out and start torturing you to death. They are all equally "real", and they occur the same cardinality number of times. Unless you're the sort of person who thinks you die if you enter a star trek teleporter, I think the only correct thing to say is that you would have ALL of these experiences.

Anyway, the question of how to do probability theory in such "mutiverse" type settings is highly controversial, and I'm not aware of any satisfactory general prescription which doesn't lead to horrible paradoxes in certain cases. But, provisionally, because it seems to me the least absurd, I incline to the view that by far the best way to explain the (seeming fact that) some things happen but not others, is that (in reality) some things happen but not others. This requires that the universe not be too large and uniform.

10. g says:

(I know that this is all rather off topic, and you've said you're going to be posting on this issue in the future -- so unless you specifically request otherwise this will be the last I have to say on the matter in this discussion.)

I really don't see how the word "smuggle" is a reasonable description of what I described. We have the wavefunction. We have an obvious metric on the space of possible wavefunctions. I remark that the axiom "probabilities are a continuous function of Psi" is enough to get you (close enough for practical purposes to) the Born rule. Where's the smuggling?

the assumption that "sufficient tiny norm events never happen" seems rather contrary to the premise that "all possible events happen".

But I never suggested making the assumption that sufficiently-tiny-norm events never happen. I suggested making an assumption that implies that as norm -> 0, the probability of the event happening (on any particular occasion) also -> 0. That's an entirely different matter.

about such situations I would be inclined, hesitantly, to say that it is also meaningless what you roll (and therefore that we know we don't live in such a universe)

It seems to me that you should have, at least, a niggling feeling in the back of your mind that you're deriving too strong a conclusion from too little information, when you say "therefore we know we don't live in such a universe".

I suggest the following thought experiment. Consider a one-parameter family of universes, all very much like this one (and, in particular, all having us in them) but with parameterized size. Once the size gets large enough, there are almost certainly "copies" of us with indistinguishable life histories such that (e.g.) any given die roll comes out each possible way; and apparently you know on (for want of a better term) metaphysical grounds that that's absurd and meaningless and "therefore we know we don't live in such a universe". For smaller sizes, this doesn't happen and (so far as I know) you're happy regarding us as living in such a universe. So what does the transition from possible to impossible look like? Is a world where there is, let's say, a 10% chance that there's just one other indistinguishable copy of you "meaningless" and impossible? One where there's a 0.01% chance? 10^-100? Even in our world, and even assuming it isn't terribly large (for all we know, last I heard, it might well be), the probability isn't zero. Should we be saying that Pr(roll a 1) = ... = Pr(roll a 6) = something just a little bigger than 1/6?

It seems to me that that whole line of thinking must be wrong. The probability that you roll a 6 isn't made any larger by the possibility that a copy of you somewhere else might be rolling a 6. Your probabilities have to add up to 1, not to 1 + a fudge factor accounting somehow for the possibility that there are other versions of you elsewhere.

And it also seems to me that if all these finite-but-ever-larger universes are OK and give us the same probabilities (as they must) then their infinite limit is also OK and gives us the same probabilities; and that cardinality is a mere red herring. I should in fairness add that although I think I've just given a reason to think it's a red herring, that isn't "my" reason -- it simply seems obvious to me from the outset that "they all have equal cardinality" is no more reason to assign equal probabilities than e.g. the fact that (assuming a traditional continuously-divisible spacetime) the states-of-the-world in which a die comes up 1 and comes up not-1 "have equal cardinality" is reason to assign equal probabilities to those.

11. A quick note about Noah and Abraham - I don't see why you think this is a far-fetched idea. It actually seems to be implied by the text itself. What did Jacob say to Pharaoh in Genesis 47:9? "The years of my pilgrimage are a hundred and thirty. My years have been few and difficult, and they do not equal the years of the pilgrimage of my fathers".

He lived to be 130 years old, but his years were *few* and *shorter* than that of his ancestors. By all accounts, even incidental ones like this, human longevity shortened dramatically in those years. In addition, if you have a group of people who are living that much longer than their offspring, you can see where the Greek and Roman heroic stories come from. You have a group of people who really do seem to be immune from death giving birth to children who are mortal. Eventually they did die, but this must have been how it seemed to those living at the time.

12. Aron Wall says:

Welcome to my blog, Jonathan. It is of course true that Genesis seems to portray prehistoric human beings as living longer than other humans. There are also other ancient texts which describe mythologically long lifespans (e.g. Sumerian kings reigning 72,000 years, which seems excessive even by the standards of Genesis).

However, archaeological evidence shows that prehistoric people (at least those whose remains we can examine) did not live longer than modern day humans; in fact their life expectancy, and the age of the oldest people, are noticably lower. Thus, in general, they did not live longer than us. Which should not be surprising given the much worse medical technology of that time.

If long life were only achieved by a tiny fraction of the population, then of course we would not necessarily know it from archaeology. One could imagine that God supernaturally extended the ages of certain people (given the basic facts of human biology as we know it now, I think this would require a miracle), but we would not be able to scientifically test this unless those people were a part of our sample. This seems especially likely in the case of Abraham, where the whole point of the story is that he and Sarah were much to old to have a child, his body being "dead" as Paul says---and that he had faith anyway that God would do the impossible.

But long lifespans are hardly the worst conflict between modern Science and a literal interpretation of Genesis. The fact is, that any Christian who accepts the modern scientific consensus must interpret the early chapters of Genesis nonliterally. Leaving aside the age of the earth and human evolution, the geological evidence simply cannot be squared with a universal Flood. Thus, at least the extreme old ages of the antediluvian patriarchs are squarely inside a portion of the text which we know for other reasons to be mythological (although nonetheless divinely inspired by God, and revealing deep truths in a symbolic way). The symbolic nature of these ages seems reinforced by the fact that some of them seem to have numerological singificance (most strikingly Enoch (365) and Lamech (777)), and that they keep coming tantalyzingly close to 1,000 without ever reaching it, suggesting the inadequacy of even the longest lifespan for attaining complete fulfillment. This lesson from Genesis will be of even greater practical significance if future medical technology allows us to extend the maximum lifespan beyond 120 years.