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Falsifiability Is Falsifiable

We’ve talked many times before, and at greater length in Uncertanity, about the concept of falsifiability. It has come up again lately.

The term shouldn’t be but is equivocal. I mean it is used in an equivocal sense, which is always a danger, because it happens that an argument is started with one sense of the word, but finished with another, invalidating the argument.

The first, and what I say should be the only, is the logical interpretation. To falsify is to prove something false. To prove is to demonstrate by a sound, valid argument. Thus if a man holds the proposition “7 is less than 4”, we can falsify that proposition with a simple proof which takes as its premises basic arithmetic. Indeed, for every proof we have (in math, logic, philosophy) we have also proved a contrary is false. Falsifications are thus not rare—but they are restricted, as we shall see.

Theories make predictions, or rather it is possible to infer predictions from theories. If a theory says, “X is impossible” and X is observed, then the theory has been falsified, i.e. proved false. We here take impossible in its strictest sense.

But if the theory merely says, “X is very unlikely” and X happens, then the theory has not been falsified. Not according to the logical definition of the word. Rare things will happen. The theory admitted this rare thing was not an impossibility; it admitted that the rare thing was possible. The rare thing did happen. Therefore, if anything, the theory has been given support!

Falsification was, as we all know, made popular by Karl Popper. He relied upon it for both philosophical and practical reasons. About the latter, he was frustrated by certain ridiculous theories that could not, by the use of the common tools of the day, be shown to be false. Every observation, said the believers in these queer theories, was consistent with their cherished models.

Take the theory that UFOs have visited earth. The lack of clear or unambiguous photographs means that the UFOs are clever in evading cameras. That NASA denies the existence of UFOs shows the government is in on the conspiracy. And so on. There is no way to falsify the theory that UFOs are real.

Indeed, there does not exist a definitive proof, in the logical sense. Such a proof would have to demonstrate both why other spaceship-building lifeforms could not exist or that even if they could, they could not have got to earth. These demonstrations cannot say such feats are unlikely; they have to say they are impossible. And that’s not possible. UFOs therefore cannot be falsified.

True theories also cannot be falsified; and they have the happy bonus of being right about everything. That is, every observation also supports true theories. No observation anywhere falsifies the theory “7 > 4”.

Enter the second, and incorrect, use of falsified. People will say that the UFO theory has been “practically falsified”, because no evidence of little green men has ever withstood scrutiny. These people are right about about the lack of evidence, and even right according to my lights about their judgement not to take UFOs seriously. But they are wrong to say that the theory has been falsified, practically or not.

Practically falsified is to falsified as practically a virgin is to virgin. They are not in the same philosophical ballpark.

Back to our rare X. A theory has said X is rare, but not impossible. X is seen. Depending on the rarity, for rarity is a loose word with many interpretations, people will incorrectly say the theory has been “practically falsified”. Suppose it was judged Pr(X|theory) = ε > 0, and X is observed. If ε is “small enough”, the criterion for “practical falsification” has been met. Yet once people allow themselves the phrase “practically falsified”, they generously given themselves permission to strip off the qualifier and say just plain “falsified”.

If this doesn’t sound familiar, then you have not been paying attention, dear reader. For this is the basis of the use of p-values — where ε stands in for the magic number. As some of us recall, it was Fisher’s intent to follow Popper’s lead here.

Now it may be the case that every other theory that we know also says X is rare; in notation Pr(X|other theories) = rare. Or we may not know of any other theory; or the theories we know do not allow us to compute a numerical probability.

In the logical sense, all we can say about X is that, perhaps, some theories give it higher probabilities than others. It is natural also to think that the theory which said X was more likely is itself more useful, which it might very well be. But that depends on the use of theory, and how the probabilities affect our decisions. This is why I said I agree about the decision to treat UFOs as unimportant (mistakes or hoaxes etc.), and why I did not say UFOs are false.

We are on the familiar ground of the predictive method, where we recognize that probability is not decision, and understanding how a theory can be useful to one man, but useless to a second, and so forth. See the on-going class for details.

This leads to the conclusion that “practical falsification” is an act, a decision, and not a demonstration. Nothing has been proved with “practical falsification”; something has been judged. “Practical falsification” is in this sense an opinion. In statistics, p-values are a one-size-fits-all decision, because the magic number is, well, magic. One theory is judged false (the “null”), while another has been judged true (the “alternate”).

Wait. Not judged true. Judged “not falsified”. Popper could never bring himself to believe anything; all theories were to him temporary and waiting to be supplanted. That accounts for the screwy “not falsified”, which isn’t wrong, but it is odd. See Uncertainty for more details on this.

21 thoughts on “Falsifiability Is Falsifiable Leave a comment

  1. While not all religious people fall into the trap of describing their faith as some kind of non-falsifiable theory, many of them do, and here (along with strongly held political ideologies) is where you find the mother load.

    I even recently encountered a fellow who claimed that the absence of any contemporaneous texts doubting the reality of Jesus’ miracles was somehow evidence that those miracles, as described in the gospels, actually happened, even though there is also no account outside the scriptures confirming their reality. In other words, to this Christian, the absence of evidence was itself confirming evidence. And this fellow is prone to trumpet his mastery of logic, and, even, the statistical treatment of evidence!

  2. Lee – absence of evidence is not evidence of absence. Evidence for the truth of the teachings and resurrection of Christ abound – there are no less than four different eyewitness testimonies written shortly after the events themselves. There was no profit in being a disciple – all but one were murdered, and he was nearly killed, then banished. Yet, they persisted in speaking what they perceived as the truth, and spreading the word to other at no profit to themselves.

    There is no logical proof that humans are capable of independent cognition and creativity. There is no proof of the fundamental axioms of mathematics and logic. Yet, we still base our entire edifice of thought upon these provably unprovable assertions.


    “All right,” said Susan. “I’m not stupid. You’re saying humans need… fantasies to make life bearable.”


    “Tooth fairies? Hogfathers? Little—”


    “So we can believe the big ones?”


    “They’re not the same at all!”


    “Yes, but people have got to believe that, or what’s the point—”


    ? Terry Pratchett, Hogfather

  3. The evidence for UFOs is much stronger than the evidence that Jesus performed miracles. For UFOs we have photos, videos, eyewitness accounts, and radar tracking. For miracles, we have contradictory accounts written down 70 years after Jesus (supposedly) died, in another country, and in a different language, by activists.

    In addition, as you say in the article, there isn’t anything inherently impossible about UFOs. Miracles, by definition, go against known laws of nature, so according to the same criterea, are falsified.

  4. Consider this remark from Briggs’ essay today:

    “Take the theory that UFOs have visited earth. The lack of clear or unambiguous photographs means that the UFOs are clever in evading cameras. That NASA denies the existence of UFOs shows the government is in on the conspiracy. And so on. There is no way to falsify the theory that UFOs are real.”

    Or, consider other similar remarks before the ‘little green men’ remarks appear.

    See the problem?

    The statements are not well presented nor are key terms defined. Of course we know what was meant — extraterritorial visitors arriving via spacecraft. Or something like that.

    But to say UFOs are or are not real without precision about what’s being addressed invites all sorts of confusion, and worse, openings for others to wedge in reasonable doubts in an unreasonable way. UFOs include, for example, extraterrestrial events of no real controversy such as small meteors and so forth, and/or, other explainable events of terrestrial origin (e.g. USAF fighter pilots “training” at a distance, turning on & off their lights to make it appear [from a distance] impossible maneuvers are occurring, dumping fuel and lighting the afterburners to create otherworldly displays and so forth. And, yes, they do that on purpose).

    Properly defining the problem, or issue, or whatever it is, helps focus analysis — including the pursuit of additional info [an omitted topic around here] — to get at all the various issues, including ferreting out factors that render the “problem” into multiple other “problemS.”

  5. Lee Phillips writes: “…you find the mother load.”

    That’s “lode”.

    “I even recently encountered a fellow who claimed that the absence of any contemporaneous texts doubting the reality of Jesus’ miracles was somehow evidence that those miracles”

    Mr. Briggs hints at this phenomenon; the less evidence existing for a conspiracy the more effective must be the conspiracy.

  6. Missing evidence of UFO is somewhat similar to missing evidence for God. A problem is that people decide in advance of observation what a UFO (or God) must look like or resemble; and the definition could thus be wrong, in which case you have seen many UFO’s that closely resemble a Cessna Jet while you have been looking for giant pie tins.

  7. Lee Phillips, 1st post, touches on another behavioral issue:


    “… a fellow who claimed that the absence of any contemporaneous texts doubting the reality of Jesus’ miracles was somehow evidence that those miracles … actually happened, even though there is also no account outside the scriptures confirming their reality. In other words, … the absence of evidence was itself confirming evidence. And this fellow is prone to trumpet his mastery of logic, and, even, the statistical treatment of evidence!”

    Humans are notoriously biased — its called “confirmation bias” and it manifests in a variety of ways. In the brief description, above, we see a tale about someone that chooses to believe certain reports. Ignored is the bias of the sources reporting the spectacular reports (the authors of the Gospels are highly biased — how does one know if they are objective or wannabe cult leaders concocting a tall tale to seduce exploitable drones, for example?).

    The absence of corroborating info is perceived as no problem [doesn’t seem to be addressed], and, the absence of disputing evidence is perceive as proof there is nothing to dispute the stories. This inconsistent treatment of unknown or nonexistent evidence is a certain indication of confirmation bias.

    Further, we can be pretty certain the person described as arguing the veracity of the miracle stories has not explored the implications of the purges by the Catholic Church of heretical beliefs — purges we know were VERY effective, but not entirely complete as enough has survived directly and in the descriptions by Church officials disputing various heresies. Is the absence of evidence disputing those stories evidence there was none?, or, is the surviving evidence just harder to find and evidence of the thoroughness of the Church’s efforts to maintain a particular myth? I bet we can be nearly certain that the individual described has neither considered, nor would he consider, such alternatives as these would challenge a cherished belief.

    It’s a curious thing about human bias — especially when it manifests in conjunction with a religious topic: The search for “truth” is so easily hijacked and shunted to cherry-picking and force-fitting data to fit a preconceived and poorly founded belief. People lie most and lie best when they are lying to themselves.

    The real “trick” (if that’s the word) is knowing how to step outside oneself to pick up on one’s own biases clouding and distorting the data/evidence one is evaluating.

    The movie, 12 Angry Men (jurors deliberating), delves into this masterfully.

  8. The point about UFO’s is that they are supposedly flown by Aliens, beings from another planet. Nobody has encountered such beings in different settings, like meeting them in a bar, or passing them in a shopping mall, and a gazillion other ways one could be meeting them. UFO’s being flown by Aliens is therefore unreasonable, as there is no *other* evidence such beings exist.

    The existence of Jesus is not unreasonable, as there have been plenty of people claming some kind of Godly connection. But Jesus’ existence is not proof that Jesus is God.

  9. Sander van der Wal writes: “Nobody has encountered such beings in different settings, like meeting them in a bar, or passing them in a shopping mall…”</i?

    How would you know? You presume upon the appearance of aliens.

  10. swordfishtrombone writes: “Miracles, by definition, go against known laws of nature, so according to the same criterea, are falsified.”

    They are falsified to you because you have defined it that way. Miracles to me do not go against the laws of nature (but might exceed KNOWN laws of nature). I suppose I would define it as uncommon, beneficial, with no obvious scientific explanation. I believe eventually science and religion must merge, or at least the true parts of both. Science is limited by its own definition; if a thing cannot be tested, or repeated, or measured, then it isn’t subject to science but it may well exist (or have briefly existed). Almost any description of God cannot be tested because apparently he wishes not to be tested. It isn’t that you cannot; but science works poorly or not at all on self-willed beings. That is why Sociology is such a mess. It is difficult or impossible to precisely repeat an experiment on self-willed subjects even if they are cooperative.

  11. Popper’s falsifiability test is based on specific assumptions and which attempts to reunite the Descartian rationalist with the Humean empiricist into a exhaustive (methodological) test for all truth. That his framework allowed for adjustment to the assumptions if they followed the same rules as the theory itself, was internally consistent although ultimately self-referential.

    We all start with a small circle of authoritative assumptions which are the basis of our worldview. Because these ideas are the core of our understanding, they are our epistemological frame or lens through which we view the world – how we determine truth or weigh truth claims.

    The defining circle of biblical presuppositions is that the Biblical God exists and has revealed Himself authoritatively in Scriptures alone as the base for this worldview. It is His being that makes the possibilities real and why falsifiability has (limited) validity.

    “The fear of the Lord is the beginning of wisdom” (Pr. 9:10)

  12. Mr Briggs has again shot his own foot off by basing his argument on a ridiculous assertion; namely that any fanciful speculation, conjecture, fairy story, or cunning deceit can be a “theory” and if such are “based” in a complete detachment from reality and logic so that they are untestable then the falsifiability scientific requirement is invalid.

    Scientifically, a theory is an hypothesis (which is a reasonable possible explanation for observations) that has not been repudiated (falsified) by other observations and/or logic which is then accepted as a likely explanation… still liable to falsification or modification.

    You galahs are busting to elevate your favourite fraud “Evolution” to the status of a “theory” by redefining terms and precepts and concocting statistical “possibilities” to override the well known Laws of Nature and the almost unknown Laws of Logic.

    Blardy mathemagicians should have been condemned along with the Scribes, Pharisees and Lawyers.

  13. All,

    The paper here is of course highly relevant:


    Your friend might have been arguing like this:

    Pr(Miracles true | no contemporary skeptical account exists and we would expect them because people are anxious to dismiss miracles and other evidence) = a + d, where d>0.

    Pr(Miracles true | other evidence) = a.

    (Of course, a and d do not have to be strict.)

    You are saying

    Pr(Miracles true | No accounts except by certain eye-witnesses and their contemporaries exist and miracles aren’t possible) = 0.

    You’re both right. I mean, given the assumptions you both made, your probabilities follow.

    As I have been emphasizing, again and again, the premises are the most important part of any argument (i.e. probability assessment).

  14. What is the definition of a miracle? For us ordinary folk a miracle is something that does not occur according to the nature of things. It requires a prerequisite that there is a natural order of cause and effect and if an effect cannot be the result of a natural progression of natural processes then it can be described as “miraculous”.

    A pox on “probability assessment”. Either it is or it isn’t.

  15. The “friend”’s argument is weak at best, and seems fallacious as well. I’m sure any motivated reader could construct an argument with the same form that was obviously invalid (for example, why is d > 0? Assuming the conclusion?). Also, I understand that it is easier to argue with a position that you invent in order to oppose it than with a real position, but, once again, you’ve put words into my mouth. I never said what you said I said.

  16. Dr. Briggs has not refuted falsifiability, contrary to his claim. The shortcomings that Briggs alleges in the principle of falsifiability are avoided by those methods for selecting the inferences that are made by a model through maximization or minimization of the missing information in each such inference for a deductive conclusion to be reached by it per event, the so-called “entropy.” These methods are enabled by the fact the the entropy is the unique measure of an inference under the “probabilistic logic”; this logic is formed from the classical logic through replacement of the rule that each proposition that is stated by a model has a truth value by the rule that each proposition that is stated by a model has a probability of being true. The generalization that is formed in this way is falsified if and only if the associated inference fails to maximize or, as required by the description of this inference, minimize the entropy of it. A wealth of observational data suggests tha this does not happen in the real world. Thus, for example, one does not
    observe cars observe cars spontaniously leaping to the tops of tall buildings while cooling to the extent required for energy to be conserved; were cars of this description to be observed, the principle of entropy maximization would be falsified by the evidence.

    The principle of seeking an extremum in the entropies of the inferences that are made by a model solves the ancient, previously unsolved “problem of induction. The problem is of how, in a logically defensible manner, to select the inferences that are made by a model.

  17. Nice to see you here, Terry. Even though I might not live long enough to translate your comments into practical concepts that I can conceive, I think I have a vague concept of the “problem of induction”. To my rather unsophisticated mind it seems specious.

    Let’s imagine that some inducted idea is proposed as a possible “solution” to a problem, real or imagined. That proposed idea is nothing more than an hypothesis; a “possible” solution that has no probability attached… it’s either demonstrably wrong (impossible according to certainly known principles) or it remains just a possibility without any real probability of being either right or wrong. As long as it remains “unproved to be wrong” it might be regarded as a “theory” to be challenged by any scientific (logical) observations.

    If it can be proved by logic and observation that there are no, and can be no, exceptions to the “theory” then it’s a “Law”… such as the Law of Non-Contradiction. Again, no “probability” attached.

    These crazy statisticians bust themselves to make the impossible into the improbable into the remotely possible into the “it is”.

    Long ago I read a blurb from Julian Huxley flogging “enlightenment” to hapless university students. He quoted the “chance” of even one simple protein forming by series of accidents… “it’s impossible” he said “but it has happened because here we are!”

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