Saturday, January 9, 2016

Falsifiability isn't empirical validity


@UnlearningEcon links us to a discussion of Popperian falsification here. Here is an earlier post and it's an interesting read. However I think the discussion confuses falsifiability with something that is maybe best described as empirical validity. At least if I understand what the discussion is about. The original author states:
Falsificationism has only two little problems: neither real scientists apply falsificationism, nor should they. If the very concrete 19th century astronomers John Couch Adams and Urbain Le Verrier had applied abstract, manichean falsificationism, (1) Newtonian mechanics and Kepler's laws of planetary motion would have been unfairly falsified, and (2) Neptune would not have been discovered. One can only imagine their dilemma: stick to the recently "falsified" Newton/Kepler or go back to the also falsified Aristotle/Ptolemy?
Emphasis in the original. Newton's laws are essentially a statement of the conservation of momentum and energy (and the definitions of mass, momentum and energy). Quantum mechanics adds expected values to these, but sufficiently accurate experiments weren't available at the time to tell the difference. I don't recall any violations of these principles measured at the time, so I am not certain what evidence was falsifying Newton's or Kepler's laws -- plus both used to this day. Newton calculates many things in the course of the Principia that are compared to experimental data; for example, he calculates the motion of comets observed by Halley and even the mechanism generating the tides. These are falsifiable in the Popperian sense -- they say the universe will behave in a certain way and not another. Neptune was discovered because the predictions of Newton's laws were off without the planet. This has nothing to do with the principle of whether Newton's laws are falsifiable (they would be falsifiable regardless of the existence or subsequent discovery of Neptune). So I do not understand the discussion in terms of falsification here.

A commenter named Hedlund adds:


E.g., Feyerabend, in Against Method, gives examples of theories that were by all appearances falsified, yet still advanced our understanding (and in some cases were later vindicated). In other words, falsification must be flexible and open to calibration rather than naively absolute; no theory is consistent with all facts.

A theory that was falsified is a fortiori falsifiable, and therefore science according to Popper. There is no conflict between being falsified (empirically invalid) and advancing understanding.

Falsification has nothing to do with a theory being "falsified" or its empirical validity. Falsification is about a theory having the capability to be falsified. All empirically invalid theories are falsifiable and hence science in the Popperian sense. Falsification is fairly metaphysical -- it is about the potential for a theory to be empirically invalid in some universe.

I think an example would be good here. A physical "theory of everything" isn't falsifiable in the narrow sense in the quotes above -- no experiment should ever prove it wrong because it is correct. But it is falsifiable in the Popperian sense -- for example, the theory of everything should predict zero macroscopic violations of momentum conservation. Observing non-conservation of momentum would constitute a path towards being falsified and hence Popperian falsifiability. We can't never prove it empirically invalid (falsify it) in our universe, but there is a conceivable universe in which there is some violation of the theory.

Additionally real scientists do consider falsification -- at least if they ever consider how to experimentally test their theory (which they should). The theory has to posit states of the world that will not occur. If a science is an experimental one (particle physics), it can help bring about those states that can't happen according to the theory and therefore demonstrate it to be empirically invalid. If not, the process of gathering evidence is harder (astronomy, economics).

Falsifiability is not in any way related to the idea that "all models are wrong" (which is about simplicity -- or better yet, complexity that can be supported by the quantity of data available). It is related to the "no true Scotsman" problem -- pseudoscientific theories have a way of explaining away any falsifying results (empirical invalidity) and therefore aren't falsifiable.

So a hard-nosed approach to falsifiability wouldn't have caused any problems in the history of science as it exists on Earth (maybe we can construct a case where it would be a problem -- I'm not fully versed on the critical takes on Popper). All scientific theories I know about are falsifiable. So are many economic theories. Second, empirical validity/invalidity is not the same thing as falsification. If you are considering empirical validity, you've already answered the question of falsifiability.  Finally, real scientists do consider falsifiability.

I wrote a bit about falsifiability before in a post titled  Falsifiabilité, simplicité, succès ... ou la mort. A good set of heuristics is that a valid theory should in general 1) be falsifiable, 2) not be too complex to be falsifiable, and finally 3) not be falsified. If you want to drop one or more of these, you better have a convincing explanation.

Economics has tried to get around these from time to time. For example I once read this line and shuddered: 
I recall Bob Lucas and Ed Prescott both telling me that [empirical tests] were rejecting too many good models
I think this was trying to get around number 3 in favor of number 2 without any convincing argument. But at least RBC was falsifiable -- it was falsified! Market monetarism isn't falsifiable as far as I can tell, violating number 1. The information transfer model is fully falsifiable and it has several predictions that should eventually show it. So there's me: a scientist considering falsifiability.

...

Update 11 January 2016:

Here is a good link for Popper:

http://plato.stanford.edu/entries/popper/

Some good quotes:
This elucidates the nature of science as Popper sees it: at any given time there will be a number of conflicting theories or conjectures, some of which will explain more than others. The latter will consequently be provisionally adopted. In short, for Popper any theory X is better than a ‘rival’ theory Y if X has greater empirical content, and hence greater predictive power, than Y.
...
What, [Lakatos] asks, would have happened if Galle had not found the planet Neptune? Would Newtonian physics have been abandoned, or would Newton's theory have been falsified? The answer is clearly not, for Galle's failure could have been attributed to any number of causes other than the falsity of Newtonian physics (e.g., the interference of the earth's atmosphere with the telescope, the existence of an asteroid belt which hides the new planet from the earth, etc). The point here is that the ‘falsification/corroboration’ disjunction offered by Popper is far too logically neat: non-corroboration is not necessarily falsification, and falsification of a high-level scientific theory is never brought about by an isolated observation or set of observations.

I've talked a bit about Lakatos before.

This latter quote gives me the impression that Popper hadn't really delved into science so much as into defining pseudoscience (particularly Marxism and psychoanalysis).

21 comments:

  1. Falsification goes along with faute de mieux. Suppose that Neptune had not been discovered, even though the most likely places for its position had been searched. That would have left the anomalies in the orbit of Uranus unexplained. Astronomers would have known that Newton's universal law of gravity might not be so universal. I.e., it would have been at least provisionally falsified. Falsification is fuzzy.

    Of more concern were the anomalies in the orbit of Mercury. Can we say that Newton's law of gravity was truly falsified before Einstein came up with a better one? One which explained the orbit of Mercury.

    As for induction, which has made something of a comeback, at least in machine learning, Holland points out that there is often a problem of coming up with any theory at all. ;) That applies to falsification, as well. If Newton's law of gravity did not apply, what did?

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    1. Both of those examples represent cases of scope (the realm of empirical validity), and have nothing to do with Popper's falsification. Newton's law of gravity is an approximation to general relativity -- it is true under certain scope conditions.

      If Neptune had never been discovered, you would have some other possible theory (such as "MOND", which is also falsifiable) to which Newton's law would be an approximation.

      I think a good way to think about falsifiability is that it has nothing to do with "being falsified" or "not being falsified". It is about whether there exist states of the universe that aren't allowed by the theory.

      Once you are questioning scope of a theory (applying to Neptune or Mercury), you've answered that the theory is falsifiable and are now just considering empirical accuracy.

      The orbit of mercury was proposed to be perturbed by the motion of another planet called "Vulcan" at the time to explain the precession.

      Here's another way to think about it. Since discovering the Higgs boson we are now presented with a major problem. There cannot be fundamental scalar fields because their mass is renormalized to infinity. So the Higgs boson was both a major success of the standard model and falsified the theory.

      That doesn't make sense. It's better to say the Higgs was a success and helped determine the scope of the theory (setting a scale for unified theories).

      The standard model has long been a falsifiable theory --there were fears that the Higgs might not be found!

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    2. I love the post and the discussion!... though I don't understand it all (e.g. I have no idea what a fundamental scalar field is, and what that has to do with the Higgs boson... but that doesn't bother me too much).

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    3. https://en.wikipedia.org/wiki/Scalar_field

      The Higgs is a scalar field (spin-0). If it is fundamental (not composite or like a string excitation) the sum of Feynman diagrams for the mass are infinite, requiring a new scale (set by strings or some other field) to regularize (i.e. make not-infinite).

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    4. I don't think that the questions about the orbits of Uranus and Mercury were simply those of empirical accuracy. They arose because there were predictable violations of expected empirical error. They had already gone beyond the question of accuracy. The phenomena were not considered noise.

      If everything is a question of scope, we get economics. Pick your model. ;)

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    5. There are a few kinds of error in science: systematic, random, model error, etc. Only random errors are considered noise. The others do not average to zero. The errors in the orbits were model errors ... i.e. the model was valid up to terms on the order of Rsun/Rneptune (both R's measured from Uranus; Neptune was effectively assumed to be infinitely far away). A model that makes the assumption that Neptune is infinitely far away is not as empirically accurate as one that doesn't.

      Another way to look at it: the differences could not have been observed until better clocks had been developed. The invention of better clocks (a historical event) has nothing to do with the question of falsifiability of Newton's theory of gravity (a philosophical question about the nature of science).

      Everything should be a question of scope! Economics is weird because it ignores questions of scope.

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    6. "Everything should be a question of scope!"

      Is scope a bigger issue in physics than in some other sciences? Do biologists, geologists, neuroscientists, geneticists, chemists, climatologists, etc. also contend with scope issues? Or do some of those other scientific fields limit their scope by their very nature? I'd imagine physics to be the king of scope issues: dealing with problems on the extremes of scale, time, force, etc.

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    7. Geologists and biologists definitely consider scope: evolution and various geological processes take place over the course of tens of thousands (ice ages) to millions of years. Different kinds of selection pressures operate over different time scales.

      Chemistry might be considered physics with a specific scope -- at certain temperatures (high, and low), chemistry becomes more physics (nucleosythesis, bose-einstein condensation).

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  2. I really like the "don't fool yourself" concept for a prime directive of science. That covers falsifiability, empirical validity and scope conditions, doesn't it? There may be valid criticisms of Popper, but "don't fool yourself" seems pretty bullet proof. Wherever beings [do/will do/have done] science It's hard to imagine they could be very successful w/o doing all they could to avoid fooling themselves. Unless they were studying self deception and using themselves as test subjects... Lol.

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    1. It is a good one, except a singular "you" shouldn't be doing the theory and the empirical data all by yourself. "Don't fool people" is better ... which means that everything that is not science is just fooling people: politics, religion, art ... :)

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    2. "that everything that is not science is just fooling people: politics, religion, art ... :)" ... Lol, yes, well that's not to say that fooling people isn't of value. It can be the basis of a profitable business and many satisfied customers.

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  3. "I don't recall any violations of these principles measured at the time, so I am not certain what evidence was falsifying Newton's or Kepler's laws".

    I wrote that post. That is explained in the post linked to in the text (link added below).

    In a nutshell: after the discovery of Uranus, astronomers calculated its orbit. However, they found there was a systematic and increasing discrepancy between Uranus' actual observed position and the corresponding prediction.

    At the time three main explanations were advanced to that:

    (1) Perhaps gravity, at such great distances, operated in a manner slightly different to what Newton described;
    (2) Maybe the predictions were based on observations containing systematic measurement errors;
    (3) A yet undiscovered planet could be perturbing Uranus' orbit.

    No quantum effects were considered or could have been considered, as you rightly note.

    Alternative (1) is tantamount to the falsification of Newton/Kepler. (2) and (3) could be understood as ad hoc justifications to the Newton/Kepler "failure".

    John Couch Adams and Urbain Le Verrier chose to investigate (3). They calculated the orbit of the still hypothetical planet perturbing Uranus' orbit and commissioned the observatories at Greenwich and Berlin, respectively, to conduct the search.

    Berlin found the planet (later named Neptune) in the place Le Verrier indicated: the so-called "ad hoc" explanation was right. If astronomers had rushed to embrace (1) -- as extreme Popperians would have advised, had one been present -- an unfair doubt would have been cast on Newton/Keppler and the discovery of Neptune would have been delayed, at least.

    Incidentally, a similar story was behind the discovery of Pluto.

    The whole story is here:
    http://aussiemagpie.blogspot.com/2010/10/observation-vs-deduction.html

    Cheers.

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    1. Hello Magpie,

      I think I understand better what you were trying to say given your last paragraph above. I think it would be better characterized as extreme adherence to empirical accuracy ... only perfectly accurate theories are accepted.

      However, I don't think that is what Popper is about. Newtonian theory makes a bad prediction for Uranus without Neptune and Popper has his answer: Newtonian theory is falsifiable. In a sense Popper doesn't care what scientists do with their theory anymore. The theory is falsifiable and that's good enough for him. It qualifies as science.

      Scientists are concerned with the empirical accuracy of the theory, but probably wouldn't throw Newton out -- there are all the successes for the other planets, the moons of Jupiter and various comets.

      Popper wasn't concerned with empirical accuracy; he was concerned with pseudoscience evading all questions of empirical accuracy. He would be fine with science using an empirically inaccurate theory.

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    2. "However, I don't think that is what Popper is about.

      That's a matter of opinion, I suppose. In support of your point of view, I'll say that Popper, like many other thinkers. has his interpreters. Some may have a more generous and flexible interpretation.

      But I've seen many speaking on his authority, expressing what I call the Queen of Hearts Philosophy of Science: off with their heads at one strike.

      "Newtonian theory makes a bad prediction for Uranus without Neptune and Popper has his answer: Newtonian theory is falsifiable. In a sense Popper doesn't care what scientists do with their theory anymore. The theory is falsifiable and that's good enough for him. It qualifies as science.

      "Scientists are concerned with the empirical accuracy of the theory, but probably wouldn't throw Newton out -- there are all the successes for the other planets, the moons of Jupiter and various comets."


      Here I am afraid I'll disagree. For Popper, a falsified theory, once falsified, cannot be justified. To justify a predictive failure by ad hoc means, according to Popper, renders the theory unfalsifiable.

      But justify Newton/Keppler is precisely what Le Verrier and Couch Adams did (rightly, in my opinion): they did not "throw Newton out" without first trying to find a reason for its apparent failure. And, as it turns out, they were right and there really was a very good reason for its "failure": Neptune.

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    3. After reading more from Popper, I am coming around to a view that he a) didn't really understand science as it operates and b) was ambiguous.

      Popper expressed a view that if something had more empirical content (more accurate than other theories), then it was a better theory. In your discussion, that would seem to point to not "throwing Newton out" because the alternative was the even less accurate Ptolemaic/Aristotelian model. Newton stays even though it has a bad observation regarding the orbit of Uranus.

      But Popper also seems to express a view that one bad observation "falsified" a theory.

      This is incoherent. In one scenario you have degrees of "truth" (relative empirical accuracy); in the other you have a binary.

      Operationally, science has been conducted -- even in Popper's time -- with degrees of truth. Some models are better than others, but only at given approximations under different domains of applicability. Thermodynamics breaks the time symmetry of Newtonian physics so that observations of nature seem to prefer a direction of time "falsifying" Newtonian physics and it's time reversal symmetry. But time reversal is a good symmetry at the micro scale, while entropy is important at the macro scale.

      A binary "truth/falsified" would mean all theories are falsified and should be thrown out. Even the standard model of physics -- the most accurate things known by humans are calculated with it -- is falsified because neutrinos appear to have mass.

      General relativity, one of Popper's favorite examples, is inconsistent with quantum mechanics and is therefore "false" if we have to choose a binary.

      That makes me think that Popper, if confronted with these facts, would take a less binary view.

      It's true that is interpretation, but it is interpretation of something that would otherwise be incoherent.

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  4. Falsification has nothing to do with a theory being "falsified" or its empirical validity.

    True. I stepped too far out into the bailey and conflated the practical matter with the logical form. Good catch.

    That said, I do believe the problem of closure to be important when we're considering the parameters of falsifiability. Because of the problem of experimental closure in the former, one can virtually always explain divergent outcomes in terms of exogenous causality without ever challenging the theory, in effect rendering it unfalsifiable without it strictly following that the theory in question is pseudoscientific. That is, hypotheses of events and phenomena may be falsified much as they are in the social sciences, but hypothesized mechanisms are not so clear cut -- and it is these one must seek out to find the "law-like" aspects of social life, in which Popper did indeed profess an interest. In this case, the falsifiability criterion by itself contradicts his ostensible aims, as illustrated by his preference for instrumentalism.

    The most generous reading would probably say the above holds because the inquiry preserves the logical quality of being testable despite the practical difficulties of ever realizing this. But to my mind that just shunts the tension out of falsifiability and into the "falsifiability and trial-and-error" dyad in general, without addressing the practical implications for a doctrine of unity of method.

    I do agree that the dual- (or even triple-, such as in your articulation) criteria reading is nevertheless far more palatable than the one that holds falsifiability as "necessary and sufficient" by itself. (Unfortunately, per the passage I linked, he's not always crystal clear on this point.)

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    1. Correction:

      *"That is, hypotheses of events and phenomena may be falsified much in the social sciences as they are in the natural sciences..."

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    2. You said:

      "That is, hypotheses of events and phenomena may be falsified much as they are in the social sciences, but hypothesized mechanisms are not so clear cut ..."

      I completely agree with this. There is often more than one way to come to a specific result. A good example is economist Gary Becker's derivation of demand curves using irrational agents versus the standard way using utility functions and optimizing agents (see here).

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  5. I was curious about Sean Carroll's take: [1], [2]

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