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Sunday, November 21, 2004

How Popper Went Wrong on Confirmation

Karl Popper is famous for declaring that theories can never be confirmed, only falsified. It seems to me he is wrong about this, and his error turns on viewing falsification and confirmation as all or nothing affairs.

But they are not. As pointed out by Duhem, Quine, Lakatos, Feyerabend, and others, no theory is ever so thoroughly falsified that there is no way to rehabilitate it. The Duhem-Quine thesis notes that, given an experimental result that apparently refutes a theory, one can always change an auxilliary hypothesis instead of the central tenet of the theory, and so rescue the theory. For example, Copernicus did not regard the absence of observed parallax in the stars as refuting his heliocentric theory. Instead, he simply moved the sphere of stars ten times as far away as it was previously thought to be. As my history of science lecturer, John Milton, pointed out, in this respect a Popperian has to regard Ptolemy's model as scientific and Copernicus's as unscientific, since Ptolemy's would be falsified by observered parallax, while, if newer, more accurate instruments still failed to detect parallax, Copernicus could simply place the sphere of the stars even farther away!

And so it is for confirmation. It is true that no theory is ever completely confirmed. But each piece of evidence supporting the theory raises the degree to which it is confirmed. Let's look at a hypothetical example from historiography to see how the Popperian view fails to capture the true state of our knowledge of the world. Imagine that two historians present you with two theories: One of them tells you that Caesar crossed the Rubicon in a deliberate act of defiance of the Roman Senate and constitution. The second says that King Arthur took on a dozen wives in order to cement diplomatic relationships with neighbouring kingdoms.

From a Popperian point of view, we have no cause to consider either theory more or less confirmed than the other. Confirmation is impossible. All we can say is that neither theory has been falsified. But this is clearly absurd: there is abundant, indeed, overwhelming evidence that leads us to believe the first historian's theory, while no one is even sure if King Arthur was a real person. (And, not knowing if he ever existed, we certainly cannot falsify a theory that says he had a dozen wives as of yet.)

One need not be a naïve or even a strict Bayesian to suspect that Bayesians are on the right track in holding that hypotheses are more or less confirmed, and that positive evidence rightly up our degree of belief in them. Scientists may not really formulate numerical estimates of the prior probability of different hypotheses. It is enough, as noted by Paul Horwich, that we can use an idealized model of how they might do so to dispel certain common errors, such as the failure to recognize that different hypotheses are held with different degrees of belief, and that different pieces of evidence do offer varying degrees of confirmation for a theory. Per Horwich, if Bayesianism can help in that process, it simply does not matter if it offers a complete, or even a very realistic, account of how scientists operate. Furthermore, if other models can also help to clear away the fog, there is no reason not to supplement Bayesianism with such models.

5 comments:

  1. Anonymous10:05 AM

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  2. Anonymous4:33 PM

    >Karl Popper is famous for declaring that theories can never be confirmed, only falsified.

    And, less famously but very importantly for the correct understanding of his epistemology, that falsifications are themselves within a conjectural framework.

    >It seems to me he is wrong about this, and his error turns on viewing falsification and confirmation as all or nothing affairs.

    Logically they are (by the law of excluded middle). Either a theory is falsified/verified or it isn't. That we can be mistaken about the apparent evidence does not affect this. Popper's fundamental epistemological argument relates to the logic of human observation. We could, in principle, observe a single refuting instance of a universal theory. We could not, in principle (though maybe God could), observe all possible instances that fit a universal theory. And anything short of all possible instances means the universal theory might be false. If "All swans are white" is the theory, then if X is a black swan then X absolutely falsifies the theory. But if Y is a white swan that adds absolutely no support to a genuinely universal theory. Only once this situational-logical point is grasped do we move on to applying it in practice. It is reasonable to look for non-white swans as it is in principle possible to falsify the white-swan theory. It is not reasonable to look for ever more white swans as it is in principle impossible to confirm the white-swan theory.

    >But they are not. As pointed out by Duhem, Quine, Lakatos, Feyerabend, and others, no theory is ever so thoroughly falsified that there is no way to rehabilitate it.

    Why is Popper missing from your list? If a theory really was falsified (by a genuine counterinstance) then it is, ipso facto, false. But falsifications operate within conjectural frameworks. An apparent falsification may later turn out to be flawed. That practical problem does not affect the situational logic.

    > The Duhem-Quine thesis notes that, given an experimental result that apparently refutes a theory, one can always change an auxilliary hypothesis instead of the central tenet of the theory, and so rescue the theory.

    But some new auxiliary hypotheses will look distinctly ad hoc. And given that we can only hope, in principle, to falsify the theory why would we seek ad hoc ones to save it (unless they withstand new tests themselves)?

    >For example, Copernicus did not regard the absence of observed parallax in the stars as refuting his heliocentric theory. Instead, he simply moved the sphere of stars ten times as far away as it was previously thought to be.

    This is, of course, exactly accepting a refutation of the whole theory and coming up with a new theory that puts the stars ten times farther away. Nothing un-falsificationist about that!

    >As my history of science lecturer, John Milton, pointed out, in this respect a Popperian has to regard Ptolemy's model as scientific and Copernicus's as unscientific, since Ptolemy's would be falsified by observered parallax, while, if newer, more accurate instruments still failed to detect parallax, Copernicus could simply place the sphere of the stars even farther away!

    Again, accepting the refutation! Or do you mistakenly think that he kept the 'essence' of his theory by doing this? Theories are wholes and do not have essences. In any case, that some theories were at one time not scientific because not yet testable, yet later went on to being testable and surviving the tests, does not show a fault in the epistemology does it? Atomism was once untestable. Later it was tested and survived (until the 'atom' was split).

    >And so it is for confirmation. It is true that no theory is ever completely confirmed. But each piece of evidence supporting the theory raises the degree to which it is confirmed.

    Remember the logical point. A single instance--even if certain--of a genuinely universal theory cannot support the theory, can it? A refuting instance can still exist undetected.

    >Let's look at a hypothetical example from historiography to see how the Popperian view fails to capture the true state of our knowledge of the world. Imagine that two historians present you with two theories: One of them tells you that Caesar crossed the Rubicon in a deliberate act of defiance of the Roman Senate and constitution. The second says that King Arthur took on a dozen wives in order to cement diplomatic relationships with neighbouring kingdoms.

    Note first here, that you have switched from universal theories in physics to very specific singular theories in history. This is hardly comparing like with like to make your point as forceful as possible. It muddies the waters that ought to be kept as clear as possible.

    >From a Popperian point of view, we have no cause to consider either theory more or less confirmed than the other. Confirmation is impossible. All we can say is that neither theory has been falsified. But this is clearly absurd: there is abundant, indeed, overwhelming evidence that leads us to believe the first historian's theory,

    You are merely lapsing into common sense. How can you hope to refute an epistemological argument with common sense? You have to engage with the epistemological argument in detail and show, if possible, exactly where it goes wrong. Now, strictly speaking, even apparently singular theories are universal in their implications. So the fact that all the, highly theory-laden, evidence so far is compatible with the theory counts for nothing. It might, for instance, be refuted by a new discovery of a contemporary text stating that Caesar had actually crossed the Rubicon thinking it was some other river, or that he was unconscious in one of his fits while carried across (and had not made the actual decision), ad infinitum. I am not saying that such things are true or likely but that the evidence that 'supports' the theory you mention is as relevant as the evidence that once 'supported' all swans being white (before a black one was discovered).

    > while no one is even sure if King Arthur was a real person. (And, not knowing if he ever existed, we certainly cannot falsify a theory that says he had a dozen wives as of yet.)


    The theory of King Arthur's existence seems to have been falsified. Hence so is the wives theory. The Arthur myth developed over 900 years with earlier authors being ignorant of latter additions to the myth (like the round table being added in the 12th century). All was most famously summed up with new additions in Malory's _Morte d'Arthur_ (1470). This is a typical pattern of myth growth that also fits the likes of Jesus and Robin Hood (neither of whom existed either).

    >One need not be a naïve or even a strict Bayesian to suspect that Bayesians are on the right track in holding that hypotheses are more or less confirmed, and that positive evidence rightly up our degree of belief in them.

    That's right, it is common sense. But where are the answers to Popper's arguments?

    >Scientists may not really formulate numerical estimates of the prior probability of different hypotheses.

    Even if they did, probability only makes sense within a framework that is itself conjectural. Hence it does not leave the realm of conjecture.

    > It is enough, as noted by Paul Horwich, that we can use an idealized model of how they might do so to dispel certain common errors, such as the failure to recognize that different hypotheses are held with different degrees of belief, and that different pieces of evidence do offer varying degrees of confirmation for a theory.

    How can strength of belief be relevant? How is any confirmation possible?

    > Per Horwich, if Bayesianism can help in that process, it simply does not matter if it offers a complete, or even a very realistic, account of how scientists operate. Furthermore, if other models can also help to clear away the fog, there is no reason not to supplement Bayesianism with such models.

    And that is what the critical rationalist model has done.

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  3. This is not an effective criticism of Popper's views. According to Popper the best we can manage is a critical preference for a theory that has stood up to criticism, including the test of evidence. Five forms of criticism can be identified: first, does the theory solve the problem, second, is it internally consistent, third, is it consistent with other well tested theories, fourth, the test of evidence including experiemental tests, fifth, the test of metaphysics (is it consistent with out larger program?).

    Inductivists and Bayesians attempt to quantify the goodness of theories but they have not yet proposed any measure that stands up to criticism or is more helpful to working scientists than a Popperian critical preference.

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  4. Anonymous8:56 AM

    Testing comments.

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