Increasing Marginal Utility

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Guest Post: Lee Kelly on Callahan on Popper

Guest blogging is Lee Kelly in response to last night’s post by Gene Callahan on Karl Popper.

Yesterday, on his blog, Gene Callahan claimed that Popper did not solve the problem of induction. He produced familiar arguments claiming that Popper ‘sneaked induction in through the back door.’. These arguments, which have already been ably refuted by David Miller in his Critical Rationalism: A Restatement and Defence, are either logically flawed or radically misconstrue the position they suppose to be attacking. Contrary to these arguments, Popper’s solution to the problem of induction is not so much to be found in the act of falsification, but rather in the conjectural (unjustified and unjustifiable) character of our knowledge, especially our scientific knowledge.

I’ll break down my response into three separate counterarguments, each against a slightly different and more sophisticated manifestation of this kind of argument.

(1) A theory which is falsified by some observation-statement today is still falsified by it tomorrow, next week, a month later, and forever after. This is not induction. The falsifying relation is deductive and timeless–to say that it will continue to hold in the future is to be merely logically consistent.

A mathematician is not inducing when he concludes that ‘1 + 1 = 2’, which is true today, will continue to be true tomorrow. If there is no pretense of having derived the future from the past, then there is no attempted induction. The mathematician concludes that ‘1 + 1 = 2’ will continue to be true tomorrow because its negation is inconsistent–a deductive inference.

The falsifying relations between statements are analogous to the above equation. If a theory is falsified by some statement today, then it will continue to be falsified by it tomorrow. Whether we will continue to believe that the falsifying statement is true tomorrow is irrelevant to the logic of the situation.

(2) Gene equivocates between a theory’s falsity and its instrumental value. Past evidence, even falsification, does not imply anything about a theory’s future usefulness. Indeed, many falsified theories continue to have instrumental value within a limited domain, e.g. building bridges with Newtonian physics.

Indeed, we actually have falsifiable hypotheses about the instrumental value of different theories, and we regularly, by stress testing technology built with their aid, push the boundaries of their application.

(3) However, Gene is presumably hinting at a more specific issue: what about repeated instances of the same experiment? Just because an experiment falsified a theory today, it does not follow that repeating the same experiment will produce another falsification tomorrow. There are two sides to this argument that I wish to address.

(a) In practice, what counts as the ‘same experiment’ is a tricky matter. By assumption, our two experiments occur today and tomorrow, but tomorrow the earth will be in a slightly different position, it’ll be Saturday rather than Friday, the universe will have expanded some, and we will have used the restroom a few more times, and that is to name only a handful of facts we’re aware of. One experiment is only the same as another relative to higher-order hypotheses about which facts are relevant–those particular facts we want to replicate and those we are free to ignore. These higher-order hypotheses may themselves be mistaken, and so there is no guarantee we are, objectively, performing the ‘same experiment’ at all.

This is, of course, a classic argument against the utility of induction–what counts as two or more instances of the same observation depends on which facts we arbitrarily deem irrelevant to the situation. In principle, infinitely many different conclusions could be induced from the same set of observations–unaided induction has no power to select between competing interpretations.

In any case, this is not a problem for the logic of falsifiability, since it is entirely deductive. All the necessary assumptions are included in the premises. Of course, some of the premises of our argument may be false, such as the higher-order hypotheses mentioned before, but that is merely a reflection of our fallibility rather than the logic of falsifiability itself. This contrasts, for example, with unaided induction where, even if we assume different parties had the same observations, no particular conclusion follows.

(b) Putting such issues aside, let us assume, for the sake argument, that our experiment tomorrow really will be the same as today’s, i.e. all relevant facts to the experimental situation will hold constant. In this case, does it follow from our past falsifying observations that a theory will continue to be falsified by the same experiment in the future? Of course not, because induction is invalid.

Past observations, falsifying or otherwise, cannot inform us whether, or to what degree, the universe exhibits regular patterns. For example, as Popper argued, the universe may be intrinsically indeterminate and its fundamental laws only describable as probabilities. (In which case ‘an experimental test’ may actually involve many individual experiments to generate a comparable sequence of results.) Alternately, perhaps there are no stable regularities at all, deterministic or otherwise, and any apparent uniformity is mere illusion or fluke.

As I describe in this post on the Critical Rationalism Blog, falsifiability need not assume anything like the uniformity of nature. We search for regularities, but we don’t have to presuppose our own success in finding them.

Just as we may conjecture that a theory is true, without any pretense of having derived it from observation, so we can also conjecture that a theory falsified by an experiment will continue to be falsified by repeating the experiment in the future. Sometimes such conjectures are, in their turn, falsified, and we may be led to question other assumptions we had made about the experimental situation, even metaphysical ideas like determinism. So it is that science might progress, by conjecturing regularities about the universe (not assuming them), including regularities about the results of repeated experiments, and ruthlessly criticising them by any means at our disposal.

It may seem trivial, but the way to avoid induction is merely to argue validly. That is, we should not pretend, per impossibile, to logically derive our theories from observation. While observations, interpreted in the light of theories, may inspire a new conjecture, there is no logical inference from one to the other. Logic is best reserved for a critical role, i.e. to help select between competing conjectures, whether they’re inspired by particular observations or discovered after banging one’s head on the bathroom sink while trying to hang a clock. Even should an adequate theory of inductive inference be formulated, it would serve no purpose, because it betrays a preoccupation with where theories come from, or what justifies them, rather than their truth or falsity–it’s the genetic fallacy applied to epistemology.

Gene is right to say that ‘these arguments are well known in the literature, and considered decisive by almost all professionals in the philosophy of science, which is why there are only a handful of Popperians left in the field.’ But these arguments are also wrong, and radically misunderstand the position which they purport to refute. Moreover, the counterarguments I make here are not elusive, neither in Popper’s original works nor that of his students. To me, this all speaks very badly of professionals in the philosophy of science; it suggests that something is very rotten, either with the institutions or the prevailing assumptions of the professional philosophic community. That’s not an idea that I welcome, but the treatment, both intellectually and personally, that Popper and others like him have received is nothing short of scandalous.

The problem of induction is solved, and we’re still waiting for the professionals to catch up.

13 responses to “Guest Post: Lee Kelly on Callahan on Popper

  1. dkuehn May 4, 2012 at 3:23 pm

    Your (2.) is why I’ve never been able to get all that excited about Popper. My take is that we try to know things for two reasons: because it’s useful and because we like to have an understanding of how things work. Obviously the two are not unrelated, but the point is understanding has intrinsic value.

    Both of these things (not just usefulness) are like your bridge-building point. Within a limited domain, falsified theories can still be valuable. Newtonian physics still helps me understand the world in a more general sense, just as it helps build bridges in an applied sense.

    That just leads me to ask “well then who cares about falsification?”.

    You get at this sort of thing later when you write: “Even should an adequate theory of inductive inference be formulated, it would serve no purpose, because it betrays a preoccupation with where theories come from, or what justifies them, rather than their truth or falsity–it’s the genetic fallacy applied to epistemology.”

    My question to you would be: since when is purpose contingent on the establishment of truth or falsity?

    Another way of putting it is that it’s only a genetic fallacy if it’s epistemology that you’re trying to do in the first place.

    • Lee Kelly May 4, 2012 at 4:19 pm


      I’m confused.You seem to be repeating more or less exactly what I said but as though we disagree. That is, theories are both instrumental and attempts to describe an independent reality. Usually, when experiments demonstrate that a theory is inadequate for explaining reality, it may remain useful within a limited domain, either for prediction or approximate understanding of said reality.

      That somehow leads you ask ‘well then who cares about falsification?’ I suppose I’ll answer anyway:

      (1) Any finite set of statements interpreting observations, even if true, cannot verify any explanatory scientific hypothesis, but they can be falsified. That is, the logical relation between statements about experience and our theories is a falsifying one.

      (2) We have theories about the instrumental limits of otherwise falsified theories, and these theories can, in their turn, be tested and potentially falsified against experience.

      My question to you would be: since when is purpose contingent on the establishment of truth or falsity?

      What I mean is that inductive logic is useless in critical argument: it cannot be used to refute or falsify anything. It’s superfluous in the context of testing conjectures–it does naught but demonstrate that some conclusion is not falsified by its premises.

      • dkuehn May 4, 2012 at 4:32 pm

        re: “That is, theories are both instrumental and attempts to describe an independent reality.”

        But I don’t think we agree. You seem to be identifying “describe an independent reality” with “truth”. I don’t necessarily. In fact I care very little about “truth”, at least in the sense that Popperians seem to worry about it. This is why I highlight Newton. He’s not just good for building bridges – he’s good for describing reality too. But, as you point out, he’s not true. My question is – if something that’s not true can be awfully good at building bridges and describing reality, why exactly should I care about falsifiability?

        It may ultimately be a question of emphasis, but I’ve never seen reason to put falsification at the center of things. It seems to have so little to do with what scientists actually do and not a whole lot to do with why we care about science. Falsification only seems to really offer careful way cataloging claims.

      • Lee Kelly May 4, 2012 at 4:58 pm


        I don’t mean to put falsification ‘at the center of things’. There is a lot going on that has nothing to do with falsifiability, but it is important if you have any pretense of doing an empirical investigation. A test that cannot be failed is no test at all, whether that’s because the logic of a theory prohibits failure or because you have decided to protect it from refutation come what may.

        Even when considering theories as instruments, we have theories about the limits of their applicability. For example, the theory that Newtonian physics would be sufficient for calculating GPS coordinates is wrong. Even if we didn’t have an alternative theory from which to deduce this result, we could test the instrumental limits of Newtonian physics by trying to falsify some conjecture about them. Perhaps more to the point, theories only have instrumental value at all because they prohibitive, because they are, in principle, falsifiable

        Truth is, in general, important as a regulative ideal. We criticise by trying to demonstrate that two claims, discoveries, beliefs, or assumptions contradict. The conflict presents us with a problem that we try to solve, either by showing the apparent contradiction to be illusory or modifying one or both of the claims, assumptions, and whatnot. Whether our claim is about physical objects out there in the world, or about the instrumental value of a theory to describe and predict, we are making claims about the truth or falsity of something, and they are rightly criticised by attempting to demonstrate their conflict with something else. When that “something else” happens to be a statement describing some empirical observation, we call that criticism, if successful, a falsification.

  2. dkuehn May 4, 2012 at 3:28 pm

    For what it’s worth, I think what Gene is getting at is your 3b.

    Again, if this is the situation – with an irregular universe (which has to be the conjecture in order to avoid the sort of conservative induction that Gene identifies), one starts to wonder what Popper really does for us.

    In an irregular universe Popper avoids the inductionist charge but he renders falsification useless and all scientific progress is through increasingly useful conjecture.

    But scientific progress through increasingly useful (but never falsifiable) conjecture doesn’t sound very Popperian to me! But then, I don’t know Popper very well.

    • Lee Kelly May 4, 2012 at 4:30 pm

      Again, I’m confused at your response. I mustn’t have explained myself clearly enough.

      • dkuehn May 4, 2012 at 4:39 pm

        So Gene seems to be saying that assuming a falsified conjecture can be considered good and falsified for time immemorial is itself an induction drawn from the past experiment. That’s one possibility. You seemed like you were countering that it is not, in fact, and induction. Instead it’s a new conjecture about the regularity of the universe. That, I actually think, is an OK way of avoiding the inductionist charge. But it then it again makes me wonder why we think falsification is so great it seems like we have to conjecture its very relevance (which is fine because I think of science more in terms of increasingly more useful conjectures anyway). I just don’t think of that as being the Popperian point. But two caveats to once again stress – (1.) I’m not Popper expert, and (2.) I often have trouble talking epistemology because I don’t think in those terms myself.

  3. Lee Kelly May 4, 2012 at 3:40 pm

    One clarification, when I wrote of conjecturing that a theory will continue to be falsified by the same experiment in the future, I had in mind an alternative theory from which that is deduced. For example, observations of light deflected by the sun are generally accepted as falsifying Newtonian physics, but we don’t just conjecture that result will continue in the future. Instead, we have a competing theory that explains why Newtonian physics fails and predicts that it will continue to fail it in the future. That is, the conjecture that an experiment will continue to falsify a theory is normally the deductive consequence of an alternative theory.

  4. gcallah May 4, 2012 at 4:04 pm

    Lee, these arguments are why Miller is not a prominent philosopher of science except amongst Popperians! #1, for instance, is just awful, and entirely misses the point of the problem situation being posited. But there is no arguing with someone in the thrall of Popper worship. Or, as a reviewer refers to Miller, “a peevish Popperian.”

    You claim:
    “That’s not an idea that I welcome, but the treatment, both intellectually and personally, that Popper and others like him have received is nothing short of scandalous.”

    Yes, the way he was made the head of a department of philosophy at a top school, the way they hang his picture in the halls, the way he is regarded as one of the two top philosophers of science of the last century: what shabby treatment!

  5. gcallah May 4, 2012 at 4:24 pm

    But Lee, you have demonstrated that some theories are immune to falsification!

    • Lee Kelly May 4, 2012 at 4:36 pm

      I can demonstrate that in a million and one different ways and none would be relevant to this discussion. If at any point you got the impression that I ever said otherwise, then you spectacularly missed the point.

      • gcallah May 5, 2012 at 3:03 pm

        Lee, does following Popper make your sense of humor disappear? I was teasing you, implying that your theories on falsification are immune to falsification.

  6. Rafe Champion May 5, 2012 at 9:49 am

    Daniel, you wonder what Popper does for us. Lee has explained the logic of the situation in response to Gene’s concern with induction, and it might help to see Popper’s ideas in a larger context. In brief, he introduced what you could call four “turns” or shifts of emphasis in the philosophy of science as traditionally practiced, or at least as it was done by the logical positivists and the logical empiricists who represented the mainstream at the time.

    First the conjectural or “hermeneutic” turn (some time in advance of the POMOs), coming to grips with the implications of fallibilism and the conjectural nature of even our best tested theories without relativism or irrationalism.

    Second, an “objective turn” to shift the focus of epistemology from subjective beliefs to public, scientific or inter-subjective knowledge.

    Third, to pay critical atteniton to the social aspect of science and the conventions or “rules of the game” of scientific practice. He did the the same thing in his political philosophy and it is the “rules fo the game” approach more than falsification which unifies his work on science and society. That is apparent in The Logic of Scientific Discovery (1935 and 1959) and also in chapter 23 of The Open Society (1945) which can be read as a pre-emptive strike on the sociology of knowledge!

    Finally, to rehabilitate metaphysics in the heart of the philosophy of science with his theory of metaphysical research programs which was stuck in galleys from the 1950s to 1982 when it appeared in an Addendum to the third volume of The Postscript to the Logic of Scientific Discovery. This was the inspiration for Lakatos when he produced his methodology of scientific research programs but Lakaots left out the vital ingredient of criticism and so his theory was as useless as paradigm theory for scientists.

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