Tethering Icarus: A Response to Popper’s “Conjectures and Refutations”

by Shaun Terry

On page 57 of “Conjectures and Refutations,” Popper states, “One should also be careful not to confuse the problem of the reasonableness of the scientific procedure and the (tentative) acceptance of the results of this procedure—i.e. the scientific theories—with the problem of the rationality or otherwise of the belief that this procedure will succeed.” Here, Popper means to point out that the degree to which we can feel confident in a theory is not the basis on which we should determine the value in a scientific theory; instead, a theory’s value should lie in the degree to which a theory is corroborable. In Section 82 of Popper’s “The Logic of Scientific Discovery,” Popper defines corroborability by whether or not we can test a theory and its constituent aspects.

I agree that it is important for a theory to be testable; in fact, I think that is an important aspect of what makes a theory scientific and I think that Popper made important discoveries that helped to shape more accurate and useful science. But I have a few contentions. My first problem is that his definition of corroborability is a bit amorphous. On page 264 of “The Logic of Scientific Discovery,” Popper explains: “[Corroboration] asserts the fact that these basic statements do not contradict the theory, and it does this with due regard to the degree of testability of the theory, and to the severity of the tests to which the theory has been subjected, up to a stated period of time.”

What does Popper mean by “up to a stated period of time?” It seems that Popper is suggesting that there is some timeframe within which one is to attempt to falsify a theory before which we come to tentatively accept its truthfulness. I think that Popper might even agree in hindsight that this definition gives too much leeway to the theorizer and that it can lead to the acceptance of untrue theories. Even if we altered Popper’s statement to speak to a volume of attempts at discreditation, it would still be problematic. After all, the ability to uncover new evidence means that a theory could always be disproved. Maybe a better definition would have ended by saying that a theory is indefinitely subject to its verification. Still, the idea that we should ever accept a theory, tentatively or not, is one that I am disinclined to buy into.

I think that it is right to presume that humans tend to seek out and establish patterns, and that we act on the basis that those patterns are true, but, in this way, science should be distinct from unscientific human behaviors. If we accept that we can never know whether or not a theory is true, then why should we accept any theory at all? Discussing theories in terms of degrees of confidence makes some sense and I would advocate that we could act on the basis that some theories appear to be true, but in discourse over theories, themselves, I am not convinced of the wisdom in tentatively accepting any scientific theory, as opposed to simply claiming that some appear to be more true than others do.

But these are minor issues when compared with how Popper treats probability and the valuation of theories. Popper argues that a scientific theory that tells us very little about the world is of little value to us and that the value in a theory should rest solely on the degree to which it can be tested and disproved. He supports this idea on page 58 of “Conjectures and Refutations,” by saying that “…the probability of a statement (or set of statements) is always the greater the less the statement says: it is inverse to the content or the deductive power of the statement, and thus to its explanatory power.” Viewed in a certain way, this makes perfect sense: a theory that accurately explains everything is more valuable than a theory that explains nearly nothing. If one were to theorize with this idea as a guide, they might view their success as having something to do with coming up with the most comprehensive and unlikely theory they can, given what Popper has to say, on page 58, about how the value of a theory relates to its probability.

To some degree, the danger of overtheorizing is mitigated by Popper’s claims about the importance of corroboration, but that does not fully negate the problem. It may be that the improbability of a theory is immaterial, so long as one can effectively test the theory, but it is also true that there is value in attaining some level of confidence in simple theories and that the value is less clear when the testing of a theory is prohibitively complicated. To be clear, a simple theory at least has the virtue of being more clearly verifiable (regardless of what exactly is meant by “verifiable”) than a more complicated theory. Borrowing an idea from calculus, the problem with a theory of everything is, in some sense, opposite to the problem with a theory of something infinitesimally small: one requires so much that you never achieve its corroboration while the other’s significance is imperceptible. I would argue that lesser significance is less dangerous than is complication in verification, which supports a preference for simpler theories.

Popper’s work has been important and has ignited advancements in how we conduct science but, like many philosophers, Popper gives a degree of lip service to the idea that induction is a fundamentally flawed proposition while arguing for induction’s virtues. It may be that the question of value in induction is discussed in terms of a spectrum—after all, I have yet to discover a modern philosopher who argues that you can prove things through induction—but where I would argue the flaw lies (Popper included) in the thinking of some philosophers is that they seem to make statements on the problem of induction as a way to qualify their arguments which run counter to this fundamental problem.