Howson and Urbach vs Popper

Howson and Urbach claim to have refuted Popper’s ideas in “Scientific Reasoning: The Bayesian Approach”. In Section 4g they write:

Philosophers, such as Popper and Lakatos, who deny any inductive role for evidence, and who oppose, in particular, the Bayesian approach take note of the that scientists often do deal with particular instances of the Duhem problem by proposing alternative hypotheses; some of these philosophers have suggested certain normative rules that purport to say when such alternatives are acceptable and when they are not. Their idea is that a theory that was introduced ad hoc, that is, “for the sole purpose of saving a hypothesis seriously threatened by adverse evidence” (Hempel 1966, p. 29), is in some way inferior. The adhocness idea was largely inspired by certain types of scientific example, which appeared to endorse it, but in our view, the examples are misinterpreted and the idea badly flawed. The following are four such examples.

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In each of these examples, the theory that was proposed in place of the refuted one seems highly unsatisfactory. It is not likely that any of them would have been advanced, save in response to particular anomalies and in order to evade the consequent difficulty, hence the label ‘ad hoc’. But philosophers who attach inductive significance to adhocness recognize that the mere fact that the theory was proposed under such circumstances is not by itself grounds for condemnation. For there are examples, like the following, where a theory that was proposed for the sole purpose of dealing with an anomaly was nevertheless very successful.

4 William Herschel, in 1781, discovered the planet Uranus. Astronomers quickly sought to describe the orbit of the new planet in Newtonian terms, taking account of the perturbing influence of the other known planets, and were able to deduce predictions concerning its future positions. But discrepancies between predicted and observed positions of Uranus substantially exceeded the accepted limits of experimental error, and grew year by year. A few astronomers mooted the possibility that the fault lay with Newton’s laws but the prevailing opinion was that there must be some unknown planet acting as an extra source of gravitational attraction on Uranus, which ought to be included in the Newtonian calculations. Two astronomers in particular, Adams and Le Verrier, working independently, were convinced of this and using all the known sightings of Uranus, they calculated in a mathematical tour de force where the hypothetical planet must be. The hypothesis was ad hoc, yet it was vindicated when careful telescopic observations as well as studies of old astronomical charts revealed in 1846 the presence of a planet with the anticipated characteristics. The planet was later called Neptune. Newton’s theory was saved, for the time being. (See Smart 1947.)

Their account of Popper’s position is wrong. In “The Logic of Scientific Discovery”, Chapter 4, Section 20, Popper writes:

As regards auxiliary hypotheses we propose to lay down the rule that only those are acceptable whose introduction does not diminish the degree of falsifiability or testability of the system in question, but, on the contrary, increases it. (How degrees of falsifiability are to be estimated will be explained in sections 31 to 40.) If the degree of falsifiability is increased, then introducing the hypothesis has actually strengthened the theory: the system now rules out more than it did previously: it prohibits more. The introduction of an auxiliary hypothesis should always be regarded as an attempt to construct a new system; and this new system should then always be judged on the issue of whether it would, if adopted, constitute a real advance in our knowledge of the world. An example of an auxiliary hypothesis which is eminently acceptable in this sense is Pauli’s exclusion principle (cf. section 38). An example of an unsatisfactory auxiliary hypothesis would be the contraction hypothesis of Fitzgerald and Lorentz which had no falsifiable consequences but merely served to restore the agreement between theory and experiment—mainly the findings of Michelson and Morley. An advance was here achieved only by the theory of relativity which predicted new consequences, new physical effects, and thereby opened up new possibilities for testing, and for falsifying, the theory. Our methodological rule may be qualified by the remark that we need not reject, as conventionalistic, every auxiliary hypothesis that fails to satisfy these standards. In particular, there are singular statements which do not really belong to the theoretical system at all. They are sometimes called ‘auxiliary hypotheses’, and although they are introduced to assist the theory, they are quite harmless.

So Popper does not say that every hypothesis introduced to save an existing theory is bad. Rather, he sez that if a new hypothesis is introduced to save an existing theory it should be a real advance in our understanding and should be testable. The Neptune theory passes this test since knowing there is a new planet is an advance in our understanding and can be tested. So the Neptune example doesn’t refute Popper’s actual position, as opposed to the position that Howson and Urbach invented and then attributed to Popper.