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Science Rules: A Historical Introduction to Scientific Methods Hardcover – August 13, 2004
The Amazon Book Review
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About the Author
Peter Achinstein is a professor of philosophy at the Johns Hopkins University. His previous books include Concepts of Science, Law and Explanation, The Nature of Explanation, Particles and Waves, and The Book of Evidence.
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I will comment in detail only on part 3 because it upset me. This part concerns hypothetico-deductivism versus inductivism, and is centred on a "debate" between Whewell and Mill.
Whewell's excerpt is delightful. He approves of an hypothetico-deductivism of sorts by saying that if a theory can explain both what it was intended to explain and things beyond its original scope, and if it becomes simpler and more coherent (rather than weighed down by auxiliary hypotheses) as its domain is extended, then it has "a stamp of truth beyond the power of ingenuity to counterfeit" (p. 161). Whewell's proof is historical and supported by numerous examples. "No example can be pointed out, in the whole history of science, so far as I am aware, in which [these rules have] given testimony in favour of an hypothesis afterwards discovered to be false" (p. 162).
According to Achinstein's rather unbalanced introduction, Mill now offered a "simple and powerful" objection (p. 135), namely that the truth of a theory cannot be established in this way since there could conceivably be another hypothesis that performs equally well. This "powerful" counter-argument Achinstein construes to have cornered Whewell into admitting the groundlessness of his argument: "Whewell simply asserts that it is so" (p. 136), i.e. that an equally successful hypothesis is exceedingly unlikely. But, as we saw, Whewell did not "simply assert," but rather supported with lots of historical evidence. And he was of course also well aware of the "powerful" objection long before Mill confronted him; he implicitly acknowledged it in the quotation above, for example (why offer historical evidence if your thesis is logically irrefutable?).
It is actually Mill who is the pinhead, putting his nose in matters he does not understand. Let me illustrate by two examples.
Mill's dumb account of the law of ellipses. On the one hand (p. 225), Mill's "major objection" (p. 236) against Whewell is that an hypothesis is not proven true by fitting the facts etc. better than the other hypotheses under consideration since there may be further hypotheses which we have failed to perceive (it hardly takes a professor of logic to notice this trivial point, but it does take one to mistake it for important). On the other hand (pp. 181-185), Mill thinks that he can simultaneously admit as true the law of ellipses ("a fact surely"); this since he is under the foolish misconception that Kepler's discovery of the law of ellipses avoided the danger by being an instance of pure induction: "it was the sum of the different observations," says Mill, believing it to have been literally a matter of connecting the dots, so that "verification is proof" (p. 220) in this case. But the data in this care are not points in space but directions of sight from the earth; obviously many hypotheses (including geostatic ones, for instance) could account for these data.
Mill's dumb account of Newton's laws. "If it had not been previously known that the planets were hindered from moving in straight lines by some force tending towards the interior of their orbit ... Newton's argument [for the inverse square law of gravitation] would not have proved his conclusion. These facts, however, being already certain ..." etc. (p. 219). But these facts were far from "already certain" at the time, even to Newton (cf. e.g. the Newton-Hooke correspondence), and alternative hypotheses were plentiful: Galileo's circular inertia, Kepler's magnetic sun theory, etc. Whatever proof we may have for these facts would be terrestrial (and consistent with things like circular inertia), so surely we would not be allowed to extend them into space, since, according to Mill, we are not allowed to do so with gravity: "it would not have been allowable for [Newton], without any lunar data, to assume that the moon was attracted towards the earth with a force as the inverse square of the distance, merely because that ratio would enable him to account for terrestrial gravity" (p. 219). Let me emphasise that this quarrel with Mill is not a quarrel with Newton, who avoids such predicaments by his rules for philosophising (pp. 78-80).
Mill's understanding is as deficient elsewhere, e.g. on Newton and the binomial theorem (pp. 179-180), but after that I ran out of the patience to keep count.
Let us note also that Achinstein choses to represent this "debate" by an 18-page excerpt from Whewell written before the debate took place, and a 61-page excerpt of Mill written after the debate (that Mill still manages to come off as a fool is quite an accomplishment). The other selections in this part of the book are also curious: 13 pages by Young which is all science and no philosophy, 5 pages of Popper drifting aimlessly in the wind, and Achinstein's concluding discussion which gets bogged down in some rather trivial probability formulas (which have typos in them; p. 241).