Whewell described the reasoning just as it appeared to a man deeply conversant with several branches of science as only a genuine researcher can know them, and adding to that knowledge a full acquaintance with the history of science. These results, as might be expected, are of the highest value, although there are important distinctions and reasons which he overlooked. John Stuart Mill endeavored to explain the reasonings of science by the nominalistic metaphysics of his father. The superficial perspicuity of that kind of metaphysics rendered his logic extremely popular with those who think, but do not think profoundly; who know something of science, but more from the outside than the inside, and who for one reason or another delight in the simplest theories even if they fail to cover the facts.
Harsh but fair, I think. In any case, I wanted to look at one particular disagreement between Mill and Whewell that is relevant to natural classification. This is Mill's claim that natural groups should be arranged in a natural series. As he says, almost everyone, including Dr. Whewell, stops short of such a claim; only Auguste Comte goes so far as to treat of it. Mill's reasoning is that, as a general instrument for investigating nature, the purpose of classification is merely to arrange the most similar things next to each other; but when we are using it to facilitate a particular inductive inquiry, we have to expect more from it. Not only must we arrange the phenomena into kinds; we must "arrange those Kinds in a series according to the degree in which they exhibit it, beginning with those which exhibit most of it, and terminating with those which exhibit least." The argument for this last point is rather obscure and for fear of not conveying it properly, I'll quote it:
We must consider as the type of the class, that among the Kinds included in it, which exhibits the properties constitutive of the class, in the highest degree; conceiving the other varieties as instances of degeneracy, as it were, from that type; deviations from it by inferior intensity of the characteristic property or properties. For every phenomenon is best studied (ceteris paribus) where it exists in the greatest intensity. It is there that the effects which either depend on it, or depend on the same causes with it, will also exist in the greatest degree. It is there, consequently, and only there, that those effects of it, or joint effects with it, can become fully known to us, so that we may learn to recognise their smaller degrees, or even their mere rudiments, in cases in which the direct study would have been difficult or even impossible. Not to mention that the phenomenon in its higher degrees may be attended by effects or collateral circumstances which in its smaller degrees do not occur at all, requiting for their production in any sensible amount a greater degree of intensity of the cause than is there met with.
So, to use Mill's example, human beings are the animals with the greatest 'intensity' of the phenomena of organic life. So human beings need to be put in the highest place, and all the other animals arranged in a series below it; because (apparently) we can only get the most accurate understanding of lower animal life by studying human beings. Not only does Mill think this is the best way to go about studying things; he thinks that this principle of natural series is more fundamental than the principle of natural affinity, which is subordinated to it. He also thinks that this is the way biologists have tended to classify animal life, and that implicit reference to a natural series is the only explanation for the high degree of agreement among different classifications.
Whewell will have none of it, since he thinks this whole idea is absurd. As he puts in a footnote on Mill's Logic in the Philosophy of Discovery:
There are some points in my doctrines on the subject of the Classificatory Sciences to which Mr. Mill objects, (ii. 314, &c.), but there is nothing which I think it necessary to remark here except one point. After speaking of Classification of organized beings in general, Mr. Mill notices (ii. 321) as an additional subject, the arrangement of natural groups into a Natural Series; and he says, that "all who have attempted a theory of natural arrangment, including among the rest Mr. Whewell, have stopped short of this: all except M. Comte." On this I have to observe, that I stopped short of, or rather passed by, the doctrine of a Series of organized beings, because I thought it bad and narrow philosophy: and that I sufficiently indicated that I did this. In the History (b. xvi. c. vi.) I have spoken of the doctrine of Circular Progression propounded by Mr. Macleay, and have said, "so far as this view negatives a mere linear progression in nature, which would place each genus in contact with the preceding and succeeding ones, and so far as it requires us to attend to the more varied and ramified resemblances, there can be no doubt that it is supported by the result of all the attempts to form natural systems." And with regard to the difference between Cuvier and M. de Blainville, to which Mr. Mill refers (ii. 321), I certainly cannot think that M. Comte's suffrage can add any weight to the opinion of either of those great naturalists.
(It should be pointed out that, despite the quotation marks, Whewell is only paraphrasing Mill; although it is an accurate paraphrase.) Mill replies in a later edition:
Dr. Whewell, in his reply (Philosophy of Discovery, p. 270) says that he "stopped short of, or rather passed by, the doctrine of a series of organized beings," because he "thought bad and narrow philosophy." If he did, bit was evidently without understanding this form of the doctrine; for he proceeds to quote a passage from his History, in which the doctrine he condemns is designated as that of "a mere linear progression in nature, which would place each genus in contact only with the preceding and succeeding ones." Now the series treated of in the text agrees with this linear progression in nothing whatever but in being a progression.
It would surely be possible to arrange all places (for example) in the order of their distance from the North Pole, though there would be not merely a plurality, but a whole circle of places at every single gradation in the scale.
It can be granted, I think, that Mill's natural series doesn't have to be a linear progression, and thus that Whewell's reply is not entirely adequate; but Mill misses, I think, the not-so-subtle barb in Whewell's last sentence, which puts forward a complaint that Whewell makes many times against Mill's Logic in many different forms: that Mill fits his account of science to presupposed philosophy instead of doing the hard work Whewell does to find out what scientists have actually done and build the account of science on that. Whewell's response would have been stronger had he pointed out the vagueness of Mill's 'natural series' (what does it mean to say that the phenomena of sensation are more 'intense' or are found in a 'greater degree' in human animals than in other animals?) and that it seems otiose (given that the natural series is simply a gradation, it seems that the typological classification of natural affinities, which both Mill and Whewell agree is a very important part of the classification process, would do everything already in the way of 'gradations' useful for scientific purposes).
Quotation from Whewell is from On the Philosophy of Discovery (1860), Lenox Hill (New York: 1971), 270. Quotations from Mill are from A System of Logic.