Whewell’s Logic of Induction

  • Robert E. Butts
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 155)


Although the literature on nineteenth-century methodology includes some discussion of the Mill-Whewell controversy over the nature of induction, Whewell’s own theory of induction has not received much attention. Especially lacking is any attempt at a philosophically interesting reconstruction of his logic of induction against the background of recent discussions of problems of inductive logic. Like Herschel, and unlike Mill, Whewell did not attempt a direct solution of the so-called “problem of induction,” perhaps because he and Herschel did not think that such a problem existed. This omission from his work—if it be one—must have made his theory of induction somewhat less interesting philosophically than Mill’s, and so Mill’s theory achieved some stature in late nineteenth-century discussions of induction, and those of Herschel and Whewell became all but forgotten until quite recently.1 This historical situation is unfortunate for two reasons. The ascendancy of Mill’s way of dealing with problems of induction obscured the historical derivativeness of much that seemed novel in his Logic. For example, Mill’s canons of induction are first set forth in Herschel’s Preliminary discourse, and much of Mill’s understanding of actual science is derived from Whewell’s historical treatment of inductive science. But more important, emphasis upon Mill as the Victorian philosopher of induction distorts the philosophical and historical picture of the development of nineteenth-century British scientific methodology. Herschel and Whewell were scientists writing about science; their forebears were Aristotle and Newton. Mill was a philosopher using scientific examples to help in the solution of philosophical problems; Hume was his progenitor.


Inductive Logic Successive Generalization Confirmation Theory Deductive Form Valid Induction 
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  1. 1.
    Whewell’s work is finally receiving much-needed attention. See Butts (1965a, 1965b, 1967, 1968) and paper in Butts and Davis 1970; Ducasse in Madden 1960, pp. 183-217; Walsh 1962a, 1962b. Herschel’s methodological work is still largely neglected, though a new issue of his Preliminary discourse on the study of natural philosophy in 1966 may help. See Ducasse in Madden 1960, 153-182; and Agassi 1969, pp. 1-36.Google Scholar
  2. 2.
    Whewell, Novum organon renovatum, Aphorism I, “MAN is the Interpreter of Nature, Science the right interpretation”; and Whewell, History of scientific ideas, “The course of real knowledge is, to obtain from thought and experience the right interpretation of our general terms, the real import of our maxims, the true generalizations which our abstractions involve” (268).Google Scholar
  3. 3.
    Whewell’s Platonism is discussed by Marcucci (1963 and 1969, pp. 298-301), and by Butts (1967).Google Scholar
  4. 4.
    Whewell, Novum organon renovatum, in Butts 1968, pp. 149-151. All references to Whewell’s works, unless otherwise specified, will be to selections in Butts (1968).Google Scholar
  5. 5.
    DeMorgan, 1859, 1860. The exchange is discussed in the introduction to Butts 1968, pp. 24-26.Google Scholar
  6. 6.
    Butts, 1968, p. 173.Google Scholar
  7. 7.
    Butts, 1968, pp. 138-177.Google Scholar
  8. 8.
    Even on this interpretation of colligation there remains some novelty and interest, however. For Whewell’s objection to Mill’s claim that we see the ellipse in the data (the discussion had to do with Kepler’s discovery of the elliptical paths of the planets) can be read as suggesting that if this is all there was to Kepler’s discovery, then either he simply observed the ellipse, or the ellipsoid nature of the paths was an idea already ingredient in earlier parts of Kepler’s theory, in which case the elliptical path laws are deductive consequences of other parts of that theory. But observation and deduction are not induction. Thus, on any sensible reading of Mill’s claim that the ellipse was in the data, he was quite wrong in having thought that Kepler performed an induction. Such considerations seem to have convinced Whewell that he was right. In fairness to Mill, however, it should be mentioned that he thought that Kepler’s induction was an argument to the conclusion that the paths will remain elliptical. Whewell seems not to have understood the nature of such generalizing arguments, at least in the context of his exchange with Mill. See Whewell, “Mr. Mill’s Logic,” (Butts 1968, pp. 272-77); and John Stuart Mill, A System of Logic, bk. III, ch. II, sections 2-4.Google Scholar
  9. 9.
    Whewell expresses this point in language quite different from that used in this paper. In “On the Fundamental Antithesis of Philosophy” (Butts, 1968, pp. 54-75), he argues for the ultimate indistinguishability of theories and facts. In Novum Organon Renovatum (Butts, 1968, pp. 176-77), he argues that the distinction is only relative and that it is in any case untenable.Google Scholar
  10. The following passage from “On the Fundamental Antithesis” makes my point about the connectedness of theory and observation languageGoogle Scholar
  11. In the progress of science, both the elements of our knowledge are constantly expanded and augmented. By the exercise of observation and experiment, we have a perpetual accumulation of facts, the materials of knowledge, the objective element. By thought and discussion, we have a perpetual development of man’s ideas going on: theories are framed, the materials of knowledge are shaped into form; the subjective element is evolved; and by the necessary coincidence of the objective and subjective elements, the matter and the form, the theory and the facts, each of these processes furthers and corrects each other: each element moulds and unfolds the other. (Butts, 1968, p. 75)Google Scholar
  12. Whewell makes the same point by suggesting a form of entrenchment as a characteristic of the building up of observation languagesGoogle Scholar
  13. Theory and Fact are the elements which correspond to our Ideas and our Senses. The Facts are facts so far as the Ideas have been combined with the sensations and absorbed in them: the Theories are Theories so far as the Ideas are kept distinct from the sensations, and so far as it is considered as still a question whether they can be made to agree with them. A true Theory is a fact, a Fact is a familiar theory. (Butts 1968, p. 59, emphasis added).Google Scholar
  14. 10.
    Butts, 1968, p. 153.Google Scholar
  15. 11.
    Ibid., p. 152.Google Scholar
  16. 12.
  17. 13.
    Ibid., p. 153.Google Scholar
  18. 14.
  19. 15.
    Of course the results in a consilience are unexpected; they have to be, given that an inductive idea maps out completely the domain that it will cover. But no ordinary deductive, or probabilistic, explication of consilience evidence can capture the sense in which consilience makes a law more acceptable. I hope to show this more clearly below.Google Scholar
  20. 16.
    Butts, 1968, p. 153.Google Scholar
  21. 17.
    A similar model has been provided by J. L. Mackie, “A Simple Model of Consilience,” in Lakatos 1968, pp. 250-51.Google Scholar
  22. 18.
    Mary Hesse’s “Consilience of Inductions,” in Lakatos 1968, pp. 232-246, is extremely helpful in displaying what I take to be the typically Whewellian point that “a confirmation theory can only explicate consilience of inductions if the language that is built into it is the language of the relevant scientific theory” (p. 239). On a somewhat different path, Mackie holds that “we get confirmation by consilience only where the consilient inductions exemplify a single principle or theoretical iaw” (Mackie, p. 252).I have found both of these papers enormously helpful in trying to get a good grip on Whewell’s concept of consilience.Google Scholar
  23. 19.
    Surely Whewell would want to say this, given his position on the coincidence of theory and data outlined in note 9 above. Whewell’s writings abound with references to semantic and conceptual change, although, unhappily, a great many of his discussions contain more metaphor than analysis. In the wonderful essay, “Of the Transformation of Hypotheses in the History of Science” (Butts, 1968, pp. 251-262), he discusses the question of how rival explanations in science get to be decided, concludingGoogle Scholar
  24. And thus, when different and rival explanations of the same phenomena are held, till one of them, though long defended by ingenious men, is at last driven out of the field by the pressure of facts, the defeated hypothesis is transformed before it is extinguished. Before it has disappeared, it has been modified so as to have all palpable falsities squeezed out of it, and subsidiary provisions added, in order to reconcile it with the phenomena. It has, in short, been penetrated, infiltrated, and metamorphosed by the surrounding medium of truth, before the merely arbitrary and erroneous residuum has been finally ejected out of the body of permanent and certain knowledge, (p. 262)Google Scholar
  25. Whewell’s stress upon the imposition of a concept in cases of induction (and hence of consilience) serves to underscore his view of progress in science as involving semantic changes in scientific theories. For example, in his discussion of the inductive table of optics, he regards the undulatory theory of light as having won the field, largely through successive consiliences achieved by the use of the theoretical concept of polarization. But on his own admission, polarization achieves consiliences of the various phenomena of light only on the supposition that undulations are transverse (Butts, 1968, p. 157). That vibrations are transverse is not a newly discovered datum, it is introduced as a new and partial meaning of the term “undulation,” and, thus understood, polarization in terms of the undulatory theory of light accommodates all of the phenomena of light. Whewell is quite prepared to generalize from such examples. Thus he writesGoogle Scholar
  26. In Induction..., besides mere collection of particulars, there is always a new conception, a principle of connexion and unity, supplied by the mind, and superinduced upon the particulars. There is not merely a juxta-position of materials, by which the new proposition contains all that its component parts contained; but also a formative act exerted by the understanding, so that these materials are contained in a new shape.... Our Inductive Tables, although they represent the elements and the order of these Inductive steps, do not fully represent the whole signification of the process in each case. (Butts 1968, p. 163, emphasis added)Google Scholar
  27. In addition, Whewell himself admits that cases of induction, and hence also cases of consilience, are not fully explicable in terms of inclusion of less general propositions in more general ones.Google Scholar
  28. But when we say that the more general proposition includes the several more particular ones, we must recollect what has before been said, that these particulars form the general truth, not by being merely enumerated and added together, but by being seen in a new light. (Butts 1968, p. 169-170).Google Scholar
  29. 20.
    Butts, 1968, pp. 173-76.Google Scholar
  30. 21.
    For example, see Butts, 1968, pp. 154-55.Google Scholar
  31. 22.
    Whewell’s theory of induction is much more complex and rich than he himself often took it to be. Driven by an almost Hegelian delight in unified theories, he tended to read the history of science as a quest for deductive structure and deductive unity. The novel features of his theory of method do not rest well on the procrustean bed of this ancient doctrine. Whewell’s own realization of the tensions within his system seems to have come in debate rather than in exposition. Thus in the exchanges with both DeMorgan and Mill he appears willing to abandon questions of deductive form in favor of stressing the new insights of his theory, e.g., colligation of facts as imposition of a new concept, inductive acceptance of total theories on the basis of extraevidential principles like simplicity.Google Scholar
  32. 23.
    Butts, 1968, pp. 160-177.Google Scholar
  33. 24.
  34. 25.
    When, in the discussion of the inductive tables, he refers to the special “act of attention” required to see that the facts actually do fit the hypothesis (Ibid., pp. 168-69), and when, in discussion of Newton’s rules of philosophizing, he distinguishes rather clearly between the process of confirmation and that of refinement of a law already taken to be true (Ibid., pp. 333-36; also see my paper in Butts and Davis 1970, pp. 143-47). I will return to these points below.Google Scholar
  35. 26.
    Butts, 1968, p. 176.Google Scholar
  36. 27.
    Ibid., p. 174.Google Scholar
  37. 28.
    Ibid., p. 173.Google Scholar
  38. 29.
  39. 30.
    Ibid., pp. 175-76.Google Scholar
  40. 31.
    I have discussed some of the novel non-hypothetico-deductive features of Whewell’s discussion of the inductive tables in the Introduction to Butts, 1968, pp. 18-24. Since my aims in this paper are somewhat different from those in the Introduction, I will not repeat those remarks here.Google Scholar
  41. 32.
    Ducasse seems to have done so in Madden 1960, pp. 216-17.Google Scholar
  42. 33.
    Laurens Laudan, 1970, review of Butts 1968.Google Scholar
  43. 34.
    Though I thus concede Laudan’s point that consilience is not always or uniquely bound up with content increase in theories, I will not concede what I take to be the implications of his remark that the Popperian notion of severe tests must be considered in explicating Whewell’s notion of consilience. Consilience is not achieved when increase in content is achieved; neither is it achieved when increase in corroboration has been achieved. What I say below about Whewell’s concept of an experiment may help to clarify the points of this new disagreement with Laudan.Google Scholar
  44. While writing this paper I read Laudan 1971a and b and Hesse 1971 in typescript. I am much indebted to both authors (and to Laudan for acute private discussion of the issues involved in consilience). In a recent lecture delivered in the University of Pittsburgh Series in the Philosophy of Science (“Consilience of Inductions and the Problem of Conceptual Change in Science,” October, 1971), I argued that Hesse’s formalization of the concept of consilience is preferable to Laudan’s, and that the concept of consilience adds nothing to our ordinary understanding of the probabilistic confirmation of laws or theories. The new papers by Laudan and Hesse do not seem to force any important changes in the interpretation of Whewell’s inductive logic offered in the present essay.Google Scholar
  45. 35.
    Butts, 1968, pp. 159-160.Google Scholar
  46. 36.
    Ibid., p. 159.Google Scholar
  47. 37.
    Additional evidence for my way of reading what I am calling Whewell’s second theory of scientific method may be gotten from Whewell’s way of interpreting Newton’s first rule of philosophizing: “We are not to admit other causes of natural things than such as both are true, and suffice for explaining their phenomena.” Briefly, Whewell collapses the distinction between “true cause” and “adequate explanation,” arguing that direct ontological criteria be replaced by an ontological criterion having to do with the success of theories. Both consilience and simplicity play a role in this argument. Again, briefly, scientific entities are said to exist (to be “true causes”) when hypothetical constructs naming them are ingredients in successful scientific theories, where those theories are powerful in explanation, i.e., exhibit consilience and simplicity. I have discussed these matters in Butts and Davis 1970, pp. 139-142.Google Scholar
  48. 38.
    For detailed discussion of Whewell’s concept of necessary truth, see Walsh (1962b); and Butts (1965a, 1965b).Google Scholar
  49. 39.
    “On the Nature of the Truth of the Laws of Motion,” in Butts 1968, pp. 79-100. Additional discussion of this paper is in Butts 1965aGoogle Scholar
  50. 40.
    Ibid., p. 98, italics added.Google Scholar
  51. 41.
    Ibid., italics added.Google Scholar
  52. 42.
    Ibid., p. 99.Google Scholar
  53. 43.
    Ibid., p. 100.Google Scholar
  54. 44.
    Ibid., p. 97.Google Scholar
  55. 45.
    Sir John Herschel, in his early review of Whewell’s History and Philosophy (Herschel, 1841), noticed this feature of Whewell’s theory of experimentation. He wroteGoogle Scholar
  56. Experience, according to [Whewell], only exemplifies, cannot prove a general proposition. Its truth stands on the higher and independent ground of inherent necessity, and is recognized to do so by the mind so soon as it becomes thoroughly familiarized with the terms of its expression, (p. 173)Google Scholar
  57. Mackie (see note 18 above) also picks out this exemplification feature of Whewell’s theory of science.Google Scholar
  58. 46.
    Adventures of Ideas, p. 94.Google Scholar
  59. 47.
    P. K. Feyerabend 1965, pp. 159-160; see also his discussion in Butts and Davis (1970); and application to Whewell in Butts and Davis (1970, pp. 140-46).Google Scholar
  60. 48.
    In this respect, Whewell appears to have also hit upon what is now called Duhem’s thesis about the non-falsifiability of physical laws.Google Scholar
  61. 49.
    In Butts, 1968, pp. 333-36.Google Scholar
  62. 50.
    I discuss this in detail in Butts and Davis (1970, pp. 143-47).Google Scholar
  63. 51.
    Whewell, 1848, “Second Memoir on the Fundmental Antithesis of Philosophy,” pp. 33-35.Google Scholar
  64. 52.
    Butts, 1965a, pp. 13-19.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Robert E. Butts
    • 1
  1. 1.Department of PhilosophyThe University of Western OntarioCanada

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