Necessary Truth in Whewell’s Theory of Science

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


William Whewell’s fifty-year long career as scientist and historian and philosopher of science was in many ways a perverse one. In keeping with his training, his interests, and the most influential intellectual trends of his age, Whewell should have been a philosophical empiricist.1 His own work in science was for the most part of the most narrow empirical kind. He collected and classified minerals, attempted to measure the density of the earth at the bottom of Dolcoath coal mine shaft, made a monumental descriptive study of the tides off the coast of England, invented an instrument, called an ‘anemometer,’ for measuring the force and direction of the wind, and prepared detailed notes on the architecture of German churches. The tenor of the intellectual times in Britain was also clearly empirical: the utilitarianism of John Stuart Mill rose to popularity; in Scotland Dougald Stewart continued to develop the fortunes of Scottish common sense empiricism; William Hamilton loudly proclaimed the virtues of his variety of empiricism; and even in Cambridge great friends of Whewell—like Sir John Herschel—championed a different variation on empiricism. Yet, in spite of what his own scientific work and the philosophical tendencies of his age might have suggested to him, Whewell’s philosophy of science emerged as one of the last great rationalist systems, complete with a metaphysics, a theology, and a theory of morals. In its finished or nearly finished form, Whewell’s philosophy was, in Britain at least, an anomaly. For his system was, in its basic features and in many of its details, much more like the systems of Leibniz and other seventeenth-century rationalists than like those of his British contemporaries.2


Trinity College Fundamental Idea General Proposition Cambridge Philosophical Society Universal Truth 
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  1. 1.
    In this paper, ‘empiricism’ refers to that epistemology that holds that all non-trivial and non-analytic knowledge is based on experience, and that no such knowledge is certain or necessary.Google Scholar
  2. 2.
    Dr. Walter Cannon of the Smithsonian Institution has pointed out to me in conversation that pre-Darwin Victorian English men of science—one thinks at once of Sir John Herschel and of Whewell in this context—held to an implicit ‘world picture’ that included acceptance of an orderly, divinely designed universe, of physical science as the rational paradigm, and of mathematics as the language in which natural laws were originally written. Indeed, most of the key ingredients that went into seventeenth-century rationalism were to some extent reproduced in nineteenth-century England, especially in the thought of those associated with Cambridge. In one sense, then, Whewell’s philosophy can be regarded as having made explicit what was implicit in the attitudes of some of his contemporaries.Google Scholar
  3. 3.
    To James Garth Marshall, Dec. 25, 1849; to Richard Jones, Aug. 21, 1834.Google Scholar
  4. 4.
    On Sept. 6, 1837, he wrote to Richard Jones asking him to “Put down on paper, as clearly and strongly as you can, the reasons which you can find for the opinion you held a little while ago; namcly, that the simplest mechanical truths depend upon experience in a manner in which the simplest geometrical truths do not: that the axioms of geometry may be self-evident, and known a priori; but that there are not axioms of mechanics so known and so evident. I am very desirous of getting this opinion in its best and most definite shape, because the negation of it is a very leading point of my philosophy. This tenet separates me from the German schools as well as from the Scotch metaphysicians, and is the basis of a long series of results both speculative and practical. The whole art of induction depends upon it.”.Google Scholar
  5. 5.
    My account of Whewell’s theory of the Ideas, and some parts of my account of his theory of necessary truth, parallel the account in (Ducasse, 1951a, pp. 56-59). This paper by Ducasse, together with Ducasse, 1951b (both papers are reprinted as one under the title, “William Whewell’s Philosophy of Scientific Discovery,” in Blake, et. al. (eds.), 1960 is the only reasonably accurate and detailed exposition of the fundamental elements in Whewell’s theory of science written in this century. But Ducasse’s purpose—to expose clearly the fundamentals of Whewell’s philosophy of discovery—is more limited than mine. I wish to show both the essential features of Whewell’s theory of necessary truth and to say something about its development in the broader context of Whewell’s philosophical thought. My account makes good one defect of Ducasse’s work: it shows that Whewell did make some attempt to justify his otherwise purely psychologistic theory of necessary truth. Thus I hope to have gone beyond Ducasse’s papers in the direction of a fuller exposition of both Whewell’s theory and the context of discussion and thought in which it developed.Google Scholar
  6. 6.
    Capital letters are used throughout this paper to abbreviate the titles of Whewell’s works. A complete list of Whewell’s works cited appears on pp. 209-211.Google Scholar
  7. 7.
    Whewell attempted to find synonyms for the term “idea” in a letter written to Richard Jones (Aug. 21, 1834): “I expect to shew clearly that in order to arrive at knowledge or science we must have, besides impressions of sense, certain mental bonds of connexion, ideal relations, combinatory modes of conception, sciential conditions, or whatever else you can help me to call them: they are what I called Ideas in my former letter....” In his notebooks (1830–33) Whewell calls the Ideas “regulative conceptions,” “interpretative conceptions,” and “conditions of inductivity,” Inductuon, I, II, IV. (Uncatalogued manuscript notebooks, Wren Library, Trinity College, Cambridge.).Google Scholar
  8. 8.
    In HSI, vol I, p. 87, Whewell states that his discussion of space and time contains “... the leading arguments respecting Space and Time, in Kant’s Kritik.” See also PD, p. 335.Google Scholar
  9. 9.
    In (Blanche, 1935, p. 2) it is argued that there are two fundamental problems in arriving at a fair interpretation of Whewell’s philosophy. First, are ideas constitutive elements of the structure of reason, or contingent creations of individual genius? Second, are ideas forms in the Kantian sense, or substantive notions as in Descartes and Plato? Blanché thinks that Whewell never entirely answers either question, and thus that there is “...l’indécision fondamentale de sa philosophie, oscillant sans cesse entre l’idéalisme et le réalisme, entre l’épistémologie et ll’ontologie. “ I hope to be able to show that Whewell does make a decision on both questions, though the attempted solution that results is hardly satisfactory.Google Scholar
  10. 10.
    NOR, pp. 70, 88-90. Aphorism XIV: “The Consilience of Inductions takes place when an Induction, obtained from one class of facts, coincides with an Induction, obtained from another different class. This consilience is a test of the truth of the Theory in which it occurs.” Thus a consilience of inductions takes place when a hypothesis predicts facts of a kind different from those it was introduced to explain. In NOR, Whewell has made much of the fact that hypotheses (and hence the Ideas that they introduce) are invented by scientists, an admission that has led some to suppose that for Whewell hypotheses are conventions. This supposition is patently false, for Whewell insists that the conceptions introduced by hypotheses be clear and distinct, appropriate to the matter they are to deal with, and carefully verified by subsequent observations and experiments. Invention was for Whewell a most important step in discovery, but not in proof, which requires a patient and exact comparison of hypotheses with facts. Finally, Whewell thought that sound inductive proofs are demonstrative, so that some inductions show that the facts are expressible only by means of certain ideas and not by others. (NOR, pp. 111-12).Google Scholar
  11. 11.
    See, for example, FA; PIS, vol. I, pp. 62, 66, 74-78; HSI, vol. I, pp. 65, 68, 76-80.Google Scholar
  12. 12.
    Cf. TD, pp. v-vii. It is this second sense of “experience” that Whewell employs in answering some of his critics. For example, he writes of Mill: “Mr. Mill cannot deny that our knowledge of geometrical axioms and the like, seems to be necessary. I cannot deny that our knowledge, axiomatic as well as other, never is acquired without experience.” (IM, p. 79; PD, p. 286).Google Scholar
  13. 13.
    See for example (PIS, p. 276) where, when speaking of necessary truths, Whewell writes “Truths thus necessarily acquired in the course of all experience, cannot be said to be learnt from experience, in the same sense in which particular facts at definite times, are learnt from experience, learnt by some persons and not by others, learnt with more or less of certainty.”Google Scholar
  14. 14.
    Immanuel Kant, Kritik der reinen Vernunft [1781, 1787], Bi.Google Scholar
  15. 15.
    None of Whewell’s previous commentators have realized that his description of the avenues to the discovery (intuition) of necessary truth is throughout Platonic. We begin with confused and untrustworthy perceptions. These must first be rendered more orderly and less confusing by introducing precise scientific ideas. Discussion of the ideas plus accumulation of refined experiences eventually, so to speak, overcome the limitations of the ‘perceptual cave’ in which we live, and we have then the power to intuit the necessity of some propositions whose ideas are clear and distinct. (Shades of the ‘Divided Line’?) Indeed, even Whewell’s theory of induction has clear but frequently unrecognized Platonic motives.Google Scholar
  16. 16.
    The developmental or progressive character of the intuition of necessity was an essential aspect of four of Whewell’s theories: (1) his theory of necessary truth; (2) his theory of mathematical reasoning; (3) his theory of the historical development of science; and (4) his theory of education. For (1) see especially his answers to his critics in PD, chs. XXVIII, XXIX, For (2) see ME, appendix, “Remarks on Mathematical Reasoning and on the Logic of Induction.” For (3) see HIS, HSI, and NOR. For (4) see TSM, pp. 5-33, and PEU, pp. 12-50.Google Scholar
  17. 17.
    This accounts for the central place Whewell accorded to training in mathematics in a liberal education. See TSM and PEU. Whewell’s view of the intuitive necessity of the basic principles (Axioms) of the sciences also led him to attempt to construct statics, dynamics, and parts of other physical sciences as deductive systems. See TM and ME.Google Scholar
  18. 18.
    For Whewell’s interpretation of Plato’s theory of ideas in terms of his (Whewell’s) own conception of Ideas, see PTI, and PD, pp. 12 ff. For his almost incredible misunderstanding of Descartes, see HIS, vol. II, Bk. VII, pp. 140-45. Whewell was so intent on establishing Bacon and Newton as the heroes of the scientific revolution that he even criticized Descartes for holding a form of the view of science that Whewell himself held: “At the same time we may venture to say that a system of doctrine thus deduced from assumed principles by a long chain of reasoning, and not verified and confirmed at every step by detailed and exact facts, has hardly a chance of containing any truth. Descartes said that he should think it little to show how the world is constructed, if he could not also show that it must of necessity have been so constructed. The more modest philosophy which has survived the boastings of his school is content to receive all its knowledge of facts from experience, and never dreams of interposing its peremptory must be when nature is ready to tell us what is.”.Google Scholar
  19. 19.
    TM; see also ME, p. 159: “... I say that the axioms of Statics are self-evidently true.”.Google Scholar
  20. 20.
    TM, p. 264 note. The seeming self-evidence of dynamical laws is also admitted by Whewell in a number of early works, for example, in BT, pp. 231-32.Google Scholar
  21. 21.
    PIS, vol. I, p. 192; HSI, vol. I, p. 212. This might not seem much of a change in Whewell’s position until one understands that for Whewell experience Can render propositions general, but it cannot show them to be universal. Universal truths are necessary truths depending upon Fundamental Ideas. Sce PIS, vol. I, pp. 62-66; HSI, vol. I, pp. 65-67.Google Scholar
  22. 22.
    NTM. Much of the material of this essay is included in PIS, vol. I, pp. 177-185, 215-254, and in HSI, vol. I, pp. 184-204, 235-270. The essay was also reprinted as an appendix to the second edition of PIS.Google Scholar
  23. 23.
    The basic problem of Whewell’s philosophy was for him the establishment of the truth of the proposition, “Man is the Interpreter of Nature, and Science is the right Interpretation” (PIS, vol. I, p. 37; HSI, vol. I, p. 41). Thus it might be said that he was seeking adequate ‘bridge rules,’ ‘epistemic correlations,’’ semantical rules,’ or ‘rules of interpretation’ that would provide an epistemological link between theoretical scientific terms and experiments, or between theoretical laws and empirical laws. But given his theory that there are (synthetic a priori) axioms that are the ultimate epistemoiogical justification-sources of the sciences, his solution to the bridge rule problem (the problem of showing that theoretical systems say something true about the empirical world even though theoretical terms have no direct empirical referents) takes, in the end, a partly Kantian, partly theological form, as will be shown later in this paper.Google Scholar
  24. 24.
    Whewell was aware that his position that “... all that we learn from experience is, that she has nothing to teach us concerning the laws of motion...” was similar to d’Alembert’s position. (NTM, p. 24) Surely Whewell could have agreed with d’Alembert’s statement of the problem of necessity in science in Traité de dynamique (1758), p. xxiv: “The great metaphysical problem has been put recently: are the laws of nature necessary or contingent? To settle our ideas on this question, we must first reduce it to the only reasonable meaning it can possibly have... viz., whether the laws of equilibrium and motion that we observe in nature are different from those that matter would have followed, if abandoned to itself. Hence this is the way the scientist should follow: first he should try to discover through reason alone which would be the laws of mechanics in matter abandoned to itself; then he should investigate empirically what are really such laws in the universe. If the two sets of laws be different, he should conclude that the laws of mechanics, such as those yielded by experiment, are of contingent truth, since they appear to spring from a particular and express decision of the Supreme Being: if, on the other side, the laws yielded by experiment agree with those that could be deduced by logic alone [the position of Whewell, and, in a somewhat different form, of d’Alembert], he shall conclude that those laws are of necessary truth: which does not mean that the Creator could not have established a wholly different set of laws, but that he did not hold it right to establish other laws than those which resulted from the very existence of matter.” Quoted in Georgio de Santillana,1950, p. 10. For an interpretation of d’Alembert’s rationalistic philosophy of science see Butts, 1959. As will emerge shortly from the exposition of this paper, even the theological framework of d’Alembert’s posing of the question of necessary truth can be seen to be of vital importance to Whewell’s later position on the justification of necessary truths.Google Scholar
  25. 25.
    In his notebooks (uncatalogued mss. in Wren Library, Trinity College), Whewell lists the Ideas that will later play a key role in the Philosophy: space, time, number, cause, opposition, resemblance, substance, etc. (Induction, I, II). In Induction I he also lists “regulative conceptions” of political economy—property, exchangeable value, labor, etc., and in Induction, IV, under the date Apr. 12, 1831, he lists the “regulative or interpretative conceptions” of “notional” (subjective) sciences—character, countenance, wisdom, God, right, pleasure, etc., which are Ideas that come to play a large role in Whewell’s theory of morality (see EM, vol. I, p. 50; vol. II, p. 6). Whewell’s main contention is that each science must be based upon such Ideas, but he was perfectly willing to admit that what he suggested as ideal bases of some sciences, namely the imperfectly developed ones, might not turn out to be distinctly intuitable in the course of history. A recent commentator (Walsh, 1962, pp. 141, 145) has been misled by this tentativeness of Whewell’s attitude into thinking that Whewell took the Ideas to be sources of merely hypothetical or relational necessity, a position Whewell explicitly denies in PIS, vol. I, p. 100; HSI, vol. I, p. 101. Mill also misunderstood the tentative nature of the attitude that Whewell took toward some of the Ideas, like the Ideas of demmite composition and definite quantity in chemistry. Whewell explained that “... what I meant to do [in the Philosophy] was, to throw out an opinion, that if we could conceive the composition of bodies distinctly, we might be able to see that it is necessary that the modes of composition should be definite.... The thought of such a necessity was rather an anticipation of what the intuitions of philosophical chemists in another generation would be, than an assertion of what they now are or ought to be....” (PD, p. 340). For Whewell mathematical physics was the paradigm science, and he was far from thinking that other sciences matched exactly its intuitive certainty.Google Scholar
  26. 26.
    Walsh, 1962, p. 141; Ducasse, 1959a, and Ducasse 1959b.Google Scholar
  27. 27.
    Letter to Sir John Herschel, Apr. 11, 1844 (uncatalogued mss. copy, Wren Library, Trinity College, Cambridge). Printed as an appendix in PIS and PD.Google Scholar
  28. 28.
    For example, (Walsh, 1962, pp. 141-42) completely misrepresents the role that the two memoirs on the fundamental antithesis of philosophy play in the development of Whewell’s philosophy. I hope in what follows that I can put this matter right.Google Scholar
  29. 29.
    FA and FAIL.Google Scholar
  30. 30.
    I do not think that Whewell was explicitly aware how far his final attempted justification of the Ideas would depart from his earlier Kantianism. Part of the puzzle rests on the fact that Whewell’s own definition of ‘metaphysical’ underwent several significant changes. In the early 1820’s (e.g., in his letter to Richard Jones, Sept. 23, 1882), he wanted to be rid of the term ‘metaphysical’ because what it signified stood in opposition to the inductive philosophy. He also condemned seventeenth-century metaphysicians for using what Bacon had called the “method of anticipation,” a condemnation with which Kant’s philosophy agrees. But during the same period he wrote the following in a letter to Jones (Aug. 16, 1822): “And so by the metaphysics of mathematics I mean the examination of the laws and powers of the mind on which their evidence depends, the analysis of their principles into the most simple form and if you choose the history of their development. It is not easy to stick to the distinction between this and the logic of the science; but the latter examines the accuracy of your mode of deducing consequences from your principles and the former your way of getting your principles.” In NOR (p. viii) he wrote: “Metaphysics is the process of ascertaining that thought is consistent with itself: and if it be not so, our supposed knowledge is not knowledge.” But Whewell never fully recognized anything like Kant’s distinction between critical theory of knowledge and metaphysics as empirically empty speculation, perhaps because as his thought developed, he saw more clearly that the consistency of thought with itself could only be established on completely non-Kantian grounds.Google Scholar
  31. 31.
    FAII, “Continuation of the Second Memoir.” Originally printed for private circulation.Google Scholar
  32. 32.
    Galileo Galilei, 1953, p. 114 (Dialogue on the great world systems 1632, Salisbury translation 1661, revised by Georgio de Santillana): “... We should have recourse to a philosophical distinction and say that the understanding is to be taken two ways, that is intensively or extensively. Extensively, that is, as to the multitude of intelligibles, which are infinite, the understanding of man is as nothing, though he should understand a thousand propositions; for a thousand in respect of infinity is but as zero. But as for the understanding intensively, inasmuch as that term imports perfectly some propositions, I say that human wisdom understands some propositions as perfectly and is as absolutely certain thereof, as Nature herself; and such are the pure mathematical sciences, to wit, Geometry and Arithmetic. In these Divine Wisdom knows infinitely more propositions, because it knows them all; but I believe that the knowledge of those few comprehended by human understanding equals the Divine, as to objective certainty, for it arrives to comprehend the necessity of it, than which there can be no greater certainty.”.Google Scholar
  33. 33.
    PW, pp. 276-78. This quoted material is from Whewell’s printer’s copy of PW, dated 1853 and bearing the catalogue number ADV.C. 16.27 in the Wren Library, Trinity College, Cambridge. This copy of PW contains five chapters that Whewell had printed but then later deleted from the published edition. Apparently he suppressed this material at the suggestion of Sir James Stephen who complained that these five chapters on metaphysics could not appeal to the same audience to which the main body of the book was addressed. In a letter to Sidgwick (MSS. in Wren Library, Trinity College, dated June 8, 1854) Whewell explains why he suppressed these chapters: “In the first printing of my essay I had pursued my speculations about the Divine Mind a good deal further than in the published book. I suppressed what I had printed because I thought that the greater part of my readers would be repelled by what they would call metaphysics; but if you could find time to read my cancelled pages, I think they would interest you; and I should be very much pleased to hear your opinion about my speculations.” It should be pointed out that Whewell did not suppress all theological material from the essay on Plurality of Worlds. For example, in the finally printed version of PW, Whewell argues on pp. 109-110 that the Ideas are both epistemological conditions of human knowledge and ontological conditions of the creation of the world by God. The five suppressed chapters express this position much more fully, but the point is that it was Whewell’s published position. It seems clear, then, that Whewell was yielding to editorial advice in the act of suppressing these five chapters, and that he had not come to disagree with what he wrote there. That these five chapters do represent a metaphysical position that Whewell accepted toward the end of his life is amply confirmed by the fact that Chapters XXX–XXXI in PD essentially reproduce this once suppressed metaphysical material. In addition there is also some discussion of the relation between the Divine and the human mind closely resembling a discussion of this topic in one of the suppressed chapters of PW in an uncatalogued manuscript notebook entitled Philosophy and Theology dated August 27, 1851 (Wren Library).Google Scholar
  34. 34.
    FAII, “Additional Note to two Memoirs ‘On the Fundamental Antithesis of Philosophy.’”.Google Scholar
  35. 35.
    Of course in one sense the theology had not rested at all, for one clear statement of it in the Bridgewater Treatise, which appeared unchanged in seven editions between 1833 and 1864, was always available. But Whewell’s theology in PW and PD differs from that in BT. The differences, however, must await discussion in another place.Google Scholar
  36. 36.
    One of Whewell’s reviewers praises the Kantian spirit of his Philosophy and the merits of its anti-empiricist effects. But he warns Whewell not to take Kant too seriously, since his ‘ultra-rationalism’ in religion would corrupt Cambridge. “Whewell’s ‘Philosophy of the Inductive Sciences,’” Dublin University Magazine, no. 98 (Feb. 1841). I think that Whewell was more prone to accept this sort of remark than his earlier commentators seem to have realized. The religious and moralistic background of Whewell’s philosophy has yet to be studied.Google Scholar
  37. 37.
    See H.L. Mansel, 1860, pp. 189-293; and Mansel, 1853. Also see Whewell, “A Letter to the Author of Prolegomena Logica by the author of the History and Philosophy of the Inductive Sciences” (Sept. 20, 1852), and PD, pp. 335-39.Google Scholar

References to Whewell’s Works Cited

  1. BT.
    Astronomy and General Physics Considered with Reference to Natural Theology (London, 1833).Google Scholar
  2. DMH.
    “Demonstration that All Matter is Heavy,” Transactions of the Cambridge Philosophical Society, vol. 7, pt. H (1841). Reprinted as an appendix in PD and PIS.Google Scholar
  3. EM.
    The Elements of Morality, including Polity (London, 1845), 2 vols..Google Scholar
  4. FA.
    “On the Fundamental Antithesis of Philosophy,” Transactions of the Cambridge Philosophical Society, vol. 7, pt. H (1844). Reprinted as an appendix in PD and PIS.Google Scholar
  5. FAII.
    “Second Memoir on the Fundamental Antithesis of Philosophy,” Transactions of the Cambridge Philosophical Society, vol. 7, pt. V (1848).Google Scholar
  6. HIS.
    History of the Inductive Sciences, 1st ed. (London, PEU 1837), 3 vols.Google Scholar
  7. HSI.
    The History of Scientific Ideas (London, 1858), 2 PIS vols. Part I of the 3d. ed. of PIS.Google Scholar
  8. IM.
    Of Induction, with Especial Reference to Mr. Mill’s PTI System of Logic (London, 1849). Reprinted as part of PD.Google Scholar
  9. ME.
    Mechanical Euclid (Cambridge, 1837). One section, “Remarks on Mathematical Reasoning and on the Logic of Induction,” reprinted as an appendix in PIS, 2d. ed.Google Scholar
  10. NOR.
    Novum Organon Renovatum (London, 1858). Part II of the 3d. ed. of PIS.Google Scholar
  11. NTM.
    “On the Nature of the Truth of the Laws of Motion,” Transactions of the Cambridge Philosophical Society, vol. 5, pt. II (1834). Reprinted as an appendix in PIS.Google Scholar
  12. PD.
    On the Philosophy of Discovery (London, 1860), pt. III of the 3d. ed. of PIS.Google Scholar
  13. PEU.
    On the Principles of English University Education (London, 1837).Google Scholar
  14. PIS.
    The Philosophy of the Inductive Sciences, 2d. ed. (London, 1847), 2 vols.Google Scholar
  15. PTI.
    “Of the Platonic Theory of Ideas,” Transactions of the Cambridge Philosophical Society, vol 10, pt. I (1857).Google Scholar
  16. PW.
    Of the Plurality of Worlds (London, 1853). Also the copy (dated also 1853) containing 5 chapters, printed, but cancelled, in the published work (Wren Library, Trinity College, Cambridge).Google Scholar
  17. TD.
    On the Motion of Points Constrained and Resisted, and on the Motion of a Rigid Body. The Second Part of a new edition of A Treatise on Dynamics (Cambridge, 1834).Google Scholar
  18. TM.
    An Elementary Treatise on Mechanics, 1st ed. (Cambridge, 1819), and 5th ed. (Cambridge, 836).Google Scholar
  19. TSM.
    Thoughts on the Study of Mathematics as Part of a Liberal Education (Cambridge, 1835).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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