(b. Lancaster, England, 24 May 1794;
d. Cambridge, England, 6 March 1866), theology, history and philosophy of science, physical astronomy, mineralogy, tidal theory, science education, political economy, architectural history, moral philosophy. For the original article on Whewell see DSB, vol. 14.
An avalanche of research on William Whewell since the 1970s added considerably to an understanding of him and his nineteenth-century context. Scholars always recognized Whewell as a religious man, for example, but have come to better see exactly how his religion mixed with other areas of thought—especially his philosophy of science, itself better understood in the early twenty-first century. Publications have examined his collaboration with Richard Jones in developing political economic theory, including their debates with other political economists. Much scholarship has addressed the institutional and social contexts of Whewell’s life, such as the nature of education at Cambridge University and the creation of scientific societies in Britain. Whewell’s conceptual controversies included his rejection of Darwinian evolution, that with David Brewster on the extent of life in the universe, and those with John Stuart Mill involving philosophy, moral theory, and economics.
Cambridge University immersed the young would-be carpenter Whewell in a network of like-minded intellectuals who would collectively contemplate many subjects. He was one of the poor scholarship students (sizars) at Trinity College, all of whom received contributions from better-off students. He took his BA degree in 1816 as second wrangler and second Smith’s prizeman, that is, with the second-highest honors in his class. Succeeding the next year in the highly competitive fellowship examination at Trinity College, he virtually guaranteed himself a lifelong Cambridge career, which is what came to pass. He held professorships in two quite different subjects, mineralogy from 1828 to 1832 and moral philosophy from 1838 to 1855. Surely spurred significantly by his own example, he praised the socially transforming power of English universities to enable sons of peasants to become country clergymen. Physically as well as intellectually vigorous, Whewell died when thrown from the horse he was riding near Cambridge when he was nearly seventy-three years old. He outlived two wives, the second dying in 1865. He had no children.
Religion and Science. Theology provided Whewell his deepest knowledge. He wrote religious letters of comfort to his mortally ill sister, who died in 1821. He assured his colleague Hugh James Rose that science would not undermine religion, and in his Cambridge sermons of 1827 he explained that revelation provided more secure theological insights than did natural theology, as valuable as the latter was. In a Cambridge sermon of 1828 Whewell underscored the point he had made to Rose by citing the religion of the likes of Isaac Newton. Natural theology’s value appeared strikingly in Whewell’s Bridgewater Treatise, Astronomy and General Physics, Considered with Reference to Natural Theology, published in 1833 and many times thereafter. Design in the physical world certainly disclosed the existence of a designing God, but it revealed more than that. God also designed man’s morality and intellect, for instance. Though decidedly inferior to God’s mind, man’s mind mirrored God's. Hence, man’s degree of pleasure in contemplating a particular scientific theory was a measure of God’s own pleasure in creating the world with
that theory in mind. That is, such pleasure suggested, but did not guarantee, the theory’s truth. Whewell’s theology would provide a context for his philosophy of science, and as master of Trinity he delivered sermons into the 1860s.
Geology was the current science most responsible for disagreements involving science and religion. The conflict, however, was not simply between religion and geology but, even more, between competing views of scripture. Whewell had been reading works by leading geologists as early as 1818, and he went on geological field trips in the 1820s with Cambridge’s new professor of geology, Adam Sedgwick. Sedgwick and Whewell established a Cambridge approach to geology that emphasized probing the geometrical form of geological strata and comprehending their configuration in dynamical terms, that is, in terms of the laws of motion. In the early 1830s Whewell praised Charles Lyell’s contribution to geological dynamics, but he disagreed with Lyell’s “uniformitarian” (Whewell’s word) conclusions that the Earth had remained essentially the same, experiencing only nonprogressive and rather gradual changes. Both Lyell and the “catastrophist” (Whewell’s word) geologists concluded that the Earth had a vast age, and Whewell agreed. That is, Whewell was not one of the young-Earth, scriptural geologists of the day but one who valued scripture primarily for its revelation of such as God, Christ, and the afterlife. Earth’s changing life and the fossil record’s discontinuities, however, did bespeak miraculous interventions to Whewell, scripture and geology essentially agreeing in this regard.
Political Economy. Whewell’s partner in the study of political economy was Richard Jones, another Trinity man who had taken his degree in 1816. David Ricardo’s recent books on economic theory roused their inductivist ire. Compared to mechanics and astronomy, political economy was far too immature a science for Ricardo to make the assumptions and deductions that he did, they argued. Though claiming universal conclusions, Ricardo actually ignored agricultural economic arrangements for most of the world. Contrary to Ricardo, they asserted, there was no perpetual equilibrium, as was disclosed by other sciences. Whewell rejected Ricardo’s conclusion that landowners’ interests conflicted with those of others in society. Whewell endorsed the English class system as a judicious social control. Jones inductively amassed the evidence that Whewell could draw upon in his mathematical demonstration of Ricardo’s errors. Whewell presented papers on political economy to the Cambridge Philosophical Society in 1829 and 1831. Also in 1831 appeared Jones’s long-awaited Essay on the Distribution of Wealth and on the Sources of Taxation.
Natural Science. In addition to his significant research on mineralogy and the tides, Whewell kept careful track of other physical sciences within an increasingly institutional scientific context. In the early 1820s he was reading French works in physics and taking detailed notes on Michael Faraday’s earliest research concerning connections between electricity and magnetism. A few years later Whewell contributed the extensive mathematical portion of Francis Lunn’s article on “Electricity” in the Encyclopaedia Metropolitana. A Cambridge graduate of 1818, Lunn became a fellow of the Royal Society of London the next year and helped sponsor Whewell’s successful application for membership in 1820. Whewell presented his paper on mineralogy to the Royal Society in 1824 and others on the subject to the Cambridge Philosophical Society, which he had helped found in 1819. By around 1830 Whewell strongly advocated the new undulatory theory of light with its concept of a luminiferous ether. The British Association for the Advancement of Science was established in 1831, and Whewell presented to it long reports on the current state of mineralogy in 1832 and on the current state of mathematical theories of electricity, magnetism, and heat in 1835. He became president of the Geological Society of London in 1837, the next year inducing Charles Darwin to assume the burdens of secretary. Though the word scientist gained currency only well after Whewell’s lifetime, his invention of it in the 1830s symbolized the increasing professionalization of science.
Education. Whewell helped change Cambridge education in important ways. In 1816, instruction within colleges prepared pupils for the university’s Senate House examination upon which a Cambridge honors degree depended. Lectures by university professors could be interesting but were generally not relevant to Senate House examination subjects, which were classics, moral philosophy, and especially mathematics. The last included pure mathematics (with Isaac Newton’s fluxional notation for the calculus) and mixed mathematics—that is, those successfully mathematized areas of science: mechanics, observational astronomy, gravitational theory, hydrostatics, and geometrical optics. During the previous century French savants using the Continental version of the calculus had dramatically developed Newton’s gravitational theory. That was excellent motivation for John Herschel, Charles Babbage, and George Peacock to form their Analytical Society and to try to alter the Cambridge curriculum. Whewell joined their cause with his Elementary Treatise on Mechanics(1819) and Treatise on Dynamics (1823), both of which employed the Continental calculus. In addition, Whewell essentially separated statics from dynamics, rewriting Newton’s laws of motion in the process. More fundamental, he declared those laws to be necessary truths—a conclusion that would eventually provide a basis for his philosophy of science.
Whewell continued to influence Cambridge studies into mid-century. He departed somewhat from the Analytical Society’s exuberance for the calculus, arguing that students must first master more elementary mathematics in preparation for logical thinking in other—and ultimately more significant—areas of thought. In his Principles of English University Education (1837), he emphasized the university’s role in converting undergraduates into Englishmen during that crisis period when youth became man. England was something like a present-day Greece or Rome, and the university bore much of the duty to maintain that reality. He identified permanent knowledge as classics and mathematics, which at Cambridge were the preserve of college instruction. Progressive knowledge included not-yet-mathematized areas of science, which at Cambridge were part of professorial instruction. With both the fate of the nation and his own success in mastering many subjects undoubtedly in mind, Whewell pursued his convictions. He succeeded in getting some questions on heat, electricity, and magnetism included in the mathematical tripos (as the Senate House examination came to be called). As master of Trinity he was one of the examiners for the Smith’s prize examination, and his questions included a few on heat, electricity, and magnetism as well as engineering. As chair of key committees in the 1840s he was instrumental in establishing the natural sciences tripos and the moral sciences tripos at mid-century, thus making professorial lectures (including his own) directly relevant to Cambridge education.
Philosophy. Whewell’s philosophy of science combined primarily the philosophies of Francis Bacon and Immanuel Kant. Bacon was one of the most famous of Trinity men, and his legacy would have been ever present to the young Whewell. Whewell’s diaries reveal his awareness of Kant by spring 1820 and of Kant’s nonutilitarian moral philosophy by February 1821, evidently from reading Madame de Staël’s advocacy of Kant in her Germany(1813). Though the mature philosophy that Whewell formulated in the 1830s would have totally pleased neither Bacon nor Kant, it did explain how an empirical study of nature had led to necessary truths. Not merely a random gathering of information, induction required an active mind, seeking patterns and forming explanations— though without jumping to conclusions or pursuing wild hypotheses. Whewell termed resultant successes the “colligation” of facts and the “consilience” of inductions. Colligation involved one idea explaining different but similar observations. The more powerful consilience required an idea to explain quite different phenomena, the classic example being Newton’s gravitational theory, which united the celestial and terrestrial worlds. Moreover, such successful theories could disclose “true causes”—causes known actually to exist in nature, even though unobservable. The luminiferous ether was a prime example. No Kantian-like doubt of a real, external world arose. God had created both humans and nature, designing them for each other.
Whewell’s Kantian-like “fundamental ideas” provided necessary truths. The history of science showed that knowledge of such fundamental ideas emerged through long and careful empirical studies of nature. Because of colligation and consilience, laws of motion would appear first as powerful inductive truths that were still subject to refutation. Eventually, though, one recognized their necessity, that their truth depended not upon experience but upon their logical connection to the fundamental idea of cause. Gravitational theory, then, must accord with the laws of motion, but not the reverse. That is, gravitational theory was not a necessary truth because, in principle, contrary evidence could disprove it. Whewell identified several fundamental ideas, such as that of affinity for chemical knowledge. However, the existence of necessary truths did not preclude change in scientific understanding. The future could bring additional fundamental ideas, for example, including more inclusive ones that could effect something like a consilience of already known fundamental ideas. Fundamental ideas allowed the human mind glimpses of God's.
Such glimpses of course were relevant to Whewell’s moral philosophy. Indeed, he articulated such a view in his Foundation of Morals, the published version of four sermons he delivered in Cambridge in 1837. As with the Ten Commandments, revelation provided moral guidance, but scriptural passages such as Romans 2:14 also signaled the presence of innate moral ideas in man’s mind. Whewell’s prime opponent here was utilitarianism, especially that of William Paley, whose Principles of Moral and Political Philosophy (1785) argued that when scripture was not specific enough, the happiness produced by proper behavior indicated the morality of that behavior. Because Paley’s book was required reading at Cambridge, Whewell once more confronted the Cambridge curriculum. As professor of moral philosophy and in later publications, Whewell pursued his anti-utilitarian theme. For Whewell, the history of innate ideas in moral philosophy resembled that of fundamental ideas in science.
Controversies. Controversies were not confined to Cambridge. John Stuart Mill disagreed with Whewell not only about utilitarianism but about political economy and induction as well. Whewell’s Of Induction (1849) responded at length to Mill. The eminent Scottish scientist David Brewster engaged Whewell in acrimonious and entangled debate on the plurality of worlds—that is, on whether the rest of the universe was also inhabited. Supporting the widely held plurality view, Brewster declared, for example, that God would not create wasted worlds, that is, worlds absent life. Geology, Whewell countered, demonstrated that the Earth itself had existed for eons with no life, indicating by analogy that God could create such worlds. In his Origin of Species (1859), Darwin quoted from Whewell’s Bridgewater Treatise regarding God’s law-governed universe. Darwin may have called upon Whewell’s formulation of scientific knowledge in defending his theory of evolution, but he was also obviously rejecting Whewell’s published opposition to any such theory. Whewell added a preface to the 1864 edition of his Bridgewater Treatise confirming that opposition.
Thus, at an Anglican university where competing theologies vied, William Whewell endorsed a theology that supported a philosophy of human knowledge. It in turn provided what he regarded as the proper understanding of the true science that had emerged historically in the epoch of Isaac Newton. The man who invented the word scientist was not himself a scientist in exactly the modern sense of the word. Indeed, he was more interesting than that.
The bibliography in Fisch and Schaffer 1991 (see Other Sources) lists some 130 works by Whewell. The bibliography that follows here includes none of those works nor any in the original DSB bibliography.
WORKS BY WHEWELL
Sermons Preached in the Chapel of Trinity College, Cambridge. London: John W. Parker; Cambridge, U.K.: J. & J. J. Deighton, 1847.
Collected Works of William Whewell. 16 vols. Edited with an introduction by Richard Yeo. Bristol, U.K.: Thoemmes Press, 2001. Includes one edition or another of most of Whewell’s major works as well as the two-volume biography of him by Isaac Todhunter published in 1876.
Of the Plurality of Worlds: A Facsimile of the First Edition of 1853; Plus Previously Unpublished Material Excised by the Author Just before the Book Went to Press; and Whewell’s Dialogue Rebutting His Critics, Reprinted from the Second Edition. Edited with new introductory material by Michael Ruse. Chicago: University of Chicago Press, 2001.
Becher, Harvey W. “William Whewell and Cambridge Mathematics.” Historical Studies in the Physical Sciences 11 (1980): 1–48.
Brooke, John H. “Natural Theology and the Plurality of Worlds: Observations on the Brewster-Whewell Debate.” Annals of Science 34 (1977): 221–286.
———. “Indications of a Creator: Whewell as Apologist and Priest.” In William Whewell: A Composite Portrait, edited by Menachim Fisch and Simon Schaffer. Oxford: Clarendon Press, 1991. Explores the complexities for Whewell of the empirical argument from design, including the superiority of revelation as a way of knowing God’s existence.
Butts, Robert E. Historical Pragmatics: Philosophical Essays. Dordrecht and Boston: Kluwer, 1993. Reprints thirteen articles by Butts, five dealing with Whewell. Fisch, Menachim. William Whewell: Philosopher of Science. Oxford: Clarendon Press, 1991.
———, and Simon Schaffer, eds. William Whewell: A Composite Portrait. Oxford: Clarendon Press, 1991. Contains thirteen chapters by thirteen authors.
Henderson, James P. Early Mathematical Economics: William Whewell and the British Case. Lanham, MD: Rowman & Littlefield, 1996.
Marsden, Ben. “‘The Progeny of These Two “Fellows”’: Robert Willis, William Whewell, and the Sciences of Mechanism, Mechanics, and Machinery in Early Victorian Britain.” British Journal for the History of Science 37 (2004): 401–434.
Reidy, Michael. Tides of History: Ocean Science and Her Majesty’s Navy. Chicago: University of Chicago Press, forthcoming 2008. Places Whewell’s tidal research thoroughly within its practical and social contexts.
Ross, Sydney. “‘Scientist’: The Story of a Word.” Annals of Science 18 (1962): 65–85.
Ruse, Michael. “William Whewell and the Argument from Design.” Monist 60 (1977): 244–268.
Schneewind, Jerome B. “Whewell’s Ethics.” American Philosophical Quarterly Monograph Series 1 (1968): 108–141.
Smith, Crosbie. “Geologists and Mathematicians: The Rise of Physical Geology.” In Wranglers and Physicists: Studies on Cambridge Physics in the Nineteenth Century, edited by Peter M. Harman. Manchester, U.K.: Manchester University Press, 1985.
Snyder, Laura J. “William Whewell.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. Spring 2004. Available from http://plato.stanford.edu/archives Discusses and evaluates previous interpretations of Whewell’s philosophy of science.
———. Reforming Philosophy: A Victorian Debate on Science and Society. Chicago: University of Chicago Press, 2006. Examines the many aspects of the Whewell-Mill debate.
Wettersten, John R. Whewell’s Critics: Have They Prevented Him from Doing Good? Edited by James A. Bell. Amsterdam: Rodopi, 2005.
Wilson, David B. “Herschel and Whewell’s Version of Newtonianism.” Journal of the History of Ideas 35 (1974): 79–97.
———. “Convergence: Metaphysical Pleasure versus Physical Constraint.” In William Whewell: A Composite Portrait, edited by Menachim Fisch and Simon Schaffer. Oxford: Clarendon Press, 1991.
———. “Arbiters of Victorian Science: George Gabriel Stokes and Joshua King.” In From Newton to Hawking: A History of Cambridge University’s Lucasian Professors of Mathematics, edited by Kevin C. Knox and Richard Noakes. Cambridge, U.K.: Cambridge University Press, 2003. Indicates various ways in which Whewell’s ideas and committees helped shape the context of two of Cambridge’s Lucasian professors.
Wise, M. Norton, and Crosbie Smith. “Work and Waste: Political Economy and Natural Philosophy in Nineteenth Century Britain (II).” History of Science 27 (1989): 391–449. Discusses Whewell at length.
Yanni, Carla. “On Nature and Nomenclature: William Whewell and the Production of Architectural Knowledge in Early Victorian Britain.” Architectural History 40 (1997): 204–221.
Yeo, Richard. Defining Science: William Whewell, Natural Knowledge, and Public Debate in Early Victorian Britain. Cambridge, U.K.: Cambridge University Press, 1993.
David B. Wilson
(b. Lancaster, England, 24 May 1794; D. Cambridge, England, 6 March 1866),history and philosophy of science, physical astronomy, science education.
Whewell was the eldest son of a master carpenter, who hoped his son would follow him in his trade. Early displays of intellectual ability convinced the father, however, to send him to the grammar school at Heversham, in Westmorland. In 1812 Whewell began a lifelong career at Trinity College, Cambridge, where he received a classical literary education and what he soon recognized as outdated training in mathematics and science. After election as fellow of the college in 1817, Whewell took his M.A. degree in 1819 and his D.D. degree in 1844. He was ordained deacon around 1825 and then priest (1826) in the Church of England. In 1841 Whewell was appointed master of Trinity, a post he held until his death. He was named vice-chancellor of the University of Cambridge in 1842 and again in 1855. In 1841 he married Cordelia Marshall, who died in 1855; three years later he married Lady Evering Affleck.
Tall and massively built, Whewell enjoyed good health throughout his life. Friends and foes alike admired his intelligence and breadth of scholarship, his capacity for profound affection, and his generosity. Whewell was self-consciously awkward in dealing with others, however, and he cannot be said to have been a generally popular figure at Cambridge. There can be no doubt about his qucik-tempered resentament of criticism, his autocratic and often arbitrary exercise of academic power, and his jealous defense of his own position. Nevertheles, he was widely recongnized as one of the central figures in Victorian science. He was a member or honorary member of at least twenty-five British and foreign scientific societies, including the Royal Society, the Royal Astronomical Society, the Royal Irish Academy, and the Royal Society of Edinburgh.
The range of Whewell’s scholarly and scientific interests was immense. He composed sermons, English hexameter verses, translations of German literary works, and essays on architecture, theology, philosophy, political economy, and university education. He translated Plato’s dialogues into English.
In response to the need for more accurate instruments for use in meteorology Whewell invented a self-registering anemometer that measured the direction, velocity, and temporal duration of the velocity of the wind. Anemometers in use at the time measured direction and pressure of the wind, but did not permit charting of the total movement of the air as did Whewell’s device. Whewell’s instrument failed to show accurate results in measuring slow movements of the air. The technical problem was solved by the Reverend T. R. Robinson in 1846 by modifying Whewell’s instrument by the introduction of the now-familiar windmill with hemispherical cups.
Whewell was especially adept in coining new scientific terms. In correspondence with Michael Faraday he contributed “ion” , “anode” , and “cathode,” among others. To geology he contributed “Eocene,” “Miocene,” and “Pliocene,” and he introduced the terms “physicist” and “scientist.”
Apart from his teaching, Whewell’s major work in the decade beginning with 1819 was in science education, architecture, experimental physics, and mineralogy. As a member of a group of reformers in which John Herschel, Charles Babbage, and George Peacock were prominent, Whewell contributed to the attempt to bring the mathematical methods of the French analysts into Cambridge scientific education. In textbooks on mechanics and dynamics, he introduced the calculus for solving problems, while insisting that analysis is no substitute for experimental physics. The reformers were successful; as a college tutor in the 1820’s and later as a major figure in guiding educational changes at Cambridge, Whewell contributed to the development of British physics and to the centrality of Cambridge in that development. In architecture Whewell attempted to refute the contention that the pointed arch is the defining property of Gothic style, arguing that in the history of German architecture the flying buttress, not the pointed arch, completed the transition from Romanesque to high Gothic.
In 1826 and 1828 Whewell and Airy made unsuccessful attempts to measure the density of the earth at a copper mine in Cornwall. Of greater importance was Whewell’s work in mineralogy. In a paper read before the Royal Society in 1824, Whewell, according to Herbert Deas, “laid the foundations of mathematical crystallography.” His system for calculating the angles of planes of crystals assumed that crystals are aggregates of small rhomboids that can be thought to shrink below the level of possible measurement, thus suggesting that crystals are latticelike. In 1825 Whewell visited Mohs in Germany. In 1828, the year in which Whewell became professor of mineralogy, he published a revision of Mohs’s system of mineralogical classification.
Between 1833 and 1850 Whewell published fourteen memoirs on the tides. Before the 1830’s little reliable observation of the tides had been undertaken: and the two leading theories, the Newton-Bernoulli equilibrium theory and the Laplace dynamical theory, were largely untested. The British Admiralty and the British Association initiated work on the tides that soon became international in scale. Whewell, with the help of John Lubbock, received and interpreted observations from all over the world; their work earned them the Royal Medal. Whewell’s investigation of the tides began with an attempt to apply Thomas Young’s idea of cotidal lines to the world’s oceans. Had the idea applied, it would have allowed plotting the movements of tidal waves through all the oceans on the basis of initial observations of simultaneous high tides at different places. Whewell abandoned the idea in its general application, however, although the application of the idea did obtain some results for small, confined bodies of water and for shorelines.
Whewell stressed the “diurnal inequality” of the tides (“that which makes the tide of the morning and evening of the same day at the same place, differ both in height and time of high water, according to a law depending on the time of the year”). He showed large variations in this effect in accordance with local circumstances and thought the inequality to be more basic than other features of the tides. From the failure of the idea of cotidal lines and the empirical prominence of the daily inequality, Whewell concluded that no theory of physical astronomy could account for tidal phenomena in a general way. Instead, the variety and multiplicity of the data suggested that detailed study of each individual shoreline was required. Given this conclusion, it is not surprising that Whewell’s work did not contribute directly to theory of the tides. Consistent with the principles of his own philosophy of science, however, he could regard himself as having fathered the science of the tides. He thought that the beginning of a science involved the laborious collection and organization of data; full theoretical generality, if any, would come later.
From the late 1830’s until his death, Whewell worked mainly in the history and philosophy of science. His three-volume History of the Inductive Sciences appeared in 1837; in 1838 he was appointed professor of moral philosophy; and the first edition of his two-volume the Philosophy of the Inductive Sciences, Founded Upon Their History was published in 1840. Both the History and the Philosophy were ambitious works, and together they constitute Whewell’s major scholarly achievement. The History had no rivals in its day and remains, despite unevenness, one of the important surveys of science from the Greeks to the nineteenth century. Whewell appreciated the importance of Greek science, especially astronomy, but showed typical disregard for the contributions of medieval scientists. His assessment of the importance of contributions of such major figures as Galileo and Descartes suffers from a heavy intrusion of religious and philosophical biases. But his treatment of Newton and other modern mathematical scientists is fair and sometime brilliant, and is based throughout upon detailed considerations of texts. Whewee’s Philosophy stimulated major philosophical exchanges between its author and Sir John Herschel, Augustus De Morgan, Henry L. Mansel, and John Stuart Mill. Alongside Mill’s System of Logic and Herschel’s Preliminary Discourseon the Study of Natural Philosophy, the work ranks as one of the masterpieces of Victorian philosophy of science.
Whewell’s effort in these works was unique in his attempt to derive a philosophy of science from the general features of the historical development of empirical science. The importance of this attempt has not been fully appreciated. Whewell thought that the history of science displayed a progressive movement from less to more general theories, from imperfectly understood facts to basic sciences built upon a priori foundations that he called “Fundamental Ideas.” All science was theoretical in that no body of data comes to us selforganized; even collection of data involves the imposition of a guiding interpretive idea. Major advances in science occur in what Whewell called an “Inductive Epoch,” a period in which the basic ideas of a science are well understood by one or more scientists, and in which the generality and explanatory power of a science are seen to be much more illuminating than those of rival theories. Each such “Epoch” had a “Prelude,” a period in which older theories experienced difficulties and new ideas were seen to be required, and a “Sequel,” a period in which the new theory was applied and refined.
Largely ignoring the British tradition of empiricist philosophy and methodology, Whewell erected a philosophy of science upon his understanding of history that derived partly from Kant and Plato, and partly from an anachronistic theological position. Like his British predecessors, he thought that induction was the basic method of science. He understood induction not as a form of inference from particulars to generalizations, but as a conceptual act of coming to see that a group of data can best be understood and organized (his term was “colligated”) under a certain idea. Furthermore, induction was demonstrative in that it yields necessary truths, propositions the logical opposites of which cannot be clearly conceived. The zenith of the inductive process was reached when a “consilience of inductions” took place-when sets of data previously considered disjoint came to be seen as derivable from the same, much richer theory. Although Whewell thought that the paradigm form of a scientific theory was deductive, he departed from the orthodox hypothetico-deductivist view of science by claiming that tests of the acceptability of given theories are extraevidential, based on considerations of simplicity and consilience. He made some attempt to justify the necessity of the conclusions that induction yields by arguing for the identity of facts and theories, and for the theological view that we know the world the way it is because that is the way God made it.
In physical astronomy Whewell’s work on the tides ranks second only to that of Newton. Also of great importance was his lifelong effort to modernize and improve science education at Cambridge. The achievement in history and philosophy of science probably is less significant, although recent revival of interest in Whewell has centered mainly upon his insights in philosophy of science and methodology. Interest is growing in the interrelations of history and philosophy of science; and so long as this interest continues to be fruitful, it will be well worthwhile considering what Whewell had to say on the nature of scientific discovery, inductive methodology, and the characteristics of scientific progress.
I. Original Works. Whewell’s papers are in the Wren Library, Trinity College, Cambridge. A catalog of these papers is available (to libraries) from the Royal commission on Historical Manuscripts, Quality House, Quality Court, Chancery Lane, London WC2A 1 HP. Unfortunately no complete bibliography of his works exists, although fairly complete ones in history and philosophy of science are available. The projected 10-vol. collection of facsimiles. The Historical and Philosophical Works of William Whewell, G. Buchdahl and L. L. Laudan, eds. (London, 1967–), will help make his works in those areas more easily available. A selection of Whewell’s central works in methodology appears in William Whewell’s Theory of Scientific Method, Robert E. Butts, ed. (Pittsburgy, 1968).
Whewell’s major writings in science include An Elementary Treatise on Mechanics (Cambridge, 1819); A Treatise on Dynamics (Cambridge, 1823); “A General Method of Calculating the Angles Made by Any Planes of Crystals, and the Laws According to Which They Are Formed,” in Philosophical Transactions of the Royal Society, 115 (1825), 87–130; An Essay on Mineralogical Classification and Nomenclature; With Tables of the Orders and Species of Minerals (Cambridge, 1828); Architectural Notes on German Churches, With Remarks on the Origin of Gothic Architecture (Cambridge, 1830); Analytical Statics (Cambridge, 1833); “Essay Towards a First Approximation to a Map of Cotidal Lines,” in Philosophical Transactions of the Royal Society, 123 (1833), 147–236; “On the Results of an Extensive System of Tide Observations Made on the Coasts of Europe and America in June 1835,” ibid., 126 (1836), 289–341; “On the Diurnal Inequality Wave Along the Coasts of Europe,” ibid., 127 (1837), 227–244; The Mechanical Euclid (Cambridge, 1837); and “On the Results of Continued Tide Observations at Several Places on the British Coasts,” in Philosophical Transactions of the Royal Society, 140 (1850), 227–233.
Major writings in history and philosophy of science include “On the Nature of the Truth of the Laws of Motion,” in Transactions of the Cambridge Philosophical Society, 5 (1834), 149–172; History of the Inductive Sciences, 3 vols. (London, 1837); The Philosophy of the Inductive Sciences, Forsuled Upon Their History, 2 vols, (London, 1840), the 3rd ed. of which appeared as 3 separate vols.: The History of Scientific Ideas, 2 pts. (London, 1858), Norusn organon renovatum (London, 1858), and On the Philosophy of Discovery (London, 1860).
II. Secondary Literature. There is very little informed and up-to-date commentary on Whewell’s scientific achievements; in recent years his philosophy of science has begun to receive the attention it deserves. There are two biographies: Mrs. Stair Douglas, Life and Selections From the Correspondence of William Whernell (London, 1881), on his personal, including university, life: and Isaac Todhunter, William Whenell (London, 1876), which surveys his scientific and scholarly work. Both works contain large collections of letters; Todhunter is the best source of bibliography. Of considerable interest are Robert Robson, “William Whewell, F.R.S. (1794-1866), I. Academic Life,” and Walter F. Cannon “II. Contributions to Science and Learning,” in Notes and Records. Royal Society of London, 19 , no. 2 (Dec. 1964), 168–191. Cannon’s paper is the first attempt at a general assessment of Whewell’s scientific achievements. Robert Willis, Remarks on the Architecture of the Middle Ages, Especially of Italy (Cambridge, 1835), extends and improves upon Whewell’s work in architecture. George Airy, “Tides and Waves,” in Encyclopaedia metropolitana, V (London, 1845), secs. VII and VIII, esp. arts. 496 and 571, praises Whewell’s work on the tides, especially his methods of graphical representation of results of observations. Airy preferred the Laplace theory, however, and argued against Whewell’s continuing reliance upon the Bernoulli equilibrium theory. Herbert Deas, “Crystallography and Crystallographers in Early 19th-Century England,” in Centaurus, 6 (1959), 129–148, presents a sympathetic evaluation of Whewell’s work in that area.
Whewell’s philosophy attracted no disciples; and except for various references to his work in the writings of C.S. Peirce, his system received no serious study until the early 1930’s. There are two book-length studies: Robert Blanché, Le rationalisme de Whewell (Paris, 1935); and Silvestro Marcucci, L’ “idealismo” scientifico di William Whewell (Pisa, 1963). British and American studies of Whewell’s philosophy in the context of contemporary problems in philosophy of science have taken the form of monographs and papers on specific problems. A potentially quite productive exchange of views on Whewell’s concept of consilience of inductions exemplifies the richness and novelty of his insights in methodology. Among the relevant papers are Robert E. Butts, “Whewell’s Logic of Induction.” in Ronald Giere and Richard Westfall, eds., Foundations of Scientific Methods: The Nineteenth Century (Bloomington, Ind., 1973), 53–85; Mary Hesse, “Consilience of Inductions,” in Imre Lakatos, ed., The Problem of Inductive Logic (Amsterdam, 1968), 232–247; and Larry Laudan, “William Whewell on the Consilience of Inductions,” in Monist, 55 , no. 3 (1971), 368–391
Robert E. Butts
William Whewell (1794–1866), English mathematical economist, was born in Lancashire. He was educated at Trinity College, Cambridge, and remained there as a fellow and tutor. In 1841 he was appointed master of the college. He served from 1828 to 1832 as professor of mineralogy and from 1838 to 1855 as professor of moral philosophy.
Whewell was primarily a philosopher and a mathematician, and he published his major works in these fields. He was also, however, one of a small group of British authors, which included Samuel Turner, T. Perronet Thompson, Denis G. Lube, and the anonymous “E.R.,” who made contributions to the early development of mathematical economics. Whewell’s contribution was contained in a paper, “Mathematical Exposition of Some Doctrines of Political Economy,” delivered before the Cambridge Philosophical Society in 1829. In this paper, he pointed out that some parts of the science of political economy could be presented in a more systematic and connected form, and also more clearly and simply, by the use of mathematical language.
To illustrate his argument, Whewell used mathematics to discuss Ricardo’s theory of the incidence of a tax on wages. Ricardo had argued against Adam Smith’s view that a tax on wages would ultimately be borne by the employer of labor. Such a supposition, Ricardo asserted, would lead to the absurd conclusion that, as a rise in the prices of goods due to a rise in wages would again operate on wages, the action and reaction first of wages on goods and then of goods on wages would continue “without any assignable limits” (Ricardo  1962, p. 301).
Whewell showed in his 1830 paper that if Ricardo had considered the mathematical implications of his theory, he would have found that a limitless rise in prices and wages was not only absurd but impossible. To demonstrate this, he assumed that wages would rise by the whole amount of the tax, which would be, say, 1/10. On the assumption that only a part, say 1/2, of the value of goods is wages, the rise in the price of manufactured goods would be 1/20. And on the assumption that only 1/2 of the laborers’ consumption is manufactured goods, the resulting rise in wages due to the rise in price would be 1/40, and so on. The whole rise in wages would then be
and the whole rise in the price of goods would be
Whewell concluded that as both these geometrical series have limits, Ricardo’s argument about quantities with no assignable limits is not valid. A similar argument can be found in T. Perronet Thompson’s An Exposition of Fallacies on Rent, Tithes, etc. (see 1826, pp. 39–40).
Whewell also sought in his paper to make a distinction between the moral axioms of political economy and the conclusions that might be deduced from them, a task for which mathematics could be of considerable help.
Using certain axioms as a foundation, Whewell discussed the difference between those who, following Ricardo, maintained that all taxes on the produce of land were ultimately paid by the consumer and those who maintained that most such taxes were paid by the landlord. He showed that the tax would fall solely on rent only in the absence of marginal soil. The existence of marginal soil, however, would mean that the tax would not only fall on rent but also lead to a diminution of the return on capital and an increase of price.
In a second memoir to the Cambridge Philosophical Society in 1831, Whewell presented a mathematical exposition of Ricardo’s doctrines and in a third memoir in 1850, an examination of questions of demand, supply, price, and international exchange.
Whewell was more than a translator of existing doctrine into mathematical language, as he has sometimes been described. His contributions to mathematical economics and, especially, his first approximation to a solution of the problem of the dynamic stability of equilibrium, in the discussion of the effect of a tax on wages, are really noteworthy.
(1819) 1847 An Elementary Treatise on Mechanics. 7th ed. London: Whittaker.
1823 A Treatise on Dynamics, Containing a Considerable Collection of Mechanical Problems. Cambridge:Deighton.
1830 Mathematical Exposition of Some Doctrines of Political Economy. Cambridge Philosophical Society, Transactions 3:191–230.
1831 Mathematical Exposition of Some of the Leading Doctrines in Mr. Ricardo’s Principles of Political Economy and Taxation. Cambridge Philosophical Society, Transactions 4:155–198.
1832 An Introduction to Dynamics, Containing the Laws of Motion and the First Three Sections of the Principia. Cambridge: Deighton.
(1837) 1890 History of the Inductive Sciences, From the Earliest to the Present Time. 3d ed., with additions. New York: Appleton.
(1840) 1847 The Philosophy of the Inductive Sciences, Founded Upon Their History. 2 vols. A new edition, with corrections and additions, and an appendix containing philosophical essays previously published. London: Parker.
1850 Mathematical Exposition of Some Doctrines of Political Economy. Cambridge Philosophical Society, Transactions 9, part 1:128–149; part 2:1–7.
Ricardo, David (1817) 1962 Principles of Political Economy and Taxation. London: Dent; New York: Dutton. → A paperback edition was published in 1963 by Irwin.
Robertson, Ross M. 1949 Mathematical Economics Before Cournot. Journal of Political Economy 57:523–536.
Schumpeter, Joseph A. (1954) 1960 History of Economic Analysis. Edited by E. B. Schumpeter. New York: Oxford Univ. Press.
Theocharis, Reghinos D. 1961 Early Developments in Mathematical Economics. London: Macmillan.
Thompson, T. Perronet (1826)1832 The True Theory of Rent, in Opposition to Mr. Ricardo and Others, Being an Exposition of Fallacies on Rent, Tithes, etc. 9th ed. London: Heward. → First published as An Exposition of Fallacies on Rent, Tithes, etc. Containing an Examination of Mr. Ricardo’s Theory of Rent….