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What is most often remarked about Whewell is the breadth of his endeavors. In a time of increasing specialization, Whewell appears a throwback to an earlier era when natural philosophers dabbled in a bit of everything. He published work in the disciplines of mechanics, physics, geology, astronomy, and economics, while also finding the time to compose poetry, author a Bridgewater Treatise, translate the works of Goethe, and write sermons and theological tracts. In mathematics, Whewell introduced what is now called the Whewell equation, an equation defining the shape of a curve without reference to an arbitrarily chosen coordinate system. He also organized thousands of volunteers internationally to study ocean tides, in what is now considered one of the first citizen science projects. He received the Royal Medal for this work in 1837.
His best-known works are two voluminous books that attempt to systematize the development of the sciences, History of the Inductive Sciences (1837) and The Philosophy of the Inductive Sciences, Founded Upon Their History (1840, 1847, 1858-60). While the History traced how each branch of the sciences had evolved since antiquity, Whewell viewed the Philosophy as the "Moral" of the previous work as it sought to extract a universal theory of knowledge through history.
In the latter, he attempted to follow Francis Bacon's plan for discovery. He examined ideas ("explication of conceptions") and by the "colligation of facts" endeavored to unite these ideas with the facts and so construct science. This colligation is an "act of thought", a mental operation consisting of bringing together a number of empirical facts by "superinducing" upon them a conception which unites the facts and renders them capable of being expressed in general laws. Whewell refers to as an example Kepler and the discovery of the elliptical orbit: the orbit's points were colligated by the conception of the ellipse, not by the discovery of new facts. These conceptions are not "innate" (as in Kant), but being the fruits of the "progress of scientific thought (history) are unfolded in clearness and distinctness".
Upon these follow special methods of induction applicable to quantity: the method of curves, the method of means, the method of least squares and the method of residues, and special methods depending on resemblance (to which the transition is made through the law of continuity), such as the method of gradation and the method of natural classification. In Philosophy of the Inductive Sciences Whewell was the first to use the term "consilience" to discuss the unification of knowledge between the different branches of learning.
Opponent of English empiricism
Here, as in his ethical doctrine, Whewell was moved by opposition to contemporary English empiricism. Following Immanuel Kant, he asserted against John Stuart Mill the a priori nature of necessary truth, and by his rules for the construction of conceptions he dispensed with the inductive methods of Mill. Yet, according to Laura J. Snyder, "surprisingly, the received view of Whewell's methodology in the 20th century has tended to describe him as an anti-inductivist in the Popperian mold, that is it is claimed that Whewell endorses a 'conjectures and refutations' view of scientific discovery. Whewell explicitly rejects the hypothetico-deductive claim that hypotheses discovered by non-rational guesswork can be confirmed by consequentialist testing. Whewell explained that new hypotheses are 'collected from the facts' (Philosophy of Inductive Sciences, 1849, 17)". In sum, the scientific discovery is a partly empirical and partly rational process; the "discovery of the conceptions is neither guesswork nor merely a matter of observations", we infer more than we see.
One of Whewell's greatest gifts to science was his wordsmithing. He often corresponded with many in his field and helped them come up with new terms for their discoveries. In fact, Whewell came up with the term scientist itself in 1833, and it was first published in Whewell's anonymous 1834 review of Mary Somerville's On the Connexion of the Physical Sciences published in the Quarterly Review. (They had previously been known as "natural philosophers" or "men of science").
Whewell was prominent not only in scientific research and philosophy but also in university and college administration. His first work, An Elementary Treatise on Mechanics (1819), cooperated with those of George Peacock and John Herschel in reforming the Cambridge method of mathematical teaching. His work and publications also helped influence the recognition of the moral and natural sciences as an integral part of the Cambridge curriculum.
In general, however, especially in later years, he opposed reform: he defended the tutorial system, and in a controversy with Connop Thirlwall (1834), opposed the admission of Dissenters; he upheld the clerical fellowship system, the privileged class of "fellow-commoners," and the authority of heads of colleges in university affairs.
He opposed the appointment of the University Commission (1850) and wrote two pamphlets (Remarks) against the reform of the university (1855). He stood against the scheme of entrusting elections to the members of the senate and instead, advocated the use of college funds and the subvention of scientific and professorial work.
Aside from Science, Whewell was also interested in the history of architecture throughout his life. He is best known for his writings on Gothic architecture, specifically his book, Architectural Notes on German Churches (first published in 1830). In this work, Whewell established a strict nomenclature for German Gothic churches and came up with a theory of stylistic development. His work is associated with the "scientific trend" of architectural writers, along with Thomas Rickman and Robert Willis.
He paid from his own resources for the construction of two new courts of rooms at Trinity College, Cambridge, built in a Gothic style. The two courts were completed in 1860 and (posthumously) in 1868, and are now collectively named Whewell's Court (in the singular).
Between 1835 and 1861 Whewell produced various works on the philosophy of morals and politics, the chief of which, Elements of Morality, including Polity, was published in 1845. The peculiarity of this work--written from what is known as the intuitional point of view--is its fivefold division of the springs of action and of their objects, of the primary and universal rights of man (personal security, property, contract, family rights, and government), and of the cardinal virtues (benevolence, justice, truth, purity and order).
Among Whewell's other works--too numerous to mention--were popular writings such as:
the third Bridgewater Treatise, Astronomy and General Physics considered with reference to Natural Theology (1833),
the two volumes treatise The Philosophy of the Inductive Sciences: Founded Upon Their History (1840),
But with regard to the material world, we can at least go so far as this--we can perceive that events are brought about not by insulated interpositions of Divine power, exerted in each particular case, but by the establishment of general laws.
In the 1857 novel Barchester Towers Charlotte Stanhope uses the topic of the theological arguments, concerning the possibility of intelligent life on other planets, between Whewell and David Brewster in an attempt to start up a conversation between her impecunious brother and the wealthy young widow Eleanor Bold.
^Lewis, Christopher (2007). "Chapter 5: Energy and Entropy: The Birth of Thermodynamics". Heat and Thermodynamics: A Historical Perspective. United States of America: Greenwood Press. p. 95. ISBN978-0-313-33332-3.
^GRO Register of Deaths: MAR 1866 3b 353 CAMBRIDGE - William Whewell, aged 71
^Full bibliographical details are given by Isaac Todhunter, William Whewell: An Account of his Writings, with a selection from his literary and scientific correspondence, London: Macmillan, 1876, (volume 1, volume 2). See also Mrs Stair Douglas The Life and Selections from the Correspondence of William Whewell, D.D., London: C. Kegan Paul & Co., 1881, at Internet Archive
^L.J. Snyder, entry: "W. Whewell" in "Stanford Encyclopedia of Philosophy".
^W. Whewell "The Philosophy of the Inductive Sciences, Founded Upon Their History" (1860, 373), London J.W. Parker.
^L.J. Snyder, entry: "Whewell" in "Stanford Encyclopedia of Philosophy".
^W. Whewell "The History of Scientific Ideas", 1858, I, 46, two volumes, London: John W. Parker.
Losee, J. (1983), "Whewell and Mill on the relation between philosophy of science and history of science", Studies in History and Philosophy of Science (published June 1983), 14 (2), pp. 113-126, doi:10.1016/0039-3681(83)90016-X, PMID11615935
Fisch, M. (1991), William Whewell Philosopher of Science, Oxford: Oxford University Press.
Fisch, M. and Schaffer S. J. (eds.) (1991), William Whewell: A Composite Portrait, Oxford: Oxford University Press.
Henderson, James P. (1996). Early Mathematical Economics: William Whewell and the British Case. Lanham: Rowman & Littlefield. ISBN978-0-8476-8201-0.
Metcalfe, J. F. (1991), "Whewell's developmental psychologism: a Victorian account of scientific progress", Studies in History and Philosophy of Science (published March 1991), 22 (1), pp. 117-139, doi:10.1016/0039-3681(91)90017-M, PMID11622706
Morrison, M. (1997), "Whewell on the ultimate problem of philosophy", Studies in History and Philosophy of Science Part A, 28 (3), pp. 417-437, doi:10.1016/S0039-3681(96)00028-3
Ruse, M. (1975), "Darwin's debt to philosophy: an examination of the influence of the philosophical ideas of John F. W. Herschel and William Whewell on the development of Charles Darwin's theory of evolution", Studies in History and Philosophy of Science (published June 1975), 6 (2), pp. 159-181, doi:10.1016/0039-3681(75)90019-9, PMID11615591
Yeo, R. (1991), Defining Science: William Whewell, Natural Knowledge and Public Debate in Early Victorian Britain, Cambridge: Cambridge University Press.
Zamecki, Stefan, Komentarze do naukoznawczych pogl?dów Williama Whewella (1794-1866): studium historyczno-metodologiczne [Commentaries to the Logological Views of William Whewell (1794-1866): A Historical-Methodological Study], Warsaw, Wydawnictwa IHN PAN, 2012, ISBN978-83-86062-09-6, English-language summary: pp. 741-43.