William Whewell was born on 24 May 1794 and died on 6 March 1866. Harvey Becher in the essay “William Whewell’s Odyssey: From Mathematics to Moral Philosophy” gives a good sense of both the polymath quality of Whewell’s inquiries and the fundamental reality that his interdisciplinary stance reveals about Victorian science. Becher notes, in a somewhat “heroic” fashion, “During his fifty-four years at Trinity College in Cambridge University, in an age when knowledge reverberated throughout an intellectual world unencumbered by barriers erected by disciplines narrowly defined as means and ends of themselves, Whewell incessantly studied and promoted the science and pedagogy which engulfed him.” (See William Whewell: A Composite Portrait, p. 1.) Whewell wrote on subjects as diverse as geology, mineralogy, mechanics, mathematics, political economy, political theory, and architecture.
Whewell was both a founding member and one of the first presidents of the British Association for the Advancement of Science, a fellow of the Royal Society, a president of the Geological Society, and was the Master, with intermittent controversy, of Trinity College, Cambridge. He exchanged ideas and letters with such well-known men of Victorian science as John Herschel and Charles Lyell, and exerted considerable influence on Michael Faraday. Whewell’s Bridgewater Treatise, Astronomy and general physics considered with reference to Natural Theology, published in 1830, was an important text in natural theology. His Of the Plurality of Worlds, published in 1853, sought to assess the limits of human agency given the new accounts of the universal action of geological laws in Lyell’s “uniformitarian” picture of the earth and to eliminate the threat to man’s exceptional place in the universe given the possibility of life on alien worlds.
Philosophers and historians of science know Whewell today in the context of John Stuart Mill’s attack on his The Philosophy of the Inductive Sciences, founded upon their history, published in 1840. The specific issue, according to Peter Achinstein, in his “Hypotheses, Probability, and Waves” in The British Journal for the Philosophy of Science, was problem of “verification” or the ability of the hypothesis to explain known, and to predict, future phenomenon. Mill, in his System of Logic, defined hypothesis as “any supposition which we make (either without actual evidence, or on evidence avowedly insufficient) in order to endeavor to deduce from it conclusions in accordance with facts which are known to be real; under the idea that if the conclusions to which the hypothesis leads are known truths, the hypothesis itself either must be, or at least is likely to be, true.” ([1843]: A System of Logic. 1959 Impression. Longmans, Green, and Co.)
The “method of hypothesis” consisted in assessing the consequences of the hypothesis. If the consequences derived from the hypothesis were found to be true, the hypothesis was true, or at the very least, probable. Mill, as Achinstein notes, “rejects this as a method for establishing either the truth or the probability of hypotheses, on the grounds that conflicting hypotheses are possible from which the same true consequences can be derived; unless such alternatives can be excluded, nothing can be inferred about the truth or probability of any hypothesis being considered” (Achinstein, p. 73.) The fact that a hypothesis could explain given phenomenon only assured that a hypothesis could be true insofar as it fit the evidence observed thus far. As Achinstein concluded in his later article, “Waves and Scientific Method,” this type of reasoning was a “simple hypothesis.” (PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1992, Volume Two: Symposia and Invited Papers (1992), pp. 193-204.)
Whewell, however, had a four-stage model of hypothetical deduction, which was more complex than Mill’s characterization of the method of hypothesis. For Whewell, a hypothesis first had to explain given phenomenon or “the phenomenon which initially prompted it” (Achinstein, pg. 194.) Second, a hypothesis should also be able to predict new phenomenon. So much better if the hypothesis, third, could explain or predict phenomenon of a distinct class from that which it was originally designed to explain. If this occurred than it represented, in Whewell’s phrase, “a concilliance of inductions.” The fourth test for the efficacy of a hypothesis was the degree to which a series of interrelated hypotheses, as a theoretical system, became simpler and more coherent over time. If a hypothesis met all four of these criteria then, for Whewell, the hypothesis was virtually certain (Achinstein, p.194.)