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6. What is the difference between these
methods
and Holmes's?
Holmes's reasoning by elimination has a strong affinity with Mill's; his reasoning backward, i.e. imagining several hypotheses for explaining the given facts and selecting the best one, also has a strong affinity with Whewell's idea of the colligation of facts. But however strong these affinities may be, there is one essential factor which is present in Holmes's method but absent in Herschel-Mill's or Whewell's method. That is the consideration of probabilities of hypotheses, and of the probabilistic connections between hypotheses and data. Only by taking these into consideration, it can make sense to speak of "the balance of probabilities."
Comments: Unlike Whewell and Mill, who were unsympathetic to statistical or probabilistic methods, Herschell clearly saw the merits of these methods in a well-known article in Edinburgh Review (1850), in which he reviewed Quetelet's work. [Maxwell is said to be influenced by this article, and began his research on the kinetic theory of gases.] However, we can find no such views in his 1830 book on scientific methodology (and we know that he was unsympathetic or hostile to Darwin's theory of natural selection, which essentially depends on a statistical principle). Thus Herschel comes in between one extreme of Whewell and Mill, and the other extreme of de Morgan and Jevons.
June 21, 1998; last modified, April 16, 2006. (c) Soshichi Uchii
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