Whewell described the reasoning just as it appeared to a man deeply conversant with several branches of science as only a genuine researcher can know them, and adding to that knowledge a full acquaintance with the history of science. These results, as might be expected, are of the highest value, although there are important distinctions and reasons which he overlooked. John Stuart Mill endeavored to explain the reasonings of science by the nominalistic metaphysics of his father. The superficial perspicuity of that kind of metaphysics rendered his logic extremely popular with those who think, but do not think profoundly; who know something of science, but more from the outside than the inside, and how for one reason or another delight in the simplest theories even if they fail to cover the facts.
Quite a good description of the Omniscientist, I'd say; and I like the description of Mill. He says elsewhere:
I am very far from holding that experience is our only light; Whewell's views of scientific method seem to me truer than Mill's; so much so that I should pronounce the known principles of physics to be but a development of original instinctive beliefs.
This is C. S. Peirce, quoted in John Wettersten, Whewell's Critics, Rodopi (New York: 2005) 102. (The citations are to Peirce 1960, vol. I, sect. 70, and Peirce 1960, vol. I, sect. 404.) Wettersten's work is a good history of the non-reception of Whewell's philosophy of science after the general prevalence of Mill's Baconian/Newtonian inductivism.