It may be objected, indeed, as the Spectator objects, that Mill’s System of Logic is particularly strong in the discussion of the psychological foundations of reasoning, so that Mill would appear to have successfully treated that which I feel myself to be incapable of attempting at present. If Mill’s analysis of knowledge is correct, then I have nothing to say in excuse for my own deficiencies. But it is well to do one thing at a time, and therefore I have not occupied any considerable part of this book with controversy and refutation. What I have to say of Mill’s logic will be said in a separate work, in which his analysis of knowledge will be somewhat minutely analysed. It will then be shown, I believe, that Mill’s psychological and philosophical treatment of logic has not yielded such satisfactory results as some writers seem to believe.18
Various minor but still important criticisms were made by Professor Robertson, a few of which have been noticed in the text (pp. 27, 101). In other cases his objections hardly admit of any other answer than such as consists in asking the reader to judge between the work and the criticism. Thus Mr. Robertson asserts19 that the most complex logical problems solved in this book (up to p. 102 of this edition) might be more easily and shortly dealt with upon the principles and with the recognised methods of the traditional logic. The burden of proof here lies upon Mr. Robertson, and his only proof consists in a single case, where he is able, as it seems to me accidentally, to get a special conclusion by the old form of dilemma. It would be a long labour to test the old logic upon every result obtained by my notation, and I must leave such readers as are well acquainted with the syllogistic logic to pronounce upon the comparative simplicity and power of the new and old systems. For other acute objections brought forward by Mr. Robertson, I must refer the reader to the article in question.
One point in my last chapter, that on the Results and Limits of Scientific Method, has been criticised by Professor W. K. Clifford in his lecture20 on “The First and the Last Catastrophe.” In vol. ii. p. 438 of the first edition (p. 744 of this edition) I referred to certain inferences drawn by eminent physicists as to a limit to the antiquity of the present order of things. “According to Sir W. Thomson’s deductions from Fourier’s theory of heat, we can trace down the dissipation of heat by conduction and radiation to an infinitely distant time when all things will be uniformly cold. But we cannot similarly trace the Heat-history of the Universe to an infinite distance in the past. For a certain negative value of the time, the formulæ give impossible values, indicating that there was some initial distribution of heat which could not have resulted, according to known laws of nature, from any previous distribution.”
Now according to Professor Clifford I have here misstated Thomson’s results. “It is not according to the known laws of nature, it is according to the known laws of conduction of heat, that Sir William Thomson is speaking. . . . All these physical writers, knowing what they were writing about, simply drew such conclusions from the facts which were before them as could be reasonably drawn. They say, here is a state of things which could not have been produced by the circumstances we are at present investigating. Then your speculator comes, he reads a sentence and says, ‘Here is an opportunity for me to have my fling.’ And he has his fling, and makes a purely baseless theory about the necessary origin of the present order of nature at some definite point of time, which might be calculated.”
Professor Clifford proceeds to explain that Thomson’s formulæ only give a limit to the heat history of, say, the earth’s crust in the solid state. We are led back to the time when it became solidified from the fluid