that I should take Professor Tait's interpretion of its meaning.1 "In his new work On some Recent Advances in Physical Science, Professor Tait has recurred to the subject as follows: "A profound lesson may be learned from one of the earliest little papers of Sir W. Thomson, published while he was an undergraduate at Cambridge, where he shows that Fourier's magnificent treatment of the conduction of heat [in a solid body] leads to formulæ for its distribution which are intelligible (and of course capable of being fully verified by experiment) for all time future, but which, except in particular cases, when extended to time past, remain intelligible for a finite period only, and then indicate a state of things which could not have resulted under known laws from any conceivable previous distribution [of heat in the body]. So far as heat is concerned, modern investigations have shown that a previous distribution of the matter involved may, by its potential energy, be capable of producing such a state of things at the moment of its aggregation; but the example is now adduced not for its bearing on heat alone, but as a simple illustration of the fact that all portions of our Science, especially that beautiful one, the Dissipation of Energy, point unanimously to a beginning, to a state of things incapable of being derived by present laws [of tangible matter and its energy] from any conceivable previous arrangement." As this was published nearly a year after Professor Clifford's lecture, it may be inferred 1 Sir W. Thomson's words are as follows (Cambridge Mathematical Journal, Nov. 1842, vol. iii. p. 174). "When a is negative, the state represented cannot be the result of any possible distribution of temperature which has previously existed." There is no limitation in the sentence to the laws of conduction, but, as the whole paper treats of the results of conduction in a solid, it may no doubt be understood that there is a tacit limitation. See also a second paper on the subject in the same journal for February, 1844, vol. iv. p. 67, where again there is no expressed limitation. Pp. 25-26. The parentheses are in the original, and show Professor Tait's corrections in the verbatim reports of his lectures. The subject is treated again on pp. 168-9. that Professor Tait adheres to his original opinion that the theory of heat does give evidence of "a beginning." 1 I may add that Professor Clerk Maxwell's words seem to countenance the same view, for he says, "This is only one of the cases in which a consideration of the dissipation of energy leads to the determination of a superior limit to the antiquity of the observed order of things." The expression "observed order of things" is open to much ambiguity, but in the absence of qualification I should take it to include the aggregate of the laws of nature known to us. I should interpret Professor Maxwell as meaning that the theory of heat indicates the occurrence of some event of which our science cannot give any further explanation. The physical writers thus seem not to be so clear about the matter as Professor Clifford assumes. So far as I may venture to form an independent opinion on the subject, it is to the effect that Professor Clifford is right, and that the known laws of nature do not enable us to assign a "beginning." Science leads us backwards into infinite past duration. But that Professor Clifford is right on this point, is no reason why we should suppose him to be right in his other opinions, some of which I am sure are wrong. Nor is it a reason why other parts of my last chapter should be wrong. The question only affects the single paragraph on pp. 744-5 of this book, which might, I believe, be struck out without necessitating any alteration in the rest of the text. is always to be remembered that the failure of an argument in favour of a proposition does not, generally speaking, add much, if any, probability to the contradictory proposition. I cannot conclude without expressing my acknowledgments to Professor Clifford for his kind expressions regarding my work as a whole. 1 Theory of Heat, 1871, p. 245. 2, THE CHESTNUTS, WEST HEATH, August 15, 1877. HAMPSTEAD, N.W. It CONTENTS. 2. The Powers of Mind concerned in the Creation of Science 3. Laws of Identity and Difference 4. The Nature of the Laws of Identity and Difference 7. Symbolic Expression of Logical Inference. 8. Expression of Identity and Difference 9. General Formula of Logical Inference 10. The Propagating Power of Similarity C 3. Inference with Two Simple Identities 4. Inference with a Simple and a Partial Identity 5. Inference of a Partial from Two Partial Identities 6. On the Ellipsis of Terms in Partial Identities 7. Inference of a Simple from Two Partial Identities 8. Inference of a Limited from Two Partial Identities 61 7. The Inverse Logical Problem, involving Three Classes 8. Professor Clifford on the Types of Compound Statement in- 2. Induction an Inverse Operation 3. Inductive Problems for Solution by the Reader. 4. Induction of Simple Identities 5. Induction of Partial Identities . 6. Solution of the Inverse or Inductive Problem, involving Two 122 |