Mental Science. This very mischievous locution, which although countenanced by the practice of some of our best authors, suggests a view of Kant's doctrine diametrically opposed to its most characteristic feature, and that which differentiates it from all preceding systems of Philosophy, it is believed has hereby received its death-blow, and must henceforth disappear from the face of English literature. P.S.-In the prefatory letter to the volume of collected 'Lay Sermons, Addresses, and Reviews,' with which Professor Huxley has recently gratified the public, I notice some remarks which he has made on the inaugural address above referred to. He says, addressing himself to Dr. Tyndall: In the same paper (On the Educational Value of the Natural History Sciences) there is a statement concerning the method of the mathematical sciences, which repeated and expanded elsewhere brought upon me, during the meeting of the British Association at Exeter, the artillery of our eminent friend Professor Sylvester. 'No one knows better than you do, how readily I should defer to the opinion of so great a mathematician if the question at issue were really, as he seems to think it is, a mathematical one. But I submit, that the dictum of a mathematical athlete upon a difficult problem which mathematics offer to philosophy, has no more special weight than the verdict of that great pedestrian Captain Barclay would have had in settling a disputed point in the physiology of locomotion.' To this I need only reply that I am not aware what reason Professor Huxley has for attributing to me the opinion that it is a mathematical question to determine the place of mathematics among the sciences. I have only ventured to express my belief that had the distinguished lay preacher been better acquainted with the real aim and scope of mathematics he would scarcely have committed himself to saying that the teaching of languages is of the same general nature as ‘mathematical training.' I remain of that belief still. Supposing that Professor Huxley had had no acquaintance with the anatomy, physiology, and habits of the human subject, would he have felt himself justified in writing as he has done, On the Place of Man in Nature;' or, supposing he had done so, would what he wrote have been likely to achieve the world-wide celebrity of his actual work on the subject?* I may possibly have misquoted the title. I remember seeing a translation into German of the book I mean, lying on the counter of an Italian bookseller in Florence. a He further adds, The genius which sighs for new worlds to conquer beyond that surprising region in which "geometry, algebra, and the theory of numbers melt into one another like sunset tints, or the colours of a dying dolphin," may be of comparatively little service in the cold domain (mostly lighted by the moon, some say) of philosophy. And the more I think of it, the more does our friend seem to me to fall into the position of one of those "verständige Leute," about whom he makes so apt a quotation from Goethe. Surely he has not duly considered two points. The first, that I am in no way answerable for the origination of the doctrine he criticises: and the second, that if we are to employ the terms observation, induction, and experiment, in the sense in which he uses them, logic is as much an observational, inductive, and experimental science as mathematics; and that, I confess, appears to me to be a reductio ad absurdum of his argument.' With regard to the first of the two points' here raised, I would say that Professor Huxley, whether or not answerable for the origination, is certainly answerable for the vindication and propagation, with 'repetition and expansion,' of the erroneous doctrine which formed the subject of my criticism. I felt no call to go into so purely subjective a question as that of ascertaining the sources from which he had drawn the erroneous opinions which found in him their advocate. As regards the second of the two points I am perfectly at a loss to understand how Professor Huxley can suppose that the observational, inductive, and experimental processes which I have referred to and illustrated in their bearing on the illimitable sphere of mathematical discovery and invention, can be shown to have any place in the confined and circumscribed area of pure logic. In a word, without the slightest intention of saying anything unkind or discourteous, I cannot conceal my opinion that what my estimable and eminent adversary calls a reductio ad absurdum might with much greater propriety be termed a deductio ex absurdo: for it seems to me absurd to suppose that there exists in the science of pure logic anything that bears a resemblance to the infinitely developable and interminable euristic processes of mathematical science. J. J. S. ATHENAEUM CLUB, |