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XIII. — Hegel and the Metaphysics of the Fluxional Calculus. By W. Robertson 

 Smith, M.A., Assistant to the Professor of Natural Philosophy in the 

 University of Edinburgh. Communicated by Professor Tait. 



(Read 17th May 1869.) 



It is now many years since Dr Whewell drew the attention of the Cambridge 

 Philosophical Society to the courageous, if somewhat Quixotic, attempts of Hegel 

 to cast discredit on Newton's law of gravitation, and on the mathematical 

 demonstrations of Kepler's laws given in the " Principia." At the time when 

 Whewell wrote, it would probably have been difficult to find in Britain any one 

 ready to maintain the cause of Hegel in this matter, or even to hint that the 

 astounding arguments of the Naturphilosophie flowed from any deeper source 

 than self-complacent ignorance. 



The present state of matters is different. The philosophy of Hegel is now for 

 the first time beginning to have a direct and powerful influence on British specula- 

 tion. Men are beginning to study Hegel ; and an author whose works con- 

 fessedly demand the labour of years, if they are to be fully understood, can hardly 

 be studied at all except by devoted disciples. A man whose determination to 

 master Hegel's philosophy survives the repelling impression which the obscurity 

 and arrogance of the philosopher are sure to produce at first, is very likely to be 

 carried away by the calm assumption of omniscience which runs through Hegel's 

 writings. It is not, therefore, surprising that Dr Stirling extends his admira- 

 tion to Hegel's physical positions ; and if he does not venture to say that Hegel's 

 proof of Kepler's laws is right, at least feels sure that it would repay the attention 

 of mathematicians. 



It would not, perhaps, be impossible to rob Dr Stirling of even this sorry 

 consolation ; but there is the less occasion for retracing any part of the ground 

 gone over by Whewell, in so much as " The Secret of Hegel" calls attention 

 to another point, in which Hegel criticises Newton, and in which Dr Stirling 

 has no hesitation in pronouncing Hegel's findings " perfectly safe from assault," 

 and Newton guilty of an obvious mathematical blunder. 



Such a statement, proceeding from the most powerful of our living metaphy- 

 sicians, and recently reiterated in the newspaper press, as a sort of challenge to 

 mathematicians, seems to call for some remark from a mathematical point of 

 view. It is true that a confirmed Hegelian is not likely to be influenced by any 

 reasoning that we can offer. " The judgment of a pure mathematician," we are 



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