76 LECTURES AND ESSAYS [1869- 



inaccuracy,&quot; when I venture to state that the German 

 philosopher represents Newton as having fallen into &quot; real 

 errors,&quot; and as having determined the unlucky fluxion 

 before us &quot;in a manner analytically unsound.&quot; The 

 expressions &quot; real errors,&quot; &quot; analytically unsound,&quot; are 

 quoted from my Royal Society paper, and the second 

 expression is recurred to by Dr. Stirling on p. 127, as a 

 clear proof that I have misunderstood Hegel. The latter 

 &quot; knows the result to be analytically sound ; he only 

 objects to an apparent arithmetical &quot; (more correctly 

 algebraical, since the operation is performed on letters, 

 not on numbers) &quot; stratagem in deduction of it.&quot; At 

 first sight this sentence appears meaningless, for every 

 arithmetical or algebraic operation falls as species under 

 the genus Analysis ; and so the objectionable arithmetical 

 (algebraical) stratagem involves of necessity analytical 

 unsoundness. But Dr. Stirling, as we learn at page 124, 

 has a meaning of his own for the word analysis, which 

 shall indicate what concerns the higher calculus, as 

 opposed to what is merely arithmetical. Dr. Stirling 

 seems to have concluded that I must necessarily take the 

 word in this sense because I had taken objection to Hegel 

 for identifying analytical with arithmetical process. In 

 fact my objection was directed against the identification 

 of the genus with the species. This would have been 

 obvious to any one familiar with mathematical language ; 

 and it is simply the lack of such familiarity that has led 

 Dr. Stirling to say that I have &quot; utterly failed to see what 

 Hegel meant, whether arithmetically or analytically.&quot; l 



The sum of our argument then is this : Hegel admits 

 the correctness of Newton s result, in the sense of admit 

 ting that the fluxion which Newton gives is that which, 

 applied in concrete problems say of geometry gives 

 correct results. But he denies that Newton has got the 



1 I am thus not called upon to go into the lesson on the etymological 

 sense of the word &quot; analytical &quot; which Dr. Stirling reads me at p. 124. 

 But a very moderate knowledge of Greek would have shown that the 

 word cannot possibly mean &quot; dissoluble.&quot; 



