i 4 LECTURES AND ESSAYS [1869- 



surprising that Dr. Stirling extends his admiration 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 mathe 

 maticians. 



It would not, perhaps, be impossible to rob Dr. Stirling 

 of even this sorry consolation ; but there is 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 &quot; perfectly safe from assault,&quot; and 

 Newton guilty of an obvious mathematical blunder. 



Such a statement, proceeding from the most powerful 

 of our living metaphysicians, and recently reiterated in 

 the newspaper press, as a sort of challenge to mathe 

 maticians, seems to call for some remark from a mathe 

 matical point of view. It is true that a confirmed Hegelian 

 is not likely to be influenced by any reasoning that we can 

 offer. &quot; The judgment of a pure mathematician,&quot; we 

 are told, &quot; has really been so peculiarly trained that, 

 perhaps, any such will never prove decisive as regards 

 any Hegelian element.&quot; We are told, too, that Hegel s 

 &quot; most important note &quot; on the mathematical infinite 

 &quot; has remained hitherto absolutely sealed,&quot; for C. Frantz, 

 who does take up the subject &quot; as in opposition to, is to be 

 assumed ignorant of, the views of Hegel, which plainly, so 

 far as they go, are inexpugnable &quot; (!) 



Now I do not profess to be able to treat this question 

 from the standpoint of Hegel s own philosophy. I have 

 no desire to criticise Hegel s doctrine of the Infinite, in so 

 far as it forms an integral part of his system. But the 

 note to which Dr. Stirling calls attention is itself a critical 

 note, in which Hegel proposes &quot; to consider in detail the 

 most remarkable attempts to justify the use of the mathe 

 matical notion of the Infinite, and get rid of the difficulties 

 by which the method feels itself burdened &quot; (Hegel s 



