8o LECTURES AND ESSAYS [1869- 



second, that be the Notion what it may, we need not look 

 for light from it on this matter, since it has lighted its great 

 master himself into a mathematical ditch. 



Now the first of my two points seems really to be proved 

 when we find Hegel vitally wrong in so essential a matter 

 as the fluxion of a product. Dr. Stirling, however, is too 

 little of a mathematician to be able to distinguish between 

 vital and venial error in such a subject, and finds that 

 &quot; on the whole Hegel made himself very sufficiently 

 acquainted with whatever he was minded to talk upon.&quot; 

 If this means only, as regards the case before us, that 

 Hegel had glanced through a number of mathematical 

 books, new and old, I have nothing to object ; but if 

 it is claimed that he understood what he read, I can only 

 say that he thoroughly miscomprehended Newton and 

 Lagrange, and that he never learned what mathematicians 

 mean by a Limit, by Continuity, and by Evaluation. I 

 offered in my former paper a few of the many proofs of 

 these assertions, which are heaped up a misura di carboni 

 in Hegel s writings. The proofs were given by me as far 

 as possible in the precise and unambiguous language and 

 formulae of mathematics ; and I am the less called upon 

 to repeat these technical arguments, that it is perfectly 

 evident that Dr. Stirling was unable to follow my symbolic 

 statements. But as this inability has not modified the 

 fierceness of assertion with which he condemns all this 

 portion of my work as absolute misapprehension, I may 

 be permitted to offer some examples of the way in which 

 he has thought it fair to cut knots that he cannot untie. 



My first example shall be one in which Dr. Stirling rests 

 his case on a charge of garbling Hegel s words. In my 

 paper of 1869 I wrote as follows : 



&quot; Purely analytical considerations without any physical 

 basis were held, Hegel thinks, to furnish in this way 

 physical laws. In support of this view, Hegel triumph 

 antly refers to the Newtonian proof of his fundamental 

 proposition in the theory of gravitation, compared with 

 Schubert s Astronomy, where it is admitted that ... in 



