i8 7 3] HEGEL AND THE CALCULUS 15 



Werke, in. 286). l What Hegel seeks to show is, &quot; that 

 the mathematical Infinite is at the bottom the true 

 Infinite &quot; (p. 283) ; imperfectly conceived, however, by 

 the mathematicians, who have therefore never been able 

 to put the higher calculus on a basis thoroughly free from 

 confusion, or even error. Thus, not to speak of Fermat, 

 Leibnitz, Euler, and others, whose views Hegel takes up 

 more or less fully, we are told that Newton himself, 

 although his fundamental thought was quite in harmony 

 with Hegel s views, was not so far master of his own 

 thought as to be able fairly to deduce the practical rules 

 of his method. In the actual application of the new 

 instrument, Newton clung &quot; to the formal and superficial 

 principle of omission because of relative smallness.&quot; He 

 thus fell into real errors ; and even so fundamental a 

 problem as the determination of the fluxion of a product 

 was solved in a manner analytically unsound. Now 

 these, I maintain, are assertions that can fairly be 

 examined by one who does not profess to have mastered 

 Hegel s system. They even afford a fair test whether 

 that system is really so complete in all its parts, and so 

 light-giving in its applications, as we are told to believe. 

 If Newton is really confused and in error, it must be 

 possible to make this clear by an argument based on 

 Newton s own principles. For if to the mathematician 

 Newton s method is perfectly clear and self-contained, 

 and if its errors can only be observed from an entirely 

 different point of view, we have not one truth, but two 

 truths, mutually destructive. And this surely Dr. Stirling 

 will not assert. 



It is possible, however, to go further than this. To 

 the subject of the calculus Hegel devotes two notes. The 

 first of these alone is taken up by Dr. Stirling. And in 

 this note Hegel adds to the destructive criticism of which 



1 Here and elsewhere I adopt, as far as possible, the language of 

 Dr. Stirling s own translations from Hegel, which may be viewed as 

 authoritative. 



