492 MR W. ROBERTSON SMITH ON HEGEL 



told, " has really been so peculiarly trained that, perhaps, any such will never 

 prove decisive as regards any Hegelian element.'" We are told, too, that Hegel's 

 " most important note" on the mathematical infinite " has remained hitherto 

 absolutely sealed," for C. Frantz, who does take up the subject " as in opposition 

 to, is to be assumed ignorant of, the views of Hegel, which plainly, so far as they 

 go, are inexpugnable" (!) 



Now I do not profess to be able to treat this question from the stand-point 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 

 " to consider in detail the most remarkable attempts to justify the use of the 

 mathematical notion of the Infinite, and get rid of the difficulties by which the 

 method feels itself burdened" (Hegel's Werke, iii. 286).* What Hegel seeks to 

 show is, " that the mathematical Infinite is at bottom the true Infinite" (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 con- 

 fusion, 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 instru- 

 ment, Newton clung " to the formal and superficial principle of omission because 

 of relative smallness." 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 we have been 

 speaking only a very general account of the principles on which he would base 

 the calculus. These general principles are, as Hegel saj's, " abstract" (we would 

 rather say vague), " and therefore in themselves also easy" (p. 327). The real 



* 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. 



