i873] STIRLING AND HEGEL 79 



But on the whole the result to which my investigation led 

 me was, that the darkness experienced by Hegel was due 

 to his imperfect training, not to any defect in the mathe 

 matical theory, notably at least not in Newton s theory. 

 And I found that in this darkness Hegel was so unlucky as 

 to stumble upon the method of Lagrange, and to accept 

 it as relatively best as his guide. This method he proposes 

 to bring &quot; into its due abstraction &quot; (cf. Stirling, p. 134), 

 but, while still darkly labouring at his task, is clumsy 

 enough to make modifications on the method, which not 

 only changes its mathematical character and analytical 

 accuracy, but really (though, of course, unconsciously) 

 amount to the suggestion of what I have ironically called 

 &quot; a Hegelian calculus.&quot; On these results Dr. Stirling 

 joins issue with me, and, curiously overlooking the obvious 

 irony of my statements, assumes that I imagine that Hegel 

 intended to suggest new mathematical processes. I am 

 assured, therefore, that I have simply deluded myself, 

 and that Hegel never made a mathematical suggestion 

 in his life. I shall show in due time that he made more 

 than one such suggestion ; but of course I shall not deny 

 that he did so in ignorance, out of sheer incompetence 

 to distinguish between metaphysical and mathematical 

 modification of the statements of Lagrange. And thus 

 Hegel points to his own disciples the lesson that no one has 

 a right to speak on the principles of a science which he has 

 not mastered in its essential detail. 



My work, then, falls very clearly into two parts. 

 Hegel and Dr. Stirling detect in the calculus an obscurity, 

 manifesting itself to their eyes in the logical inconsistency 

 of processes correct in result ; and they claim a light 

 thrown on the method by the introduction of the &quot;Notion&quot; 

 which suggests that the operation shall be made &quot; to 

 depend not on the quantity but on the quality required &quot; 

 (Stirling, p. 129). To this I object, jfo s/, that the supposed 

 obscurity and logical inconsistency are to be found in the 

 mind of Hegel, not in the processes of Newton ; and 



