V 



DR. STIRLING, HEGEL, AND THE 

 MATHEMATICIANS 



(From the Fortnightly Review, April 1873) 



THE names which head this paper will suggest to those 

 who are interested in metaphysical and scientific dis 

 cussion a controversy which has never been quite extinct 

 since Dr. Whewell attacked Hegel s statements on the law 

 of gravitation, and which from time to time has burst 

 into somewhat lurid flame. The controversy as opened 

 by Dr. Whewell dealt with questions of physics. But in 

 the year 1865, Dr. Stirling, in the second volume of The 

 Secret of Hegel, enlarged the field of discussion by trans 

 lating Hegel s note on the precise nature of the notion 

 of the mathematical Infinite, in which the philosopher 

 joins issue with the mathematicians, particularly with 

 Newton, on certain alleged imperfections in their treat 

 ment of the fluxional calculus. To his translation Dr. 

 Stirling subjoins remarks laudatory of Hegel, and emphas 

 ising those defects in the mathematical doctrine on which 

 Hegel animadverts. Such imperfections are 



&quot; Quanta by very definition no longer Quanta, yet 

 treated as Quanta ; omission because of insignificance, 

 but omission obligatory and indispensable in spite of 

 insignificance, proof necessary from elsewhere, yet pre 

 tensions above any elsewhere ; great results of the 

 operation, but the operation itself granted incorrect ; an 

 incorrect operation, but absolutely correct results/ 

 (Secret, ii. 380.) 



Dr. Stirling further refers to striking and instructive 



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