OF KNOWLEDGE. 303 



represents nineteenth century thought more fully than 

 any other, who influenced men's minds more lastingly, 

 and gave them certainly a higher flight, that of Goethe, 

 sympathised with almost every fruitful line of thought 

 and aspiration except the mathematical. And in Eng- 

 land also the wisdom of Bacon was blind to the power 

 of the mathematical methods. Thus it comes that what 

 was wanting in the theories of knowledge in the school 

 of Mill and had to be supplemented by his later fol- 

 lowers was an appreciation of just that factor which 

 dominated French thought, being reflected in the best 

 style of some of the classical French writers. But the 

 clearness, simplicity, and elegance which this dominant 

 trait imparted to French thought misled it also into 

 the belief that psychological theories, in which English 

 and German philosophy abounded, were superfluous for 

 the attainment of exact knowledge, even in the region of 

 morals, economics, and politics. It led to that neglect 

 or contempt of logic and psychology which is charac- 

 teristic of the positivism of Auguste Comte, whose ideal 



and Universities ; he was an acade- 

 mician, not a professor, and passed 

 a great part of his life outside of 

 Germany. And as concerns Gauss, 

 he stood outside and above the 

 general current of German thought. 

 His earliest and most original mathe- 

 matical work was written in Latin, 

 and was practically unknown in 

 Germany. He was a younger con- 

 temporary of Goethe, and, along- 

 side of him, probably the greatest 

 German intellect of the age. Per- 

 sonally they seem to have been 

 unknown to each other, nor is there 



the other. The mathematical pre- 

 cision which Wolif gave to his 

 philosophical writings was purely 

 formal, as was also that of Spinoza, 

 after the manner of Euclid. The 

 modern analytical methods of 

 Leibniz, developed and perfected 

 by mathematicians such as the 

 BernouUis and Euler, and most 

 successfully applied by French 

 physicists, remained, as it seems, 

 unknown to the majority of Ger- 

 man mathematicians, and possibly 

 also to Kant. Even the study of 

 the ' Principia ' would hardly leveal 



any reference, so far as I know, in to him the power of the analytical 

 the writings of either of them to method. 



