GROWTH AND DIFFUSION OF CRITICAL SPIRIT. 107 



reason why they have not succumbed, sharing the same 

 fate as the purely philosophical theories of earlier times, 

 can be traced to the following causes. The first consists u. 



. . Reasons 



in this, that science has a definite obiect to deal with — whysciei.ce 



^ has not 



namely, the phenomena of nature, which present at least succumbed, 

 as much uniformity and regularity as is necessary to 

 afford a firm and unaltering foundation for human thought, 

 a strong foothold for the searcher and explorer. Of 

 this sine qua non scientific workers have continually 

 availed themselves wherever their results have been 

 attacked; they have always retired into the stronghold 

 of a small number of undisputed facts based upon 

 observation and verifiable by every beginner or any 

 critic who is qualified or willing to take the trouble. 

 The philosophical or introspective thinker cannot do the 

 same, and this is owing partly to the subjective nature 

 of the object of his research, but equally perhaps to the 

 fact that he is not so far removed from his object as is 



recently by Stanley Jevons and 

 Karl Pearson. In Germany they 

 have two quite independent begin- 

 nings, the first in the ' Critique ' 

 of Kant, who looked upon mathe- 

 matics and natural philosophy as 

 proving by their existence and their 

 results the possibility of scientific 

 knowledge. Somewhat later, and 

 for a long time unknown to the 

 scientific world, the great mathema- 

 tician Gauss began to question for 

 himself, and in correspondence with 

 some friends, the fundamental 

 axioms of geometry. In the sequel 

 there arose out of these speculations 

 the non - Euclidean geometry of 

 Vasiliev Lobatchevsky and others. 

 As this seeming paradox led to an 

 extension of geometrical ideas, .«o 

 in arithmetic the so-called imagin- 



ary quantities led Gauss in Ger- 

 many, De Morgan and Hamilton in 

 England, to an extension of our 

 algebraical and arithmetical con- 

 ceptions. Kirchhoff, and following 

 him Mach, in Germanj', and, as it 

 appears, independently, Karl Pear- 

 son in England, defined more clear- 

 ly the real processes of dynami- 

 cal reasoning and the fundamental 

 notions of mathematical physics. 

 Of this subject, which belongs as 

 much to science as to philosopliy, 

 I have treated in the last chapter 

 of the first section of this History. 

 In so far as it affects philosophical 

 thought, I shall deal with it in a 

 later chapter of the present section, 

 which will be occupied with the 

 problem of Nature as a whole. 



