INTRODUCTION. 



71 



almost as unknown l as agreement in the latter. There 

 we have an almost universal unity of thought ; here unity 

 of thought probably never existed ; it is unknown. Popu- 

 larly we can say that at the one extreme lie knowledge 

 and certainty, at the other faith and belief. There is, 

 however, a very large extent of ground between these two 

 extremes. This is covered by all such intermediate thought 

 as rests partly on knowledge, partly on faith, where cer- 

 tainty is largely mingled with belief. This large inter- 20. 



' J Philosophy 



mediate region, where changes and fluctuations are fre- intermedi- 

 ate between 



quent and rapid, is the proper home of philosophy, which "f^^" 

 occupies itself with the grounds of certainty and belief, and religion ' 

 the origin of knowledge and faith, and the relations in 

 which both stand to each other. Were all our thoughts 

 either purely mathematical i.e., referring to number, 

 measurement, and calculation, or purely religious i.e., 

 referring to our individual concerns and personal convic- 

 tions, the need of a continued compromise or mediation 

 would be unnecessary, the question as to the grounds of 

 certainty or belief would never arise. But no sooner 

 do we wish either to apply our strict mathematical no- 

 tions and processes, or to bring our personal convictions 

 into practical use, than the two kinds of thought come 

 into contact, not to say into conflict, and there is need 

 of some theory according to which this contact may be 

 regulated, this conflict settled. And as the occasions for 

 such contact change with the demands of practical life, or 



1 It may be doubted whether this 

 is quite correct, looking at the con- 

 troversies which have been connec- 

 ted with many mathematical theo- 

 ries such as the theory of parallel 

 Hues, the meaning of infinitesimals, 



the correct measure of force. 

 These controversies, however, re- 

 ferred really to applied, not to pure 

 mathematics, and were settled by 

 introducing corrector and more 

 stringent definitions. 



