INTRODUCTION. Vl 



almost as unknown 1 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 frequent 

 and rapid, is the proper home of philosophy, which occupies 

 itself with the grounds of certainty and belief, the origin of 

 knowledge and faith, and the relations in which both stand 

 to each other. Were all our thoughts either purely mathe- 

 matical i.e., referring to number, measurement, and calcu- 

 lation, or purely religious i.e., referring to our individual 

 concerns and personal convictions, 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 mathe- 

 matical notions and processes, or to bring our personal con- 

 victions 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 

 the progress of applied science, these theories must them- 



1 It may be doubted whether this 

 is quite correct, looking at the con- 

 troversies which have been connec- 

 ted with many mathematical theo- 

 riessuch as the theory of parallel 



lines, the meaning of infinitesimals, definitions. 



the correct measure of force. These 

 controversies, however, referred 

 really to applied, not to pure mathe- 

 matics, and were settled by intro- 

 ducing correcter and more stringent 



