64 THE GENETIC AND 



first principles of mathematics might be attacked by 

 scepticism and shaken by philosophical speculation, 

 we may remember the recent discussions as to the 

 three dimensions of space and the possibility of a 

 fourth dimension ; disputes which are carried on even 

 at the present day by the most eminent mathe- 

 maticians, physicists, and philosophers. So much as 

 this is certain, that mathematics as little constitute 

 an absolutely objective science as any other, but by 

 the very nature of man are subjectively conditioned. 

 A man's subjective power of knowing can only discern 

 the objective facts of the outer world in general so far 

 as his organs of sense and his brain admit in his own 

 individual degree of cultivation. 



However, granting that mathematics practically 

 constitute an absolutely certain and objective science, 

 how is it with the rest of the sciences ? Un- 

 doubtedly the most certain among them are those 

 " exact sciences " whose principles are to be directly 

 proved by mathematics ; thus, in the first place, a great 

 part of physics. We say, " a great part," for another 

 large part to speak accurately, by far the greatest 

 is incapable of any exact mathematical proof. For 

 what do we know for certain of the essential nature 

 of matter, or the essential nature of force ? What do 

 we know for certain of gravitation, of the attraction of 

 mass, ot its effects at great distances, and so on ? 



