468 THE PRINCIPLES OF SCIENCE. 



its sign by passing, as mathematicians say, either through 

 zero or through infinity. In the latter case there must be 

 one intermediate value of the variable for which the 

 variant is indifferently negative infinity and positive in 

 finity. Mathematicians may shirk the difficulty, but they 

 cannot make this common result of mathematical principles 

 appear otherwise than contradictory to our common 

 notions of space. 



The hypothesis that there is a Creator at once ah 1 

 powerful and all benevolent is surrounded, as it must 

 seem to every candid investigator, with difficulties verging 

 closely upon logical contradiction. The existence of the 

 smallest amount of pain and evil would seem to show that 

 He is either not perfectly benevolent, or not all-powerful. 

 No one can have lived long without experiencing sorrow 

 ful events of which the significance is inexplicable. But 

 if we cannot succeed in avoiding contradiction in our 

 notions of elementary geometry, can we expect that the 

 ultimate purposes of existence shall present themselves to 

 us with perfect clearness ? I can see nothing to forbid 

 the notion that in a higher state of intelligence much that 

 is now obscure may become clear. We perpetually find 

 ourselves in the position of finite minds attempting in 

 finite problems, and can we be sure that where we see 

 contradiction, an infinite intelligence might not discover 

 perfect logical harmony? 



From science, modestly pursued, with a due conscious 

 ness of the extreme finitude of our intellectual powers, 

 there can arise only nobler and wider notions of the pur 

 pose of Creation. Our philosophy will be an affirmative 

 one, not that false and negative one of Auguste Comte, 

 which has usurped the name, and misrepresented th 

 tendencies of a true positive philosophy. Our science wi 

 not deny the existence of things because they cannot bet- 

 weighed and measured. It will rather lead us to believe 



