Darwinism in Ethics. 159 



covery that twice two are four. An intelligence 

 advanced to that point is on the way to geometry, 

 trigonometry, and the calculus, to all those sciences 

 whose application has changed the face of the 

 material world. As the highest mathematics is 

 useful to us, so was the first germ useful to our 

 ancestors. But it does not, therefore, follow that 

 arithmetic is merely a social utility. On the 

 contrary, it is useful for the reason that it brings 

 man into deepening relation with fact ; but its 

 validity is wholly independent of its advantage 

 to mankind, and only the satirist could suggest 

 that twice two would be five if that product 

 were more advantageous to us. Arithmetical 

 facts cannot be determined by a plebiscite of 

 utilitarians. And the same is true of the de 

 liverance of conscience that injustice is wrong. 

 Ultimate mathematical principles and ultimate 

 moral principles have the same intuitive evi 

 dence ; and it is not weakened by the assumption 

 that man owes his bodily organism to animals in 

 which there was no trace either of a moral or a 

 mathematical faculty. Fact is fact ; and neither 

 morality nor geometry ceases to be objectively 

 grounded from the accident that our ancestors 

 only gradually came to an apprehension of them. 

 From all points of view, then, we are led to the 



