VI CONCERNING NECESSARY TRUTHS 139 



mere operation of thought without dependence 

 on what is anywhere existent in the universe " ? 



Suppose that there were no such things as 

 impressions of sight and touch anywhere in the 

 universe, what idea could we have even of a 

 straight line, much less of a triangle and of the 

 relations between its sides ? The fundamental 

 proposition of all Hume's philosophy is that ideas 

 are copied from impressions; and, therefore, if 

 there were no impressions of straight lines and 

 triangles there could be no ideas of straight 

 lines and triangles. But what we mean by the 

 universe is the sum of our actual and possible 

 impressions. 



So, again, whether our conception of number is 

 derived from relations of impressions in space or 

 in time, the impressions must exist in nature, that 

 is, in experience, before their relations can be per- 

 ceived. Form and number are mere names for 

 certain relations between matters of fact ; unless 

 a man had seen or felt the difference between a 

 straight line and a crooked one, straight and 

 crooked would have no more meaning to him, than 

 red and blue to the blind. 



The axiom, that things which are equal to the 

 same are equal to one another, is only a particular 

 case of the predication of similarity ; if there were 

 no impressions, it is obvious that there could be no 

 predicates. But what is an existence in the uni- 

 verse but an impression ? 



