30 THE PRINCIPLES OF SCIENCE. 



they are at once like and unlike. Two fragments of 

 rock may differ entirely in outward form, yet they may 

 have the same colour, hardness, and texture. Flowers 

 which agree in colour may differ in odour. The mind 

 learns to regard each object as an aggregate of qualities, 

 and acquires the power of dwelling at will upon one or 

 other of those qualities to the exclusion of the rest. 

 Logical abstraction, in short, comes into play, and the 

 mind becomes capable of reasoning, not merely about 

 objects which are physically complete and concrete, but 

 about things which may be thought of separately in 

 the mind though they exist not separately in nature. 

 We can think of the hardness of a rock, or the colour 

 of a flower, and thus produce abstract notions, denoted 

 by abstract terms which will form a subject for further 

 consideration. 



At the same time arise general notions and classes of 

 objects. We cannot fail to observe that the quality 

 hardness exists in many objects, for instance in many 

 fragments of rock ; and mentally joining these we create 

 the class hard object, which will include, not only the 

 actual objects examined, but all others which may 

 happen to agree with them as they agree with each 

 other. As our senses cannot possibly report to us all 

 the contents of space, we cannot usually set any limits 

 to the number of objects which may fall into any such 

 class. At this point we begin to perceive the power and 

 generality of thought which enables us at once to treat 

 of indefinitely or even infinitely numerous objects. We 

 can safely assert that whatever is true of any one object 

 coming under a general notion or class is true of any of 

 the other objects so far as they possess the common 

 qualities implied in their belonging to the class. We 

 must not place an individual thing in a class unless we 

 are prepared to believe of it all that is believed of the 



