OEIGIN OF IDEAS OF EQUALITY. 193 



ual formation of the first germs of science. This idea oi 

 likeness which underlies classification, nomenclature, Ian- 

 guage spoken and written, reasoning, and art ; and which 

 plays so important a part because all acts of intelligence 

 are made possible only by distinguishing among surround 

 ing things, or grouping them into like and unlike ; this 

 idea we shall find to be the one of which science is the es 

 pecial product. Already dxiring the stage we have been 

 describing, there has existed qualitative prevision in re 

 spect to the commoner phenomena with which savage life 

 is familiar ; and we have now to inquire how the elements 

 of quantitative prevision are evolved. We shall find that 

 they originate by the perfecting of this same idea of like 

 ness ; that they have their rise in that conception of com 

 plete likeness which, as we have seen, necessarily results 

 from the continued process of classification. 



For when the process of classification has been carried 

 as far as it is possible for the uncivilized to carry it when 

 the animal kingdom has been grouped not merely into 

 quadrupeds, birds, fishes, and insects, but each of these di 

 vided into kinds when there come to be sub-classes, in 

 each of which the members differ only as individuals, and 

 not specifically ; it is clear that there must occur a frequent 

 observation of objects which differ so little as to be indis 

 tinguishable. Among several creatures which the savage 

 has killed and carried home, it must often happen that 

 some one, which he wished to identify, is so exactly like 

 another that he cannot tell which is which. Thus, then, 

 there originates the notion of equality. The things which 

 among ourselves are called equal whether lines, angles, 

 weights, temperatures, sounds or colours are things which 

 produce in us sensations that cannot be distinguished from 

 each other. It is true that we noAV apply the word equal 

 chiefly to the separate phenomena which objects exhibit, 

 and not to groups of phenomena ; but this limitation of the 

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