154 THE GEXESIS OF SCIENCE. 



[t is manifest that the fundamental conception of similarity 

 is equality of relations. 



"With this explanation we shall be understood when we 

 say that the notion of equality of relations is the basis of 

 all exact reasoning. Already it has been shown that reasoning 

 in general is a recognition of likeness of relations ; and 

 here we further find that while the notion of likeness of 

 things ultimately evolves the idea of simple equality, the 

 notion of Hkeness of relations evolves the idea of equality 

 of relations : of which the one is the concrete germ of ex- 

 act science, while the other is its abstract germ. 



Those who cannot understand how the recognition of 

 similarity in creatures of the same kind, can have any alli- 

 ance with reasoning, will get over the difficulty on remem- 

 bering that the phenomena among which equality of rela- 

 tions is thus perceived, are phenomena of the same order 

 and are present to the senses at the same time ; while those 

 among which developed reason perceives relations, are gen- 

 erally neither of the same order, nor simultaneously present. 

 And if further, they will call to mind how Cuvier and Owen, 

 from a single part of a creature, as a tooth, construct the 

 rest by a process of reasoning based on this equality of re- 

 lations, they will see that the two things are intimately 

 connected, remote as they at first seem. But we anticipate. 

 What it concerns us here to observe is, that from familiari- 

 ty with organic forms there simultaneously arose the ideas 

 of simple equality^ and equality of relations. 



At the same time, too, and out of the same mental pro- 

 cesses, came the first distinct ideas of miniber. In the earli- 

 est stages, the presentation of several hke objects produced 

 merely an indefinite concejDtion of multiplicity ; as it still 

 does among Australians, and Bushmen, and Damaras, when 

 the number presented exceeds three or four. With such a 

 fact before us we may safely infer that the first clear numer- 

 ical conception was that of duality as contrasted with uni- 



