EQUALITY OF THINGS AND RELATIONS. 195 



it 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 likeness 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 Cuvierand 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 number. In the earli 

 est stages, the presentation of several like objects produced 

 merely an indefinite conception 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- 



