374 THE PRINCIPLES OF SCIENCE. 



ABCtZ = Mammifera, 

 ABcD = Birds, 

 ABcc/ = Reptiles, 

 Abed =Fish, 



and we imply at the same time that the other four con 

 ceivable combinations containing B, C, or D, namely 

 ABCD, AJCD, A6CW, and KbcD, do not exist in nature. 



The bifurcate form of classification seems to be needless 

 when the property according to which we classify any 

 group of things admits of numerical discrimination. It 

 would seem absurd to arrange things according as they 

 have one degree of the property or not one degree, two 

 degrees or not two degrees, and so on. The elements, for 

 instance, are classified according as the atom of each satu 

 rates, one, two, three or more atoms of a monad element, 

 such as chlorine, and they are called accordingly Monad, 

 Dyad, Triad, Tetrad elements, and so on. It would be 

 wholly useless to apply the bifid arrangement, thus : 



r 



Element 

 I 



Monad not-Monad 



Dyad riot-Dyad 



-- L - 



Triad not-Triad 



I &quot;I 



Tetrad not-Tetrad. 



The reason of this is that, by the very nature of number 

 as described in Chapter VIII, every number is logically 

 discriminated from every other number. There can thus 

 be no logical confusion in a numerical arrangement, and 

 the series of numbers indefinitely extended is also exhaus 

 tive. Every thing admitting of a property expressible in 

 numbers must find its place somewhere in the series of 

 numbers. The chords in music correspond to the various 

 simpler numerical ratios and must admit of complete 



