xxx.J CLASSIFICATION. 695 



of the minor classes are not represented among existing 

 things. If we take the genus A and divide it into the 

 species AB and AC, we imply two propositions, namely 

 that in the class A, the properties of B and C never occur 

 together, and that they are never both absent ; these 

 propositions are logically equivalent to one, namely 

 AB = Ac. Our classification is then identical with the 

 following bifurcate one : — 



r 1 



AB Ab 



I 



ABC = A Be AbV Abe = 



If, again, we divide the genus A into three species, AB, 

 AC, AD, we are either logically in error, or else we must 

 be understood to imply that, as regards the other letters, 

 there exist oidv three combinations containing A, namely 

 ABcd, AhCd, cuid AkD. 



The logical necessity of bifurcate classification has been 

 clearly and correctly stated in the Outline of a New System, 

 of Lofjic by George Bentham, the eminent botanist, a work 

 of which the logical value has been quite overlooked until 

 lately. Mr. Bentham points out, in p. 113, that every 

 classiiication must be essentially bifurcate, and takes, as 

 an example, the division of vertebrate animals into four 

 sub-classes, as follows : — 



Mammifera — end(jwed with mammse and lungs. 



liirds withoi:^\mamm8e but with lungs and wings. 



Fish deprive 1 of lungs. 



Reptiles deprived of mammae and wings but with 



lungs. 



Wq, liave, then, as Mj-. Bentham says, three bifid divi- 

 sions, thus represented : — 



Vertebrata 



\ . 



> > 



Endowed witli luiig3 deprived of lungs 



I = Fish. 



I ' 



Kndowed with deprived of 



riiainm;c mainiiiOR 



= Mammifera | 



( \ I 



witli wings without wings 



= Birds. = Keptiles, 



