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: 



A 



AB Ab 



\ I 



ABC = ABc AbC Abe = O 



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 only three combinations containing A, namely 

 ABoZ, AbCd, and A&cD. 



The logical necessity of bifurcate classification has been 

 clearly and correctly stated in the Outline of a New System 

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

 of which the logical value has been quite overlooked until 

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

 classification must be essentially bifurcate, and takes, as 

 an example, the division of vertebrate animals into four 

 sub-classes, as follows : 



Mammifera endowed with mammae and lungs. 



Birds without mamma3 but with lungs and wings. 



Fish deprived of lungs. 



lleptiles deprived of mammae and wings but with 

 lungs. 



We have, then, as Mr. Beutham says, three bifid divi- 

 sions, thus represented : 



Vertebrata 



Endowed with lungs deprived of lungs 



= Fish. 



i ' 1 



Endowed with deprived of 



mammae 

 = Mammifera 



with wiiigs without wings 



= Birds. ~ Reptiles. 



