CHAPTER XXX. CLASSIFICATION.

to regard this arrangement as in any way a peculiar or special method; it is not only a natural and important one, but it is the inevitable and only system which is logically perfect, according to the fundamental laws of thought. All other arrangements of classes correspond to the bifurcate arrangement, with the implication that some 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:‍—

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 ABcd, AbCd, and AbcD.

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. Bentham 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:‍—

We have, then, as Mr. Bentham says, three bifid divisions, thus represented:‍—

It is quite evident that according to the laws of thought even this arrangement is incomplete. The sub-class mammifera must either have wings or be deprived of them; we must either subdivide this class, or assume that none of the mammifera have