| A | |||||||
AB | Ab | ||||||
ABC = 0 | ABc | AbC | Abc = 0 | ||||
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:—
| Mammifera— | endowed with mammæ and lungs. |
| Birds | without mammæ but with lungs and wings. |
| Fish | deprived of lungs. |
| Reptiles | deprived of mammæ and wings but with lungs. |
We have, then, as Mr. Bentham says, three bifid divisions, thus represented:—
Vertebrata | |||||||
Endowed with | deprived of lungs | ||||||
Endowed with | deprived of | ||||||
with wings | without wings | ||||||
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 wings, which is, as a matter of fact, the case, the wings of bats not being true wings in the meaning of the term as applied to birds. Fish, again, ought to be considered with regard to the possession of mammæ and wings; and in leaving them undivided we really imply that they never have mammæ nor wings, the wings of the flying-fish, again, being no exception. If we resort to the use of our letters and define them as follows—
A = vertebrata,
B = having lungs,
C = having mammæ,
D = having wings,
then there are four existent classes of vertebrata which appear to be thus described—
ABC ABcD ABcd Ab.