The principles of science

by William Stanley Jevons

But in reality the combinations are implied to be

ABCd = Mammifera,
ABcD = Birds,
ABcd = Reptiles,
Abcd = Fish,

and we imply at the same time that the other four conceivable combinations containing B, C, or D, namely ABCD, AbCD, AbCd, and AbcD, do not exist in nature.

Mr. Bentham points out‍[573] that it is really this method of classification which was employed by Lamarck and De Candolle in their so-called analytical arrangement of the French Flora. He gives as an example a table of the principal classes of De Candolle’s system, as also a bifurcate arrangement of animals after the method proposed by Duméril in his Zoologie Analytique, this naturalist being distinguished by his clear perception of the logical importance of the method. A bifurcate classification of the animal kingdom may also be found in Professor Reay Greene’s Manual of the Cœlenterata, p. 18.

The bifurcate form of classification seems to be needless when the quality 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 quality or not one degree, two degrees or not two degrees, and so on. The elements are classified according as the atom of each saturates 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 useless to apply the bifid arrangement, thus:‍—

Element
Monad				not-Monad
		Dyad				not-Dyad
				Triad				not-Triad
						Tetrad				not-Tetrad.

The reason of this is that, by the nature of number (p. [157]) 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 exhaustive. Every thing admitting of a quality expressible in numbers must find its place somewhere in the series of numbers. The chords in music correspond to the simpler numerical ratios and must admit of complete exhaustive classification in respect to the complexity of the ratios forming them. Plane rectilinear figures may be classified according to the numbers of their sides, as triangles, quadrilateral figures, pentagons, hexagons, heptagons, &c. The bifurcate arrangement is not false when applied to such series of objects; it is even necessarily involved in the arrangement which we do apply, so that its formal statement is needless and tedious. The same may be said of the division of portions of space. Reid and Kames endeavoured to cast ridicule on the bifurcate arrangement‍[574] by proposing to classify the parts of England into Middlesex and what is not Middlesex, dividing the latter again into Kent and what is not Kent, Sussex and what is not Sussex; and so on. This is so far, however, from being an absurd proceeding that it is requisite to assure us that we have made an exhaustive enumeration of the parts of England.

The Five Predicables.

As a rule it is highly desirable to consign to oblivion the ancient logical names and expressions, which have infested the science for many centuries past. If logic is ever to be a useful and progressive science, logicians must distinguish between logic and the history of logic. As in the case of any other science it may be desirable to examine the course of thought by which logic has, before or since the time of Aristotle, been brought to its present state; the history of a science is always instructive as giving instances of the mode in which discoveries take place. But at the same time we ought carefully to disencumber the statement of the science itself of all names and other vestiges of antiquity which are not actually useful at the present day.

Among the ancient expressions which may well be excepted from such considerations and retained in use, are the “Five Words” or “Five Predicables” which were described by Porphyry in his introduction to Aristotle’s Organum. Two of them, Genus and Species, are the most venerable names in philosophy, having probably been first employed in their present logical meanings by Socrates. In the present day it requires some mental effort, as remarked by Grote, to see anything important in the invention of notions now so familiar as those of Genus and Species. But in reality the introduction of such terms showed the rise of the first germs of logic and scientific method; it showed that men were beginning to analyse their processes of thought.