CHAPTER XXX. CLASSIFICATION.

monad, dyad, triad, tetrad elements, and so on. It would be useless to apply the bifid arrangement, thus:‍—

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 arrangement‍¹⁵ 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