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

The bifurcate form of classification seems to be needless when the property 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 property or not one degree, two degrees or not two degrees, and so on. The elements, for instance, 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 wholly useless to apply the bifid arrangement, thus :—

The reason of this is that, by the very nature of number as described in Chapter VIII, 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 property expressible in numbers must find its place somewhere in the series of numbers. The chords in music correspond to the various simpler numerical ratios and must admit of complete

exhaustive classification in respect to the complexity of the ratios forming them. Plane rectilinear figures may also be classified according to the number 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 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, the latter again into 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.

n

The Five Predicables.

As a general rule it is highly desirable to consign to oblivion all 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

n George Bentham, 'Outline of a New System of Logic,' p. 115.

itself of all names and other vestiges of antiquity which are not actually useful at the present day.

6

Among those ancient expressions which may well be excepted from such considerations and ever 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 indeed, namely 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 Mr. Georges Lewes has remarked,' 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.

The Five Predicables are Genus, Species, Difference, Property, and Accident, or in the original Greek yévos, εἶδος, διαφορὰ, ἴδιον, συμβεβηκός. Of these, Genus may be taken to mean any class of objects which is regarded as broken up into two minor classes, which form Species of it. The Genus is defined by a certain number of qualities or circumstances which belong to all objects included in the class, and which are sufficient to mark out these objects from all others which we do not intend to include. Interpreted as regards intension, then, the Genus is a group of qualities; interpreted as regards extension, it is a group of objects possessing those qualities. If now another quality be taken into account which is possessed by some of the objects and not by the others, this quality becomes a Difference which divides the Genus into two Species. We may interpret the Species Biographical History of Philosophy,' (1857) vol. i. p. 126. Grote's History of Greece,' vol. viii. p. 578.

either in intension or extension; in the former respect it is more than the Genus as containing one more quality, the Difference in the latter respect it is less than the Genus as containing only a portion of the group constituting the Genus. We may say then, with Aristotle, that in one sense the Genus is in the Species, namely in intension, and in another sense the Species is in the Genus, namely in extension. The Difference, it is evident, can be interpreted in intension only.

A Property is a quality which belongs to the whole of a class, but does not enter into the definition of that class. Thus if it be a generic property it belongs to every individual object contained in the genus. It is a property of the genus Parallelogram that the opposite angles are equal. If we regard a Rectangle as a species of parallelogram, the difference being that one angle is a right angle, it follows as a specific property that all the angles are right angles. Though a property in the strict logical sense must belong to each of the objects included in the class of which it is a property, it may or may not belong to other objects. The property of having the opposite angles equal may belong to many figures besides parallelograms, for instance, regular hexagons. It is a property of the circle that all triangles constructed upon the diameter with the apex upon the circumference are right angled triangles, and vice versa, all closed curves of which this is true must be circles. We might with advantage distinguish properties which thus belong to a class, and only to that class, as peculiar properties. They enable us to make statements in the form of simple identities (vol. i. p. 44). Thus we know it to be a peculiar property of the circle that for a given length of perimeter it encloses a greater area than any other possible curve; hence we may say—

Curve of equal curvature curve of greatest area.

It is a peculiar property of equilateral triangles that they are equiangular, or, vice versa, it is a peculiar property of equiangular triangles that they are equilateral. It is a property of crystals of the regular system that they are devoid of the power of double refraction, but this is not a property peculiar to them, because vitreous and other amorphous transparent solids, such as glass, together with all liquids and gases, are also devoid of the same property.

An Accident, the fifth and last of the Predicables, is any quality, which may or may not belong to certain objects, and which has no connexion with the classification adopted. The particular size of a crystal does not in the slightest degree affect the nature of the crystal, nor does the manner in which it may be grouped with other crystals: these, then, are Accidents as regards a crystallographic classification. With respect to the chemical composition of a substance, again, it is an accident whether the substance be crystallized or not, or whether it be organized or not. As regards botanical classification the absolute size of a plant is an accident, due to external circumThus we see that a logical accident is any quality or circumstance which is not known to be correlated with those qualities or circumstances forming the definition of the species.

The use of the Predicables can be very concisely explained by our symbols. Thus, let A be any definite group of qualities and B another quality; then A will constitute a genus, and AB, Ab will be species of it, B being the difference. Let C, D and E be other qualities, and on examining the combinations in which A, B, C, D, E occur let them be as follows: