objects and not by the others, this quality becomes a difference which divides the genus into two species. We may interpret the species 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. A generic property 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 versâ, all curves of which this is true must be circles. A property which thus belongs to the whole of a class and only to that class, corresponds to the ἴδιον of Aristotle and Porphyry; we might conveniently call it a peculiar property. Every such property enables us to make a statement in the form of a simple identity (p. 37). 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—
It is a peculiar property of equilateral triangles that they are equiangular, and vice versâ, 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 liquids and gases are 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 form of the crystal, nor does the manner in which it is 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 crystallised or not, or whether it be organised or not. As regards botanical classification the absolute size of a plant is an accident. Thus 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 meanings of the Predicables can be clearly explained by our symbols. Let A be any definite group of qualities and B another quality or group of qualities; 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 or groups of qualities, and on examining the combinations in which A, B, C, D, E occur let them