xxx.] CLASSIFICATION. 



from all others which we do not intend to include. Inter- 

 preted 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 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 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 aU 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 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 'i8iov 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 

 cuive ; hence we may say 



Curve of equal curvature = curve of greatest area. 



