exhibit all these species in one scheme. He also points out the apparent loss of labour in making any large bifurcate classification; but this he considers to be fully recompensed by the logical value of the result, and the logical training acquired in its execution. Jeremy Bentham, then, fully recognises the value of the Logical Alphabet under another name, though he apprehends also the limit to its use placed by the finiteness of our mental and manual powers.
Does Abstraction imply Generalisation?
Before we can acquire a sound comprehension of the subject of classification we must answer the very difficult question whether logical abstraction does or does not imply generalisation. It comes to exactly the same thing if we ask whether a species may be coextensive with its genus, or whether, on the other hand, the genus must contain more than the species. To abstract logically is (p. 27), to overlook or withdraw our notice from some point of difference. Whenever we form a class we abstract, for the time being, the differences of the objects so united in respect of some common quality. If we class together a great number of objects as dwelling-houses, we overlook the fact that some dwelling-houses are constructed of stone, others of brick, wood, iron, &c. Often at least the abstraction of a circumstance increases the number of objects included under a class according to the law of the inverse relation of the quantities of extension and intension (p. 26). Dwelling-house is a wider term than brick-dwelling-house. House is more general than dwelling-house. But the question before us is, whether abstraction always increases the number of objects included in a class, which amounts to asking whether the law of the inverse relation of logical quantities is always true. The interest of the question partly arises from the fact, that so high a philosophical authority as Mr. Herbert Spencer has denied that generalisation is implied in abstraction,20 making this doctrine the ground for rejecting previous methods of classifying the sciences, and for forming an ingenious but peculiar method of his own. The question is also a fundamental one of the highest logical importance, and involves subtle difficulties which have made me long hesitate in forming a decisive opinion.
Let us attempt to answer the question by examination of a few examples. Compare the two classes gun and iron gun. It is certain that there are many guns which are not made of iron, so that abstraction of the circumstance “made of iron” increases the extent of the notion. Next compare gun and metallic gun. All guns made at the present day consist of metal, so that the two notions seem to be coextensive; but guns were at first made of pieces of wood bound together like a tub, and as the logical term gun takes no account of time, it must include all guns that have ever existed. Here again extension increases as intension decreases. Compare once more “steam-locomotive engine” and “locomotive engine.” In the present day, as far as I am aware, all locomotives are worked by steam, so that the omission of that qualification might seem not to widen the term; but it is quite possible that in some future age a different motive power may be used in locomotives; and as there is no limitation of time in the use of logical terms, we must certainly assume that there is a class of locomotives not worked by steam, as well as a class that is worked by steam. When the natural class of Euphorbiaceæ was originally formed, all the plants known to belong to it were devoid of corollas; it would have seemed therefore that the two classes “Euphorbiaceæ,” and “Euphorbiaceæ devoid of Corollas,” were of equal extent. Subsequently a number of plants plainly belonging to the same class were found in tropical countries, and they possessed bright coloured corollas. Naturalists