[m] See Grote, Plato and the other Companions of Sokrates, Vol. III., ch. 38, p. 523.
[n] Prantl, Geschichte der Logik, Vol. III., Sect. 19, p. 327.
[o] Berkeley, Principles of Human Knowledge, Introduction, Sect. 12, 15, 16.
There is one other remark to be made, respecting the view of Classification presented in the eighth Chapter of the Analysis. We read in the beginning of that Chapter—[p. 249]—“Forming a class of things is a mode of regarding them. But what is meant by a mode of regarding things? This is mysterious: 283 and is as mysteriously explained, when it is said to be the taking into view the particulars in which individuals agree. For what is there which it is possible for the mind to take into view, in that in which individuals agree? Every colour is an individual colour, every size is an individual size, every shape is an individual shape. But things have no individual colour in common, no individual shape in common, no individual size in common: that is to say, they have neither shape, colour, nor size in common. What then is it which they have in common which the mind can take into view? Those who affirmed that it was something, could by no means tell. They substituted words for things: using vague and mystical phrases, which when examined meant nothing.”
Here we find certain phrases, often used both in common speech and in philosophy, condemned us mystical and obscure. In the next or ninth Chapter (on Abstraction, [p. 295] seq.), we shall see the language substituted for them, and the theory by which the mystery is supposed to be removed. I cannot but think that the theory of Mr. James Mill himself is open to quite as many objections as that which he impugns. He finds fault with those who affirm that the word cube or sphere is applied to a great many different objects by reason of the shape which they have in common; and that they may be regarded so far forth as cube or sphere. But surely this would not have been considered as either incorrect or mysterious by any philosopher, from Aristotle downward. When I am told that it is incorrect, because the shape of each object is an individual shape, I dissent from the reason given. In my judgment, the term individual is a term applicable, properly and specially, to a concrete object—to that which Aristotle would have called a Hoc Aliquid. The term is not applicable to a quality or attribute. The same quality that belongs to one object, may also belong to an indefinite number of others. It is this common quality that is connoted (in the sense of that word employed by Mr. John Stuart Mill) by the class-term: and if there were no common quality, the class-term would have no connotation. In other words, there would be no class: nor 284 would it be correct to apply to any two objects the same concrete appellative name.
But when we come to the following Chapter of the Analysis (ch. ix. on Abstraction, [p. 296]), we read as follows—“Let us suppose that we apply the adjective black first to the word Man. We say ‘black man.’ But we speedily see that for the same reason for which we say black man, we may say black horse, black cow, black coat, and so on. The word black is thus associated with innumerable modifications of the sensation black. By frequent repetition, and the gradual strengthening of the association, these modifications are at last called up in such rapid succession that they appear commingled, and no longer many ideas, but one. Black is therefore no longer an individual, but a general name. It marks not the particular black of a particular individual, but the black of every individual and of all individuals.”
To say that we apply the word black to the horse for the same reason as we applied it to the man, is surely equivalent to saying that the colour of the horse is the same as that of the man: that blackness is the colour which they have in common. It is quite true that we begin by applying the name to one individual object, then apply it to another, and another, &c.; but always for the same reason—to designate (or connote, in the phraseology of Mr. John Stuart Mill) the same colour in them all, and to denote the objects considered under one and the same point of view. It may be that in fact there are differences in shade of colour: but the class-name leaves these out of sight. When we desire to call attention to them, we employ other words in addition to it. Every attribute is considered and named as One, which is or may be common to many individual objects: the objects only are individual.
It is to be regretted, I think, that Mr. James Mill disconnected Classification so pointedly from Abstraction, and insisted on explaining the former without taking account of the latter. Such disconnection is a novelty, as he himself states ([p. 294]): previous expositors thought that “abstraction was included in classification”—and, in my judgment, they were 285 right in thinking so, if (with Mr. James Mill) we are to consider Classification as a “great operation.” An aggregate of concretes is not sufficient to constitute a Class, in any scientific sense, or as available in the march of reasoned truth. You must have, besides, the peculiar mode of regarding the aggregate: (a phrase which Mr. James Mill deprecates as mysterious, but which it is difficult to exchange for any other words more intelligible) you must have “that separating one or more of the ingredients of a complex idea from the rest, which has received the name of Abstraction”—to repeat the very just explanation given by him, [p. 295]—though that too, if we look at [p. 249], he seems to consider as tainted with mystery.
We proceed afterwards to some clear and good additional remarks—[p. 298]. A class-term, as black, “is associated with two distinguishable things, but with the one much more than with the other: the clusters, with which it is associated, are variable: the peculiar sensation with which it is associated, is invariable. It is constantly, and therefore much more strongly, associated with the sensation, than with any of the clusters. It is at once a name of the clusters and a name of the sensation: but it is more peculiarly a name of the sensation.” Again shortly afterwards, the abstract term is justly described as “marking exclusively one part (of the cluster), upon which such and such effects depend, no alteration being supposed in any other part of it.”[p]
[p] The abstract term is coined for the express purpose of marking one part of a cluster simultaneously present to the mind, and fixing attention upon it without the other parts—but the concrete term is often made to serve the same purpose, by means of the adverb quatenus, κάθοσον, ᾗ &c. These phrases are frequent both in Plato and Aristotle: the stock of abstract terms was in their day comparatively small. It is needless to multiply illustrations of that which pervades the compositions of both: a very good one appears in Plato, Republ. I., p. 340 D, 341 C, 342.