of the idea to which it is supposed to give rise, has been matter of considerable controversy among modern philosophers. Bishop Berkeley, and subsequently Hume, denied altogether the possibility of such an operation, on the following grounds. The general idea of a triangle, it was argued by Locke', is an imperfect idea, wherein parts of several different and inconsistent ideas are put together. As limited to no particular kind of triangle, but comprehending all, it must be neither oblique nor rectangle, neither equilateral, equicrural, nor scalene, but all and none of these at once. The abstract idea, as thus described, Berkeley easily perceived to be self-contradictory, and the doctrine suicidal. "I have a faculty," he says, "of imagining or representing to myself the ideas of those particular things I have perceived, and of variously compounding and dividing them. I can imagine a man with two heads, or the upper parts of a man joined to the body of a horse. I can consider the hand, the eye, the nose, each by itself, abstracted or separated from the rest of the body. But then

In the former, we are said to abstract the attention from certain distinctive features of objects presented, (abstrahere a differentiis.) In the latter, we are said to abstract certain portions of a given concept from the remainder, (abstrahere differentias.) The former sense must be understood here, where we are considering the mental process by which concepts are formed. To the latter, as a conscious process of thought, the following remarks do not apply.

whatever hand or eye I imagine, it must have some particular shape and colour. Likewise the idea of man that I frame to myself, must be either of a white, or a black, or a tawny, a straight, or a crooked, a tall, or a low, or a middle-sized man. To be plain, I own myself able to abstract in one sense, as when I consider some particular parts or qualities separated from others, with which though they are united in some object, yet it is possible they may really exist without them. But I deny that I can abstract one from another, or conceive separately, those qualities which it is impossible should exist so separated; or that I can frame a general notion by abstracting from particulars in the manner aforesaid *."

"It is, I know," continues the Bishop, " a point much insisted on, that all knowledge and demonstration are about universal notions, to which I fully agree: but then it doth not appear to me that those notions are formed by abstraction in the manner premised; universality, so far as I can comprehend, not consisting in the absolute, positive nature or conception of any thing, but in the relation it bears to the particulars signified or represented by it by virtue whereof it is that things, names, or notions, being in their own nature particular, are rendered universal. Thus when I demonstrate any proposition concerning triangles, it is to be supposed that I have in view the universal Principles of Human Knowledge, Introduction, §. x.

X

idea of a triangle; which ought not to be understood as if I could frame an idea of a triangle which was neither equilateral, nor scalenon, nor equicrural. But only that the particular triangle I consider, whether of this or that sort it matters not, doth equally stand for and represent all rectilinear triangles whatever, and is in that sense universal..... Though the idea I have in view whilst I make the demonstration be, for instance, that of an isosceles rectangular triangle, whose sides are of a determinate length, I may nevertheless be certain it extends to all other rectilinear triangles, of what sort or bigness soever. And that, because neither the right angle, nor the equality, nor determinate length of the sides, are at all concerned in the demonstration. It is true, the diagram I have in view includes all these particulars, but then there is not the least mention made of them in the proof of the proposition. . . . . And here it must be acknowledged, that a man may consider a figure merely as triangular, without attending to the particular qualities of the angles or relations of the sides. So far he may abstract but this will never prove that he can frame an abstract general inconsistent idea of a triangle." On the other hand, it was argued by Reid, that if a man may consider a figure simply as triangular, without attending to the particular qualities of the angles or relations of the sides, he must have some conception of this object of his y Ibid. §. xv. xvi.

consideration; for no man can consider a thing which he does not conceive. He has a conception, therefore, of a triangular figure, merely as such; and this is all that is meant by an abstract general conception of a triangle”.

In this controversy, the question has been needlessly confused by the vague and inaccurate use of terms. Idea has been indifferently employed by modern philosophers, to denote the object of thought, of imagination, and even (under the representative hypothesis) of perception. Conception, again, has not been sufficiently distinguished, on the one side, from imagination, and, on the other, from a mere understanding of the meaning of words, such as is sufficient to carry on a process of reasoning. To clear up the point at issue, it will be necessary to bear in mind two facts which have just been noticed; viz. firstly, that in every complete act of conception, the attributes forming the concept are contemplated as coexisting in a possible object of intuition; and, secondly, that all concepts are formed by means of signs which have previously been representative of individual objects

- Intellectual Powers, Essay v. ch. 6.

As it is sometimes convenient to have a general term indifferently applicable to any object of internal consciousness, I have in the present work occasionally availed myself in this extent of the term Idea, rejecting, however, the representative idea of perception. The term, however, has been avoided, wherever it is necessary to distinguish between two different states of consciousness.

only. Berkeley, therefore, is thus far right, that we cannot, in any single act of conception, think of a triangle as neither equilateral, isosceles, nor scalene, nor yet as all three at once; for such an individual triangle is not a possible object of intuition. But, on the other hand, in different acts of conception, we may think of a triangle successively as equilateral, isosceles, and scalene; and in every single act we regard it as one or another. The concept cannot, at any one time, that is, in any one act of thought, contain attributes contradictory of each other; but it may, at different times, be combined with individual attributes that are so contradictory. It can therefore potentially, i. e. out of relation to this or that act of conception, be said, in different points of view, to contain all or none of such attributes; but actually, in this or that act of conception, it is limited to this or that combination. Berkeley is also in one sense right in denying that we gain general notions by an operation of abstraction, at least after the manner in which this operation is frequently explained. Similarities are noticed earlier than differences; and our first abstractions may be said to be performed for us, as we learn to give the same name to individuals presented to us under slight, and at first unnoticed, circumstances of

b A contrary theory on this point has occasioned most of the difficulty which Rousseau professes to find in accounting for the origin of general language from proper names.