Page:Mind (Old Series) Volume 11.djvu/201

 190 G. S. FULLEETON I Berkeley, Locke's great opponent on the subject of the abstract idea : "Whether cithers have this wonderful faculty of abstracting their ideas, they best can tell : for myself, I find indeed I have indeed a faculty nf imagining, or representing to myself, the ideas of those particular things [ 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 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. I cannot by any effort of thought conceive the abstract idea above described. And it is equally impossible for me to form the abstract idea of motion distinct from the body moving, and which is neither swift nor slow, curvilinear nor rectilinear; and the like may be said of all other abstract general ideas whatsoever. 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 from one 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 which last are the two proper acceptations of abstraction. And there is ground to think most men will acknowledge themselves to be in my case. The generality of men which are simple and illiterate never pretend to abstract notions. It is said they are difficult, and not to be attained without pains and study; we ma} T therefore reasonably conclude that, if such there be, they are confined only to the learned." (1'rinciples of Human Knowledge, Introd., 10.) So much for Berkeley's position with respect to the abstract notion. But mark the concessions which he is forced to make in a later section (16) : "But here it will be demanded, how we can know any proposition to In- true of all particular triangles, except we have first seen it denii'nstrated of the abstract idea of a triangle which equally a-i-e.-.- to all? For, because a property may be demonstrated to agree to some one particular triangle, it will not thence follow that it equally belongs to any other triangle, which in all respects is not the same with it. For example, having demonstrated that the three angles of an isosceles rectangular triangle an- equal to two right ones, I cannot therefore conclude this affection agrees to all other triangles which have neither a right angle nor two equal sides. It seems therefore that, to be certain this proposition is universally true, we must either make a particular demonstration for every particular triangle, which is impo.-sible. or once for all demonstrate it of the abstract idea of a triangle, in which all the particulars do indifl'eieiitly partake and by which they are all equally iepre>ented. To which 1 answer, that, though the idea I have in view whilst 1 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 Hie demonstration. It is true the diagram 1 have in view includes all these particulars, but then there is not the least mention made of them in