we have no general notions of squares and triangles, our demonstration of the properties of these figures never can go beyond those particular squares or triangles conceived by us in our demonstration. Thus, says Berkeley, who states the objection, and endeavours to answer it," having demonstrated that the three angles of an isosceles rectangular triangle, are 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 impossible, or once for all, demonstrate it of the abstract idea of a triangle, in which all the particulars so indifferently partake, and by which they are all equally represented. To which I answer, that though the idea I have in view while 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. It is not said the three angles are equal to two right ones, because one of them is a right angle, or because the sides comprehending it are of the same length; which sufficiently shows that the right angle might have been oblique, and the sides unequal, and, for all that, the demonstration have held good; and for this reason it is that I conclude that to be true, of any oblique angular or scalenon, which I had demonstrated, of a particular rightangled equicrural triangle, and not because I demonstrated the proposition of the abstract idea of a triangle."*

"This answer," I have said in my observation on Dr Darwin's Zoonomia, "This answer evidently takes for granted the truth of the opinion which it was intended to confute, by supposing us, during the demonstration, to have a general idea of triangles, without particular reference to the diagram before us. It will be admitted, that the right angle, and the equality of two of the sides, and the determinate length of the whole, are not expressed in the

Berkeley's Works, Lond. 1784, v. i. p. 13.

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words of the demonstration; but words are of consequence only as they suggest ideas, and the ideas, suggested by the demonstration, are the same as if these particular relations of the triangle had been mentioned at every step. It is not said, that the three angles are equal to two right angles, because one of them is a right angle, or because the sides, which comprehend that angle, are of the same length; but it is proved, that the three angles of the triangle, which has one of its angles a right angle, and the sides, which comprehend that angle, of equal length, are together equal to two right angles. This particular demonstration is applicable only to triangles, of one particular form. I cannot infer from it the existence of the same property, in figures, essentially different for, unless we admit the existence of general ideas, an equilateral triangle differs as much from a scalene rectangular triangle, as from a square. In both cases, there is no medium of comparison. To say that the two triangles agree, in having three sides, and three angles, is to say, that there are general ideas of sides and angles; for if they be particularised, and if by the words sides and angles, be meant equal sides, and equal angles, it is evident, that the two triangles do not agree in the slightest cir cumstance. Admitting, therefore, that I can enunciate a general proposition, the conception of which is impossible, I can be certain that the three angles of every triangle are together equal to two right angles, only when it has been demonstrated of triangles of every variety of figure; and, before this can be done, I must have it in my power to limit space, and chain down imagination.”*

In Dr Campbell's illustrations of the power of signs, in his very ingenious work on the Philosophy of Rhetoric, he adopts and defends this doctrine, of the general representative power of particu lar ideas,-making, of course, the same inconsistent assumption which Berkeley makes, and which every Nominalist must make, of those general notions of orders, sorts, or kinds, which his argument would lead us to deny.." When a geometrician," says he, "makes a diagram with chalk upon a board, and from it demonstrates some property of a straight-lined figure, no spectator ever imagines, that he is demonstrating a property of nothing else but that individual white figure of five inches long, which is before him

* Brown's Observations on Darwin's Zoonomia, p. 142-144.

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Every one is satisfied, that he is demonstrating a property of all that order, whether more or less extensive, of which it is both an example and a sign; all the order being understood to agree with it in certain characters, however different in other respects."* There can be no question that every one is, as Dr Campbell says, satisfied that the demonstration extends to a whole order of figures, and the reason of this is, that the mind is capable of forming a general notion of an order of figures; for it really is not easy to be understood, how the mind should extend any demonstration to a whole order of figures, and to that order only, of which order itself, it is said to be incapable of any notion. The mind,' continues Dr Campbell, with the utmost facility, "extends or contracts the representative power of the sign as the particular occasion requires. Thus, the same equilateral triangle will, with equal propriety, serve for the demonstration, not only of a property of all equilateral triangles, but of a property of all isosceles triangles, or even of a property of all triangles whatever." The same diagram does, indeed, serve this purpose, but not from any extension or contraction of the representative power of the sign according to occasion. It is because we had a general notion of the nature of triangles,-or of the common circumstances in which the figures, to which alone we give the name of triangles, agree,-before we looked at the diagram, and had this general notion, common to the whole order, in view, during the whole demonstration. "Nay, so perfectly is this matter understood," Dr Campbell adds, "that, if the demonstrator, in any part, should recur to some property as to the length of a side, belonging to the particular figure he hath constructed, but not essential to the kind mentioned in the proposition, and which the particular figure is solely intended to represent, every intelligent observer would instantly detect the fallacy. So entirely, for all the purposes of science, doth a particular serve for a whole species or genus." But, on Dr Campbell's principles, what is the species or genus, and how does it differ from other species or genera? Instead of the explanation, therefore, which he gives, I would rather say, so certain is it, that, during the whole demonstration, or, at least, as often as any mention of the figures occurs, the general notion of the species or genus of figures, that is to say,

of the circumstance of resemblance of these figures, has been present to the mind; since, if it had no such general notion, it could not instantly detect the slightest circumstance which the species or genus does not include. The particular idea is said to be representative of other ideas" that agree with it in certain characters." But what are these characters? If we do not understand what they are, we cannot, by our knowledge of them, make one idea representative of others; and if we do know what the general characters are, we have already that general notion, which renders the supposed representation unnecessary.

In this case as in many other cases, I have no doubt,-notwithstanding the apparent extravagance of the paradox,-that it is because the doctrine of the Nominalists is very contrary to our feelings, we do not immediately discover it to be so. If it were nearer the truth, we should probably discover the error which it involves, much more readily. The error escapes us, because our general terms convey so immediately to our mind that common relation which they denote, that we supply, of ourselves, what is wanting in the process as described by the Nominalist,-the feeling of the circumstances of resemblance, specific or generic, that are to guide us in the application, as they led us to the invention of our terms. We know what it is which he means, when he speaks of particular terms, or particular ideas, that become more generally significant, by standing for ideas of the same sort, or the same order, or species, or genus, or kind; and we therefore make, for him, by the natural spontaneous suggestions of our own minds, the extension and limitation, which would be impossible on his own system. But for such an illusion, it seems to me scarcely possible to understand, how so many of the first names, of which our science can boast, should be found among the defenders of an opinion which makes reasoning nothing more than a mere play upon words, or, at best, reduces very nearly to the same level, the profoundest ratiocinations of intellectual, or physical, or mathematical philosophy, and the technical labours of the grammarian, or the lexicographer.

The system of the Nominalists, then, I must contend, though more simple than the system of the Realists, is not any more than that system, a faithful statement of the process of generalization.

It is true, as it rejects the existence of any universal form or species, distinct from our mere feeling of general resemblance. But it is false, as it rejects the general relative feeling itself, which every general term denotes, and without which, to direct us in the extension and limitation of our terms, we should be in danger of giving the name of triangle, as much to a square or a circle, as to any three-sided figure. We perceive objects,-we have a feeling, or general notion of their resemblance, we express this general notion by a general term. Such is the process of which we are conscious; and no system, which omits any part of the process, can be a faithful picture of our consciousness.