of which is followed by the same feeling of resemblance, and no objects but these alone. If this be a faithful statement of the process, and for its fidelity I may safely appeal to your consciousness,-the doctrine of the Nominalists is not less false than that of the Realists. It is false, because it excludes that general feeling of resemblance, the relative suggestion,-which is all that the general name itself truly designates, and without which, therefore, it never would have been invented; while the doctrine of the Realists is false, by inserting in the process those supposed separate entities which form no part of it. The one errs, as I have already said, by excess, the other by deficiency. Even in professing to exclude the general notion of resemblance, however, the Nominalist unconsciously proceeds on it; and no stronger proof can be imagined of the imperfectness of the view which his system gives of our generalizations, than the constant necessity under which we perceive him to labour, of assuming, at every stage of his argument, the existence of those very notions, or feelings of relative suggestion, against which his argument is directed. The general term, we are told, is significant of all objects of a certain kind, or a particular idea is made to represent various other ideas of the same sort; as if the very doctrine did not necessarily exclude all notion of a kind or sort, independent of the application of the term itself. "An idea," says Berkeley," which, considered in itself, is particular, becomes general, by being made to represent or stand for all other particular ideas of the same sort; and he instances this in the case of a line of any particular length, an inch, for example,-which, to a geometer, he says, becomes general, as "it represents all particular lines whatsoever; so that what is demonstrated of it, is demonstrated of all lines, or in other words, of a line in general." It is truly inconceivable that he should not have discovered, in this very statement, that he had taken for granted the existence of general notions, the very states of mind which he denied; since, without these, there can be no meaning in the restriction of any sign, to "ideas of the same sort." If we have previously a notion of what he himself, rather inconsistently, calls a line in general, we can easily understand how the word line may be limited to ideas of one sort; but if we have no such previous general notion, we cannot have any knowledge of the sort to which we are, notwithstanding, said to limit our term. An inch, which is certainly not the same figure as a foot or a yard is, on the principles of Nominalism, which exclude all knowledge of the nature of lines in general, essentially different from these; and might as well, but for that general notion of the resemblance of lines which all have, independently of the term, and previously to the term, but which Nominalism does not allow to exist, be significant of a square, or a circle, as of any other simple length. To say that it represents all particular lines whatsoever, is either to say nothing, or it is to say that certain general notions of resemblance exist truly, as a part of our consciousness, and that we are hence able to attach a meaning to the phrase, "all particular lines whatsoever;" which we could not if a foot, a yard, or a mile, did not appear to us to resemble each other in some respect. It is in vain that Berkeley, who is aware of the objection which may be brought from the universal truths of geometry, against a system which denies every thing but particular ideas, and the signs of particular ideas, endeavours to reconcile this denial of the conception of universality, with that very universality which it denies. It is quite evident, that if 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 do 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 right-angled equicrural triangle, and not because I demonstrated the proposition of the abstract idea of a triangle."* "This answer," I have said in my observations 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 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 particularized, 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 circumstance. Admitting, therefore, that I can enunciate a general proposition, the concepBerkeley's Works, Lond. 1784, v. i. p. 13. tion 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 particular 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," say 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. 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 this 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 * Brown's Observations on Darwin's Zoonomia, p. 142-144. § Ibid. + Philosophy of Rhetoric, B. ii. c. 7. 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. hon different form compterallerian, LECTURE XLVII. TRUE THEORY OF GENERALIZATION REPEATED.-INCONGRUITY IN THE My last Lecture, gentlemen, was employed on a subject which has engaged, in an eminent degree, the attention of philosophers, both from the difficulty which was supposed to attend it, and from the extensive applications which were to be made of it, as the ground-work of every proposition, and consequently, of all our knowledge. It was necessary, therefore, to give you a sketch of the great controversy as to Universals, that so long divided the schools, of which one party, that of the Realists,-formerly so powerful, when the general theory of the primary mental functions of perception accorded with the Realism,-may now, when our theory of perception is too simple to accord with it, be considered as altogether extinct. It was scarcely possible that universal forms, or species, should continue to hold a place in the philosophy of mind, or in our systems of dialectics, when even sensible species had been universally abandoned. In stating the opinion, on the subject of this controversy, which I consider as the only one worthy of your assent, and indeed so obviously just, that it seems to me as if it could scarcely have failed to occur to every mind, but for the darkness of insignificant terms and phrases, with which the controversy itself had enveloped it, I endeavoured to free it, as much as possible, from this mere verbal darkness, and to exhibit the process to you in that simple order of succession in which it appears to me to take place. The process I stated to be the following: We perceive two, or more objects,-this is one state of the mind. We are struck with the feeling of their resemblance in certain respects. This is a second state of the mind. We then, in the third stage, give a name to these circumstances of felt resemblance, a name which is, of course, applied afterwards only where this relation of similarity is felt. It is unquestionably not the name which produces the feeling of resemblance, but the feeling of faut resemblance which leads to the invention, or application of the name; for it would be equally just and philosophic to say, that it is the name of the individual, John, or William, which gives existence to the individual John or William, and that he was nobody, or nothing, till the name, which made him something, was given, as to say, that the name man, which includes both John and William is that which constitutes our relative notion of the resemblance of John and William, expressed by their common appellation; and that, but for the name, we could not have conceived them to have any common or similar properties, that is to say, could not have had any general relative notion, or general idea, as it has been wrongly called, of human nature, of the respects in which John, William, and all other individual men agree. So far is the general term from being essential to the rise of that state of mind which constitutes the feeling of resemblance, or, in other words, to the geneVOL. I. 60 ньше |