first published it, was justly regarded "as a notable instance of the "great use and comprehensiveness of algebraic solutions." I allude to his formula for finding universally the foci of optic lenses; an example which I purposely select, as it cannot fail to be familiarly known to all who have the slightest tincture of mathematical and physical science.

In such instances as these, it will not surely be supposed, that while we read the geometrical demonstration, or follow the successive steps of the algebraical process, our general conceptions embrace all the various possible cases to which our reasonings extend. So very different is the fact, that the wide grasp of the conclusion is discovered only by a sort of subsequent induction; and, till habit has familiarized us with similar discoveries, they never fail to be attended with a certain degree of unexpected delight. Dr. Halley seems to have felt this strongly when the optical formula already mentioned first presented itself to his mind.

In the foregoing remarks, I have borrowed my examples from mathematics, because, at the period of life when we enter on this study, the mind has arrived at a sufficient degree of maturity to be able to reflect accurately on every step of its own progress; whereas, in those general conclusions to which we have been habituated from childhood, it is quite impossible for us to ascertain, by any direct examination, what the processes of thought were, which originally led us to adopt them. In this point of view, the first doubtful and unassured steps of the young geometer present to the logician a peculiarly interesting and instructive class of phenomena, for illustrating the growth and development of our reasoning powers. The true theory, more especially of general reasoning, may be here distinctly traced by every attentive observer; and may hence be confidently applied (under due limitations) to all the other departments of human knowledge.*

*The view of general reasoning which is given above, appears to myself to afford (without any comment) a satisfactory answer to the following argument of the late worthy and learned Dr. Price: "That the universality consists in the idea, and not merely in the name, as used to signify a number of particulars, resembling that which is the immediate object of reflection, is plain; because, was the idea to which the name answers, and which it recalls into the mind, only a particular one, we could not know to what other ideas to apply it, or what particular objects had the resemblance necessary to bring them within the meaning of the name. A person, in reading over a mathematical demonstration, certainly is conscious that it relates to somewhat else, than just that precise figure presented to him in the diagram. But if he knows not what else, of what use can the demonstra tion be to him? How is his knowledge enlarged by it? Or how shall he know afterwards to what to apply it ?"

In a note upon this passage, Dr. Price observes, that "according to Dr. Cudworth, abstract ideas are implied in the cognoscitive power of the mind; which, he says, contains in itself virtually (as the future plant or tree is contained in the seed) general notions or exemplars of all things, which are exerted by it, or unfold and discover themselves, as occa sions invite, and proper circumstances occur." "This, no doubt, (Dr. Price adds) many will very freely condemn as whimsical and extravagant. I have, I own, a different opin ion of it; but yet I should not care to be obliged to defend it.”—Review of the Principal Questions in Morals. pp. 38, 39, 2d edit.

For my own part, I have no scruple to say, that I consider this fancy of Cudworth as not only whimsical and extravagant, but as altogether unintelligible; and yet it appears

From what has been now said, it would appear, that, in order to arrive at a general conclusion in mathematics (and the same observation holds with respect to other sciences) two different processes of reasoning are necessary. The one is the demonstration of the proposition in question; in studying which, we certainly think of nothing but the individual diagram before us. The other is, the train of thought by which we transfer the particular conclusion to which we have been thus led, to any other diagram to which the same enunciation is equally applicable. As this last train of thought is, in all cases, essentially the same, we insensibly cease to repeat it when the occasion for employing it occurs, till we come at length, without any reflection, to generalize our particular conclusion, the moment it is formed; or, in other words, to consider it as a proposition comprehending an indefinite variety of particular truths. When this habit is established, we are apt to imagine,-forgetting the slow steps by which the habit was acquired, that the general conclusion is an immediate inference from a general demonstration; and that, although there was only one particular diagram present to our external senses, we must have been aware, at every step, that our thoughts were really conversant, not about this diagram, but about general ideas, or, in Dr. Reid's language, general conceptions. Hence the familiar use among logicians of these scholastic and mysterious phrases, which, whatever attempts may be made to interpret them in a manner not altogether inconsistent with good sense, have unquestionably the effect of keeping out of view the real procedure of the human mind in the generalization of its knowledge.

Dr. Reid seems to be of opinion, that it is by the power of forming general conceptions, that man is distinguished from the brutes; for he observes, that "Berkeley's system goes to destroy the bar"rier between the rational and animal natures." I must own I do not perceive the justness of this remark, at least in its application to the system of the nominalists, as I have endeavoured to explain and to limit it in the course of this work. On the contrary, it appears to me, that the account which has been just given of general reasoning, by ascribing to a process of logical deduction (presupposing the previous exercise of abstraction or analysis) what Dr. Reid attempts to explain by the scholastic, and not very intelligible phrase of general conceptions, places the distinction between man and brutes in a far clearer and stronger light, than that in which philosophers have been accustomed to view it. That it is to the exclusive possession

to me, that some confused analogy of the same sort must exist in the mind of every person who imagines that he has the power of forming general conceptions without the intermediation of language.

:

In the continuation of the same note, Dr. Price seems disposed to sanction another re. mark of Dr. Cudworth in which he pronounces the opinion of the nominalists to be so ridiculous and false, as to deserve no confutation. I suspect, that when Dr. Cudworth wrote this splenetic and oracular sentence, he was out of humour with some argument of Hobbes, which he found himself unable to answer. It is not a little remarkable, that the doctrine which he here treats with so great contempt, should, with a very few exceptions, have united the suffrages of all the soundest philosophers of the eighteenth century.

of the faculty of abstraction, and of the other powers subservient to the use of general signs, that our species is chiefly indebted for its superiority over the other animals, I shall afterwards endeavour to show.

It still remains for me to examine an attempt which Dr. Reid has made, to convict Berkeley of an inconsistency, in the statement of his argument against abstract general ideas. "Let us now consider "(says he) the Bishop's notion of generalizing. An idea (he tells "us) which, considered in itself, is particular, becomes general, by "being made to represent or stand for all other particular ideas of "the same sort. To make this plain by an example: Suppose (says "Berkeley) a geometrician is demonstrating the method of cutting "a line into two equal parts. He draws, for instance, a black line "of an inch in length. This, which is in itself a particular line, is "nevertheless, with regard to its signification, general, since, as it is "there used, 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. And as that particular line becomes "general by being made a sign, so the name line, which, taken abso"lutely, is particular, by being a sign, is made general.

"Here (continues Dr. Reid) I observe, that when a particular "idea is made a sign to represent and stand for all of a sort, this sup66 poses a distinction of things into sorts or species. To be of a sort, "implies having those attributes which characterize the sort, and "are common to all the indviduals that belong to it. There cannot "therefore be a sort, without general attributes; nor can there be 66 any conception of a sort without a conception of those general at"tributes which distinguish it. The conception of a sort, therefore, "is an abstract general conception.

"The particular idea cannot surely be made a sign of a thing of "which we have no conception. I do not say, that you must have "an idea of the sort; but surely you ought to understand or conceive "what it means, when you make a particular idea a representative "of it; otherwise your particular idea represents you know not "what."*

Although I do not consider myself as called upon to defend all the expressions which Berkeley may have employed in support of his opinion on this question, I must take the liberty of remarking, that, in the present instance, he appears to me to have been treated with an undue severity. By ideas of the same sort, it is plain he meant nothing more than things called by the same name, and, consequently, (if our illustrations are to be borrowed from mathematics) comprehended under the terms of the same definition. In such cases, the individuals thus classed together are completely identified as subjects of reasoning; in so much, that what is proved with respect to one individual, must hold equally true of all the others. As it is an axiom in geometry, that things which are equal to one and the same

*Pages 484, 485.

thing, are equal to one another; so it may be stated as a maxim in logic, that whatever things have the same name applied to them, in consequence of their being comprehended in the terms of the same definition, may all be considered as the same identical subject, in every case where that definition is the principle on which our reasoning proceeds. In reasoning, accordingly, concerning any sort or species of things, our thoughts have no occasion to wander from the individual sign or representative to which the attention happens to be directed, or to attempt the fruitless task of grasping at those specific varieties which are avowedly excluded from the number of our premises. As every conclusion which is logically deduced from the definition must, of necessity, hold equally true of all the individuals to which the common name is applicable, these individuals are regarded merely as so many units, which go to the composition of the multitude comprehended under the collective or generic term. Nor has the power of conception any thing more to do in the business, than when we think of the units expressed by a particular number in arithmetical computation.

The word sort is evidently transferred to our intellectual arrangements, from those distributions of material objects into separate heaps or collections, which the common sense of mankind universally leads them to make for the sake of the memory; or (which is perhaps nearly the same thing) with a view to the pleasure arising from the perception of order. A familiar instance of this presents itself in the shelves, and drawers, and parcels, to which every shopkeeper had recourse, for assorting, according to their respective denominations and prices, the various articles which compose his stock of goods. In one parcel (for example) he collects and incloses under one common envelope, all his gloves of a particular size and quality; in another, all his gloves of a different size and quality; and, in like manner he proceeds with the stockings, shoes, hats, and the various other commodities with which his warehouse is filled. By this means, the attention of his shopboy, instead of being bewildered among an infinitude of particulars, is confined to parcels or assortments of particulars; of each of which parcels a distinct idea may be obtained from an examination of any one of the individuals contained in it. These individuals, therefore, are, in his apprehension, nothing more than so many units in a multitude, any one of which units is perfectly equivalent to any other; while, at the same time, the parcels themselves, notwithstanding the multitude of units of which they are made up, distract his attention and burden his me, mory as little, as if they were individual articles. The truth is, that they become to his mind individual objects of thought, like a box of counters, or a rouleau of guineas, or any of the other material aggregates with which his senses are conversant; or, to take an example still more apposite to our present purpose, like the phrases one thousand, or one million, when considered merely as simple units entering into the composition of a numerical sum.

The task which I have here supposed the tradesman to perform, in order to facilitate the work of his shop-boy, is exactly analogous, in its effect, to the aid which is furnished to the infant understanding by the structure of its mother-tongue; the generic words which abound in language assorting, and (if I may use the expression) packing up, under a comparatively small number of comprehensive terms, the multifarious objects of human knowledge.* In consequence of the generic terms to which, in civilized society, the mind is early familiarized, the vast multiplicity of things which compose the furniture of this globe are presented to it, not as they occur to the senses of the untaught savage, but as they have been arranged and distributed into parcels or assortments by the successive observations and reflections of our predecessors. Were these arrangements and distributions agreeable, in every instance, to sound philosophy, the chief source of the errours to which we are liable in all our general conclusions, would be be removed; but it would be too much to expect (with some late theorists) that, even in the most advanced state either of physical or of moral science, this supposition is ever to be realized in all its extent. At the same time, it must be remembered, that the obvious tendency of the progressive reason and experience of the species, is to diminish more and more the imperfections of the classifications which have been transmitted from ages of comparative ignorance; and, of consequence, to render language more and more a safe and powerful organ for the investigation of truth.

The only science which furnishes an exception to these observations is mathematics; a science essentially distinguished from every other by this remarkable circumstance, that the precise import of its generic terms is fixed and ascertained by the definitions which form the basis of all our reasonings, and in which, of consequence, the very possibility of errour in our classifications is precluded by the virtual identity of all those hypothetical objects of thought to which the same generic term is applied.

I intend to prosecute this subject farther, before concluding my observations on general reasoning. At present, I have only to add to the foregoing remarks, that, in the comprehensive theorems of the philosopher, as well as in the assortments of the 'tradesman, I cannot perceive a single step of the understanding, which implies any thing more than the notion of number, and the use of a common

name.

Upon the whole, it appears to me, that the celebrated dispute concerning abstract general ideas, which so long divided the schools, is now reduced, among correct thinkers, to this simple question of fact, Could the human mind, without the use of signs of one kind or another, have carried on general reasonings, or formed genera! conclusions? Before arguing with any person on the subject, I should

* The same analogy had occurred to Locke. "To shorten its way to knowledge, and make each perception more comprehensive, the mind binds them into bundles."

VOL. II.

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