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And, first, of complex ideas of COMBINATION. Unity, as I have already observed, is a simple idea : and it is one of the most common simple ideas that can be presented to the mind, for every object without, and every idea within, tend equally to excite it. And, as being a simple idea, the mind, as I have also remarked, is passive on its presentation; it can neither form such an idea to itself, nor contemplate it otherwise than in its totality: but it can combine the ideas of as many units as it pleases, and hence produce the complex idea of a hundred, a thousand, or a hundred thousand. So beauty is a complex idea; for the mind, in forming it, combines a variety of separate ideas into one common aggregate. Thus Dryden, in delineating the beautiful Victoria, in his “ Love Triumphant:"

Her eyes, her lips, her cheeks, her shape, her features,
Seem to be drawn by LOVE's own hand; by Love
Himself in love.

In like manner the mind can produce complex ideas by an opposite process, and that is, by ABSTRACTION, or separation. Thus chalk, snow, and milk, though agreeing, perhaps, in no other respect, coincide in the same colour; and the mind, contemplating this agreement, may abstract or separate it from the other properties of these three objects, and form the idea which is indicated by the term whiteness; and having thus acquired a new idea by the process of abstraction, it may afterward apply it as a character to a variety of other objects: and hence particular ideas become general or universal.

Other complex ideas are produced by COMPARISON. Thus, if the mind take one idea, as that of a foot, as a determinate measure, and place it by the side of another idea, as the idea of a table, the result will be a formation of the complex idea of length, breadth, and thickness. Or if we vary the primary ideas, we may obtain as a result the secondary ideas of coarseness and fineness.

And hence, complex ideas must be almost infinitely more numerous than simple ideas, which are their elements or materials, as words must be always far more numerous than letters. I have instanced only a few of their principal kinds; but even each of these kinds is applicable to a variety of subjects, of which Mr. Locke mentions the three following:

I. IDEAS OF SUBSTANCES; or such as we have uniformly found connected in the same thing, and without which, therefore, such thing cannot be contemplated. To this head belong the complex ideas of a man, a horse, a river, a mountain.

II. IDEAS OF MODEs; or such as may be considered as representative of the mere affections, or properties of substance; of which the idea of number may once more be offered as an example: the ideas of expansion or extension and duration belong to the same stock; and in like manner those of power, time, space, and infinity, which are all modes, properties, or affections of substance; or secondary ideas derived from or excited by the primary idea of substance of some kind or other.

III. IDEAS OF RELATIONS ; which are by far the most extensive, if not the most important, branch of subjects from which our complex ideas are derived; for there is nothing whatever, whether simple idea, substance, mode, relation, or even the name of any of them, which is not capable of an almost infinite number of bearings in reference or relation to other things. It is from this source, therefore, that we derive a very large proportion of our thoughts and words. As examples under it, I may mention all those ideas that relate to or are even imported by the terms father, brother, son, master, magistrate, younger, older, cause and effect, right and wrong, and, consequently, all moral relations.

It must hence appear obvious that many of our ideas have a NATURAL CORRESPONDENCE, congruity, and connexion with each other. And as many, perhaps, on the contrary, a NATURAL REPUGNANCY, incongruity, and disconnexion. Thus if I were to speak of a cold fire, I should put together ideas that are naturally disconnected and incongruous, and should consequently make an absurd proposition, or, to adopt common language, talk nonsense. I should

be guilty of the same blunder if I were to speak of a square billiard-ball, or a soft reposing rock. But a warm fire, on the contrary, a white, or even a black billiard-ball, and a hard, rugged rock, are congruous ideas, and, consequently, consistent with good sense. Now, it is the direct office of that discursive faculty of the mind which we call reason, to trace out these natural coincidences or disjunctions, and to connect or separate them by proper relations; for it is a just perception of the natural connexion and congruity, or of the natural repugnancy and incongruity, of our ideas, that constitutes all real knowledge. The wise man is he who has industriously laid in and carefully assorted an extensive stock of ideas; as the stupid or ignorant man is he who, from natural hebetude, or having had but few opportunities, has collected and arranged but a small number. The man who discovers the natural relations of his ideas quickly is a man of sagacity; and, in popular language, is said, and correctly so, to possess a quick, sharp intellect. The man, on the contrary, who discovers these relations slowly, we call dull or heavy. If he rapidly discover and put together relations that lie remote, and perhaps touch only in a few points, but those points striking and pleasant, he is a man of wit, genius, or brilliant fancy; of agreeable allusion and metaphor. if he connect ideas of fancy with ideas of reality, and mistake the one for the other, however numerous his ideas may be, and whatever their order of succession, he is a madman: he reasons from false principles; and, as we say in popular language, and with perfect correctness, is out of his judgment.

Finally, our ideas are very apt to ASSOCIATE or run together in trains; and upon this peculiar and happy disposition of the mind we lay our chief dependence in sowing the important seeds of education. It often happens, how: ever, that some of our ideas have been associated erroneously, and even in a state of early life, before education has commenced: and hence, from the difficulty of separating them, most of the sympathies and antipathies, the whims and prejudices, that occasionally haunt us to the latest period of old age. Peter the Great, having been terrified by a fall into a sheet of water when an infant, could never, till he became a man, go over a bridge without shuddering; and even at last had no small difficulty in breaking the connex, ion of the ideas that were thus early and powerfully associated. Avarice did not by any kind of predisposition belong to the miser Elwes, for in his youth he was of gay manners, and a spendthrift; but he caught the vice by living with his uncle: uninterrupted habit, the strong power of association, gave strength to its influence, and what was originally his abhorrence, became at length his idol. í Such, then, is the manner in which the mind, at first a sheet of white paper, without characters of any kind, becomes furnished with that vast store of ideas, the materials of wisdom and knowledge, which the busy and boundless fancy of man has painted on it with an almost endless variety. The whole is derived from experience- THE EXPERIENCE OF SENSATION OR REFLECTION; from the observations of the mind employed either about external sensible objects, or the internal operations of itself, perceived and reflected upon by its own faculties.

But man is a social as well as a rational being; he is dependent, for the supply of his wants, upon his fellow-man; and his happiness is made to consist in this dependence. The ideas he possesses he feels a desire of communicating, and those possessed by others he feels an equal desire of diving into. But ideas in themselves are incommunicable: he requires here, as in the case of sensible objects, a circulating medium by which their value may be expressed. And what he requires is freely granted to him: it consists in the high faculty of speech ; in reducing ideas to articulate sounds or words, the aggregate of which constitutes language. And hence the great and valuable systematic work to which I have now chiefly directed your attention, proceeds from a general analysis of our ideas to a general analysis of their vocal representatives: a subject which every one must perceive to be of the utmost importance in the progress of human understanding. Important, however, as it is, it is a subject rather collateral than direct. We have briefly


glanced at it already,* and may perhaps return to it hereafter, but I shall postpone it for the present, that we may hasten with due speed to the goal before

Allow me, however, before we quit it, to observe that words bear precisely the same relation to ideas that ideas do to objects; for as ideas are the mere signs of objects, so words are the mere signs of ideas; and hence that every rule which applies to the variety, precision, and arrangement of our ideas, applies with equal force to the variety, precision, and arrangement of our words; and that without a clear and determinate meaning to the latter, we can no more have a clear and determinate apprehension of the former than we can have of a person's features by a confused or unlike picture. And hence the importance of attending to our vocabulary; of minutely measuring and weighing the terms we make use of, so as to adjust them exactly to the measure and weight of our ideas, must be obvious at the first glance; as it must be also that the more exact and copious a language is found, the more clear and comprehensive must be the general knowledge of the nation to which it belongs.

But ideas and words, though the materials of which knowledge is constructed, and without which it cannot among mankind be constructed at all, are no more knowledge itself than the bricks and mortar of a house are the house itself. Both, as I have indeed hinted at already, must be collected in sufficient abundance, compared with each other, duly assorted, arranged, and united together, before the proper building can be produced; and we have yet, therefore, to contemplate the most important part of the subject before us, and that to which the preceding parts are subservient-the general nature of knowledge, its kinds, degrees, and reality.

KNOWLEDGE may be defined the PERCEPTION OF TRUTH, or, in the language of Aristotle, THE SCIENCE OF TRUTH: and, consequently, he who acquires knowledge perceives or acquires truth. But what is truth? This is a question which has been asked for ages: the particular answer, however, must neces. sarily depend upon the particular subject to which it refers. We are now considering general truth, which may be defined the connexion and agreement, or repugnancy and disagreement, of our ideas.

This definition requires some attention ; but when it is thoroughly comprehended, it will be found to apply to truths of every kind, in the arts, physics, and morals, as well as in metaphysics ; for the law of adjustment, of connexion and disconnexion, of congruity and incongruity, it refers to, is a universal law or constitution of nature, and hence must hold equally every where. Thus, in a building, where the different parts of which it consists perfectly agree, the lines accurately correspond, and the dependencies fit and are proportioned to each other, every part is TRUE to every part, and the whole is TRUE to itself.

So in working a mathematical problem, or determining a fact from cir. eumstantial evidence, every separate link or idea that constitutes a part of the general chain, must have its proper connexion or agreement with the link or idea that lies next to it, as well above as below: for it is these connexions or agreements between one idea and another that constitute the proofs, and a failure in any one destroys our knowledge upon the subject; or, in other words, prevents us from perceiving its truth.

It sometimes happens that we are able to discover at once this agreement or disagreement, this connexion or repugnancy, in the ideas that are presented to us; and in such case our knowledge is instantaneous, and constitutes what we call INTUITION Or INTUITIVE KNOWLEDGE. But it happens far more generally that the agreement or disagreement is by no means obvious; and we are obliged, as in the case of circumstantial evidence, to look out for some inter... mediate idea, which the schools denominate a medius terminus, by which the separate ideas may be united. To make this research is the peculiar province of the discursive faculty of reason; and hence the information thus obtained is called RATIONAL KNOWLEDGE. Let us take a brief view of both these. When I affirm that white is not

* Series 11 Lecture viii. ix. X.

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black; or, which is a proposition of the same kind, that white is white and black is black, I affirm what I know intuitively. The colours of white and of black have excited ideas in my mind, which, whenever they occur, must be identic and true to themselves; for it is not possible for me to have any other idea of white than white, or of black than black: the agreement in this case is the AGREEMENT OF INDENTITY, the agreement of eitheridea with itself; and hence the man who asks me to prove that white is white, or that white is not black, or red, or yellow, asks me to prove what I neither can prove nor want to prove. I do not want to prove it, for I know it with certain knowledge, or, in other words, it is SELF-EVIDENT. And I cannot prove it for this reason; that every proof consists in placing between two ideas that we want to unite together by an agreement which we do not perceive an idea whose agreement with both of them is more obvious. But what idea can I place by the side of the idea of white, of black, of red, or of yellow, that can agree more fully with either of these ideas than such ideas agree with themselves ? Every one must see that there is no such idea to be had; and, consequently, that I can neither offer a proof nor want one. And the very attempt to obtain such a proof would be an absurdity: for could it possibly be acquired, it would not add to my knowledge, which is perfect and certain already, and depends upon the constant agreement of the idea with itself—the agreement of identity.

Nothing has been productive of more mischief in the science of metaphysics than this absurd restlessness in seeking after proofs in cases of intuition, where no proofs are to be had, and the knowledge is certain without them. M. Des Cartes's hypothesis, as I had occasion to notice in our last lecture, commences with an instance of this very absurdity, and it has proved the ruin of it; and the same attempt in various other hypotheses of later date that we shall yet have to touch upon, and particularly those of Bishop Berkeley and Mr. Hume, has equally proved the ruin of these. When I affirm that I am, I affirm that of which I have an intuitive knowledge: and when I affirm that I think, I only make a proposition of the same kind. The connexion between the two ideas I am, and the two ideas I think, is a connexion of coexistence or absolute necessity. It is not possible to separate them, and they want no third or intervening idea to unite them; for if it were possible for me to doubt whether I thought, or whether I existed, the very doubt itself would answer the purpose of a proof in either case. Now one of the chief absurdities of M. Des Cartes's argument, I think, therefore I am, consists in his putting two propositions equally self-evident and intuitive by the side of each other, and making the first the proof of the second: for being equally intuitive, the second must be just as good a proof of the first as the first is of the second; since the mind can no more put together the two ideas I am without thinking, than it can put together the two ideas I think, without being: But nothing is gained by their being put together in the way of proof or demonstration; for I have no more evidence of my existence by calling up the ideas I think, than I had before this proposition was conceived; and hence the attempt not only fails, but could lead to no use if it could stand its ground.

Our knowledge of personal identity is derived from the same source. It is INTUITIVE. This is a subject which has excited a great deal of learned controversy,and called forth many a different proof, or attempt at proof, from the different disputants who have engaged in it. Mr. Locke himself, with a singular deviation from the principles of his own system, has fallen into a common error and offered as a proof the idea of consciousness. No proof, however, or attempt at proof, is more imperfect; for the identity often continues when the consciousness is interrupted, as in sleep without dreaming, in apoplexy, catalepsy, drowning, and various other cases: and hence, if identity were dependent on consciousness, the same man in a dead sleep and out of it would be two or more different persons. The truth is, that our knowledge of identity is intuitive; the two ideas I am, and the two ideas I was, a combination of which constitutes the more complex idea of personal identity, are ideas of necessary connexion from the first moment the connexion can be formed: and hence they produce certain knowledge, and can have no proof; since

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there can be no intermediate idea capable of possessing a closer connexion with either proposition, and consequently fitted to enter between them. “Here, then,” to adopt the language of Bishop Butler, whose reasoning upon this subject bears a close resemblance to the present, “ we can go no farther. For it is ridiculous to attempt to prove the truth of those perceptions whose truth we can no otherwise prove than by other perceptions of exactly the same kind with them, and which there is just the same ground to suspect; or to attempt to prove the truth of our faculties, which can no otherwise be proved than by the use or means of those very suspected faculties themselves."

1 may now advance a step farther, and observe that in all cases in which the agreement or disagreement of two or more ideas can be immediately perceived and compared together, our knowledge is of a like kind, and consequently approaches to intuitive ; although to other persons such ideas may be very remote, and require a long chain of intermediate ideas to connect or separate them, or prove their agreement or repugnancy. Thus I know intuitively, or without going through the process, that the arc of a circle is less than the entire circle ; that a circle itself is a line equidistant in every part of it from its centre; that the three angles of a triangle are equal to two right” angles; that the square of four is sixteen. No man, however, can, perhaps, have any kind of knowledge at first sight upon any of these subjects; he cannot put the extreme ideas together in such a manner as to perceive their agreement or disagreement, and he is not acquainted with the intermediate ideas which are to compare them, and prove their relation. If he could perceive that relation at first sight, he would at first sight have intuitive knowledge upon the subject; and some persons have a much more comprehensive power of this kind than others; for they can perceive and compare the relations of ideas both more readily and more extensively. Euler was a striking example of this endowment, in regard to the science of abstract quantities : Jedediah Buxton appears to have obtained a similar degree of intuitive knowledge in regard to the science of numbers; and we seem in our own day to have another instance of the same kind in the very extraordinary young calculator from America, not more than eight years old.

I have already stated, that when we cannot immediately perceive the agreement or disagreement of two or more ideas, which we are desirous of bringing into comparison, we are obliged to seek out for some intervening idea whose agreement or disagreement with them is obvious to us; and I have also stated, that as this general search is the immediate office of the faculty of reason, the knowledge thus obtained is called RATIONAL KNOWLEDGE. In many cases we are so fortunate as to hit upon intervening ideas whose connexion with the one, the other, or both, as in a chain of perfect evidence, is clear and distinct; and in such case, whether the reasoning consist of a single step or of many, as soon as the mind is able to perceive the connexion or repugnancy, the agreement or disagreement, of the ideas in question, the degree of rational knowledge hereby obtained becomes equal, or nearly so to INTUITION, and is called DEMONSTRATION. If the proofs, or intervening ideas, do not quite amount to this, we have necessarily an inferior degree of rational knowledge, and we distinguish it by the name of BELIEF, ASSENT, or OPINION; and according to the nature of the proofs or intermediate ideas, as decided by the faculty of the judgment, the opinion is rendered INDUBITABLE, PROBABLE, CONJECTURAL, or SUSPICIOUS.

It is upon this comparison of two ideas, by means of a mediate idea expressed or understood, that most of our moral information or common knowledge would be found to depend, if we were to analyze it. Thus, on going into the street, and hearing a man whom I am acquainted with asking which is the way to London Bridge, I may, perhaps, observe to a by-stander, " That man ought to know the way.” The by-stander immediately compares the two

* Analogy of Religion, Natural and Revealed. Of Personal Identity, forming Diss. I.

+ See “Some account of Zerah Colburn, an American child, who possesses some very remarkable pow. er of solving questions in arithmetic, by computation without writing, or any visible contrivance.". Noboleon's Journal of Nat. Phil. vol. xxxiv. p. 5.

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