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it affects us with a certain feeling of relation when considered together with certain other numbers,-though for discovering the property originally, and for feeling it afterwards, it was necessary that the other numbers should be considered together with it; as, when I state that mercury admits of being amalgamated with other metals, I state a property included in my complex notion of mercury, though, for originally discovering the property, and for feeling it afterwards, I must have considered the mercury together with the other metals, with which I state its readiness of entering into chemical union. When I consider the same number four together with other numbers, I discover various other relations, as when I endeavour to form new combinations of mercury, or of other chemical substances, I discover new relations, which I add to my complex notions of the substances themselves. As my original conception of mercury becomes more complex by all the new relations which I trace, so my original conception of the number four, which seemed at first a very simple one, becomes gradually more complex, by the detection of the various relations of proportion, which are truly comprehended in it as a subject of our thought,-as every new relation which I discover in a chemical substance, is comprehended in my widening conception of the substance itself,-and the arithmetical or geometrical proportion, like the chemical quality, may thus strictly be reduced to the general class of the relations of comprehension.

In this way, every new proportion which is traced out, in a long series of such arithmetical or geometrical propositions, may be considered as the result of a mere analysis, by which elements existing before, but unsuspected, are evolved, as in the other species of reasoning, more obviously analytic. It is evident, indeed, that the statement of any property inherent in any subject, must, in rigid accuracy of arrangement, be analytical. But without insisting on so subtile a process, it may be easier, at least, though it should not be more accurate, to regard our reasonings of this kind, in the same manner as we formerly regarded our feelings of the simple relation of proportion, involved in each proposition of the reasoning, as forming a class apart; the reasonings we may call, in distinction from our more obvious analytic reasonings, proportional reasonings, as we termed the simple relative suggestions which they involve, relations of proportion.

Whatever be the species of reasoning, however, it is necessary, that the propositions which form the reasoning, should follow each other in a certain order, for without this order, though each proposition might involve some ittle analysis, and consequently some little accession of knowledge, the knowledge thus acquired must be very limited. There could be no deduction of remote conclusions, by which the primary subject of a distant proposition might be shown, through a long succession of analyses, to have properties, which required all these various evolutions, before they could themselves be evolved to view. In the proportional reasonings of geometry, we know well, that the omission of a single proposition, or even a change of its place, might render apparently false, and almost inconceivable by us, a conclusion, which, but for such omission or change of place of a few words of the demonstration, we should have adopted instantly, with a feeling of the absolute impossibility of resisting its evidence.

How is it then, that, when order is so essential to discovery, the propositions which we form in our own silent reasoning, arrange themselves, as they rise in succession, in this necessary order; and what are we to think of that

art, which, for so many ages, was held out, not so much as an auxiliary to reason, as with the still higher praise of being an instrument that might almost supply its place, by the possession of which, the acute and accurate might argue still more acutely and accurately, and imbecility itself become a champion worthy of encountering them; and though not perhaps the victor, at least not always the vanquished.

But to these subjects I must not proceed till my next Lecture.




GENTLEMEN, after considering and classing our feelings of relation,-as they arise in any particular case, from the simple perception or conception of two or more objects, I proceeded in my last Lecture, to consider them, as they arise in those series which are denominated reasoning-series, that correspond, of course, with the division which we have made of the species of relations involved in the separate propositions that compose them; but of which the most important are those which I termed analytical, as involving in every stage the consideration of a whole and its parts, or those which I termed proportional, as involving some common relation of intellectual measurement. To the former of these orders, indeed, the analytical-the others might, as I stated to you, and endeavoured to prove, admit of being reduced; but as the process which reduces them all to this one great order, might seem too subtile, and could afford no additional advantage in our inquiry, I conceived it more advisable, upon the whole, to retain our original division.

Every reasoning is a series of propositions; but every series of propositions is not reasoning; however just the separate propositions may be,-the half of eighteen is equal to the cube of three-man is liable to error-marble is a carbonate of lime-these propositions following each other lead to no conclusion different from those which each separately implies and expresses. To constitute reasoning, it is necessary that there should be some mutual relation of the subjects and predicates of the different propositions. The order in which the different propositions arrange themselves, so as to present to us this mutual relation of the successive subjects and predicates, is, therefore, of the utmost importance to our consecutive analysis, in the reasonings that are strictly analytic, and to our consecutive measurements in the reasonings which I have termed proportional.

On what does this order depend?

Let us suppose, for example, that A is equal to D,—that we are ignorant of this exact relation,-that we wish to estimate it precisely,—that we have no mode of considering them together, but that without knowing the relation of equality of A to D, we know the relation which these bear to some other objects which may be termed intermediate-that, for example, we know A to be equal to B, which we know to be equal to the half of C, and that C is known by us to be the double of D. If the proportional relative A is equal to B, which is the half of C, which is the double of D, follow each other in our mind in this order, it will be absolutely impossible for us to doubt, that A is exactly equal to D, since it is equal to that which is the half of the double of D. But, if any one of these relations of the intermediate objects do not arise in our mind-whether it be the relation of A to B, of B to C, of C to D, the relation of equality of A to D, which is instantly and irresistibly felt by us, after the former series, will not be felt, though the series should be exactly the same in every respect, with the exception of this single proposition omitted in it. It is not enough that we may have formerly observed and measured B and C, and known their relation to D, unless B occur to us while A is in our thought; and we might thus have all the knowledge which is necessary for discovering the proportional relation of A and D, without the slightest knowledge of the proportion, or even the slightest possibility of knowing it, unless our thoughts should arrange themselves in a certain order. It is quite essential to our demonstration, that B and C should arise at certain times; and they do arise at certain times. How is it that this happens?

The common opinion, on the subject, makes this order a very easy matter. We have a certain sagacity, it is said, by which we find out the intervening propositions that are so, and they are arranged in this order, because we have discovered them to be suitable for our measurement, and put them in their proper place." Those intervening ideas, which serve to show the agreement of any two others," says Locke, " are called proofs. A quickness in the mind to find out these intermediate ideas (that shall discover the agreement or disagreement of any other) and to apply them rightly, is, I suppose, that which is called sagacity. And reason itself, in another part of his work, he defines to be the faculty which finds out these means, and rightly applies them." I need not quote to you the common expressions, to the same purport,which are to be found in other writers.

That, in some minds, these intervening conceptions, on which demonstration depends, do arise more readily than in others, there can be no question; and it is by a very natural and obvious metaphor, that minds, able to detect those secret relations, which are not perceived by others, to whom the same intervening conceptions have not arisen, or have arisen without suggesting the same feeling of common relation, are said to have peculiar sagacity. But it is a metaphor only, and is far from solving the difficulty. The question still remains, what that process truly is, which the word sagacity is borrowed to denote,-whether the intermediate conceptions, that arise more readily, in certain minds, than in others, arise in consequence of any skill in discovering them, or any voluntary effort in producing them, or whether they do not arise in consequence of laws of suggestion, that are independent alike of * Essay concerning Human Understanding, B. iv. c. ii. sect. 2.

t Ibid. B. iv. c. xvii. sect. 2.

our skill, and of any efforts which that skill might direct? A and D are before us, and have a relation, which is at present unknown, but a relation which would be evolved to us, if B and C were to arise to our mind. Do they then arise at our bidding? Or do they arise without being subject to our command, and without obeying it?

After the remarks which I made, in reference to intellectual phenomena, in some degree analogous, I trust that you are able, of yourselves, to decide this question, by the argument which I used on the occasions to which I refer. The mind, it can scarcely fail to occur to you, cannot will the conception of B or C, however essential they may be to our reasoning; since to will them, at least if we know what we will, which is surely essential to volition, implies the existence of the very conceptions which we are said to will, as states of the mind present, and prior to the exercise of that sagacity which is said to produce them. If B and C, therefore, rise to our thought, in the case supposed by us, it cannot be because we have willed them; but they must rise in consequence of laws of mind, that are independent of our volition. In short, we do not find them out, as Locke says, but they come to us; and when they have thus risen in our mind, we do not apply them, as he says, because we regard them as suitable; but the relation which is involved in them, is felt, without any intentional application, merely in consequence of their presence together in the mind. The skilful application, indeed, of which he speaks, involves an error of precisely the same kind as that which is involved in the assertion of the volition of the particular conceptions, which are said to be thus applied. It necessarily assumes the existence of the very relative feeling, for the rise of which it professes to account; since, without this previous feeling, the comparative suitableness of one medium of proof, rather than another, could not be known. The right application of fit conceptions to fit conceptions, in the choice of intermediate ideas, presupposes then, in the very sagacity which is said to apply them rightly, a knowledge of the relation which the intermediate idea bears to the object to which it is applied,-of the very relation for discovering which alone, it is of any consequence that the intermediate idea should be applied. The subjects of our intervening propositions, in our trains of reasoning,B and C, for example, by which we discover the relation of A to D, do not, then, and cannot arise in consequence of our willing them since to will them, would be to have those very subjects of comparison, which we will to exist, already present to our mind, which wills them; and to will them, with peculiar sagacity, on account of their fitness as subjects of comparison, would be to have already felt that relation, for the mere purpose of discovering which, they are said to be willed. Though arising in conformity with our general desire, then, they do not arise in consequence of any particular volitions; and yet they arise, and arise in the very order that is necessary for developing the remote relation. The whole seeming mystery of this order, in the propositions which form our longest processes of reasoning, depends on the regularity of the laws, which guide our simple suggestions, in the phenomena of mere association formerly considered by us. Our various conceptions, in our trains of thought, we found, do not follow each other loosely, but according to certain relations. It is not wonderful, therefore, that A should suggest B, which is related to it,-B C,-C D. All this might take place by simple suggestion, though no relation were felt, and consequently no proposition or verbal statement of relation framed. But, it is not a train of VOL. I.


simple suggestions only which the laws of mind evolve. We are susceptible of the feeling of relation of parts of the train, as much as of the conceptions themselves; and when A has excited the relative conception of B, it is not wonderful that we should feel the relation of A and B; or, when C is excited, the relation of B and C, more than that any other feeling of our mind should arise in its ordinary circumstances,-that we should hear the sound of a cannon, in consequence of the vibration of a few invisible particles of air, or see the flash which precedes it, in consequence of some slight affection of our visual nerves. It is impossible for us to will any one of the conceptions in the series A, B, C, D, though we may have the general wish of discovering the relation of A and D, and consequently their relation to any common objects of comparison. It is equally impossible for us to will our feeling of any one of the relations of these to each other, though we may be desirous of discovering their relations; since to will any particular feeling of relation, would be to have already felt that relation. But the conceptions rise after each other, in a certain order, in consequence of the natural order of the course of suggestion; and our feelings of relation, therefore, and consequently our propositions, which are only our feelings of relations expressed in language, correspond, as might be supposed, with the regularity of the conceptions which suggest them.

The sagacity of which Locke and other writers speak, may then, since it is nothing more than a form of our simple suggestion itself, be reduced to that peculiar tendency of the suggesting principle, varying in different minds, of which I before treated, when considering the Secondary Laws of Suggestion, in their relation to Original Genius. The same objects do not suggest to all the same objects, even where past observation and experience may have been the same; because the peculiar suggestions of the objects, the relations of which are afterwards felt, depend, in a great measure, on constitutional tendencies, varying in different individuals, and, in a great measure, also on tendencies modified by long habit; and, therefore, varying in different individuals, as these habits may have been different. To some minds, -the common minds, which, in the great multitudes of our race, think what others have thought, as they do what others have done, the conceptions which form their trains of memory, that scarcely can be called trains of reflection, rise, as we have seen, according to the relation of mere contiguity, or former proximity in time, of the related images. The conceptions of minds of a higher order, rise in almost infinite variety, because they rise according to a relation which does not depend on former co-existence of the very images themselves, but is itself almost infinitely various.

It is this tendency of our suggestions, to rise according to the relation of analogy, which gives inventive vigour to our reasoning, as it gives richness and novelty to our products of mere imagination. By continually presenting to us new objects, in succession, it, of course, presents to us new relations, and leads the philosophic genius from the simplest perceptions of objects, which the dullest of mankind equally behold, but in which the objects themselves are all which they see, to those sublime relations of universal nature, which bind every thing to every thing, in the whole infinity of worlds, and of which the knowledge of the immensity is scarcely so wonderful as the apparent insignificance of the means by which the knowledge has been acquired.

The sagacity, then, of which Locke and other writers speak, is as little

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