and so on; this is a clear proof, that the ideas of surfaces, lines, and points, admit not of any division; those of surfaces in depth, of lines in breadth and depth, and of points in any dimension.
The _schoolmen_ were so sensible of the force of this argument, that some of them maintained that nature has mixed among those particles of matter, which are divisible _in infinitum_, a number of mathematical points in order to give a termination to bodies; and others eluded the force of this reasoning by a heap of unintelligible cavils and distinctions. Both these adversaries equally yield the victory. A man who hides himself confesses as evidently the superiority of his enemy, as another, who fairly delivers his arms.
Thus it appears, that the definitions of mathematics destroy the pretended demonstrations; and that if we have the idea of indivisible points, lines, and surfaces, conformable to the definition, their existence is certainly possible; but if we have no such idea, 'tis impossible we can ever conceive the termination of any figure, without which conception there can be no geometrical demonstration.
But I go farther, and maintain, that none of these demonstrations can have sufficient weight to establish such a principle as this of infinite divisibility; and that because with regard to such minute objects, they are not properly demonstrations, being built on ideas which are not exact, and maxims which are not precisely true. When geometry decides any thing concerning the proportions of quantity, we ought not to look for the utmost _precision_ and exactness. None of its proofs extend so far: it takes the dimensions and proportions of figures justly; but roughly, and with some liberty. Its errors are never considerable, nor would it err at all, did it not aspire to such an absolute perfection.
I first ask mathematicians what they mean when they say one line or surface is _equal_ to, or _greater_, or _less_ than another? Let any of them give an answer, to whatever sect he belongs, and whether he maintains the composition of extension by indivisible points, or by quantities divisible _in infinitum_. This question will embarrass both of them.
There are few or no mathematicians who defend the hypothesis of indivisible points, and yet these have the readiest and justest answer to the present question. They need only reply, that lines or surfaces are equal, when the numbers of points in each are equal; and that as the proportion of the numbers varies, the proportion of the lines and surfaces is also varied. But though this answer be _just_ as well as obvious, yet I may affirm, that this standard of equality is entirely _useless_, and that it never is from such a comparison we determine objects to be equal or unequal with respect to each other. For as the points which enter into the composition of any line or surface, whether perceived by the sight or touch, are so minute and so confounded with each other that 'tis utterly impossible for the mind to compute their number, such a computation will never afford us a standard, by which we may judge of proportions. No one will ever be able to determine by an exact enumeration, that an inch has fewer points than a foot, or a foot fewer than an ell, or any greater measure; for which reason, we seldom or never consider this as the standard of equality or inequality.
As to those who imagine that extension is divisible _in infinitum_, 'tis impossible they can make use of this answer, or fix the equality of any line or surface by a numeration of its component parts. For since, according to their hypothesis, the least as well as greatest figures contain an infinite number of parts, and since infinite numbers, properly speaking, can neither be equal _nor_ unequal with respect to each other, the equality or inequality of any portions of space can never depend on any proportion in the number of their parts. 'Tis true, it may be said, that the inequality of an ell and a yard consists in the different numbers of the feet of which they are composed, and that of a foot and a yard in the number of inches. But as that quantity we call an inch in the one is supposed equal to what we call an inch in the other, and as 'tis impossible for the mind to find this equality by proceeding _in infinitum_ with these references to inferior quantities, 'tis evident that at last we must fix some standard of equality different from an enumeration of the parts.
There are some who pretend,[6] that equality is best defined by _congruity_, and that any two figures are equal, when upon the placing of one upon the other, all their parts correspond to and touch each other. In order to judge of this definition let us consider, that since equality is a relation, it is not, strictly speaking, a property in the figures themselves, but arises merely from the comparison which the mind makes betwixt them. If it consists therefore in this imaginary application and mutual contact of parts, we must at least have a distinct notion of these parts, and must conceive their contact. Now 'tis plain, that in this conception, we would run up these parts to the greatest minuteness which can possibly be conceived, since the contact of large parts would never render the figures equal. But the minutest parts we can conceive are mathematical points, and consequently this standard of equality is the same with that derived from the equality of the number of points, which we have already determined to be a just but an useless standard. We must therefore look to some other quarter for a solution of the present difficulty.
There are many philosophers, who refuse to assign any standard of _equality_, but assert, that 'tis sufficient to present two objects, that are equal, in order to give us a just notion of this proportion.
All definitions, say they, are fruitless without the perception of such objects; and where we perceive such objects we no longer stand in need of any definition. To this reasoning I entirely agree; and assert, that the only useful notion of equality, or inequality, is derived from the whole united appearance and the comparison of particular objects.
'Tis evident that the eye, or rather the mind, is often able at one view to determine the proportions of bodies, and pronounce them equal to, or greater or less than each other, without examining or comparing the number of their minute parts. Such judgments are not only common, but in many cases certain and infallible. When the measure of a yard and that of a foot are presented, the mind can no more question, that the first is longer than the second, than it can doubt of those principles which are the most clear and self-evident.
There are therefore three proportions, which the mind distinguishes in the general appearance of its objects, and calls by the names of _greater, less_, and _equal_. But though its decisions concerning these proportions be sometimes infallible, they are not always so; nor are our judgments of this kind more exempt from doubt and error than those on any other subject. We frequently correct our first opinion by a review and reflection; and pronounce those objects to be equal, which at first we esteemed unequal; and regard an object as less, though before it appeared greater than another. Nor is this the only correction which these judgments of our senses undergo; but we often discover our error by a juxta-position of the objects; or, where that is impracticable, by the use of some common and invariable measure, which, being successively applied to each, informs us of their different proportions. And even this correction is susceptible of a new correction, and of different degrees of exactness, according to the nature of the instrument by which we measure the bodies, and the care which we employ in the comparison.
When therefore the mind is accustomed to these judgments and their corrections, and finds that the same proportion which makes two figures have in the eye that appearance, which we call _equality_, makes them also correspond to each other, and to any common measure with which they are compared, we form a mixed notion of equality derived both from the looser and stricter methods of comparison. But we are not content with this. For as sound reason convinces us that there are bodies _vastly_ more minute than those which appear to the senses; and as a false reason would persuade us, that there are bodies _infinitely_ more minute, we clearly perceive that we are not possessed of any instrument or art of measuring which can secure us from all error and uncertainty.
We are sensible that the addition or removal of one of these minute parts is not discernible either in the appearance or measuring; and as we imagine that two figures, which were equal before, cannot be equal after this removal or addition, we therefore suppose some imaginary standard of equality, by which the appearances and measuring are exactly corrected, and the figures reduced entirely to that proportion.
This standard is plainly imaginary. For as the very idea of equality is that of such a particular appearance, corrected by juxta-position or a common measure, the notion of any correction beyond what we have instruments and art to make, is a mere fiction of the mind, and useless as well as incomprehensible. But though this standard be only imaginary, the fiction however is very natural; nor is any thing more usual, than for the mind to proceed after this manner with any action, even after the reason has ceased, which first determined it to begin.
This appears very conspicuously with regard to time; where, though 'tis evident we have no exact method of determining the proportions of parts, not even so exact as in extension, yet the various corrections of our measures, and their different degrees of exactness, have given us an obscure and implicit notion of a perfect and entire equality. The case is the same in many other subjects. A musician, finding his ear become every day more delicate, and correcting himself by reflection and attention, proceeds with the same act of the mind even when the subject fails him, and entertains a notion of a complete _tierce_ or _octave_, without being able to tell whence he derives his standard. A painter forms the same fiction with regard to colours; a mechanic with regard to motion. To the one _light_ and _shade_, to the other _swift_ and _slow_, are imagined to be capable of an exact comparison and equality beyond the judgments of the senses.
We may apply the same reasoning to _curve_ and _right_ lines. Nothing is more apparent to the senses than the distinction betwixt a curve and a right line; nor are there any ideas we more easily form than the ideas of these objects. But however easily we may form these ideas, 'tis impossible to produce any definition of them, which will fix the precise boundaries betwixt them. When we draw lines upon paper or any continued surface, there is a certain order by which the lines run along from one point to another, that they may produce the entire impression of a curve or right line; but this order is perfectly unknown, and nothing is observed but the united appearance.
Thus, even upon the system of indivisible points, we can only form a distant notion of some unknown standard to these objects. Upon that of infinite divisibility we cannot go even this length, but are reduced merely to the general appearance, as the rule by which we determine lines to be either curve or right ones. But though we can give no perfect definition of these lines, nor produce any very exact method of distinguishing the one from the other, yet this hinders us not from correcting the first appearance by a more accurate consideration, and by a comparison with some rule, of whose rectitude, from repeated trials, we have a greater assurance. And 'tis from these corrections, and by carrying on the same action of the mind, even when its reason fails us, that we form the loose idea of a perfect standard to these figures, without being able to explain or comprehend it.
'Tis true, mathematicians pretend they give an exact definition of a right line when they say, _it is the shortest way betwixt two points_. But in the first place I observe, that this is more properly the discovery of one of the properties of a right line, than a just definition of it. For I ask any one, if, upon mention of a right line, he thinks not immediately on such a particular appearance, and if 'tis not by accident only that he considers this property? A right line can be comprehended alone; but this definition is unintelligible without a comparison with other lines, which we conceive to be more extended. In common life 'tis established as a maxim, that the straightest way is always the shortest; which would be as absurd as to say, the shortest way is always the shortest, if our idea of a right line was not different from that of the shortest way betwixt two points.
Secondly, I repeat, what I have already established, that we have no precise idea of equality and inequality, shorter and longer, more than of a right line or a curve; and consequently that the one can never afford us a perfect standard for the other. An exact idea can never be built on such as are loose and undeterminate.
The idea of a _plain surface_ is as little susceptible of a precise standard as that of a right line; nor have we any other means of distinguishing such a surface, than its general appearance. 'Tis in vain that mathematicians represent a plain surface as produced by the flowing of a right line. 'Twill immediately be objected, that our idea of a surface is as independent of this method of forming a surface, as our idea of an ellipse is of that of a cone; that the idea of a right line is no more precise than that of a plain surface; that a right line may flow irregularly, and by that means form a figure quite different from a plane; and that therefore we must suppose it to flow along two right lines, parallel to each other, and on the same plane; which is a description that explains a thing by itself, and returns in a circle.
It appears then, that the ideas which are most essential to geometry, viz. those of equality and inequality, of a right line and a plain surface, are far from being exact and determinate, according to our common method of conceiving them. Not only we are incapable of telling if the case be in any degree doubtful, when such particular figures are equal; when such a line is a right one, and such a surface a plain one; but we can form no idea of that proportion, or of these figures, which is firm and invariable. Our appeal is still to the weak and fallible judgment, which we make from the appearance of the objects, and correct by a compass, or common measure; and if we join the supposition of any farther correction, 'tis of such a one as is either useless or imaginary. In vain should we have recourse to the common topic, and employ the supposition of a Deity, whose omnipotence may enable him to form a perfect geometrical figure, and describe a right line without any curve or inflection. As the ultimate standard of these figures is derived from nothing but the senses and imagination, 'tis absurd to talk of any perfection beyond what these faculties can judge of; since the true perfection of any thing consists in its conformity to its standard.
Now, since these ideas are so loose and uncertain, I would fain ask any mathematician, what infallible assurance he has, not only of the more intricate and obscure propositions of his science, but of the most vulgar and obvious principles? How can he prove to me, for instance, that two right lines cannot have one common segment? Or that 'tis impossible to draw more than one right line betwixt any two points? Should he tell me, that these opinions are obviously absurd, and repugnant to our clear ideas; I would answer, that I do not deny, where two right lines incline upon each other with a sensible angle, but 'tis absurd to imagine them to have a common segment. But supposing these two lines to approach at the rate of an inch in twenty leagues, I perceive no absurdity in asserting, that upon their contact they become one. For, I beseech you, by what rule or standard do you judge, when you assert that the line, in which I have supposed them to concur, cannot make the same right line with those two, that form so small an angle betwixt them? You must surely have some idea of a right line, to which this line does not agree. Do you therefore mean, that it takes not the points in the same order and by the same rule, as is peculiar and essential to a right line? If so, I must inform you, that besides that, in judging after this manner, you allow that extension is composed of indivisible points (which, perhaps, is more than you intend), besides this, I say, I must inform you, that neither is this the standard from which we form the idea of a right line; nor, if it were, is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserved. The original standard of a right line is in reality nothing but a certain general appearance; and 'tis evident right lines may be made to concur with each other, and yet correspond to this standard, though corrected by all the means either practicable or imaginable.
To whatever side mathematicians turn, this dilemma still meets them.
If they judge of equality, or any other proportion, by the accurate and exact standard, viz. the enumeration of the minute indivisible parts, they both employ a standard, which is useless in practice, and actually establish the indivisibility of extension, which they endeavour to explode. Or if they employ, as is usual, the inaccurate standard, derived from a comparison of objects, upon their general appearance, corrected by measuring and juxtaposition; their first principles, though certain and infallible, are too coarse to afford any such subtile inferences as they commonly draw from them. The first principles are founded on the imagination and senses; the conclusion therefore can never go beyond, much less contradict, these faculties.
This may open our eyes a little, and let us see, that no geometrical demonstration for the infinite divisibility of extension can have so much force as what we naturally attribute to every argument, which is supported by such magnificent pretensions. At the same time we may learn the reason, why geometry fails of evidence in this single point, while all its other reasonings command our fullest assent and approbation. And indeed it seems more requisite to give the reason of this exception, than to show that we really must make such an exception, and regard all the mathematical arguments for infinite divisibility as utterly sophistical. For 'tis evident, that as no idea of quantity is infinitely divisible, there cannot be imagined a more glaring absurdity, than to endeavour to prove, that quantity itself admits of such a division; and to prove this by means of ideas, which are directly opposite in that particular. And as this absurdity is very glaring in itself, so there is no argument founded on it, which is not attended with a new absurdity, and involves not an evident contradiction.
I might give as instances those arguments for infinite divisibility, which are derived from the _point of contact_. I know there is no mathematician, who will not refuse to be judged by the diagrams he describes upon paper, these being loose draughts, as he will tell us, and serving only to convey with greater facility certain ideas, which are the true foundation of all our reasoning. This I am satisfied with, and am willing to rest the controversy merely upon these ideas. I desire therefore our mathematician to form, as accurately as possible, the ideas of a circle and a right line; and I then ask, if upon the conception of their contact he can conceive them as touching in a mathematical point, or if he must necessarily imagine them to concur for some space. Whichever side he chooses, he runs himself into equal difficulties. If he affirms, that in tracing these figures in his imagination, he can imagine them to touch only in a point, he allows the possibility of that idea, and consequently of the thing. If he says, that in his conception of the contact of those lines he must make them concur, he thereby acknowledges the fallacy of geometrical demonstrations, when carried beyond a certain degree of minuteness; since, 'tis certain he has such demonstrations against the concurrence of a circle and a right line; that is, in other words, he can prove an idea, viz. that of concurrence, to be _incompatible_ with two other ideas, viz. those of a circle and right line; though at the same time he acknowledges these ideas to be _inseparable_.
[5] L'Art de penser.
[6] See Dr Barrow's Mathematical Lectures.
SECTION V.
THE SAME SUBJECT CONTINUED.
If the second part of my system be true, _that the idea of space or extension is nothing but the idea of visible or tangible points distributed in a certain order_, it follows, that we can form no idea of a vacuum, or space, where there is nothing visible or tangible. This gives rise to three objections, which I shall examine together, because the answer I shall give to one is a consequence of that which I shall make use of for the others.
First, it may be said, that men have disputed for many ages concerning a vacuum and a plenum, without being able to bring the affair to a final decision: and philosophers, even at this day, think themselves at liberty to take party on either side, as their fancy leads them.
But whatever foundation there may be for a controversy concerning the things themselves, it may be pretended that the very dispute is decisive concerning the idea, and that 'tis impossible men could so long reason about a vacuum, and either refute or defend it, without having a notion of what they refuted or defended.
Secondly, if this argument should be contested, the reality, or at least possibility, of the _idea_ of a vacuum, may be proved by the following reasoning. Every idea is possible which is a necessary and infallible consequence of such as are possible. Now, though we allow the world to be at present a plenum, we may easily conceive it to be deprived of motion; and this idea will certainly be allowed possible.
It must also be allowed possible, to conceive the annihilation of any part of matter by the omnipotence of the Deity, while the other parts remain at rest. For as every idea that is distinguishable is separable by the imagination, and as every idea that is separable by the imagination may be conceived to be separately existent, 'tis evident, that the existence of one particle of matter no more implies the existence of another, than a square figure in one body implies a square figure in every one. This being granted, I now demand what results from the concurrence of these two possible ideas of _rest_ and _annihilation_, and what must we conceive to follow upon the annihilation of all the air and subtile matter in the chamber, supposing the walls to remain the same, without any motion or alteration? There are some metaphysicians who answer, that since matter and extension are the same, the annihilation of the one necessarily implies that of the other; and there being now no distance betwixt the walls of the chamber, they touch each other; in the same manner as my hand touches the paper which is immediately before me. But though this answer be very common, I defy these metaphysicians to conceive the matter according to their hypothesis, or imagine the floor and roof, with all the opposite sides of the chamber, to touch each other, while they continue in rest, and preserve the same position. For how can the two walls, that run from south to north, touch each other, while they touch the opposite ends of two walls that run from east to west?
And how can the floor and roof ever meet, while they are separated by the four walls that lie in a contrary position? If you change their position, you suppose a motion. If you conceive any thing betwixt them, you suppose a new creation. But keeping strictly to the two ideas of _rest_ and _annihilation_, 'tis evident, that the idea which results from them is not that of a contact of parts, but something else, which is concluded to be the idea of a vacuum.
The third objection carries the matter still farther, and not only asserts, that the idea of a vacuum is real and possible, but also necessary and unavoidable. This assertion is founded on the motion we observe in bodies, which, 'tis maintained, would be impossible and inconceivable without a vacuum, into which one body must move in order to make way for another. I shall not enlarge upon this objection, because it principally belongs to natural philosophy, which lies without our present sphere.
In order to answer these objections, we must take the matter pretty deep, and consider the nature and origin of several ideas, lest we dispute without understanding perfectly the subject of the controversy.
'Tis evident the idea of darkness is no positive idea, but merely the negation of light, or, more properly speaking, of coloured and visible objects. A man who enjoys his sight, receives no other perception from turning his eyes on every side, when entirely deprived of light, than what is common to him with one born blind; and 'tis certain such a one has no idea either of light or darkness. The consequence of this is, that 'tis not from the mere removal of visible objects we receive the impression of extension without matter; and that the idea of utter darkness can never be the same with that of vacuum.
Suppose again a man to be supported in the air, and to be softly conveyed along by some invisible power; 'tis evident he is sensible of nothing, and never receives the idea of extension, nor indeed any idea, from this invariable motion. Even supposing he moves his limbs to and fro, this cannot convey to him that idea. He feels in that case a certain sensation or impression, the parts of which are successive to each other, and may give him the idea of time, but certainly are not disposed in such a manner as is necessary to convey the idea of space or extension.
Since, then, it appears that darkness and motion, with the utter removal of every thing visible and tangible, can never give us the idea of extension without matter, or of a vacuum; the next question is, whether they can convey this idea, when mixed with something visible and tangible?
'Tis commonly allowed by philosophers, that all bodies which discover themselves to the eye, appear as if painted on a plain surface, and that their different degrees of remoteness from ourselves are discovered more by reason than by the senses. When I hold up my hand before me, and spread my fingers, they are separated as perfectly by the blue colour of the firmament, as they could be by any visible object which I could place betwixt them. In order, therefore, to know whether the sight can convey the impression and idea of a vacuum, we must suppose, that amidst an entire darkness, there are luminous bodies presented to us, whose light discovers only these bodies themselves, without giving us any impression of the surrounding objects.
We must form a parallel supposition concerning the objects of our feeling. 'Tis not proper to suppose a perfect removal of all tangible objects: we must allow something to be perceived by the feeling; and after an interval and motion of the hand or other organ of sensation, another object of the touch to be met with; and upon leaving that, another; and so on, as often as we please. The question is, whether these intervals do not afford us the idea of extension without body.
To begin with the first case; 'tis evident, that when only two luminous bodies appear to the eye, we can perceive whether they be conjoined or separate; whether they be separated by a great or small distance; and if this distance varies, we can perceive its increase or diminution, with the motion of the bodies. But as the distance is not in this case any thing coloured or visible, it may be thought that there is here a vacuum or pure extension, not only intelligible to the mind, but obvious to the very senses.
This is our natural and most familiar way of thinking, but which we shall learn to correct by a little reflection. We may observe, that when two bodies present themselves, where there was formerly an entire darkness, the only change that is discoverable is in the appearance of these two objects, and that all the rest continues to be as before, a perfect negation of light, and of every coloured or visible object.
This is not only true of what may be said to be remote from these bodies, but also of the very distance which is interposed betwixt them; _that_ being nothing but darkness, or the negation of light; without parts, without composition, invariable and indivisible. Now, since this distance causes no perception different from what a blind man receives from his eyes, or what is conveyed to us in the darkest night, it must partake of the same properties; and as blindness and darkness afford us no ideas of extension, 'tis impossible that the dark and undistinguishable distance betwixt two bodies can ever produce that idea.
The sole difference betwixt an absolute darkness and the appearance of two or more visible luminous objects consists, as I said, in the objects themselves, and in the manner they affect our senses. The angles, which the rays of light flowing from them form with each other; the motion that is required in the eye, in its passage from one to the other; and the different parts of the organs which are affected by them; these produce the only perceptions from which we can judge of the distance. But as these perceptions are each of them simple and indivisible, they can never give us the idea of extension.
We may illustrate this by considering the sense of feeling, and the imaginary distance or interval interposed betwixt tangible or solid objects. I suppose two cases, viz. that of a man supported in the air, and moving his limbs to and fro, without meeting any thing tangible; and that of a man, who, feeling something tangible, leaves it, and, after a motion of which he is sensible, perceives another tangible object; and I then ask, wherein consists the difference betwixt these two cases? No one will make any scruple to affirm, that it consists merely in the perceiving those objects, and that the sensation, which arises from the motion, is in both cases the same; and as that sensation is not capable of conveying to us an idea of extension, when unaccompanied with some other perception, it can no more give us that idea, when mixed with the impressions of tangible objects, since that mixture produces no alteration upon it.
But though motion and darkness, either alone or attended with tangible and visible objects, convey no idea of a vacuum or extension without matter, yet they are the causes why we falsely imagine we can form such an idea. For there is a close relation betwixt that motion and darkness, and a real extension, or composition of visible and tangible objects.
First, we may observe, that two visible objects, appearing in the midst of utter darkness, affect the senses in the same manner, and form the same angle by the rays which flow from them, and meet in the eye, as if the distance betwixt them were filled with visible objects, that give us a true idea of extension. The sensation of motion is likewise the same, when there is nothing tangible interposed betwixt two bodies, as when we feel a compounded body, whose different parts are placed beyond each other.
Secondly, we find by experience, that two bodies, which are so placed as to affect the senses in the same manner with two others, that have a certain extent of visible objects interposed betwixt them, are capable of receiving the same extent, without any sensible impulse or penetration, and without any change on that angle, under which they appear to the senses. In like manner, where there is one object, which we cannot feel after another without an interval, and the perceiving of that sensation we call motion in our hand or organ of sensation; experience shews us, that 'tis possible the same object may be felt with the same sensation of motion, along with the interposed impression of solid and tangible objects, attending the sensation. That is, in other words, an invisible and intangible distance may be converted into a visible and tangible one, without any change on the distant objects.
Thirdly, we may observe, as another relation betwixt these two kinds of distance, that they have nearly the same effects on every natural phenomenon. For as all qualities, such as heat, cold, light, attraction, &c. diminish in proportion to the distance; there is but little difference observed, whether this distance be marked out by compounded and sensible objects, or be known only by the manner in which the distant objects affect the senses.
Here then are three relations betwixt that distance, which conveys the idea of extension, and that other, which is not filled with any coloured or solid object. The distant objects affect the senses in the same manner, whether separated by the one distance or the other; the second species of distance is found capable of receiving the first; and they both equally diminish the force of every quality.
These relations betwixt the two kinds of distance, will afford us an easy reason why the one has so often been taken for the other, and why we imagine we have an idea of extension without the idea of any object either of the sight or feeling. For we may establish it as a general maxim in this science of human nature, that wherever there is a close relation betwixt two ideas, the mind is very apt to mistake them, and in all its discourses and reasonings to use the one for the other. This phenomenon occurs on so many occasions, and is of such consequence, that I cannot forbear stopping a moment to examine its causes. I shall only premise, that we must distinguish exactly betwixt the phenomenon itself, and the causes which I shall assign for it; and must not imagine, from any uncertainty in the latter, that the former is also uncertain. The phenomenon may be real, though my explication be chimerical. The falsehood of the one is no consequence of that of the other; though at the same time we may observe, that 'tis very natural for us to draw such a consequence; which is an evident instance of that very principle, which I endeavour to explain.
When I received the relations of _resemblance, contiguity_, and _causation_, as principles of union among ideas, without examining into their causes, 'twas more in prosecution of my first maxim, that we must in the end rest contented with experience, than for want of something specious and plausible, which I might have displayed on that