A Treatise of Human Nature Part 2

Two different answers, I find, have been made to this argument; neither of which is in my opinion satisfactory. The first is, that the objects of geometry, those surfaces, lines and points, whose proportions and positions it examines, are mere ideas in the mind; I and not only never did, but never can exist in nature. They never did exist; for no one will pretend to draw a line or make a surface entirely conformable to the definition: They never can exist; for we may produce demonstrations from these very ideas to prove, that they are impossible.

But can anything be imagined more absurd and contradictory than this reasoning? Whatever can be conceived by a clear and distinct idea necessarily implies the possibility of existence; and he who pretends to prove the impossibility of its existence by any argument derived from the clear idea, in reality a.s.serts, that we have no clear idea of it, because we have a clear idea. It is in vain to search for a contradiction in any thing that is distinctly conceived by the mind. Did it imply any contradiction, it is impossible it coued ever be conceived.

There is therefore no medium betwixt allowing at least the possibility of indivisible points, and denying their idea; and it is on this latter principle, that the second answer to the foregoing argument is founded. It has been pretended [L'Art de penser.], that though it be impossible to conceive a length without any breadth, yet by an abstraction without a separation, we can consider the one without regarding the other; in the same manner as we may think of the length of the way betwixt two towns, and overlook its breadth. The length is inseparable from the breadth both in nature and in our minds; but this excludes not a partial consideration, and a distinction of reason, after the manner above explained.

In refuting this answer I shall not insist on the argument, which I have already sufficiently explained, that if it be impossible for the mind to arrive at a minimum in its ideas, its capacity must be infinite, in order to comprehend the infinite number of parts, of which its idea of any extension would be composed. I shall here endeavour to find some new absurdities in this reasoning.

A surface terminates a solid; a line terminates a surface; a point terminates a line; but I a.s.sert, that if the ideas of a point, line or surface were not indivisible, it is impossible we should ever conceive these terminations: For let these ideas be supposed infinitely divisible; and then let the fancy endeavour to fix itself on the idea of the last surface, line or point; it immediately finds this idea to break into parts; and upon its seizing the last of these parts, it loses its hold by a new division, and so on in infinitum, without any possibility of its arriving at a concluding idea. The number of fractions bring it no nearer the last division, than the first idea it formed. Every particle eludes the grasp by a new fraction; like quicksilver, when we endeavour to seize it. But as in fact there must be something, which terminates the idea of every finite quant.i.ty; and as this terminating idea cannot itself consist of parts or inferior ideas; otherwise it would be the last of its parts, which finished the idea, 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 school 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, it is 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 anything concerning the proportions of quant.i.ty, 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 quant.i.ties divisible in infinitum. This question will embarra.s.s 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 varyed. 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 it is 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 numeration, 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, it is 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 s.p.a.ce can never depend on any proportion in the number of their parts. It is 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 the inches. But as that quant.i.ty we call an inch in the one is supposed equal to what we call an inch in the other, and as it is impossible for the mind to find this equality by proceeding in infinitum with these references to inferior quant.i.ties: it is evident, that at last we must fix some standard of equality different from an enumeration of the parts.

There are some [See Dr. Barrow's mathematical lectures.], who pretend, 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 it is 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 a.s.sign any standard of equality, but a.s.sert, that it is 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 a.s.sert, that the only useful notion of equality, or inequality, is derived from the whole united appearance and the comparison of particular objects.

It is evident, that the eye, or rather the mind is often able at one view to determine the proportions of bodies, and p.r.o.nounce 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 p.r.o.nounce 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 juxtaposition 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 perswade 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 ill 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 juxtaposition 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 anything 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 it is 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 as 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 becoming 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 compleat 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, it is 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 meerly 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 rect.i.tude from repeated trials we have a greater a.s.surance. And it is 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.

It is 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 deflation 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 it is 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 it is 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 undetermined.

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. It is in vain, that mathematicians represent a plain surface as produced by the flowing of a right line. It will 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 compa.s.s or common measure; and if we join the supposition of any farther correction, it is 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 inflexion. As the ultimate standard of these figures is derived from nothing but the senses and imagination, it is 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 a.s.surance 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 it is 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 it is 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 a.s.serting, that upon their contact they become one. For, I beseech you, by what rule or standard do you judge, when you a.s.sert, 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 it is 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 coa.r.s.e 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 falls of evidence in this single point, while all its other reasonings command our fullest a.s.sent and approbation. And indeed it seems more requisite to give the reason of this exception, than to shew, that we really must make such an exception, and regard all the mathematical arguments for infinite divisibility as utterly sophistical. For it is evident, that as no idea of quant.i.ty is infinitely divisible, there cannot be imagined a more glaring absurdity, than to endeavour to prove, that quant.i.ty 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 satisfyed 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 s.p.a.ce. Whichever side he chuses, 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 carryed beyond a certain degree of minuteness; since it is 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, those of a circle and right line; though at the same time he acknowledges these ideas to be inseparable.

SECT. V. THE SAME SUBJECT CONTINUED.

If the second part of my system be true, that the idea of s.p.a.ce 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 s.p.a.ce, 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 part 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 it is impossible men coued 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 the 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; it is 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 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, it is 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 a.s.serts, that the idea of a vacuum is real and possible, but also necessary and unavoidable. This a.s.sertion is founded on the motion we observe in bodies, which, it is 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 princ.i.p.ally 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. It is 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 it is certain such-a-one has no idea either of light or darkness. The consequence of this is, that it is 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; it is 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 s.p.a.ce or the idea of s.p.a.ce 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?

It is 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 coued be by any visible object, which I coued 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. It is 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; it is 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, it is 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 pa.s.sage 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 ill.u.s.trate 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 meerly 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 unaccompanyed 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 falsly 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 find 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 it is 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 phaenomenon. 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 marled 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 phaenomenon 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 phaenomenon itself, and the causes, which I shall a.s.sign for it; and must not imagine from any uncertainty in the latter, that the former is also uncertain. The phaenomenon may be real, though my explication be chimerical. The falshood of the one is no consequence of that of the other; though at the same time we may observe, that it is 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, it was 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 subject. It would have been easy to have made an imaginary dissection of the brain, and have shewn, why upon our conception of any idea, the animal spirits run into all the contiguous traces, and rouze up the other ideas, that are related to it. But though I have neglected any advantage, which I might have drawn from this topic in explaining the relations of ideas, I am afraid I must here have recourse to it, in order to account for the mistakes that arise from these relations. I shall therefore observe, that as the mind is endowed with a power of exciting any idea it pleases; whenever it dispatches the spirits into that region of the brain, in which the idea is placed; these spirits always excite the idea, when they run precisely into the proper traces, and rummage that cell, which belongs to the idea. But as their motion is seldom direct, and naturally turns a little to the one side or the other; for this reason the animal spirits, falling into the contiguous traces, present other related ideas in lieu of that, which the mind desired at first to survey. This change we are not always sensible of; but continuing still the same train of thought, make use of the related idea, which is presented to us, and employ it in our reasoning, as if it were the same with what we demanded. This is the cause of many mistakes and sophisms in philosophy; as will naturally be imagined, and as it would be easy to show, if there was occasion.

Of the three relations above-mentioned that of resemblance is the most fertile source of error; and indeed there are few mistakes in reasoning, which do not borrow largely from that origin. Resembling ideas are not only related together, but the actions of the mind, which we employ in considering them, are so little different, that we are not able to distinguish them. This last circ.u.mstance is of great consequence, and we may in general observe, that wherever the actions of the mind in forming any two ideas are the same or resembling, we are very apt to confound these ideas, and take the one for the other. Of this we shall see many instances in the progress of this treatise. But though resemblance be the relation, which most readily produces a mistake in ideas, yet the others of causation and contiguity may also concur in the same influence. We might produce the figures of poets and orators, as sufficient proofs of this, were it as usual, as it is reasonable, in metaphysical subjects to draw our arguments from that quarter. But lest metaphysicians should esteem this below their dignity, I shall borrow a proof from an observation, which may be made on most of their own discourses, viz. that it is usual for men to use words for ideas, and to talk instead of thinking in their reasonings. We use words for ideas, because they are commonly so closely connected that the mind easily mistakes them. And this likewise is the reason, why we subst.i.tute the idea of a distance, which is not considered either as visible or tangible, in the room of extension, which is nothing but a composition of visible or tangible points disposed in a certain order. In causing this mistake there concur both the relations of causation and resemblance. As the first species of distance is found to be convertible into the second, it is in this respect a kind of cause; and the similarity of their manner of affecting the senses, and diminishing every quality, forms the relation of resemblance.

After this chain of reasoning and explication of my principles, I am now prepared to answer all the objections that have been offered, whether derived from metaphysics or mechanics. The frequent disputes concerning a vacuum, or extension without matter prove not the reality of the idea, upon which the dispute turns; there being nothing more common, than to see men deceive themselves in this particular; especially when by means of any close relation, there is another idea presented, which may be the occasion of their mistake.

We may make almost the same answer to the second objection, derived from the conjunction of the ideas of rest and annihilation. When every thing is annihilated in the chamber, and the walls continue immoveable, the chamber must be conceived much in the same manner as at present, when the air that fills it, is not an object of the senses. This annihilation leaves to the eye, that fict.i.tious distance, which is discovered by the different parts of the organ, that are affected, and by the degrees of light and shade;-and to the feeling, that which consists in a sensation of motion in the hand, or other member of the body. In vain should we. search any farther. On whichever side we turn this subject, we shall find that these are the only impressions such an object can produce after the supposed annihilation; and it has already been remarked, that impressions can give rise to no ideas, but to such as resemble them.

Since a body interposed betwixt two others may be supposed to be annihilated, without producing any change upon such as lie on each hand of it, it is easily conceived, how it may be created anew, and yet produce as little alteration. Now the motion of a body has much the same effect as its creation. The distant bodies are no more affected in the one case, than in the other. This suffices to satisfy the imagination, and proves there is no repugnance in such a motion. Afterwards experience comes in play to persuade us that two bodies, situated in the manner above-described, have really such a capacity of receiving body betwixt them, and that there is no obstacle to the conversion of the invisible and intangible distance into one that is visible and tangible. However natural that conversion may seem, we cannot be sure it is practicable, before we have had experience of it.

Thus I seem to have answered the three objections above-mentioned; though at the same time I am sensible, that few will be satisfyed with these answers, but will immediately propose new objections and difficulties. It will probably be said, that my reasoning makes nothing to the matter in hands and that I explain only the manner in which objects affect the senses, without endeavouring to account for their real nature and operations. Though there be nothing visible or tangible interposed betwixt two bodies, yet we find BY EXPERIENCE, that the bodies may be placed in the same manner, with regard to the eye, and require the same motion of the hand in pa.s.sing from one to the other, as if divided by something visible and tangible. This invisible and intangible distance is also found by experience to contain a capacity of receiving body, or of becoming visible and tangible. Here is the whole of my system; and in no part of it have I endeavoured to explain the cause, which separates bodies after this manner, and gives them a capacity of receiving others betwixt them, without any impulse or penetration.

I answer this objection, by pleading guilty, and by confessing that my intention never was to penetrate into the nature of bodies, or explain the secret causes of their operations. For besides that this belongs not to my present purpose, I am afraid, that such an enterprise is beyond the reach of human understanding, and that we can never pretend to know body otherwise than by those external properties, which discover themselves to the senses. As to those who attempt any thing farther, I cannot approve of their ambition, till I see, in some one instance at least, that they have met with success. But at present I content myself with knowing perfectly the manner in which objects affect my senses, and their connections with each other, as far as experience informs me of them. This suffices for the conduct of life; and this also suffices for my philosophy, which pretends only to explain the nature and causes of our perceptions, or impressions and ideas [FN 4.].

[FN 4. As long as we confine our speculations to the appearances of objects to our senses, without entering into disquisitions concerning their real nature and operations, we are safe from all difficulties, and can never be embarra.s.sed by any question. Thus, if it be asked, if the invisible and intangible distance, interposed betwixt two objects, be something or nothing: It is easy to answer, that it is SOMETHING, VIZ. a property of the objects, which affect the SENSES after such a particular manner. If it be asked whether two objects, having such a distance betwixt them, touch or not: it may be answered, that this depends upon the definition of the word, TOUCH. If objects be said to touch, when there is nothing SENSIBLE interposed betwixt them, these objects touch: it objects be said to touch, when their IMAGES strike contiguous parts of the eye, and when the hand FEELS both objects successively, without any interposed motion, these objects do not touch. The appearances of objects to our senses are all consistent; and no difficulties can ever arise, but from the obscurity of the terms we make use of.

If we carry our enquiry beyond the appearances of objects to the senses, I am afraid, that most of our conclusions will be full of scepticism and uncertainty. Thus if it be asked, whether or not the invisible and intangible distance be always full of body, or of something that by an improvement of our organs might become visible or tangible, I must acknowledge, that I find no very decisive arguments on either side; though I am inclined to the contrary opinion, as being more suitable to vulgar and popular notions. If THE NEWTONIAN philosophy be rightly understood, it will be found to mean no more. A vacuum is a.s.serted: That is, bodies are said to be placed after such a manner, is to receive bodies betwixt them, without impulsion or penetration. The real nature of this position of bodies is unknown. We are only acquainted with its effects on the senses, and its power of receiving body. Nothing is more suitable to that philosophy, than a modest scepticism to a certain degree, and a fair confession of ignorance in subjects, that exceed all human capacity.]

I shall conclude this subject of extension with a paradox, which will easily be explained from the foregoing reasoning. This paradox is, that if you are pleased to give to the in-visible and intangible distance, or in other words, to the capacity of becoming a visible and tangible distance, the name of a vacuum, extension and matter are the same, and yet there is a vacuum. If you will not give it that name, motion is possible in a plenum, without any impulse in infinitum, without returning in a circle, and without penetration. But however we may express ourselves, we must always confess, that we have no idea of any real extension without filling it with sensible objects, and conceiving its parts as visible or tangible.

As to the doctrine, that time is nothing but the manner, in which some real objects exist; we may observe, that it is liable to the same objections as the similar doctrine with regard to extension. If it be a sufficient proof, that we have the idea of a vacuum, because we dispute and reason concerning it; we must for the same reason have the idea of time without any changeable existence; since there is no subject of dispute more frequent and common. But that we really have no such idea, is certain. For whence should it be derived? Does it arise from an impression of sensation or of reflection? Point it out distinctly to us, that we may know its nature and qualities. But if you cannot point out any such impression, you may be certain you are mistaken, when you imagine you have any such idea.

But though it be impossible to shew the impression, from which the idea of time without a changeable existence is derived; yet we can easily point out those appearances, which make us fancy we have that idea. For we may observe, that there is a continual succession of perceptions in our mind; so that the idea of time being for ever present with us; when we consider a stedfast object at five-a-clock, and regard the same at six; we are apt to apply to it that idea in the same manner as if every moment were distinguished by a different position, or an alteration of the object. The first and second appearances of the object, being compared with the succession of our perceptions, seem equally removed as if the object had really changed. To which we may add, what experience shews us, that the object was susceptible of such a number of changes betwixt these appearances; as also that the unchangeable or rather fict.i.tious duration has the same effect upon every quality, by encreasing or diminishing it, as that succession, which is obvious to the senses. From these three relations we are apt to confound our ideas, and imagine we can form the idea of a time and duration, without any change or succession.

SECT. VI. OF THE IDEA OF EXISTENCE, AND OF EXTERNAL EXISTENCE.

It may not be amiss, before we leave this subject, to explain the ideas of existence and of external existence; which have their difficulties, as well as the ideas of s.p.a.ce and time. By this means we shall be the better prepared for the examination of knowledge and probability, when we understand perfectly all those particular ideas, which may enter into our reasoning.

There is no impression nor idea of any kind, of which we have any consciousness or memory, that is not conceived as existent; and it is evident, that from this consciousness the most perfect idea and a.s.surance of being is derived. From hence we may form a dilemma, the most clear and conclusive that can be imagined, viz. that since we never remember any idea or impression without attributing existence to it, the idea of existence must either be derived from a distinct impression, conjoined with every perception or object of our thought, or must be the very same with the idea of the perception or object.

As this dilemma is an evident consequence of the principle, that every idea arises from a similar impression, so our decision betwixt the propositions of the dilemma is no more doubtful. So far from there being any distinct impression, attending every impression and every idea, that I do not think there are any two distinct impressions, which are inseparably conjoined. Though certain sensations may at one time be united, we quickly find they admit of a separation, and may be presented apart. And thus, though every impression and idea we remember be considered as existent, the idea of existence is not derived from any particular impression.

The idea of existence, then, is the very same with the idea of what we conceive to be existent. To reflect on any thing simply, and to reflect on it as existent, are nothing different from each other. That idea, when conjoined with the idea of any object, makes no addition to it. Whatever we conceive, we conceive to be existent. Any idea we please to form is the idea of a being; and the idea of a being is any idea we please to form.

Whoever opposes this, must necessarily point out that distinct impression, from which the idea of ent.i.ty is derived, and must prove, that this impression is inseparable from every perception we believe to be existent. This we may without hesitation conclude to be impossible.

Our foregoing reasoning [Part I. Sect. 7.] concerning the distinction of ideas without any real difference will not here serve us in any stead. That kind of distinction is founded on the different resemblances, which the same simple idea may have to several different ideas. But no object can be presented resembling some object with respect to its existence, and different from others in the same particular; since every object, that is presented, must necessarily be existent.

A like reasoning will account for the idea of external existence. We may observe, that it is universally allowed by philosophers, and is besides pretty obvious of itself, that nothing is ever really present with the mind but its perceptions or impressions and ideas, and that external objects become known to us only by those perceptions they occasion. To hate, to love, to think, to feel, to see; all this is nothing but to perceive.

Now since nothing is ever present to the mind but perceptions, and since all ideas are derived from something antecedently present to the mind; it follows, that it is impossible for us so much as to conceive or form an idea of any thing specifically different from ideas and impressions. Let us fix our attention out of ourselves as much as possible: Let us chase our imagination to the heavens, or to the utmost limits of the universe; we never really advance a step beyond ourselves, nor can conceive any kind of existence, but those perceptions, which have appeared in that narrow compa.s.s. This is the universe of the imagination, nor have we any idea but what is there produced.

The farthest we can go towards a conception of external objects, when supposed SPECIFICALLY different from our perceptions, is to form a relative idea of them, without pretending to comprehend the related objects. Generally speaking we do not suppose them specifically different; but only attribute to them different relations, connections and durations. But of this more fully hereafter.[Part IV, Sect. 2.]

PART III. OF KNOWLEDGE AND PROBABILITY.

SECT. I. OF KNOWLEDGE.

There are seven [Part I. Sect. 5.] different kinds of philosophical relation, viz. RESEMBLANCE, IDENt.i.tY, RELATIONS OF TIME AND PLACE, PROPORTION IN QUANt.i.tY OR NUMBER, DEGREES IN ANY QUALITY, CONTRARIETY and CAUSATION. These relations may be divided into two cla.s.ses; into such as depend entirely on the ideas, which we compare together, and such as may be changed without any change in the ideas. It is from the idea of a triangle, that we discover the relation of equality, which its three angles bear to two right ones; and this relation is invariable, as long as our idea remains the same. On the contrary, the relations of contiguity and distance betwixt two objects may be changed merely by an alteration of their place, without any change on the objects themselves or on their ideas; and the place depends on a hundred different accidents, which cannot be foreseen by the mind. It is the same case with ident.i.ty and causation. Two objects, though perfectly resembling each other, and even appearing in the same place at different times, may be numerically different: And as the power, by which one object produces another, is never discoverable merely from their idea, it is evident cause and effect are relations, of which we receive information from experience, and not from any abstract reasoning or reflection. There is no single phaenomenon, even the most simple, which can be accounted for from the qualities of the objects, as they appear to us; or which we coued foresee without the help of our memory and experience.

It appears, therefore, that of these seven philosophical relations, there remain only four, which depending solely upon ideas, can be the objects of knowledge and certainty. These four are RESEMBLANCE, CONTRARIETY, DEGREES IN QUALITY, and PROPORTIONS IN QUANt.i.tY OR NUMBER. Three of these relations are discoverable at first sight, and fall more properly under the province of intuition than demonstration. When any objects resemble each other, the resemblance will at first strike the eye, or rather the mind; and seldom requires a second examination. The case is the same with contrariety, and with the degrees of any quality. No one can once doubt but existence and non-existence destroy each other, and are perfectly incompatible and contrary. And though it be impossible to judge exactly of the degrees of any quality, such as colour, taste, heat, cold, when the difference betwixt them is very small: yet it is easy to decide, that any of them is superior or inferior to another, when their difference is considerable. And this decision we always p.r.o.nounce at first sight, without any enquiry or reasoning.

We might proceed, after the same manner, in fixing the proportions of quant.i.ty or number, and might at one view observe a superiority or inferiority betwixt any numbers, or figures; especially where the difference is very great and remarkable. As to equality or any exact proportion, we can only guess at it from a single consideration; except in very short numbers, or very limited portions of extension; which are comprehended in an instant, and where we perceive an impossibility of falling into any considerable error. In all other cases we must settle the proportions with some liberty, or proceed in a more artificial manner.

I have already observed, that geometry, or the art, by which we fix the proportions of figures; though it much excels both in universality and exactness, the loose judgments of the senses and imagination; yet never attains a perfect precision and exactness. It's first principles are still drawn from the general appearance of the objects; and that appearance can never afford us any security, when we examine, the prodigious minuteness of which nature is susceptible. Our ideas seem to give a perfect a.s.surance, that no two right lines can have a common segment; but if we consider these ideas, we shall find, that they always suppose a sensible inclination of the two lines, and that where the angle they form is extremely small, we have no standard of a I @ right line so precise as to a.s.sure us of the truth of this proposition. It is the same case with most of the primary decisions of the mathematics.

There remain, therefore, algebra and arithmetic as the only sciences, in which we can carry on a chain of reasoning to any degree of intricacy, and yet preserve a perfect exactness and certainty. We are possest of a precise standard, by which we can judge of the equality and proportion of numbers; and according as they correspond or not to that standard, we determine their relations, without any possibility of error. When two numbers are so combined, as that the one has always an unite answering to every unite of the other, we p.r.o.nounce them equal; and it is for want of such a standard of equality in extension, that geometry can scarce be esteemed a perfect and infallible science.

But here it may not be amiss to obviate a difficulty, which may arise from my a.s.serting, that though geometry falls short of that perfect precision and certainty, which are peculiar to arithmetic and algebra, yet it excels the imperfect judgments of our senses and imagination. The reason why I impute any defect to geometry, is, because its original and fundamental principles are derived merely from appearances; and it may perhaps be imagined, that this defect must always attend it, and keep it from ever reaching a greater exactness in the comparison of objects or ideas, than what our eye or imagination alone is able to attain. I own that this defect so far attends it, as to keep it from ever aspiring to a full certainty: But since these fundamental principles depend on the easiest and least deceitful appearances, they bestow on their consequences a degree of exactness, of which these consequences are singly incapable. It is impossible for the eye to determine the angles of a chiliagon to be equal to 1996 right angles, or make any conjecture, that approaches this proportion; but when it determines, that right lines cannot concur; that we cannot draw more than one right line between two given points; it's mistakes can never be of any consequence. And this is the nature and use of geometry, to run us up to such appearances, as, by reason of their simplicity, cannot lead us into any considerable error.

I shall here take occasion to propose a second observation concerning our demonstrative reasonings, which is suggested by the same subject of the mathematics. It is usual with mathematicians, to pretend, that those ideas, which are their objects, are of so refined and spiritual a nature, that they fall not under the conception of the fancy, but must be comprehended by a pure and intellectual view, of which the superior faculties of the soul are alone capable. The same notion runs through most parts of philosophy, and is princ.i.p.ally made use of to explain oar abstract ideas, and to shew how we can form an idea of a triangle, for instance, which shall neither be an isoceles nor scalenum, nor be confined to any particular length and proportion of sides. It is easy to see, why philosophers are so fond of this notion of some spiritual and refined perceptions; since by that means they cover many of their absurdities, and may refuse to submit to the decisions of clear ideas, by appealing to such as are obscure and uncertain. But to destroy this artifice, we need but reflect on that principle so oft insisted on, that all our ideas are copyed from our impressions. For from thence we may immediately conclude, that since all impressions are clear and precise, the ideas, which are copyed from them, must be of the same nature, and can never, but from our fault, contain any thing so dark and intricate. An idea is by its very nature weaker and fainter than an impression; but being in every other respect the same, cannot imply any very great mystery. If its weakness render it obscure, it is our business to remedy that defect, as much as possible, by keeping the idea steady and precise; and till we have done so, it is in vain to pretend to reasoning and philosophy.