Chapter 7

[5]L'Art de penser.

[6]See Dr Barrow's Mathematical Lectures.

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 theideaof 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 thisidea 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 ofrestandannihilation, 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, yousuppose a new creation. But keeping strictly to the two ideas ofrestandannihilation, '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 receivesthe 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 organof 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;thatbeing 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 darkand 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 noidea 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 nearlythe 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 ofresemblance, contiguity, andcausation, 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 subject. 'Twould have been easy to have made an imaginary dissection of the brain, and have shown, 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 despatches 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 inphilosophy; 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 circumstance 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 'tis 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 substitute 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 therelations ofcausationandresemblance. As the first species of distance is found to be convertible into the second, 'tis 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 frommetaphysicsormechanics. 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 immovable, 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 theeyethat fictitious distance, which is discovered by the different parts of the organ that are affected, and by the degrees of light and shade; and to thefeeling, 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, 'tis 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 satisfied with these answers, but will immediately propose new objections and difficulties. 'Twill probably be said, that my reasoning makes nothing to the matter in hand, 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 findby 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 passing from one to the other, as if divided by something visible and tangible. This invisible and intangible distance is also foundby experienceto contain a capacity of receiving body, or of becoming visible and tangible. Here is the whole of mysystem; 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 connexions 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.[7]

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 invisible 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 impulsein 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 'tis liable to the same objections as the similar doctrinewith 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 outany such impression, you may be certain you are mistaken, when you imagine you haveany such idea.

But though it be impossible to show 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 o'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 shows us, that the object was susceptible of such a number of changes betwixt these appearances; as also that the unchangeable or rather fictitious duration has the same effect upon every quality, by increasing 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.

[7]As long as we confine our speculations tothe appearancesof objects to our senses, without entering into disquisitions concerning their real nature and operations, we are safe from all difficulties, and can never be embarrassed by any question. Thus, if it be asked, if the invisible and intangible distance, interposed betwixt two objects, be something or nothing: 'tis easy to answer, that it issomething, viz. a property of the objects, which affect thesensesafter 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 wordtouch. If objects be said to touch, when there is nothingsensibleinterposed betwixt them, these objects touch: If objects be said to touch, when theirimagesstrike contiguous parts of the eye, and when the handfeelsboth 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 inquiry 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 ofbody, 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. Ifthe Newtonianphilosophy be rightly understood, it will be found to mean no more. A vacuum is asserted; that is, bodies are said to be placed after such a manner as 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.

If we carry our inquiry 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 ofbody, 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. Ifthe Newtonianphilosophy be rightly understood, it will be found to mean no more. A vacuum is asserted; that is, bodies are said to be placed after such a manner as 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.

It may not be amiss, before we leave this subject, to explain the ideas ofexistenceand ofexternal existence; which have their difficulties, as well as the ideas of space 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 'tis evident that, from this consciousness, the most perfect idea and assurance ofbeingis 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 andevery 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 entity 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[8]concerning thedistinctionof ideas without any realdifferencewill 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 ofexternal existence. We may observe, that 'tis 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 'tis 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 compass. 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 supposedspecificallydifferent 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, connexions, and durations. But of this more fully hereafter.[9]

[8]Part I. Sect. 7.

[9]Part VI. Sect. 2.

There are seven different kinds of philosophical relation,[1]viz.resemblance, identity, relations of time and place, proportion in quantity or number, degrees in any quality, contrariety, and causation. These relations may be divided into two classes; into such as depend entirely on the ideas, which we compare together, and such as may be changed without any change in the ideas. 'Tis 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 ofcontiguityanddistancebetwixt 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 themind. 'Tis the same case withidentityandcausation. 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, 'tis evidentcauseandeffectare relations, of which we receive information from experience, and not from any abstract reasoning or reflection. There is no single phenomenon, even the most simple, which can be accounted for from the qualities of the objects, as they appear to us; or which we could 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 areresemblance, contrariety, degrees in quality, and proportions in quantity or number. Three of these relations are discoverable at first sight, and fall more properly under the province of intuition than demonstration. When any objectsresembleeach other, the resemblance will at first strike the eye, or rather the mind; and seldom requires a second examination. The case is the same withcontrariety, and with thedegreesof anyquality. 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 'tis easy to decide, that any of them is superior or inferior to another, when their difference is considerable. And this decision we always pronounce at first sight, without any inquiry or reasoning.

We might proceed, after the same manner, in fixing theproportionsofquantityornumber, 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 moreartificialmanner.

I have already observed, that geometry, or theartby 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. Its 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 assurance, 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 right line so precise as to assure us of the truth of this proposition. 'Tis 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 possessedof 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 pronounce them equal; and 'tis 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 asserting, 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. 'Tis 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; its mistakes can never be of any consequence. And this is the nature and use of geometry, to run us up to suchappearances, 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. 'Tis 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 principally made use of to explain our abstract ideas, and to show how we can form an idea of a triangle, for instance, which shall neither be an isosceles nor scalenum, nor be confined to any particular length and proportion of sides. 'Tis 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 copied from out impressions. For from thence we may immediately conclude, that since all impressions are clear and precise, the ideas, which are copied 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, 'tis our business to remedy that defect, as much as possible, by keeping the idea steady and precise; and tillwe have done so, 'tis in vain to pretend to reasoning and philosophy.

[1]Part I. Sect. 5.

This is all I think necessary to observe concerning those four relations, which are the foundation of science; but as to the other three, which depend not upon the idea, and may be absent or present even whilethatremains the same, 'twill be proper to explain them more particularly. These three relations areidentity, the situations in time and place, and causation.

All kinds of reasoning consist in nothing but acomparison, and a discovery of those relations, either constant or inconstant, which two or more objects bear to each other. This comparison we may make, either when both the objects are present to the senses, or when neither of them is present, or when only one. When both the objects are present to the senses along with the relation, we callthisperception rather than reasoning; nor is there in this case any exercise of the thought, or any action, properly speaking, but a mere passive admission of the impressions through the organs of sensation. According to this way of thinking, we ought not to receive as reasoning any of the observations we may make concerningidentity, and therelationsoftimeandplace; since in none of them the mind can go beyond what is immediately present to the senses, either to discover the real existenceor the relations of objects. 'Tis onlycausation, which produces such a connexion, as to give us assurance from the existence or action of one object, that 'twas followed or preceded by any other existence or action; nor can the other two relations ever be made use of in reasoning, except so far as they either affect or are affected by it. There is nothing in any objects to persuade us, that they are either alwaysremoteor alwayscontiguous; and when from experience and observation we discover, that their relation in this particular is invariable, we always conclude there is some secretcausewhich separates or unites them. The same reasoning extends toidentity. We readily suppose an object may continue individually the same, though several times absent from and present to the senses; and ascribe to it an identity, notwithstanding the interruption of the perception, whenever we conclude, that if we had kept our eye or hand constantly upon it, it would have conveyed an invariable and uninterrupted perception. But this conclusion beyond the impressions of our senses can be founded only on the connexion ofcause and effect; nor can we otherwise have any security that the object is not changed upon us, however much the new object may resemble that which was formerly present to the senses. Whenever we discover such a perfect resemblance, we consider whether it be common in that species of objects; whether possibly or probably any cause could operate in producing the change and resemblance; and according as we determine concerning these causes and effects, we form our judgment concerning the identity of the object.

Here then it appears, that of those three relations, which depend not upon the mere ideas, the only one that can be traced beyond our senses, and informs usof existences and objects, which we do not see or feel, iscausation. This relation therefore we shall endeavour to explain fully before we leave the subject of the Of the understanding.

To begin regularly, we must consider the idea ofcausation, and see from what origin it is derived. 'Tis impossible to reason justly, without understanding perfectly the idea concerning which we reason; and 'tis impossible perfectly to understand any idea, without tracing it up to its origin, and examining that primary impression, from which it arises. The examination of the impression bestows a clearness on the idea; and the examination of the idea bestows a like clearness on all our reasoning.

Let us therefore cast our eye on any two objects, which we call cause and effect, and turn them on all sides, in order to find that impression, which produces an idea of such prodigious consequence. At first sight I perceive, that I must not search for it in any of the particularqualitiesof the objects; since, whichever of these qualities I pitch on, I find some object that is not possessed of it, and yet falls under the denomination of cause or effect. And indeed there is nothing existent, either externally or internally, which is not to be considered either as a cause or an effect; though 'tis plain there is no one quality which universally belongs to all beings, and gives them a title to that denomination.

The idea then of causation must be derived from somerelationamong objects; and that relation we must now endeavour to discover. I find in the first place, that whatever objects are considered as causes or effects, arecontiguous; and that nothing can operate in a time or place, which is ever so little removedfrom those of its existence. Though distant objects may sometimes seem productive of each other, they are commonly found upon examination to be linked by a chain of causes, which are contiguous among themselves, and to the distant objects; and when in any particular instance we cannot discover this connexion, we still presume it to exist. We may therefore consider the relation ofcontiguityas essential to that of causation; at least may suppose it such, according to the general opinion, till we can find a more proper occasion[2]to clear up this matter, by examining what objects are or are not susceptible of juxtaposition and conjunction.

The second relation I shall observe as essential to causes and effects, is not so universally acknowledged, but is liable to some controversy. 'Tis that ofpriorityof time in the cause before the effect. Some pretend that 'tis not absolutely necessary a cause should precede its effect; but that any object or action, in the very first moment of its existence, may exert its productive quality, and give rise to another object or action, perfectly cotemporary with itself. But beside that experience in most instances seems to contradict this opinion, we may establish the relation of priority by a kind of inference or reasoning. 'Tis an established maxim both in natural and moral philosophy, that an object, which exists for any time in its full perfection without producing another, is not its sole cause; but is assisted by some other principle which pushes it from its state of inactivity, and makes it exert that energy, of which it was secretly possessed. Now if any cause may be perfectly cotemporary with its effect, 'tis certain, according to this maxim, that they mustall of them be so; since any one of them, which retards its operation for a single moment, exerts not itself at that very individual time, in which it might have operated; and therefore is no proper cause. The consequence of this would be no less than the destruction of that succession of causes, which we observe in the world; and indeed the utter annihilation of time. For if one cause were cotemporary with its effect, and this effect withitseffect, and so on, 'tis plain there would be no such thing as succession, and all objects must be co-existent.

If this argument appear satisfactory, 'tis well. If not, I beg the reader to allow me the same liberty, which I have used in the preceding case, of supposing it such. For he shall find, that the affair is of no great importance.

Having thus discovered or supposed the two relations ofcontiguityandsuccessionto be essential to causes and effects, I find I am stopped short, and can proceed no farther in considering any single instance of cause and effect. Motion in one body is regarded upon impulse as the cause of motion in another. When we consider these objects with the utmost attention, we find only that the one body approaches the other; and that the motion of it precedes that of the other, but without any sensible interval. 'Tis in vain to rack ourselves withfartherthought and reflection upon this subject. We can go nofartherin considering this particular instance.

Should any one leave this instance, and pretend to define a cause, by saying it is something productive of another, 'tis evident he would say nothing. For what does he mean byproduction? Can he give any definition of it, that will not be the same with that of causation?

If he can, I desire it maybe produced. If he cannot, he here runs in a circle, and gives a synonymous term instead of a definition.

Shall we then rest contented with these two relations of contiguity and succession, as affording a complete idea of causation? By no means. An object may be contiguous and prior to another, without being considered as its cause. There is anecessary connexionto be taken into consideration; and that relation is of much greater importance, than any of the other two above mentioned.

Here again I turn the object on all sides, in order to discover the nature of this necessary connexion, and find the impression, or impressions, from which its idea may be derived. When I cast my eye on theknown qualitiesof objects, I immediately discover that the relation of cause and effect depends not in the least onthem. When I consider theirrelations, I can find none but those of contiguity and succession; which I have already regarded as imperfect and unsatisfactory. Shall the despair of success make me assert, that I am here possessed of an idea, which is not preceded by any similar impression? This would be too strong a proof of levity and inconstancy; since the contrary principle has been already so firmly established, as to admit of no farther doubt; at least, till we have more fully examined the present difficulty.

We must therefore proceed like those who, being in search of any thing that lies concealed from them, and not finding it in the place they expected, beat about all the neighbouring fields, without any certain view or design, in hopes their good fortune will at last guide them to what they search for. 'Tis necessary for us to leave the direct survey of this question concerningthe nature of thatnecessary connexion, which enters into our idea of cause and effect; and endeavour to find some other questions, the examination of which will perhaps afford a hint, that may serve to clear up the present difficulty. Of these questions there occur two, which I shall proceed to examine, viz.

First, for what reason we pronounce itnecessary, that every thing whose existence has a beginning, should also have a cause?

Secondly, why we conclude, that such particular causes mustnecessarilyhave such particular effects; and what is the nature of thatinferencewe draw from the one to the other, and of thebeliefwe repose in it?

I shall only observe before I proceed any farther, that though the ideas of cause and effect be derived from the impressions of reflection as well as from those of sensation, yet for brevity's sake, I commonly mention only the latter as the origin of these ideas; though I desire that, whatever I say of them, may also extend to the former. Passions are connected with their objects and with one another; no less than external bodies are connected together. The same relation then of cause and effect, which belongs to one, must be common to all of them.

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