Leseprobe "Hume, David: A Treatise of Human Nature" | 

INTRODUCTION

Nothing is more usual and more natural for those, who pretend to discover anything new to the world in philosophy and the sciences, than to insinuate the praises of their own systems, by decrying all those, which have been advanced before them. And indeed were they content with lamenting that ignorance, which we still lie under in the most important questions, that can come before the tribunal of human reason, there are few, who have an acquaintance with the sciences, that would not readily agree with them. It is easy for one of judgment and learning, to perceive the weak foundation even of those systems, which have obtained the greatest credit, and have carried their pretensions highest to accurate and profound reasoning. Principles taken upon trust, consequences lamely deduced from them, want of coherence in the parts, and of evidence in the whole, these are every where to be met with in the systems of the most eminent philosophers, and seem to have drawn disgrace upon philosophy itself.

Nor is there required such profound knowledge to discover the present imperfect condition of the sciences, but even the rabble without doors may, judge from the noise and clamour, which they hear, that all goes not well within. There is nothing which is not the subject of debate, and in which men of learning are not of contrary opinions. The most trivial question escapes not our controversy, and in the most momentous we are not able to give any certain decision. Disputes are multiplied, as if every thing was uncertain; and these disputes are managed with the greatest warmth, as if every thing was certain. Amidst all this bustle it is not reason, which carries the prize, but eloquence; and no man needs ever despair of gaining proselytes to the most extravagant hypothesis, who has art enough to represent it in any favourable colours. The victory is not gained by the men at arms, who manage the pike and the sword; but by the trumpeters, drummers, and musicians of the army.

From hence in my opinion arises that common prejudice against metaphysical reasonings of all kinds, even amongst those, who profess themselves scholars, and have a just value for every other part of literature. By metaphysical reasonings, they do not understand those on any particular branch of science, but every kind of argument, which is any way abstruse, and requires some attention to be comprehended. We have so often lost our labour in such researches, that we commonly reject them without hesitation, and resolve, if we must for ever be a prey to errors and delusions, that they shall at least be natural and entertaining. And indeed nothing but the most determined scepticism, along with a great degree of indolence, can justify this aversion to metaphysics. For if truth be at all within the reach of human capacity, it is certain it must lie very deep and abstruse: and to hope we shall arrive at it without pains, while the greatest geniuses have failed with the utmost pains, must certainly be esteemed sufficiently vain and presumptuous. I pretend to no such advantage in the philosophy I am going to unfold, and would esteem it a strong presumption against it, were it so very easy and obvious.

It is evident, that all the sciences have a relation, greater or less, to human nature: and that however wide any of them may seem to run from it, they still return back by one passage or another. Even. Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since the lie under the cognizance of men, and are judged of by their powers and faculties. It is impossible to tell what changes and improvements we might make in these sciences were we thoroughly acquainted with the extent and force of human understanding, and could explain the nature of the ideas we employ, and of the operations we perform in our reasonings. And these improvements are the more to be hoped for in natural religion, as it is not content with instructing us in the nature of superior powers, but carries its views farther, to their disposition towards us, and our duties towards them; and consequently we ourselves are not only the beings, that reason, but also one of the objects, concerning which we reason.

If therefore the sciences of Mathematics, Natural Philosophy, and Natural Religion, have such a dependence on the knowledge of man, what may be expected in the other sciences, whose connexion with human nature is more close and intimate? The sole end of logic is to explain the principles and operations of our reasoning faculty, and the nature of our ideas: morals and criticism regard our tastes and sentiments: and politics consider men as united in society, and dependent on each other. In these four sciences of Logic, Morals, Criticism, and Politics, is comprehended almost everything, which it can any way import us to be acquainted with, or which can tend either to the improvement or ornament of the human mind.

Here then is the only expedient, from which we can hope for success in our philosophical researches, to leave the tedious lingering method, which we have hitherto followed, and instead of taking now and then a castle or village on the frontier, to march up directly to the capital or center of these sciences, to human nature itself; which being once masters of, we may every where else hope for an easy victory. From this station we may extend our conquests over all those sciences, which more intimately concern human life, and may afterwards proceed at leisure to discover more fully those, which are the objects of pore curiosity. There is no question of importance, whose decision is not comprised in the science of man; and there is none, which can be decided with any certainty, before we become acquainted with that science. In pretending, therefore, to explain the principles of human nature, we in effect propose a compleat system of the sciences, built on a foundation almost entirely new, and the only one upon which they can stand with any security.

And as the science of man is the-only solid foundation for the other sciences, so the only solid foundation we can give to this science itself must be laid on experience and observation. It is no astonishing reflection to consider, that the application of experimental philosophy to moral subjects should come after that to natural at the distance of above a whole century; since we find in fact, that there was about the same interval betwixt the origins of these sciences; and that reckoning from THALES to SOCRATES, the space of time is nearly equal to that betwixt, my Lord Bacon and some late philosophers [Mr. Locke, my Lord Shaftesbury, Dr. Mandeville, Mr. Hutchinson, Dr. Butler, etc.] in England, who have begun to put the science of man on a new footing, and have engaged the attention, and excited the curiosity of the public. So true it is, that however other nations may rival us in poetry, and excel us in some other agreeable arts, the improvements in reason and philosophy can only be owing to a land of toleration and of liberty.

Nor ought we to think, that this latter improvement in the science of man will do less honour to our native country than the former in natural philosophy, but ought rather to esteem it a greater glory, upon account of the greater importance of that science, as well as the necessity it lay under of such a reformation. For to me it seems evident, that the essence of the mind being equally unknown to us with that of external bodies, it must be equally impossible to form any notion of its powers and qualities otherwise than from careful and exact experiments, and the observation of those particular effects, which result from its different circumstances and situations. And though we must endeavour to render all our principles as universal as possible, by tracing up our experiments to the utmost, and explaining all effects from the simplest and fewest causes, it is still certain we cannot go beyond experience; and any hypothesis, that pretends to discover the ultimate original qualities of human nature, ought at first to be rejected as presumptuous and chimerical.

I do not think a philosopher, who would apply himself so earnestly to the explaining the ultimate principles of the soul, would show himself a great master in that very science of human nature, which he pretends to explain, or very knowing in what is naturally satisfactory to the mind of man. For nothing is more certain, than that despair has almost the same effect upon us with enjoyment, and that we are no sooner acquainted with the impossibility of satisfying any desire, than the desire itself vanishes. When we see, that we have arrived at the utmost extent of human reason, we sit down contented, though we be perfectly satisfied in the main of our ignorance, and perceive that we can give no reason for our most general and most refined principles, beside our experience of their reality; which is the reason of the mere vulgar, and what it required no study at first to have discovered for the most particular and most extraordinary phaenomenon. And as this impossibility of making any farther progress is enough to satisfy the reader, so the writer may derive a more delicate satisfaction from the free confession of his ignorance, and from his prudence in avoiding that error, into which so many have fallen, of imposing their conjectures and hypotheses on the world for the most certain principles. When this mutual contentment and satisfaction can be obtained betwixt the master and scholar, I know not what more we can require of our philosophy.

But if this impossibility of explaining ultimate principles should be esteemed a defect in the science of man, I will venture to affirm, that it is a defect common to it with all the sciences, and all the arts, in which we can employ ourselves, whether they be such as are cultivated in the schools of the philosophers, or practised in the shops of the meanest artizans. None of them can go beyond experience, or establish any principles which are not founded on that authority. Moral philosophy has, indeed, this peculiar disadvantage, which is not found in natural, that in collecting its experiments, it cannot make them purposely, with premeditation, and after such a manner as to satisfy itself concerning every particular difficulty which may be. When I am at a loss to know the effects of one body upon another in any situation, I need only put them in that situation, and observe what results from it. But should I endeavour to clear up after the same manner any doubt in moral philosophy, by placing myself in the same case with that which I consider, it is evident this reflection and premeditation would so disturb the operation of my natural principles, as must render it impossible to form any just conclusion from the phenomenon. We must therefore glean up our experiments in this science from a cautious observation of human life, and take them as they appear in the common course of the world, by men's behaviour in company, in affairs, and in their pleasures. Where experiments of this kind are judiciously collected and compared, we may hope to establish on them a science which will not be inferior in certainty, and will be much superior in utility to any other of human comprehension.

BOOK I

OF THE UNDERSTANDING.

PART I

OF IDEAS, THEIR ORIGIN, COMPOSITION, CONNEXION, ABSTRACTION, ETC.

THE ORIGIN OF OUR IDEAS

All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call IMPRESSIONS and IDEAS. The difference betwixt these consists in the degrees of force and liveliness, with which they strike upon the mind, and make their way into our thought or consciousness. Those perceptions, which enter with most force and violence, we may name impressions: and under this name I comprehend all our sensations, passions and emotions, as they make their first appearance in the soul. By ideas I mean the faint images of these in thinking and reasoning; such as, for instance, are all the perceptions excited by the present discourse, excepting only those which arise from the sight and touch, and excepting the immediate pleasure or uneasiness it may occasion. I believe it will not be very necessary to employ many words in explaining this distinction. Every one of himself will readily perceive the difference betwixt feeling and thinking. The common degrees of these are easily distinguished; though it is not impossible but in particular instances they may very nearly approach to each other. Thus in sleep, in a fever, in madness, or in any very violent emotions of soul, our ideas may approach to our impressions, As on the other hand it sometimes happens, that our impressions are so faint and low, that we cannot distinguish them from our ideas. But notwithstanding this near resemblance in a few instances, they are in general so very different, that no-one can make a scruple to rank them under distinct heads, and assign to each a peculiar name to mark the difference [FN 1.].

[FN 1. I here make use of these terms, impression and

idea, in a sense different from what is usual, and I hope

this liberty will be allowed me. Perhaps I rather restore

the word, idea, to its original sense, from which Mr LOCKE

had perverted it, in making it stand for all our

perceptions. By the terms of impression I would not be

understood to express the manner, in which our lively

perceptions are produced in the soul, but merely the

perceptions themselves; for which there is no particular

name either in the English or any other language, that I

know of.]

There is another division of our perceptions, which it will be convenient to observe, and which extends itself both to our impressions and ideas. This division is into SIMPLE and COMPLEX. Simple perceptions or impressions and ideas are such as admit of no distinction nor separation. The complex are the contrary to these, and may be distinguished into parts. Though a particular colour, taste, and smell, are qualities all united together in this apple, it is easy to perceive they are not the same, but are at least distinguishable from each other.

Having by these divisions given an order and arrangement to our objects, we may now apply ourselves to consider with the more accuracy their qualities and relations. The first circumstance, that strikes my eye, is the great resemblance betwixt our impressions and ideas in every other particular, except their degree of force and vivacity. The one seem to be in a manner the reflexion of the other; so that all the perceptions of the mind are double, and appear both as impressions and ideas. When I shut my eyes and think of my chamber, the ideas I form are exact representations of the impressions I felt; nor is there any circumstance of the one, which is not to be found in the other. In running over my other perceptions, I find still the same resemblance and representation. Ideas and impressions appear always to correspond to each other. This circumstance seems to me remarkable, and engages my attention for a moment.

Upon a more accurate survey I find I have been carried away too far by the first appearance, and that I must make use of the distinction of perceptions into simple and complex, to limit this general decision, that all our ideas and impressions are resembling. I observe, that many of our complex ideas never had impressions, that corresponded to them, and that many of our complex impressions never are exactly copied in ideas. I can imagine to myself such a city as the New Jerusalem, whose pavement is gold and walls are rubies, though I never saw any such. I have seen Paris; but shall I affirm I can form such an idea of that city, as will perfectly represent all its streets and houses in their real and just proportions?

I perceive, therefore, that though there is in general a great, resemblance betwixt our complex impressions and ideas, yet the rule is not universally true, that they are exact copies of each other. We may next consider how the case stands with our simple, perceptions. After the most accurate examination, of which I am capable, I venture to affirm, that the rule here holds without any exception, and that every simple idea has a simple impression, which resembles it, and every simple impression a correspondent idea. That idea of red, which we form in the dark, and that impression which strikes our eyes in sun-shine, differ only in degree, not in nature. That the case is the same with all our simple impressions and ideas, it is impossible to prove by a particular enumeration of them. Every one may satisfy himself in this point by running over as many as he pleases. But if any one should deny this universal resemblance, I know no way of convincing him, but by desiring him to shew a simple impression, that has not a correspondent idea, or a simple idea, that has not a correspondent impression. If he does not answer this challenge, as it is certain he cannot, we may from his silence and our own observation establish our conclusion.

Thus we find, that all simple ideas and impressions resemble each other; and as the complex are formed from them, we may affirm in general, that these two species of perception are exactly correspondent. Having discovered this relation, which requires no farther examination, I am curious to find some other of their qualities. Let us consider how they stand with regard to their existence, and which of the impressions and ideas are causes, and which effects.

The full examination of this question is the subject of the present treatise; and therefore we shall here content ourselves with establishing one general proposition, THAT ALL OUR SIMPLE IDEAS IN THEIR FIRST APPEARANCE ARE DERIVED FROM SIMPLE IMPRESSIONS, WHICH ARE CORRESPONDENT TO THEM, AND WHICH THEY EXACTLY REPRESENT.

In seeking for phenomena to prove this proposition, I find only those of two kinds; but in each kind the phenomena are obvious, numerous, and conclusive. I first make myself certain, by a new, review, of what I have already asserted, that every simple impression is attended with a correspondent idea, and every simple idea with a correspondent impression. From this constant conjunction of resembling perceptions I immediately conclude, that there is a great connexion betwixt our correspondent impressions and ideas, and that the existence of the one has a considerable influence upon that of the other. Such a constant conjunction, in such an infinite number of instances, can never arise from chance; but clearly proves a dependence of the impressions on the ideas, or of the ideas on the impressions. That I may know on which side this dependence lies, I consider the order of their first appearance; and find by constant experience, that the simple impressions always take the precedence of their correspondent ideas, but never appear in the contrary order. To give a child an idea of scarlet or orange, of sweet or bitter, I present the objects, or in other words, convey to him these impressions; but proceed not so absurdly, as to endeavour to produce the impressions by exciting the ideas. Our ideas upon their appearance produce not their correspondent impressions, nor do we perceive any colour, or feel any sensation merely upon thinking of them. On the other hand we find, that any impression either of the mind or body is constantly followed by an idea, which resembles it, and is only different in the degrees of force and liveliness, The constant conjunction of our resembling perceptions, is a convincing proof, that the one are the causes of the other; and this priority of the impressions is an equal proof, that our impressions are the causes of our ideas, not our ideas of our impressions.

To confirm this I consider Another plain and convincing phaenomenon; which is, that, where-ever by any accident the faculties, which give rise to any impressions, are obstructed in their operations, as when one is born blind or deaf; not only the impressions are lost, but also their correspondent ideas; so that there never appear in the mind the least traces of either of them. Nor is this only true, where the organs of sensation are entirely destroyed, but likewise where they have never been put in action to produce a particular impression. We cannot form to ourselves a just idea of the taste of a pine apple, without having actually tasted it.

There is however one contradictory phaenomenon, which may prove, that it is not absolutely impossible for ideas to go before their correspondent impressions. I believe it will readily be allowed that the several distinct ideas of colours, which enter by the eyes, or those of sounds, which are conveyed by the hearing, are really different from each other, though at the same time resembling. Now if this be true of different colours, it must be no less so of the different shades of the same colour, that each of them produces a distinct idea, independent of the rest. For if this should be denied, it is possible, by the continual gradation of shades, to run a colour insensibly into what is most remote from it; and if you will not allow any of the means to be different, you cannot without absurdity deny the extremes to be the same. Suppose therefore a person to have enjoyed his sight for thirty years, and to have become perfectly well acquainted with colours of all kinds, excepting one particular shade of blue, for instance, which it never has been his fortune to meet with. Let all the different shades of that colour, except that single one, be placed before him, descending gradually from the deepest to the lightest; it is plain, that he will perceive a blank, where that shade is wanting, said will be sensible, that there is a greater distance in that place betwixt the contiguous colours, than in any other. Now I ask, whether it is possible for him, from his own imagination, to supply this deficiency, and raise up to himself the idea of that particular shade, though it had never been conveyed to him by his senses? I believe there are few but will be of opinion that he can; and this may serve as a proof, that the simple ideas are not always derived from the correspondent impressions; though the instance is so particular and singular, that it is scarce worth our observing, and does not merit that for it alone we should alter our general maxim.

But besides this exception, it may not be amiss to remark on this head, that the principle of the priority of impressions to ideas must be understood with another limitation, viz., that as our ideas are images of our impressions, so we can form secondary ideas, which are images of the primary; as appears from this very reasoning concerning them. This is not, properly speaking, an exception to the rule so much as an explanation of it. Ideas produce the images of themselves in new ideas; but as the first ideas are supposed to be derived from impressions, it still remains true, that all our simple ideas proceed either mediately or immediately, from their correspondent impressions.

This then is the first principle I establish in the science of human nature; nor ought we to despise it because of the simplicity of its appearance. For it is remarkable, that the present question concerning the precedency of our impressions or ideas, is the same with what has made so much noise in other terms, when it has been disputed whether there be any INNATE IDEAS, or whether all ideas be derived from sensation and reflexion. We may observe, that in order to prove the ideas of extension and colour not to be innate, philosophers do nothing but shew that they are conveyed by our senses. To prove the ideas of passion and desire not to be innate, they observe that we have a preceding experience of these emotions in ourselves. Now if we carefully examine these arguments, we shall find that they prove nothing but that ideas are preceded by other more lively perceptions, from which the are derived, and which they represent. I hope this clear stating of the question will remove all disputes concerning it, and win render this principle of more use in our reasonings, than it seems hitherto to have been.

DIVISION OF THE SUBJECT

Since it appears, that our simple impressions are prior to their correspondent ideas, and that the exceptions are very rare, method seems to require we should examine our impressions, before we consider our ideas. Impressions way be divided into two kinds, those Of SENSATION and those of REFLEXION. The first kind arises in the soul originally, from unknown causes. The second is derived in a great measure from our ideas, and that in the following order. An impression first strikes upon the senses, and makes us perceive heat or cold, thirst or hunger, pleasure or pain of some kind or other. Of this impression there is a copy taken by the mind, which remains after the impression ceases; and this we call an idea. This idea of pleasure or pain, when it returns upon the soul, produces the new impressions of desire and aversion, hope and fear, which may properly be called impressions of reflexion, because derived from it. These again are copied by the memory and imagination, and become ideas; which perhaps in their turn give rise to other impressions and ideas. So that the impressions of reflexion are only antecedent to their correspondent ideas; but posterior to those of sensation, and derived from them. The examination of our sensations belongs more to anatomists and natural philosophers than to moral; and therefore shall not at present be entered upon. And as the impressions of reflexion, viz. passions, desires, and emotions, which principally deserve our attention, arise mostly from ideas, it will be necessary to reverse that method, which at first sight seems most natural; and in order to explain the nature and principles of the human mind, give a particular account of ideas, before we proceed to impressions. For this reason I have here chosen to begin with ideas.

MEMORY AND IMAGINATION

We find by experience, that when any impression has been present with the mind, it again makes its appearance there as an idea; and this it may do after two different ways: either when in its new appearance it retains a considerable degree of its first vivacity, and is somewhat intermediate betwixt an impression and an idea: or when it entirely loses that vivacity, and is a perfect idea. The faculty, by which we repeat our impressions in the first manner, is called the MEMORY, and the other the IMAGINATION. It is evident at first sight, that the ideas of the memory are much more lively and strong than those of the imagination, and that the former faculty paints its objects in more distinct colours, than any which are employed by the latter. When we remember any past event, the idea of it flows in upon the mind in a forcible manner; whereas in the imagination the perception is faint and languid, and cannot without difficulty be preserved by the mind steddy and uniform for any considerable time. Here then is a sensible difference betwixt one species of ideas and another. But of this more fully hereafter.

There is another difference betwixt these two kinds of ideas, which is no less evident, namely that though neither the ideas, of the memory nor imagination, neither the lively nor faint ideas can make their appearance in the mind, unless their correspondent impressions have gone before to prepare the way for them, yet the imagination is not restrained to the same order and form with the original impressions; while the memory is in a manner tied down in that respect, without any power of variation.

It is evident, that the memory preserves the original form, in which its objects were presented, and that where-ever we depart from it in recollecting any thing, it proceeds from some defect or imperfection in that faculty. An historian may, perhaps, for the more convenient Carrying on of his narration, relate an event before another, to which it was in fact posterior; but then he takes notice of this disorder, if he be exact; and by that means replaces the idea in its due position. It is the same case in our recollection of those places and persons, with which we were formerly acquainted. The chief exercise of the memory is not to preserve the simple ideas, but their order and position. In short, this principle is supported by such a number of common and vulgar phaenomena, that we may spare ourselves the trouble of insisting on it any farther.

The same evidence follows us in our second principle, OF THE LIBERTY OF THE IMAGINATION TO TRANSPOSE AND CHANGE ITS IDEAS. The fables we meet with in poems and romances put this entirely out of the question. Nature there is totally confounded, and nothing mentioned but winged horses, fiery dragons, and monstrous giants. Nor will this liberty of the fancy appear strange, when we consider, that all our ideas are copyed from our impressions, and that there are not any two impressions which are perfectly inseparable. Not to mention, that this is an evident consequence of the division of ideas into simple and complex. Where-ever the imagination perceives a difference among ideas, it can easily produce a separation.

ASSOCIATION OF IDEAS

As all simple ideas may be separated by the imagination, and may be united again in what form it pleases, nothing would be more unaccountable than the operations of that faculty, were it not guided by some universal principles, which render it, in some measure, uniform with itself in all times and places. Were ideas entirely loose and unconnected, chance alone would join them; and it is impossible the same simple ideas should fall regularly into complex ones (as they Commonly do) without some bond of union among them, some associating quality, by which one idea naturally introduces another. This uniting principle among ideas is not to be considered as an inseparable connexion; for that has been already excluded from the imagination: Nor yet are we to conclude, that without it the mind cannot join two ideas; for nothing is more free than that faculty: but we are only to regard it as a gentle force, which commonly prevails, and is the cause why, among other things, languages so nearly correspond to each other; nature in a manner pointing out to every one those simple ideas, which are most proper to be united in a complex one. The qualities, from which this association arises, and by which the mind is after this manner conveyed from one idea to another, are three, viz. RESEMBLANCE, CONTIGUITY in time or place, and CAUSE and EFFECT.

I believe it will not be very necessary to prove, that these qualities produce an association among ideas, and upon the appearance of one idea naturally introduce another. It is plain, that in the course of our thinking, and in the constant revolution of our ideas, our imagination runs easily from one idea to any other that resembles it, and that this quality alone is to the fancy a sufficient bond and association. It is likewise evident that as the senses, in changing their objects, are necessitated to change them regularly, and take them as they lie CONTIGUOUS to each other, the imagination must by long custom acquire the same method of thinking, and run along the parts of space and time in conceiving its objects. As to the connexion, that is made by the relation of cause and effect, we shall have occasion afterwards to examine it to the bottom, and therefore shall not at present insist upon it. It is sufficient to observe, that there is no relation, which produces a stronger connexion in the fancy, and makes one idea more readily recall another, than the relation of cause and effect betwixt their objects.

That we may understand the full extent of these relations, we must consider, that two objects are connected together in the imagination, not only when the one is immediately resembling, contiguous to, or the cause of the other, but also when there is interposed betwixt them a third object, which bears to both of them any of these relations. This may be carried on to a great length; though at the same time we may observe, that each remove considerably weakens the relation. Cousins in the fourth degree are connected by causation, if I may be allowed to use that term; but not so closely as brothers, much less as child and parent. In general we may observe, that all the relations of blood depend upon cause and effect, and are esteemed near or remote, according to the number of connecting causes interposed betwixt the persons.

Of the three relations above-mentioned this of causation is the most extensive. Two objects may be considered as placed in this relation, as well when one is the cause of any of the actions or motions of the other, as when the former is the cause of the existence of the latter. For as that action or motion is nothing but the object itself, considered in a certain light, and as the object continues the same in all its different situations, it is easy to imagine how such an influence of objects upon one another may connect them in the imagination.

We may carry this farther, and remark, not only that two objects are connected by the relation of cause and effect, when the one produces a motion or any action in the other, but also when it has a power of producing it. And this we may observe to be the source of all the relation, of interest and duty, by which men influence each other in society, and are placed in the ties of government and subordination. A master is such-a-one as by his situation, arising either from force or agreement, has a power of directing in certain particulars the actions of another, whom we call servant. A judge is one, who in all disputed cases can fix by his opinion the possession or property of any thing betwixt any members of the society. When a person is possessed of any power, there is no more required to convert it into action, but the exertion of the will; and that in every case is considered as possible, and in many as probable; especially in the case of authority, where the obedience of the subject is a pleasure and advantage to the superior.

These are therefore the principles of union or cohesion among our simple ideas, and in the imagination supply the place of that inseparable connexion, by which they are united in our memory. Here is a kind of ATTRACTION, which in the mental world will be found to have as extraordinary effects as in the natural, and to shew itself in as many and as various forms. Its effects are every where conspicuous; but as to its causes, they are mostly unknown, and must be resolved into original qualities of human nature, which I pretend not to explain. Nothing is more requisite for a true philosopher, than to restrain the intemperate desire of searching into causes, and having established any doctrine upon a sufficient number of experiments, rest contented with that, when he sees a farther examination would lead him into obscure and uncertain speculations. In that case his enquiry would be much better employed in examining the effects than the causes of his principle.

Amongst the effects of this union or association of ideas, there are none more remarkable, than those complex ideas, which are the common subjects of our thoughts and reasoning, and generally arise from some principle of union among our simple ideas. These complex ideas may be divided into Relations, Modes, and Substances. We shall briefly examine each of these in order, and shall subjoin some considerations concerning our general and particular ideas, before we leave the present subject, which may be considered as the elements of this philosophy.

RELATIONS

The word RELATION is commonly used in two senses considerably different from each other. Either for that quality, by which two ideas are connected together in the imagination, and the one naturally introduces the other, after the manner above-explained: or for that particular circumstance, in which, even upon the arbitrary union of two ideas in the fancy, we may think proper to compare them. In common language the former is always the sense, in which we use the word, relation; and it is only in philosophy, that we extend it to mean any particular subject of comparison, without a connecting principle. Thus distance will be allowed by philosophers to be a true relation, because we acquire an idea of it by the comparing of objects: But in a common way we say, THAT NOTHING CAN BE MORE DISTANT THAN SUCH OR SUCH THINGS FROM EACH OTHER, NOTHING CAN HAVE LESS RELATION: as if distance and relation were incompatible.

It may perhaps be esteemed an endless task to enumerate all those qualities, which make objects admit of comparison, and by which the ideas of philosophical relation are produced. But if we diligently consider them, we shall find that without difficulty they may be comprised under seven general heads, which may be considered as the sources of all philosophical relation.

(1) The first is RESEMBLANCE: And this is a relation, without which no philosophical relation can exist; since no objects will admit of comparison, but what have some degree of resemblance. But though resemblance be necessary to all philosophical relation, it does not follow, that it always produces a connexion or association of ideas. When a quality becomes very general, and is common to a great many individuals, it leads not the mind directly to any one of them; but by presenting at once too great a choice, does thereby prevent the imagination from fixing on any single object.

(2) IDENTITY may be esteemed a second species of relation. This relation I here consider as applied in its strictest sense to constant and unchangeable objects; without examining the nature and foundation of personal identity, which shall find its place afterwards. Of all relations the most universal is that of identity, being common to every being whose existence has any duration.

(3) After identity the most universal and comprehensive relations are those of SPACE and TIME, which are the sources of an infinite number of comparisons, such as distant, contiguous, above, below, before, after, etc.

(4) All those objects, which admit of QUANTITY, or NUMBER, may be compared in that particular; which is another very fertile source of relation.

(5) When any two objects possess the same QUALITY in common, the DEGREES, in which they possess it, form a fifth species of relation. Thus of two objects, which are both heavy, the one may be either of greater, or less weight than the other. Two colours, that are of the same kind, may yet be of different shades, and in that respect admit of comparison.

(6) The relation of CONTRARIETY may at first sight be regarded as an exception to the rule, THAT NO RELATION OF ANY KIND CAN SUBSIST WITHOUT SOME DEGREE OF RESEMBLANCE. But let us consider, that no two ideas are in themselves contrary, except those of existence and non-existence, which are plainly resembling, as implying both of them an idea of the object; though the latter excludes the object from all times and places, in which it is supposed not to exist.

(7) All other objects, such as fire and water, heat and cold, are only found to be contrary from experience, and from the contrariety of their causes or effects; which relation of cause and effect is a seventh philosophical relation, as well as a natural one. The resemblance implied in this relation, shall be explained afterwards.

It might naturally be expected, that I should join DIFFERENCE to the other relations. But that I consider rather as a negation of relation, than as anything real or positive. Difference is of two kinds as opposed either to identity or resemblance. The first is called a difference of number; the other of KIND.

MODES AND SUBSTANCES

I would fain ask those philosophers, who found so much of their reasonings on the distinction of substance and accident, and imagine we have clear ideas of each, whether the idea of substance be derived from the impressions of sensation or of reflection? If it be conveyed to us by our senses, I ask, which of them; and after what manner? If it be perceived by the eyes, it must be a colour; if by the ears, a sound; if by the palate, a taste; and so of the other senses. But I believe none will assert, that substance is either a colour, or sound, or a taste. The idea, of substance must therefore be derived from an impression of reflection, if it really exist. But the impressions of reflection resolve themselves into our passions and emotions: none of which can possibly represent a substance. We have therefore no idea of substance, distinct from that of a collection of particular qualities, nor have we any other meaning when we either talk or reason concerning it.

The idea of a substance as well as that of a mode, is nothing but a collection of Simple ideas, that are united by the imagination, and have a particular name assigned them, by which we are able to recall, either to ourselves or others, that collection. But the difference betwixt these ideas consists in this, that the particular qualities, which form a substance, are commonly referred to an unknown something, in which they are supposed to inhere; or granting this fiction should not take place, are at least supposed to be closely and inseparably connected by the relations of contiguity and causation. The effect of this is, that whatever new simple quality we discover to have the same connexion with the rest, we immediately comprehend it among them, even though it did not enter into the first conception of the substance. Thus our idea of gold may at first be a yellow colour, weight, malleableness, fusibility; but upon the discovery of its dissolubility in aqua regia, we join that to the other qualities, and suppose it to belong to the substance as much as if its idea had from the beginning made a part of the compound one. The principal of union being regarded as the chief part of the complex idea, gives entrance to whatever quality afterwards occurs, and is equally comprehended by it, as are the others, which first presented themselves.

That this cannot take place in modes, is evident from considering their mature. The simple ideas of which modes are formed, either represent qualities, which are not united by contiguity and causation, but are dispersed in different subjects; or if they be all united together, the uniting principle is not regarded as the foundation of the complex idea. The idea of a dance is an instance of the first kind of modes; that of beauty of the second. The reason is obvious, why such complex ideas cannot receive any new idea, without changing the name, which distinguishes the mode.

ABSTRACT IDEAS

A very material question has been started concerning ABSTRACT or GENERAL ideas, WHETHER THEY BE GENERAL OR PARTICULAR IN THE MIND'S CONCEPTION OF THEM. A great philosopher [Dr. Berkeley.] has disputed the received opinion in this particular, and has asserted, that all general ideas are nothing but particular ones, annexed to a certain term, which gives them a more extensive signification, and makes them recall upon occasion other individuals, which are similar to them. As I look upon this to be one of the greatest and most valuable discoveries that has been made of late years in the republic of letters, I shall here endeavour to confirm it by some arguments, which I hope will put it beyond all doubt and controversy.

It is evident, that in forming most of our general ideas, if not all of them, we abstract from every particular degree of quantity and quality, and that an object ceases not to be of any particular species on account of every small alteration in its extension, duration and other properties. It may therefore be thought, that here is a plain dilemma, that decides concerning the nature of those abstract ideas, which have afforded so much speculation to philosophers. The abstract idea of a man represents men of all sizes and all qualities; which it is concluded it cannot do, but either by representing at once all possible sizes and all possible qualities, or by, representing no particular one at all. Now it having been esteemed absurd to defend the former proposition, as implying an infinite capacity in the mind, it has been commonly inferred in favour of the latter: and our abstract ideas have been supposed to represent no particular degree either of quantity or quality. But that this inference is erroneous, I shall endeavour to make appear, first, by proving, that it is utterly impossible to conceive any quantity or quality, without forming a precise notion of its degrees: And secondly by showing, that though the capacity of the mind be not infinite, yet we can at once form a notion of all possible degrees of quantity and quality, in such a manner at least, as, however imperfect, may serve all the purposes of reflection and conversation.

To begin with the first proposition, THAT THE MIND CANNOT FORM ANY NOTION OF QUANTITY OR QUALITY WITHOUT FORMING A PRECISE NOTION OF DEGREES OF EACH; we may prove this by the three following arguments. First, We have observed, that whatever objects are different are distinguishable, and that whatever objects are distinguishable are separable by the thought and imagination. And we may here add, that these propositions are equally true in the inverse, and that whatever objects are separable are also distinguishable, and that whatever objects are distinguishable, are also different. For how is it possible we can separate what is not distinguishable, or distinguish what is not different? In order therefore to know, whether abstraction implies a separation, we need only consider it in this view, and examine, whether all the circumstances, which we abstract from in our general ideas, be such as are distinguishable and different from those, which we retain as essential parts of them. But it is evident at first sight, that the precise length of a line is not different nor distinguishable from the line itself nor the precise degree of any quality from the quality. These ideas, therefore, admit no more of separation than they do of distinction and difference. They are consequently conjoined with each other in the conception; and the general idea of a line, notwithstanding all our abstractions and refinements, has in its appearance in the mind a precise degree of quantity and quality; however it may be made to represent others, which have different degrees of both.

Secondly, it is contest, that no object can appear to the senses; or in other words, that no impression can become present to the mind, without being determined in its degrees both of quantity and quality. The confusion, in which impressions are sometimes involved, proceeds only from their faintness and unsteadiness, not from any capacity in the mind to receive any impression, which in its real existence has no particular degree nor proportion. That is a contradiction in terms; and even implies the flattest of all contradictions, viz. that it is possible for the same thing both to be and not to be.

Now since all ideas are derived from impressions, and are nothing but copies and representations of them, whatever is true of the one must be acknowledged concerning the other. Impressions and ideas differ only in their strength and vivacity. The foregoing conclusion is not founded on any particular degree of vivacity. It cannot therefore be affected by any variation in that particular. An idea is a weaker impression; and as a strong impression must necessarily have a determinate quantity and quality, the case must be the same with its copy or representative.

Thirdly, it is a principle generally received in philosophy that everything in nature is individual, and that it is utterly absurd to suppose a triangle really existent, which has no precise proportion of sides and angles. If this therefore be absurd in fact and reality, it must also be absurd in idea; since nothing of which we can form a clear and distinct idea is absurd and impossible. But to form the idea of an object, and to form an idea simply, is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character. Now as it is impossible to form an idea of an object, that is possest of quantity and quality, and yet is possest of no precise degree of either; it follows that there is an equal impossibility of forming an idea, that is not limited and confined in both these particulars. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, though the application of it in our reasoning be the same, as if it were universal.

This application of ideas beyond their nature proceeds from our collecting all their possible degrees of quantity and quality in such an imperfect manner as may serve the purposes of life, which is the second proposition I proposed to explain. When we have found a resemblance [FN 2.] among several objects, that often occur to us, we apply the same name to all of them, whatever differences we may observe in the degrees of their quantity and quality, and whatever other differences may appear among them. After we have acquired a custom of this kind, the hearing of that name revives the idea of one of these objects, and makes the imagination conceive it with all its particular circumstances and proportions. But as the same word is supposed to have been frequently applied to other individuals, that are different in many respects from that idea, which is immediately present to the mind; the word not being able to revive the idea of all these individuals, but only touches the soul, if I may be allowed so to speak, and revives that custom, which we have acquired by surveying them. They are not really and in fact present to the mind, but only in power; nor do we draw them all out distinctly in the imagination, but keep ourselves in a readiness to survey any of them, as we may be prompted by a present design or necessity. The word raises up an individual idea, along with a certain custom; and that custom produces any other individual one, for which we may have occasion. But as the production of all the ideas, to which the name may be applied, is in most eases impossible, we abridge that work by a more partial consideration, and find but few inconveniences to arise in our reasoning from that abridgment.

[FN 2. It is evident, that even different simple ideas

may have a similarity or resemblance to each other; nor is

it necessary, that the point or circumstance of resemblance

shoud be distinct or separable from that in which they

differ. BLUE and GREEN are different simple ideas, but are

more resembling than BLUE and SCARLET; tho their perfect

simplicity excludes all possibility of separation or

distinction. It is the same case with particular sounds, and

tastes and smells. These admit of infinite resemblances upon

the general appearance and comparison, without having any

common circumstance the same. And of this we may be certain,

even from the very abstract terms SIMPLE IDEA. They

comprehend all simple ideas under them. These resemble each

other in their simplicity. And yet from their very nature,

which excludes all composition, this circumstance, In which

they resemble, Is not distinguishable nor separable from the

rest. It is the same case with all the degrees In any

quality. They are all resembling and yet the quality, In any

individual, Is not distinct from the degree.]

For this is one of the most extraordinary circumstances in the present affair, that after the mind has produced an individual idea, upon which we reason, the attendant custom, revived by the general or abstract term, readily suggests any other individual, if by chance we form any reasoning, that agrees not with it. Thus should we mention the word triangle, and form the idea of a particular equilateral one to correspond to it, and should we afterwards assert, that the three angles of a triangle are equal to each other, the other individuals of a scalenum and isosceles, which we overlooked at first, immediately crowd in upon us, and make us perceive the falshood of this proposition, though it be true with relation to that idea, which we had formed. If the mind suggests not always these ideas upon occasion, it proceeds from some imperfection in its faculties; and such a one as is often the source of false reasoning and sophistry. But this is principally the case with those ideas which are abstruse and compounded. On other occasions the custom is more entire, and it is seldom we run into such errors.

Nay so entire is the custom, that the very same idea may be annext to several different words, and may be employed in different reasonings, without any danger of mistake. Thus the idea of an equilateral triangle of an inch perpendicular may serve us in talking of a figure, of a rectilinear figure, of a regular figure, of a triangle, and of an equilateral triangle. All these terms, therefore, are in this case attended with the same idea; but as they are wont to be applied in a greater or lesser compass, they excite their particular habits, and thereby keep the mind in a readiness to observe, that no conclusion be formed contrary to any ideas, which are usually comprized under them.

Before those habits have become entirely perfect, perhaps the mind may not be content with forming the idea of only one individual, but may run over several, in order to make itself comprehend its own meaning, and the compass of that collection, which it intends to express by the general term. That we may fix the meaning of the word, figure, we may revolve in our mind the ideas of circles, squares, parallelograms, triangles of different sizes and proportions, and may not rest on one image or idea. However this may be, it is certain that we form the idea of individuals, whenever we use any general term; that we seldom or never can exhaust these individuals; and that those, which remain, are only represented by means of that habit, by which we recall them, whenever any present occasion requires it. This then is the nature of our abstract ideas and general terms; and it is after this manner we account for the foregoing paradox, THAT SOME IDEAS ARE PARTICULAR IN THEIR NATURE, BUT GENERAL IN THEIR REPRESENTATION. A particular idea becomes general by being annexed to a general term; that is, to a term, which from a customary conjunction has a relation to many other particular ideas, and readily recalls them in the imagination.

The only difficulty, that can remain on this subject, must be with regard to that custom, which so readily recalls every particular idea, for which we may have occasion, and is excited by any word or sound, to which we commonly annex it. The most proper method, in my opinion, of giving a satisfactory explication of this act of the mind, is by producing other instances, which are analogous to it, and other principles, which facilitate its operation. To explain the ultimate causes of our mental actions is impossible. It is sufficient, if we can give any satisfactory account of them from experience and analogy.

First then I observe, that when we mention any great number, such as a thousand, the mind has generally no adequate idea of it, but only a power of producing such an idea, by its adequate idea of the decimals, under which the number is comprehended. This imperfection, however, in our ideas, is never felt in our reasonings; which seems to be an instance parallel to the present one of universal ideas.

Secondly, we have several instances of habits, which may be revived by one single word; as when a person, who has by rote any periods of a discourse, or any number of verses, will be put in remembrance of the whole, which he is at a loss to recollect, by that single word or expression, with which they begin.

Thirdly, I believe every one, who examines the situation of his mind in reasoning will agree with me, that we do not annex distinct and compleat ideas to every term we make use of, and that in talking of government, church, negotiation, conquest, we seldom spread out in our minds all the simple ideas, of which these complex ones are composed. It is however observable, that notwithstanding this imperfection we may avoid talking nonsense on these subjects, and may perceive any repugnance among the ideas, as well as if we had a fall comprehension of them. Thus if instead of saying, that in war the weaker have always recourse to negotiation, we should say, that they have always recourse to conquest, the custom, which we have acquired of attributing certain relations to ideas, still follows the words, and makes us immediately perceive the absurdity of that proposition; in the same manner as one particular idea may serve us in reasoning concerning other ideas, however different from it in several circumstances.

Fourthly, As the individuals are collected together, said placed under a general term with a view to that resemblance, which they bear to each other, this relation must facilitate their entrance in the imagination, and make them be suggested more readily upon occasion. And indeed if we consider the common progress of the thought, either in reflection or conversation, we shall find great reason to be satisfyed in this particular. Nothing is more admirable, than the readiness, with which the imagination suggests its ideas, and presents them at the very instant, in which they become necessary or useful. The fancy runs from one end of the universe to the other in collecting those ideas, which belong to any subject. One would think the whole intellectual world of ideas was at once subjected to our view, and that we did nothing but pick out such as were most proper for our purpose. There may not, however, be any present, beside those very ideas, that are thus collected by a kind of magical faculty in the soul, which, though it be always most perfect in the greatest geniuses, and is properly what we call a genius, is however inexplicable by the utmost efforts of human understanding.

Perhaps these four reflections may help to remove an difficulties to the hypothesis I have proposed concerning abstract ideas, so contrary to that, which has hitherto prevailed in philosophy, But, to tell the truth I place my chief confidence in what I have already proved concerning the impossibility of general ideas, according to the common method of explaining them. We must certainly seek some new system on this head, and there plainly is none beside what I have proposed. If ideas be particular in their nature, and at the same time finite in their number, it is only by custom they can become general in their representation, and contain an infinite number of other ideas under them.

Before I leave this subject I shall employ the same principles to explain that distinction of reason, which is so much talked of, and is so little understood, in the schools. Of this kind is the distinction betwixt figure and the body figured; motion and the body moved. The difficulty of explaining this distinction arises from the principle above explained, that all ideas, which are different, are separable. For it follows from thence, that if the figure be different from the body, their ideas must be separable as well as distinguishable: if they be not different, their ideas can neither be separable nor distinguishable. What then is meant by a distinction of reason, since it implies neither a difference nor separation.

To remove this difficulty we must have recourse to the foregoing explication of abstract ideas. It is certain that the mind would never have dreamed of distinguishing a figure from the body figured, as being in reality neither distinguishable, nor different, nor separable; did it not observe, that even in this simplicity there might be contained many different resemblances and relations. Thus when a globe of white marble is presented, we receive only the impression of a white colour disposed in a certain form, nor are we able to separate and distinguish the colour from the form. But observing afterwards a globe of black marble and a cube of white, and comparing them with our former object, we find two separate resemblances, in what formerly seemed, and really is, perfectly inseparable. After a little more practice of this kind, we begin to distinguish the figure from the colour by a distinction of reason; that is, we consider the figure and colour together, since they are in effect the same and undistinguishable; but still view them in different aspects, according to the resemblances, of which they are susceptible. When we would consider only the figure of the globe of white marble, we form in reality an idea both of the figure and colour, but tacitly carry our eye to its resemblance with the globe of black marble: And in the same manner, when we would consider its colour only, we turn our view to its resemblance with the cube of white marble. By this means we accompany our ideas with a kind of reflection, of which custom renders us, in a great measure, insensible. A person, who desires us to consider the figure of a globe of white marble without thinking on its colour, desires an impossibility but his meaning is, that we should consider the figure and colour together, but still keep in our eye the resemblance to the globe of black marble, or that to any other globe of whatever colour or substance.

PART II

OF THE IDEAS OF SPACE AND TIME.

THE INFINITE DIVISIBILITY OF SPACE AND TIME

Whatever has the air of a paradox, and is contrary to the first and most unprejudiced notions of mankind, is often greedily embraced by philosophers, as shewing the superiority of their science, which coued discover opinions so remote from vulgar conception. On the other hand, anything proposed to us, which causes surprize and admiration, gives such a satisfaction to the mind, that it indulges itself in those agreeable emotions, and will never be persuaded that its pleasure is entirely without foundation. From these dispositions in philosophers and their disciples arises that mutual complaisance betwixt them; while the former furnish such plenty of strange and unaccountable opinions, and the latter so readily believe them. Of this mutual complaisance I cannot give a more evident instance than in the doctrine of infinite divisibility, with the examination of which I shall begin this subject of the ideas of space and time.

It is universally allowed, that the capacity of the mind is limited, and can never attain a full and adequate conception of infinity: And though it were not allowed, it would be sufficiently evident from the plainest observation and experience. It is also obvious, that whatever is capable of being divided in infinitum, must consist of an infinite number of parts, and that it is impossible to set any bounds to the number of parts, without setting bounds at the same time to the division. It requires scarce any, induction to conclude from hence, that the idea, which we form of any finite quality, is not infinitely divisible, but that by proper distinctions and separations we may run up this idea to inferior ones, which will be perfectly simple and indivisible. In rejecting the infinite capacity of the mind, we suppose it may arrive at an end in the division of its ideas; nor are there any possible means of evading the evidence of this conclusion.

It is therefore certain, that the imagination reaches a minimum, and may raise up to itself an idea, of which it cannot conceive any sub-division, and which cannot be diminished without a total annihilation. When you tell me of the thousandth and ten thousandth part of a grain of sand, I have a distinct idea of these numbers and of their different proportions; but the images, which I form in my mind to represent the things themselves, are nothing different from each other, nor inferior to that image, by which I represent the grain of sand itself, which is supposed so vastly to exceed them. What consists of parts is distinguishable into them, and what is distinguishable is separable. But whatever we may imagine of the thing, the idea of a grain of sand is not distinguishable, nor separable into twenty, much less into a thousand, ten thousand, or an infinite number of different ideas.

It is the same case with the impressions of the senses as with the ideas of the imagination. Put a spot of ink upon paper, fix your eye upon that spot, and retire to such a distance, that, at last you lose sight of it; it is plain, that the moment before it vanished the image or impression was perfectly indivisible. It is not for want of rays of light striking on our eyes, that the minute parts of distant bodies convey not any sensible impression; but because they are removed beyond that distance, at which their impressions were reduced to a minimum, and were incapable of any farther diminution. A microscope or telescope, which renders them visible, produces not any new rays of light, but only spreads those, which always flowed from them; and by that means both gives parts to impressions, which to the naked eye appear simple and uncompounded, and advances to a minimum, what was formerly imperceptible.

We may hence discover the error of the common opinion, that the capacity of the mind is limited on both sides, and that it is impossible for the imagination to form an adequate idea, of what goes beyond a certain degree of minuteness as well as of greatness. Nothing can be more minute, than some ideas, which we form in the fancy; and images, which appear to the senses; since there are ideas and images perfectly simple and indivisible. The only defect of our senses is, that they give us disproportioned images of things, and represent as minute and uncompounded what is really great and composed of a vast number of parts. This mistake we are not sensible of: but taking the impressions of those minute objects, which appear to the senses, to be equal or nearly equal to the objects, and finding by reason, that there are other objects vastly more minute, we too hastily conclude, that these are inferior to any idea of our imagination or impression of our senses. This however is certain, that we can form ideas, which shall be no greater than the smallest atom of the animal spirits of an insect a thousand times less than a mite: And we ought rather to conclude, that the difficulty lies in enlarging our conceptions so much as to form a just notion of a mite, or even of an insect a thousand times less than a mite. For in order to form a just notion of these animals, we must have a distinct idea representing every part of them, which, according to the system of infinite divisibility, is utterly impossible, and, recording to that of indivisible parts or atoms, is extremely difficult, by reason of the vast number and multiplicity of these parts.

Wherever ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects; and this we may in general observe to be the foundation of all human knowledge. But our ideas are adequate representations of the most minute parts of extension; and through whatever divisions and subdivisions we may suppose these parts to be arrived at, they can never become inferior to some ideas, which we form. The plain consequence is, that whatever appears impossible and contradictory upon the comparison of these ideas, must be really impossible and contradictory, without any farther excuse or evasion.

Every thing capable of being infinitely divided contains an infinite number of parts; otherwise the division would be stopt short by the indivisible parts, which we should immediately arrive at. If therefore any finite extension be infinitely divisible, it can be no contradiction to suppose, that a finite extension contains an infinite number of parts: And vice versa, if it be a contradiction to suppose, that a finite extension contains an infinite number of parts, no finite extension can be infinitely divisible. But that this latter supposition is absurd, I easily convince myself by the consideration of my clear ideas. I first take the least idea I can form of a part of extension, and being certain that there is nothing more minute than this idea, I conclude, that whatever I discover by its means must be a real quality of extension. I then repeat this idea once, twice, thrice, &c., and find the compound idea of extension, arising from its repetition, always to augment, and become double, triple, quadruple, &c., till at last it swells up to a considerable bulk, greater or smaller, in proportion as I repeat more or less the same idea. When I stop in the addition of parts, the idea of extension ceases to augment; and were I to carry on the addition in infinitum, I clearly perceive, that the idea of extension must also become infinite. Upon the whole, I conclude, that the idea of all infinite number of parts is individually the same idea with that of an infinite extension; that no finite extension is capable of containing an infinite number of parts; and consequently that no finite extension is infinitely divisible [FN 3.].

[FN 3. It has been objected to me, that infinite

divisibility supposes only an infinite number of

PROPORTIONAL not of ALIQIOT parts, and that an infinite

number of proportional parts does not form an infinite

extension. But this distinction is entirely frivolous.

Whether these parts be calld ALIQUOT or PROPORTIONAL, they

cannot be inferior to those minute parts we conceive; and

therefore cannot form a less extension by their

conjunction.]

I may subjoin another argument proposed by a noted author [Mons. MALEZIEU], which seems to me very strong and beautiful. It is evident, that existence in itself belongs only to unity, and is never applicable to number, but on account of the unites, of which the number is composed. Twenty men may be said to exist; but it is only because one, two, three, four, &c. are existent, and if you deny the existence of the latter, that of the former falls of course. It is therefore utterly absurd to suppose any number to exist, and yet deny the existence of unites; and as extension is always a number, according to the common sentiment of metaphysicians, and never resolves itself into any unite or indivisible quantity, it follows, that extension can never at all exist. It is in vain to reply, that any determinate quantity of extension is an unite; but such-a-one as admits of an infinite number of fractions, and is inexhaustible in its sub-divisions. For by the same rule these twenty men may be considered as a unit. The whole globe of the earth, nay the whole universe, may be considered as a unit. That term of unity is merely a fictitious denomination, which the mind may apply to any quantity of objects it collects together; nor can such an unity any more exist alone than number can, as being in reality a true number. But the unity, which can exist alone, and whose existence is necessary to that of all number, is of another kind, and must be perfectly indivisible, and incapable of being resolved into any lesser unity.

All this reasoning takes place with regard to time; along with an additional argument, which it may be proper to take notice of. It is a property inseparable from time, and which in a manner constitutes its essence, that each of its parts succeeds another, and that none of them, however contiguous, can ever be co-existent. For the same reason, that the year 1737 cannot concur with the present year 1738 every moment must be distinct from, and posterior or antecedent to another. It is certain then, that time, as it exists, must be composed of indivisible moments. For if in time we could never arrive at an end of division, and if each moment, as it succeeds another, were not perfectly single and indivisible, there would be an infinite number of co-existent moments, or parts of time; which I believe will be allowed to be an arrant contradiction.

The infinite divisibility of space implies that of time, as is evident from the nature of motion. If the latter, therefore, be impossible, the former must be equally so.

I doubt not but, it will readily be allowed by the most obstinate defender of the doctrine of infinite divisibility, that these arguments are difficulties, and that it is impossible to give any answer to them which will be perfectly clear and satisfactory. But here we may observe, that nothing can be more absurd, than this custom of calling a difficulty what pretends to be a demonstration, and endeavouring by that means to elude its force and evidence. It is not in demonstrations as in probabilities, that difficulties can take place, and one argument counter-ballance another, and diminish its authority. A demonstration, if just, admits of no opposite difficulty; and if not just, it is a mere sophism, and consequently can never be a difficulty. It is either irresistible, or has no manner of force. To talk therefore of objections and replies, and ballancing of arguments in such a question as this, is to confess, either that human reason is nothing but a play of words, or that the person himself, who talks so, has not a Capacity equal to such subjects. Demonstrations may be difficult to be comprehended, because of abstractedness of the subject; but can never have such difficulties as will weaken their authority, when once they are comprehended.

It is true, mathematicians are wont to say, that there are here equally strong arguments on the other side of the question, and that the doctrine of indivisible points is also liable to unanswerable objections. Before I examine these arguments and objections in detail, I will here take them in a body, and endeavour by a short and decisive reason to prove at once, that it is utterly impossible they can have any just foundation.

It is an established maxim in metaphysics, That whatever the mind clearly conceives, includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible. We can form the idea of a golden mountain, and from thence conclude that such a mountain may actually exist. We can form no idea of a mountain without a valley, and therefore regard it as impossible.

Now it is certain we have an idea of extension; for otherwise why do we talk and reason concerning it? It is likewise certain that this idea, as conceived by the imagination, though divisible into parts or inferior ideas, is not infinitely divisible, nor consists of an infinite number of parts: For that exceeds the comprehension of our limited capacities. Here then is an idea of extension, which consists of parts or inferior ideas, that are perfectly, indivisible: consequently this idea implies no contradiction: consequently it is possible for extension really to exist conformable to it: and consequently all the arguments employed against the possibility of mathematical points are mere scholastick quibbles, and unworthy of our attention.

These consequences we may carry one step farther, and conclude that all the pretended demonstrations for the infinite divisibility of extension are equally sophistical; since it is certain these demonstrations cannot be just without proving the impossibility of mathematical points; which it is an evident absurdity to pretend to.

OUR IDEA OF SPACE AND TIME

No discovery coued have been made more happily for deciding all controversies concerning ideas, than that abovementioned, that impressions always take the precedency of them, and that every idea, with which the imagination is furnished, first makes its appearance in a correspondent impression. These latter perceptions are all so clear and evident, that they admit of no controversy; though many of our ideas are so obscure, that it is almost impossible even for the mind, which forms them, to tell exactly their nature and composition. Let us apply this principle, in order to discover farther the nature of our ideas of space and time.

Upon opening my eyes, and turning them to the surrounding objects, I perceive many visible bodies; and upon shutting them again, and considering the distance betwixt these bodies, I acquire the idea of extension. As every idea is derived from some impression, which is exactly similar to it, the impressions similar to this idea of extension, must either be some sensations derived from the sight, or some internal impressions arising from these sensations.

Our internal impressions are our passions, emotions, desires and aversions; none of which, I believe, will ever be asserted to be the model, from which the idea of space is derived. There remains therefore nothing but the senses, which can convey to us this original impression. Now what impression do oar senses here convey to us? This is the principal question, and decides without appeal concerning the nature of the idea.

The table before me is alone sufficient by its view to give me the idea of extension. This idea, then, is borrowed from, and represents some impression, which this moment appears to the senses. But my senses convey to me only the impressions of coloured points, disposed in a certain manner. If the eye is sensible of any thing farther, I desire it may be pointed out to me. But if it be impossible to shew any thing farther, we may conclude with certainty, that the idea of extension is nothing but a copy of these coloured points, and of the manner of their appearance.

Suppose that in the extended object, or composition of coloured points, from which we first received the idea of extension, the points were of a purple colour; it follows, that in every repetition of that idea we would not only place the points in the same order with respect to each other, but also bestow on them that precise colour, with which alone we are acquainted. But afterwards having experience of the other colours of violet, green, red, white, black, and of all the different compositions of these, and finding a resemblance in the disposition of coloured points, of which they are composed, we omit the peculiarities of colour, as far as possible, and found an abstract idea merely on that disposition of points, or manner of appearance, in which they agree. Nay even when the resemblance is carryed beyond the objects of one sense, and the impressions of touch are found to be Similar to those of sight in the disposition of their parts; this does not hinder the abstract idea from representing both, upon account of their resemblance. All abstract ideas are really nothing but particular ones, considered in a certain light; but being annexed to general terms, they are able to represent a vast variety, and to comprehend objects, which, as they are alike in some particulars, are in others vastly wide of each other.

The idea of time, being derived from the succession of our perceptions of every kind, ideas as well as impressions, and impressions of reflection as well as of sensations will afford us an instance of an abstract idea, which comprehends a still greater variety than that of space, and yet is represented in the fancy by some particular individual idea of a determinate quantity and quality.

As it is from the disposition of visible and tangible objects we receive the idea of space, so from the succession of ideas and impressions we form the idea of time, nor is it possible for time alone ever to make its appearance, or be taken notice of by the mind. A man in a sound sleep, or strongly occupyed with one thought, is insensible of time; and according as his perceptions succeed each other with greater or less rapidity, the same duration appears longer or shorter to his imagination. It has been remarked by a great philosopher, that our perceptions have certain bounds in this particular, which are fixed by the original nature and constitution of the mind, and beyond which no influence of external objects on the senses is ever able to hasten or retard our thought. If you wheel about a burning coal with rapidity, it will present to the senses an image of a circle of fire; nor will there seem to be any interval of time betwixt its revolutions; meerly because it is impossible for our perceptions to succeed each other with the same rapidity, that motion may be communicated to external objects. Wherever we have no successive perceptions, we have no notion of time, even though there be a real succession in the objects. From these phenomena, as well as from many others, we may conclude, that time cannot make its appearance to the mind, either alone, or attended with a steady unchangeable object, but is always discovered some PERCEIVABLE succession of changeable objects.

To confirm this we may add the following argument, which to me seems perfectly decisive and convincing. It is evident, that time or duration consists of different parts: For otherwise we coued not conceive a longer or shorter duration. It is also evident, that these parts are not co-existent: For that quality of the co-existence of parts belongs to extension, and is what distinguishes it from duration. Now as time is composed of parts, that are not coexistent: an unchangeable object, since it produces none but coexistent impressions, produces none that can give us the idea of time; and consequently that idea must be derived from a succession of changeable objects, and time in its first appearance can never be severed from such a succession.

Having therefore found, that time in its first appearance to the mind is always conjoined with a succession of changeable objects, and that otherwise it can never fall under our notice, we must now examine whether it can be conceived without our conceiving any succession of objects, and whether it can alone form a distinct idea in the imagination.

In order to know whether any objects, which are joined in impression, be inseparable in idea, we need only consider, if they be different from each other; in which case, it is plain they may be conceived apart. Every thing, that is different is distinguishable: and everything, that is distinguishable, may be separated, according to the maxims above-explained. If on the contrary they be not different, they are not distinguishable: and if they be not distinguishable, they cannot be separated. But this is precisely the case with respect to time, compared with our successive perceptions. The idea of time is not derived from a particular impression mixed up with others, and plainly distinguishable from them; but arises altogether from the manner, in which impressions appear to the mind, without making one of the number. Five notes played on a flute give us the impression and idea of time; though time be not a sixth impression, which presents itself to the hearing or any other of the senses. Nor is it a sixth impression, which the mind by reflection finds in itself. These five sounds making their appearance in this particular manner, excite no emotion in the mind, nor produce an affection of any kind, which being observed by it can give rise to a new idea. For that is necessary to produce a new idea of reflection, nor can the mind, by revolving over a thousand times all its ideas of sensation, ever extract from them any new original idea, unless nature has so framed its faculties, that it feels some new original impression arise from such a contemplation. But here it only takes notice of the manner, in which the different sounds make their appearance; and that it may afterwards consider without considering these particular sounds, but may conjoin it with any other objects. The ideas of some objects it certainly must have, nor is it possible for it without these ideas ever to arrive at any conception of time; which since it, appears not as any primary distinct impression, can plainly be nothing but different ideas, or impressions, or objects disposed in a certain manner, that is, succeeding each other.

I know there are some who pretend, that the idea of duration is applicable in a proper sense to objects, which are perfectly unchangeable; and this I take to be the common opinion of philosophers as well as of the vulgar. But to be convinced of its falsehood we need but reflect on the foregoing conclusion, that the idea of duration is always derived from a succession of changeable objects, and can never be conveyed to the mind by any thing stedfast and unchangeable. For it inevitably follows from thence, that since the idea of duration cannot be derived from such an object, it can never-in any propriety or exactness be applied to it, nor can any thing unchangeable be ever said to have duration. Ideas always represent the Objects or impressions, from which they are derived, and can never without a fiction represent or be applied to any other. By what fiction we apply the idea of time, even to what is unchangeable, and suppose, as is common, that duration is a measure of rest as well as of motion, we shall consider afterwards.

There is another very decisive argument, which establishes the present doctrine concerning our ideas of space and time, and is founded only on that simple principle, that our ideas of them are compounded of parts, which are indivisible. This argument may be worth the examining.

Every idea, that is distinguishable, being also separable, let us take one of those simple indivisible ideas, of which the compound one of extension is formed, and separating it from all others, and considering it apart, let us form a judgment of its nature and qualities.

It is plain it is not the idea of extension. For the idea of extension consists of parts; and this idea, according to t-he supposition, is perfectly simple and indivisible. Is it therefore nothing? That is absolutely impossible. For as the compound idea of extension, which is real, is composed of such ideas; were these so many non-entities, there would be a real existence composed of non-entities; which is absurd. Here therefore I must ask, What is our idea of a simple and indivisible point? No wonder if my answer appear somewhat new, since the question itself has scarce ever yet been thought of. We are wont to dispute concerning the nature of mathematical points, but seldom concerning the nature of their ideas.

The idea of space is conveyed to the mind by two senses, the sight and touch; nor does anything ever appear extended, that is not either visible or tangible. That compound impression, which represents extension, consists of several lesser impressions, that are indivisible to the eye or feeling, and may be called impressions of atoms or corpuscles endowed with colour and solidity. But this is not all. It is not only requisite, that these atoms should be coloured or tangible, in order to discover themselves to our senses; it is also necessary we should preserve the idea of their colour or tangibility in order to comprehend them by our imagination. There is nothing but the idea of their colour or tangibility, which can render them conceivable by the mind. Upon the removal of the ideas of these sensible qualities, they are utterly annihilated to the thought or imagination.

Now such as the parts are, such is the whole. If a point be not considered as coloured or tangible, it can convey to us no idea; and consequently the idea of extension, which is composed of the ideas of these points, can never possibly exist. But if the idea of extension really can exist, as we are conscious it does, its parts must also exist; and in order to that, must be considered as coloured or tangible. We have therefore no idea of space or extension, but when we regard it as an object either of our sight or feeling.

The same reasoning will prove, that the indivisible moments of time must be filled with some real object or existence, whose succession forms the duration, and makes it be conceivable by the mind.

OBJECTIONS ANSWERED

Our system concerning space and time consists of two parts, which are intimately connected together. The first depends on this chain of reasoning. The capacity of the mind is not infinite; consequently no idea of extension or duration consists of an infinite number of parts or inferior ideas, but of a finite number, and these simple and indivisible: It is therefore possible for space and time to exist conformable to this idea: And if it be possible, it is certain they actually do exist conformable to it; since their infinite divisibility is utterly impossible and contradictory.

The other part of our system is a consequence of this. The parts, into which the ideas of space and time resolve themselves, become at last indivisible; and these indivisible parts, being nothing in themselves, are inconceivable when not filled with something real and existent. The ideas of space and time are therefore no separate or distinct ideas, but merely those of the manner or order, in which objects exist: Or in other words, it is impossible to conceive either a vacuum and extension without matter, or a time, when there was no succession or change in any real existence. The intimate connexion betwixt these parts of our system is the reason why we shall examine together the objections, which have been urged against both of them, beginning with those against the finite divisibility of extension.

I. The first of these objections, which I shall take notice of, is more proper to prove this connexion and dependence of the one part upon the other, than to destroy either of them. It has often been maintained in the schools, that extension must be divisible, in infinitum, because the system of mathematical points is absurd; and that system is absurd, because a mathematical point is a non-entity, and consequently can never by its conjunction with others form a real existence. This would be perfectly decisive, were there no medium betwixt the infinite divisibility of matter, and the non-entity of mathematical points. But there is evidently a medium, viz. the bestowing a colour or solidity on these points; and the absurdity of both the extremes is a demonstration of the truth and reality of this medium. The system of physical points, which is another medium, is too absurd to need a refutation. A real extension, such as a physical point is supposed to be, can never exist without parts, different from each other; and wherever objects are different, they are distinguishable and separable by the imagination.

II. The second objection is derived from the necessity there would be of PENETRATION, if extension consisted of mathematical points. A simple and indivisible atom, that touches another, must necessarily penetrate it; for it is impossible it can touch it by its external parts, from the very supposition of its perfect simplicity, which excludes all parts. It must therefore touch it intimately, and in its whole essence, SECUNDUM SE, TOTA, ET TOTALITER; which is the very definition of penetration. But penetration is impossible: Mathematical points are of consequence equally impossible.

I answer this objection by substituting a juster idea of penetration. Suppose two bodies containing no void within their circumference, to approach each other, and to unite in such a manner that the body, which results from their union, is no more extended than either of them; it is this we must mean when we talk of penetration. But it is evident this penetration is nothing but the annihilation of one of these bodies, and the preservation of the other, without our being able to distinguish particularly which is preserved and which annihilated. Before the approach we have the idea of two bodies. After it we have the idea only of one. It is impossible for the mind to preserve any notion of difference betwixt two bodies of the same nature existing in the same place at the same time.

Taking then penetration in this sense, for the annihilation of one body upon its approach to another, I ask any one, if he sees a necessity, that a coloured or tangible point should be annihilated upon the approach of another coloured or tangible point? On the contrary, does he not evidently perceive, that from the union of these points there results an object, which is compounded and divisible, and may be distinguished into two parts, of which each preserves its existence distinct and separate, notwithstanding its contiguity to the other? Let him aid his fancy by conceiving these points to be of different colours, the better to prevent their coalition and confusion. A blue and a red point may surely lie contiguous without any penetration or annihilation. For if they cannot, what possibly can become of them? Whether shall the red or the blue be annihilated? Or if these colours unite into one, what new colour will they produce by their union?

What chiefly gives rise to these objections, and at the same time renders it so difficult to give a satisfactory answer to them, is the natural infirmity and unsteadiness both of our imagination and senses, when employed on such minute objects. Put a spot of ink upon paper, and retire to such a distance, that the spot becomes altogether invisible; you will find, that upon your return and nearer approach the spot first becomes visible by short intervals; and afterwards becomes always visible; and afterwards acquires only a new force in its colouring without augmenting its bulk; and afterwards, when it has encreased to such a degree as to be really extended, it is still difficult for the imagination to break it into its component parts, because of the uneasiness it finds in the conception of such a minute object as a single point. This infirmity affects most of our reasonings on the present subject, and makes it almost impossible to answer in an intelligible manner, and in proper expressions, many questions which may arise concerning it.

III. There have been many objections drawn from the mathematics against the indivisibility of the parts of extension: though at first sight that science seems rather favourable to the present doctrine; and if it be contrary in its DEMONSTRATIONS, it is perfectly conformable in its definitions. My present business then must be to defend the definitions, and refute the demonstrations.

A surface is DEFINed to be length and breadth without depth: A line to be length without breadth or depth: A point to be what has neither length, breadth nor depth. It is evident that all this is perfectly unintelligible upon any other supposition than that of the composition of extension by indivisible points or atoms. How else coued any thing exist without length, without breadth, or without depth?

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 asserts, 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 assert, 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 quantity; 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 quantity, we ought not to look for the utmost precision and exactness. None of its proofs extend so far. It takes the dimensions and proportions of figures justly; but roughly, and with some liberty. Its errors are never considerable; nor would it err at all, did it not aspire to such an absolute perfection.

I first ask mathematicians, what they mean when they say one line or surface is EQUAL to, or GREATER or LESS than another? Let any of them give an answer, to whatever sect he belongs, and whether he maintains the composition of extension by indivisible points, or by quantities divisible in infinitum. This question will embarrass both of them.

There are few or no mathematicians, who defend the hypothesis of indivisible points; and yet these have the readiest and justest answer to the present question. They need only reply, that lines or surfaces are equal, when the numbers of points in each are equal; and that as the proportion of the numbers varies, the proportion of the lines and surfaces is also 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 space 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 quantity 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 quantities: 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 assign any standard of equality, but assert, 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 assert, 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 pronounce them equal to, or greater or less than each other, without examining or comparing the number of their minute parts. Such judgments are not only common, but in many cases certain and infallible. When the measure of a yard and that of a foot are presented, the mind can no more question, that the first is longer than the second, than it can doubt of those principles, which are the most clear and self-evident.

There are therefore three proportions, which the mind distinguishes in the general appearance of its objects, and calls by the names of greater, less and equal. But though its decisions concerning these proportions be sometimes infallible, they are not always so; nor are our judgments of this kind more exempt from doubt and error than those on any other subject. We frequently correct our first opinion by a review and reflection; and pronounce those objects to be equal, which at first we esteemed unequal; and regard an object as less, though before it appeared greater than another. Nor is this the only correction, which these judgments of our senses undergo; but we often discover our error by a 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 rectitude from repeated trials we have a greater assurance. 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 compass 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 assurance he has, not only of the more intricate, and obscure propositions of his science, but of the most vulgar and obvious principles? How can he prove to me, for instance, that two right lines cannot have one common segment? Or that 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 asserting, that upon their contact they become one. For, I beseech you, by what rule or standard do you judge, when you assert, that the line, in which I have supposed them to concur, cannot make the same right line with those two, that form so small an angle betwixt them? You must surely have some idea of a right line, to which this line does not agree. Do you therefore mean that it takes not the points in the same order and by the same rule, as is peculiar and essential to a right line? If so, I must inform you, that besides that in judging after this manner you allow, that extension is composed of indivisible points (which, perhaps, is more than you intend) besides this, I say, I must inform you, that neither is this the standard from which we form the idea of a right line; nor, if it were, is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserved. The original standard of a right line is in reality nothing but a certain general appearance; and 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 coarse to afford any such subtile inferences as they commonly draw from them. The first principles are founded on the imagination and senses: The conclusion, therefore, can never go beyond, much less contradict these faculties.

This may open our eyes a little, and let us see, that no geometrical demonstration for the infinite divisibility of extension can have so much force as what we naturally attribute to every argument, which is supported by such magnificent pretensions. At the same time we may learn the reason, why geometry falls of evidence in this single point, while all its other reasonings command our fullest assent and approbation. And indeed it seems more requisite to give the reason of this exception, than to 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 quantity is infinitely divisible, there cannot be imagined a more glaring absurdity, than to endeavour to prove, that quantity itself admits of such a division; and to prove this by means of ideas, which are directly opposite in that particular. And as this absurdity is very glaring in itself, so there is no argument founded on it which is not attended with a new absurdity, and involves not an evident contradiction.

I might give as instances those arguments for infinite divisibility, which are derived from the point of contact. I know there is no mathematician, who will not refuse to be judged by the diagrams he describes upon paper, these being loose draughts, as he will tell us, and serving only to convey with greater facility certain ideas, which are the true foundation of all our reasoning. This I am 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 space. 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.

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 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 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, 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 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. 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 space or 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?

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 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 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.