which seems much more ingenious; to wit, that matter is composed of a definite number of mathematical points, endowed with certain powers of attraction and repulsion.

The divisibility of matter without any limit, seems to me more tenable than either of these hypotheses; nor do I lay much stress upon the metaphysical axiom, considering its origin. Metaphysicians thought proper to make the attributes common to all beings the subject of a science. It must be a matter of some difficulty to find out such attributes: and, after racking their invention, they have specified three, to wit, unity, verity, and goodness; and these, I suppose, have been invented to make a number, rather than from any clear evidence of their being universal.

There are other determinations concerning matter, which, I think, are not solely founded upon the testimony of sense: such as, that it is impossible that two bodies should occupy the same place at the same time; or that the same body should be in different places at the same time: or that a body can be moved from one place to another, without passing through the intermediate places, either in a straight course, or by some circuit. These appear to be necessary truths, and therefore cannot be conclusions of our senses; for our senses testify only what is, and not what must necessarily be.

We are next to consider our notion of space. It may be observed, that although space be not perceived by any of our senses when all matter is removed; yet, when we perceive any of the primary qualities, space presents itself as a necessary concomitant: for there can neither be extension nor motion, nor figure, nor division, nor cohesion of parts, without space.

There are only two of our senses by which the notion of space enters into the mind; to wit, touch and sight. If we suppose a man to have neither of these senses, I do not see how we could ever have any conception of space. Supposing him to have both, until he sees or feels other objects, he can have no notion of space: it has neither colour nor figure to make it an object of sight: it has no tangible quality to make it an object of touch. But other objects of sight and touch carry the notion of space along with them, and not the notion only, but the belief of it: for a body could not exist if there was no space to contain it; it could not move if there was no space: its situation, its distance, and every relation it has to other bodies, suppose space.

But though the notion of space seems not to enter at first into the mind, until it is introduced by the proper objects of sense; yet, being once introduced, it remains in our conception and belief, though the objects which introduced it be removed. We see no absurdity in supposing a body to be annihilated; but the space that contained it remains: and to suppose that annihilated, seems to be absurd. It is so much allied to nothing or emptiness, that it seems incapable of annihilation or of creation.

Space not only retains a firm hold of our belief, even when we suppose all the objects that introduced it to be annihilated, but it swells to immensity. We can set no limits to it, either of extent or of duration. Hence we call it immense, eternal, immovable, and indestructible. But it is only an immense, eternal, immovable, and indestructible void or emptiness. Perhaps we may apply to it what the Peripatetics said of their first matter, that whatever it is, it is potentially only, not actually.

When we consider parts of space that have measure and figure, there is nothing we understand better, nothing about which we can reason so clearly, and to so great extent. Extension and figure are circumscribed parts of space, and are the object of geometry, a science in which human reason has

the most ample field, and can go deeper, and with more certainty, than in any other. But when we attempt to comprehend the whole of space, and trace it to its origin, we lose ourselves in the search. The profound speculations of ingenious men upon this subject differ so widely, as may lead us to suspect, that the line of human understanding is too short to reach the bottom of it.

Bishop Berkeley, I think, was the first who observed, that the extension, figure, and space, of which we speak in common language, and of which geometry treats, are originally perceived by the sense of touch only; but that there is a notion of extension, figure, and space, which may be got by sight, without any aid from touch. To distinguish these, he calls the first tangible extension, tangible figure, and tangible space; the last he calls visible.

As I think this distinction very important in the philosophy of our senses, I shall adopt the names used by the inventor to express it; remembering what has been already observed, that space, whether tangible or visible, is not so properly an object of sense, as a necessary concomitant of the objects both of sight and touch.

The reader may likewise be pleased to attend to this, that when I use the names of tangible and visible space, I do not mean to adopt Bishop Berkeley's opinion, so far as to think that they are really different things, and altogether unlike. I take them to be different conceptions of the same thing; the one very partial, and the other more complete; but both distinct and just, as far as they reach.

Thus, when I see a spire at a very great distance, it seems like the point of a bodkin; there appears no vane at the top, no angles. But when I view the same object at a small distance, I see a huge pyramid of several angles with a vane on the top. Neither of these appearances is fallacious. Each of them is what it ought to be, and what it must be, from such an object seen at such different distances. These different appearances of the same object may serve to illustrate the different conceptions of space, according as they are drawn from the information of sight alone, or as they are drawn from the additional information of touch.

Our sight alone, unaided by touch, gives a very partial notion of space, but yet a distinct one. When it is considered according to this partial notion, I call it visible space. The sense of touch gives a much more complete notion of space; and when it is considered according to this notion, I call it tangible space. Perhaps there may be intelligent beings of a higher order, whose conceptions of space are much more complete than those we have from both senses. Another sense added to those of sight and touch, might, for what I know, give us conceptions of space, as different from those we can now attain, as tangible space is from visible; and might resolve many knotty points concerning it, which, from the imperfection of our faculties, we cannot by any labour untie.

Berkeley acknowledges that there is an exact correspondence between the visible figure and magnitude of objects, and the tangible; and that every modification of the one has a modification of the other corresponding. He acknowledges likewise, that Nature has established such a connexion between the visible figure and magnitude of an object, and the tangible, that we learn by experience to know the tangible figure and magnitude from the visible. And having been accustomed to do so from infancy, we get the habit of doing it with such facility and quickness, that we think we see tangible figure, magnitude, and distance of bodies, when, in reality,

we only collect those tangible qualities from the corresponding visible qualities, which are natural signs of them.

The correspondence and connexion which Berkeley shows to be between the visible figure and magnitude of objects, and their tangible figure and magnitude, is in some respects very similar to that which we have observed between our sensations, and the primary qualities with which they are connected. No sooner is the sensation felt, than immediately we have the conception and belief of the corresponding quality. We give no attention to the sensation; it has not a name; and it is difficult to persuade us that there was any such thing.

In like manner, no sooner is the visible figure and magnitude of an object seen, than immediately we have the conception and belief of the corresponding tangible figure and magnitude. We give no attention to the visible figure and magnitude. It is immediately forgot, as if it had never been perceived; and it has no name in common language; and indeed, until Berkeley pointed it out as a subject of speculation, and gave it a name, it had none among philosophers, excepting in one instance, relating to the heavenly bodies, which are beyond the reach of touch. With regard to them, what Berkeley calls visible magnitude was, by astronomers, called apparent magnitude.

There is surely an apparent magnitude, and an apparent figure of terrestial objects, as well as of celestial; and this is what Berkeley calls their visible figure and magnitude. But this was never made an object of thought among philosophers, until that author gave it a name, and observed the correspondence and connexion between it and tangible magnitude and figure, and how the mind gets the habit of passing so instantaneously from the visible figure, as a sign to the tangible figure, as the thing signified by it, that the first is perfectly forgot, as if it had never been perceived. Visible figure, extension, and space, may be made a subject of mathematical speculation, as well as the tangible. In the visible we find two dimensions only; in the tangible three. In the one, magnitude is measured by angles; in the other by lines. Every part of visible space bears some proportion to the whole; but tangible space being immense, any part of it bears no proportion to the whole.

Such differences in their properties led Bishop Berkeley to think, that visible and tangible magnitude and figure are things totally different and dissimilar, and cannot both belong to the same object.

And upon this dissimilitude is grounded one of the strongest arguments by which his system is supported. For it may be said, if there be external objects which have a real extension and figure, it must be either tangible extension and figure, or visible, or both. The last appears absurd; nor was it ever maintained by any man, that the same object has two kinds of extension and figure, totally dissimilar. There is then only one of the two really in the object; and the other must be ideal. But no reason can be assigned why the perceptions of one sense should be real, while those of another are only ideal; and he who is persuaded that the objects of sight are ideas only, has equal reason to believe so of the objects of touch.

This argument, however, loses all its force, if it be true, as was formerly hinted, that visible figure and extension are only a partial conception, and the tangible figure and extension a more complete conception of that figure and extension which is really in the object.

It has been proved very fully by Bishop Berkeley, that sight alone, without any aid from the informations of touch, gives us no perception, nor

But he was

even conception, of the distance of any object from the eye. not aware that this very principle overturns the argument for his system, taken from the difference between visible and tangible extension and figure: for, supposing external objects to exist, and to have that tangible extension and figure which we perceive, it follows demonstrably, from the principle now mentioned, that their visible extension and figure must be just what we see it to be.

The rules of perspective, and of the projection of the sphere, which is a branch of perspective, are demonstrable. They suppose the existence of external objects, which have a tangible extension and figure; and, upon that supposition, they demonstrate what must be the visible extension and figure of such objects, when placed in such a position, and at such a distance.

Hence, it is evident, that the visible figure and extension of objects is so far from being incompatible with the tangible, that the first is a necessary consequence from the last, in beings that see as we do. The correspondence between them is not arbitrary, like that between words and the thing they signify, as Berkeley thought; but it results necessarily from the nature of the two senses; and this correspondence being always found in experience to be exactly what the rules of perspective show that it ought to be if the senses give true information, is an argument of the truth of both.

CHAPTER XX.

OF THE EVIDENCE OF SENSE, AND OF BELIEF IN GENERAL.

THE intention of nature in the powers which we call the external senses, is evident. They are intended to give us that information of external objects which the Supreme Being saw to be proper for us in our present state; and they give to all mankind the information necessary for life, without reasoning, without any art or investigation on our part.

The most uninstructed peasant has as distinct a conception, and as firm a belief of the immediate objects of his senses, as the greatest philosopher; and with this he rests satisfied, giving himself no concern how he came by this conception and belief. But the philosopher is impatient to know how his conception of external objects, and his belief of their existence, is produced. This, I am afraid, is hid in impenetrable darkness. But where there is no knowledge, there is the more room for conjecture; and of this philosophers have always been very liberal.

The dark cave and shadows of Plato, the species of Aristotle, the films of Epicurus, and the ideas and impressions of modern philosophers, are the productions of human fancy, successively invented to satisfy the eager desire of knowing how we perceive external objects; but they are all deficient in the two essential characters of a true and philosophical account of the phenomenon: for we neither have any evidence of their existence, nor, if they did exist, can it be shown how they would produce perception. It was before observed, that there are two ingredients in this operation of perception: First, The conception or notion of the objects; and, secondly, The belief of its present existence: both are unaccountable.

That we can assign no adequate cause of our first conceptions of things, I think, is now acknowledged by the most enlightened philosophers. We know that such is our constitution, that in certain circumstances we have

certain conceptions; but how they are produced, we know no more than how we ourselves were produced.

When we have got the conception of external objects by our senses, we can analyse them in our thought into their simple ingredients; and we can compound those ingredients into various new forms, which the senses never presented. But it is beyond the power of human imagination to form any conception, whose simple ingredients have not been furnished by nature in a manner unaccountable to our understanding.

We have an immediate conception of the operations of our own minds, joined with a belief of their existence; and this we call consciousness. But this is only giving a name to this source of our knowledge. It is not a discovery of its cause. In like manner, we have, by our external senses, a conception of external objects, joined with a belief of their existence; and this we call perception. But this is only giving a name to another source of our knowledge, without discovering its cause.

We know, that when certain impressions are made upon our organs, nerves, and brain, certain corresponding sensations are felt, and certain objects are both conceived and believed to exist. But in this train of operations nature works in the dark. We can neither discover the cause of any one of them, nor any necessary connexion of one with another: and whether they are connected by any necessary tie, or only conjoined in our constitution by the will of Heaven, we know not.

That any kind of impression upon a body should be the efficient cause of sensation, appears very absurd. Nor can we perceive any necessary connexion between sensation and the conception and belief of an external object. For any thing we can discover, we might have been so framed as to have all the sensations we now have by our senses, without any impressions upon our organs, and without any conception of any external object. For any thing we know, we might have been so made as to perceive external objects, without any impressions on bodily organs, and without any of those sensations which invariably accompany perception in our present frame.

If our conception of external objects be unaccountable, the conviction and belief of their existence, which we get by our senses, is no less so.

Belief, assent, conviction, are words which I think do not admit of logical definition, because the operation of mind signified by them is perfectly simple, and of its own kind. Nor do they need to be defined, because they are common words, and well understood.

Belief must have an object. For he that believes, must believe something; and that which he believes is called the object of his belief. Of this object of his belief, he must have some conception, clear or obscure; for although there may be the most clear and distinct conception of an object without any belief of its existence, there can be no belief without conception.

Belief is always expressed in language by a proposition, wherein something is affirmed or denied. This is the form of speech which in all languages is appropriated to that purpose, and without belief there could be neither affirmation nor denial, nor should we have any form of words to express either. Belief admits of all degrees, from the slightest suspicion to the fullest assurance. These things are so evident to every man that reflects, that it would be abusing the reader's patience to dwell upon

them.

I proceed to observe, that there are many operations of mind in which,