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. SECT. V. THE SAME SUBJECT CONTINUED. If the second part of my system be true, that the idea of space or extension is nothing but the idea of visible or tangible points distributed in a certain order; it follows, that we can form no idea of a vacuum, or space, where there is nothing visible or tangible. This gives rise to three objections, which I shall examine together, because the answer I shall give to one is a consequence of that which I shall make use of for the others. First, It may be said, that men have disputed for many ages concerning a vacuum and a plenum, without being able to bring the affair to a final decision; and philosophers, even at this day, think themselves at liberty to take 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 26 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.
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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
