11.

Of

space

and time.

PART sion, which they endeavour to explode. Or if they employ, as is usual, the inaccurate standard, derived from a comparison of objects, upon their general apthe ideas of pearance, 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 fails 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 show that we really must make such an exception, and regard all the mathematical arguments for infinite divisibility as utterly sophistical. For 'tis 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

IV.

answered.

not refuse to be judged by the diagrams he describes SECT. upon paper, these being loose draughts, as he will tell us, and serving only to convey with greater facility cer- Objections tain ideas, which are the true foundation of all our reasoning. This I am satisfied 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 chooses, 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 carried beyond a certain degree of minuteness; since, 'tis 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, viz. those of a circle and right line; though at the same time he acknowledges these ideas to be inseparable.

SECTION V.

PART
II.

Of

the ideas of

space and time.

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 party on either side, as their fancy leads them. But whatever foundation there may be for a controversy concerning the things themselves, it may be pretended that the very dispute is decisive concerning the idea, and that 'tis impossible men could so long reason about a vacuum, and either refute or defend it, without having a notion of what they refuted or defended.

Secondly, if this argument should be contested, the reality, or at least possibility, of 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

V.

The same subject continued.

idea will certainly be allowed possible. It must also SECT. be allowed possible, to conceive the annihilation of any part of matter by the omnipotence of the Deity, while the other parts remain at rest. For as every idea that is distinguishable is separable by the imagination, and as every idea that is separable by the imagination may be conceived to be separately existent, 'tis evident, that the existence of one particle of matter no more implies the existence of another, than a square figure in one body implies a square figure in every one. This being granted, I now demand what results from the concurrence of these two possible ideas 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 the one necessarily implies that of the other; and there being now no distance betwixt the walls of the chamber, they touch each other; in the same manner as my hand touches the paper which is immediately before me. But though this answer be very common, I defy these metaphysicians to conceive the matter according to their hypothesis, or imagine the floor and roof, with all the opposite sides of the chamber, to touch each other, while they continue in rest, and preserve the same position. For how can the two walls, that run from south to north, touch each other, while they touch the opposite ends of two walls that run from east to west? And how can the floor and roof ever meet, while they are separated by the four walls that lie in a contrary position? If you change their position, you suppose a motion. If you conceive any thing betwixt them, you

PART
II.

Of

the ideas of

and Pace

time.

suppose a new creation. But keeping strictly to the
two ideas of rest and annihilation, 'tis evident, that the
idea which results from them is not that of a contact of
parts, but something else, which is concluded to be the
idea of a vacuum.

The third objection carries the matter still farther,
and not only asserts, that the idea of a vacuum is real
and possible, but also necessary and unavoidable. This
assertion is founded on the motion we observe in bo
dies, which, 'tis maintained, would be impossible and
inconceivable without a vacuum, into which one body
must move in order to make way for another. I shall
not enlarge upon this objection, because it principally
belongs to natural philosophy, which lies without our
present sphere.

In order to answer these objections, we must take the matter pretty deep, and consider the nature and origin of several ideas, lest we dispute without understanding perfectly the subject of the controversy. 'Tis evident the idea of darkness is no positive idea, but merely the negation of light, or, more properly speaking, of coloured and visible objects. A man who enjoys his sight, receives no other perception from turning his eyes on every side, when entirely deprived of light, than what is common to him with one born blind; and 'tis certain such a one has no idea either of light or darkness. The consequence of this is, that 'tis not from the mere removal of visible objects we receive the impression of extension without matter; and that the idea of utter darkness can never be the same with that of vacuum.

Suppose again a man to be supported in the air, and to be softly conveyed along by some invisible power; 'tis evident he is sensible of nothing, and never re

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1