ILLUSION OF FIXED POINTS IN SPACE.
96. Since space is only the extension of bodies, and there is no space where there are no bodies, it follows that the extension which we conceive distinct from bodies, with fixed points and dimensions, immovable in itself, and the receptacle of all that is movable, is a pure illusion, and there is nothing in reality corresponding to it.
In order to explain this doctrine and at the same time to solve certain objections which may be made, it will not be out of place to analyze the idea which we form of fixedness in relation to space. Because there are certain immovable points in the world in relation to which we conceive directions, we form the idea that these points are fixed, and in relation to them and because of them we imagine fixedness, immobility, as one of the properties which distinguish this ideal receptacle which we call space. The four cardinal points, East, West, North, and South, have had a great influence in producing this idea. Still it is easy to show that there is no such thing and that it is a pure illusion.
97. We shall first destroy the fixedness of East andWest. Supposing the earth to have a diurnal motion of rotation on its axis, as astronomers now hold, the points of East and West, so far from being fixed, are continually changing their position. Thus, supposing an observer at the point A of the earth, East to him will be the point B, and West the point C. If the earth revolves on its axis, the East and West of the observer will be successively at the points M, N, P, Q, etc. of the heavenly arch. Although we suppose this arch fixed, East and West have no fixed meaning.
If we deny the rotation of the earth, the appearances will be the same as though this rotation existed; and the most that we can say is that this fixedness is an appearance. Besides, if we suppose the earth to be at rest, and the heavens to move round it, it is still more impossible to determine the fixed points of East and West; for, in this case, the points in the heavens to which we refer them are in continual motion.
We repeat that all this is a mere appearance. If a man who knows not that the earth is spherical, but imagines it to be a plane surface, walks from West to East, he will believe that these two points are immovable, although they are continually changing. He would still imagine that he was going farther from the place where he started, although, after passing over the whole circumference of the earth, he would find himself where he was at first.
98. North and South seem to present greater difficulty, by reason of their fixedness in relation to us; still it is easy to show that this is not absolute, but only apparent. Let N and S represent the north and south poles. If we imagine the earth and the heavens to turn at the same time from south to north, it is evident that the fixedness of the points N and S would not exist, and yet the observer A would believe that every thing was immovable, because the appearances would be absolutely the same.
To an observer travelling from the equator toward either pole, the pole would rise over the horizon, while to another who remains in the same place, the pole would be at rest.
Even in relation to the same position on the earth the altitude of the pole changes, by the variation of the angle formed by the plane of the ecliptic with the plane of the equator, which variation is according to some calculations 8″ in a century, according to others 0″.521 in a year, or 52′.1″ in a century.
99. It follows from these reflections that the position of bodies is not absolute, but relative; that one body might exist alone, but then it would have no position, as this is entirely a relative idea, and there is no relation in this case, because there is no point of comparison; and that absolutely speaking there is no such thing asaboveorbelow; for although we imagine these to be fixed points, this imagination is only a comparison which we make between two points: below being that point toward which we gravitate, and above the opposite. Thus in the antipodes above is what we call below, and below what we call above.
100. Direction is impossible without points to which it can be referred. Therefore, without the existence of bodies, directions are purely ideal, and if only one body existed, it could have no directions out of its own extension.
101. Here arises a difficulty apparently serious, but in reality of little weight. If only one body existed, could God give it motion? To deny it seems to limit the omnipotence of God; and to concede it is to destroy all that has been said against space distinct from bodies.
This objection derives its seeming importance from a confusion of ideas, which is caused by not understanding the true state of the question. Is this motionintrinsically impossible, or is it not? If it is impossible, there is no reason why we should be afraid to say that God cannot produceit: for omnipotence does not extend to things which are contradictory. If the possibility of this motion is admitted, then we must return to the questions on the nature of space, and examine whether the reasons on which this impossibility is founded are, or are not, valid.
The questions relating to omnipotence are out of place here, and this difficulty can be solved without them. If the impossibility of the motion is demonstrated, it is no limitation of the omnipotence of God to say that he cannot produce it, no more than it is when we say that he cannot make a triangle a circle. If the impossibility is not demonstrated, then the question of omnipotence does not come in at all.
102. Neither does the argument founded on the existence of vacuum destroy the doctrine which we have established. Natural philosophers generally admit vacuum, and suppose it necessary for the explanation of motion, condensation, rarefaction, and other phenomena of nature. But to this I reply as follows:
I. The opinions of Descartes and Leibnitz are of weight in what relates to nature, whether experimental or transcendental, and neither of them admitted a vacuum.
II. No observation can prove its existence, because disseminated vacuum would occupy such small spaces that no instrument could reach them, and also because observation can only be made on those objects which affect our senses, and we know not but what there may be bodies which, on account of their excessive tenuity, are not perceptible by the senses.
III. We can determine nothing certain concerning the internal modifications of matter in motion, condensation, and rarefaction, until we know the elements of which it is composed.
IV. It is not strange that we are unable to comprehend thephenomena which seem incompatible with the denial of matter: for we can neither understand infinite divisibility, nor how extension can be composed of unextended points.
V. The existence of vacuum is a metaphysical question which does not belong to the regions of experience, and is not affected by the system of the sciences of observation.
103. By making the idea of space consist in abstract or generalized extension we reconcile all that is necessary, absolute, and infinite in it with its objective reality. This reality is the extension of bodies, while necessity and infinity are not found in the bodies themselves, but in the abstract idea. Objects themselves are confined to the sphere of reality, and are, therefore, limited and contingent. The objectiveness of the abstract idea includes both the existent and the possible, and has, therefore, no limits, and is not subject to any contingency.