NEW DIFFICULTIES.
84. If space is the extension of bodies, it follows that extension has no recipient, that is to say, no place in which it can be situated. This seems to be in direct contradiction to our most common ideas; for when we conceive any thing to be extended, we conceive the necessity of a place equal to it in which it can be contained and situated.
This difficulty, which seems so serious at first, immediately vanishes if we deny that every extended thing needs a place in which it may be situated. What is this place? It is an extension in which the thing may be contained. Does this extension also require another extension in whichit may be placed, or does it not? If it does, then the same question may be asked of this new place in which the other place is contained, and so onad infinitum. This is evidently impossible, and therefore we must admit that it is false that all extension requires another extension in which it may be placed. Just as the extension of space does not require another extension, so the extension of bodies does not require space. There is no disparity between the two cases. Therefore the necessity of a place for every extension is merely imaginary, and is opposed to reason. Extension, therefore, may exist in itself, and there is no reason why the extension of bodies may not also exist in this manner.
85. What in this case would be the meaning of changing place? It would simply mean that bodies change their respective position. This is the explanation of motion.
Suppose three bodies, A, B, and C, to be situated in space. Their respective distances are the bodies which are interposed between them. The change which a new position causes, is motion.
86. Therefore, if there were only one body there could be no motion. For motion is necessarily the passing over a distance, and, there is no distance when there is only one body.
This seems at first absurd, because it is opposed to our way of thinking and imagining; but if we carefully examine this way of thinking and imagining, we shall see that the phenomena of our mind are in accordance with this theory.
Motion has no meaning for us, we do not feel or perceive it, when we cannot refer it to the position of different bodies among themselves. If we sail down a river, shut up in the cabin of the vessel which bears us on, we really move, though we have no perception of this motion. We knowthat we move when watching the objects on the shore, we see that they are continually changing. Even then, the motion seems to be in the objects around us, not in ourselves, and the phenomena would be absolutely the same with respect to us, if, instead of the objects being at rest, and the vessel in motion, the vessel should be at rest and the objects in motion, supposing the motion of the objects to be properly combined.[47]
Therefore, take away the agitation, which is all that informs us of our own motion, and we are unable to distinguish whether the motion is in us or in the objects; and we are naturally more inclined to refer the motion to them than to ourselves. When the vessel that carries us leaves the port, we know very well that it is not the port which moves, and yet the illusion is complete, the port seems to retire from us.
Hence motion for us is only the change of the respective position of bodies. If we had not experienced this change, we should have no idea of motion. Thus no one denies that the phenomena of diurnal motion are the same, whether the heavens revolve around us from east to west, or the earth turns on its axis from west to east.
Therefore, the motion of only one body is a pure illusion; and there is no proof of the argument founded on it which is brought to oppose our doctrine of space.
Hence, also, the whole universe considered as only one body, is immovable, motion takes place only in its interior.
87. But one of the strangest results of this theory is thea prioridemonstration that the universe can only be terminated in a certain manner, to the exclusion of a multitude of figures which are essentially repugnant to it.
According to the doctrine which we have put forth, ifwe suppose only one body to exist, it cannot have any part of its surface so disposed that the shortest line from any one point to another shall pass outside of the body. For, as we suppose only one body,outsideof it is pure nothing; and can, therefore, contain no distances which can be measured by lines. This excludes a multitude of irregular figures, and thus we find geometrical regularity growing out of a metaphysical idea.
Hence if only one body were in existence, it would be impossible for it to have any angles entering into it. For, its figure requires that the point A, the vertex of the angle, should be at the distance A D from the point D, the vertex of another angle. This distance cannot exist, for there is no distance where there is no body. Therefore, the distance would exist and not exist at the same time, which is contradictory. It would also be an absurdity, because the capacities marked by the angles would not be filled.
The observation of nature confirms the former result, inasmuch as its tendency is always to terminate every thing with curved lines and surfaces. The orbits of the stars are curves, and the stars themselves terminate in curve surfaces. The great irregularities which are observed in their surfaces might seem to destroy this conclusion, but it must be remembered the limit of the figure is not in these irregularities, but in the atmosphere which surrounds them, and which, being a fluid, can have no irregularities of surface.
88. Another consequence, as strange as the former, is, that we are obliged to admit the existence of a perfect geometrical surface, and thisa priori.
If, where there is no body, distance is metaphysically impossible, this must be just as true in small as in great things, and even in infinitesimals. This is also a reason of the impossibility of vacuum. It is evident that a surface is not perfect when some of its points go farther out than others, so that the less they go out from the surface the more perfect it becomes. As there are no such points in the last surface of the universe, this surface is the realization of geometrical perfection.
We have demonstrated that it is impossible for the surface to have any angles entering into it; it is equally impossible for it to have any, even the least, prominence. The difference is only in greater or less, which does not affect the metaphysical impossibility. It is, therefore, demonstrated that in the ultimate surface of the universe there is no irregularity, but that its surface is geometrically perfect.