Fundamental Philosophy, Vol. I (of 2)

CHAPTER XII.

WHAT SPACE CONSISTS IN

77. Descartes' opinion wholly confounds space and bodies, making the essence of bodies consist in extension, and asserting that wherever there is space, there is body. This opinion we have seen to be void of all reasonable foundation. Perhaps he would come nearer the truth who should say, that in reality space is nothing more than the extension of bodies, without reference to the question whether extension does or does not constitute the essence of bodies, and denying its infinity.

78. Let us examine this last opinion. Analyzing the origin of the idea of space, we find that it is merely the idea of extension taken in the abstract. If I hold before my eyes an orange, I may, by means of abstractions, arrive at the idea of a pure extension, equal to that of the orange. In order to do this, I begin by abstracting its color, taste, smell, and all its qualities which affect the senses. I then have left only an extended being, and if I take from it its mobility, it is reduced to a part of space equal to the size of the orange.

It is plain that the same abstraction is possible in relation to the universe, and the result will be the idea of all the space which the universe occupies.

79. Here I shall answer an objection which might be made to this explanation of the idea of space, and thereby take advantage of this opportunity to throw some light upon the origin of the idea of infinite, or imaginary space.

The difficulty is this. If we form the idea of space by the mere abstraction of the qualities which accompany extension, we can only conceive a space equal to the size of the body from which we have abstracted all its sensible qualities. The abstraction made upon an orange can only give a space equal to the size of the orange, and that made upon the universe can only give a space equal to what we conceive in the universe. Consequently, we can never, by this means, obtain the idea of a space without limits which always presents itself to our mind when we think of space considered in itself.

The solution of this difficulty is in the truth that abstraction rises from the particular to the general. From the idea of gold, by abstracting those properties which constitute gold, and attending only to those which it possesses as metal, I arrive at the much more general idea of metal, which belongs not only to gold, but to all other metals. By this abstraction I pass the limit which separates gold from other metals, and form an idea which extends to all, neither specifying, nor excluding any. If from the idea of metal I abstract all that constitutes metal, and attend only to what constitutes mineral, I pass another limit, and arrive at a still more general idea. Thus passing successively the idea of inorganic, of body, and of substance, until I come to the idea of being, I thus form the most general idea possible, and which includes every thing.46

Thus passing over the limits which distinguish and, as it were, separate objects, abstraction rises to the most general. If we apply this doctrine to the abstractions made upon bodies, we shall discover the reason of the illimitability of the idea of space.

When after the abstractions made upon the orange, I have left only the idea of its extension, the abstraction has not reached the highest point possible; for my conception is not that of extension in itself, but only of the extension of the orange; I conceive its extension, not extension itself. But if I abstract all that makes this extension the extension of the orange, and attend only to extension in itself, then the idea of figure disappears, the extension expands indefinitely, it is impossible for me to assign any term to it, for any limit would make it a determinate, a particular extension, not extension in itself. Then the frontiers of the universe, so to speak, disappear; for however great the universe may be, it is limited, and can give only a particular extension, not extension itself. This is the manner in which the idea of imaginary space seems to be formed.

80. An observation of the phenomena of the imagination will confirm what we have explained by the mere order of intelligence. When I imagine the extension of an orange, I imagine it with a limit, with this or that color, and with these or those qualities; since it is not possible for me to imagine a figure without lines which terminate it. This limit in the imagination is distinct both from the extension which it encloses, and from the extension which it excludes. If it were not so distinguished, we could not imagine it as limit, and it would not answer its object, which is to enable us to distinguish that which it encloses. Therefore, the abstraction is not complete. In the imagination there is always something determinate, which is the limit or the lines which constitute the limit. Destroy these limits, and the imagination expands, until it becomes lost in a sort of dark, unbounded abyss, such as we imagine beyond the universe.

A very simple example will make this explanation clearer. Our imagination may be compared to a black board on which a figure is marked with chalk. When we see the white line on the board which forms the figure, we see the figure also; but if we rub out the line, there remains only the uniform figure of the board. If we suppose the lines which terminate the black board to be indefinitely withdrawn, we shall look in vain for a figure; we see only a black surface indefinitely extended. There is a sufficient parity between this and the manner in which the imagination pictures to itself an endless space.

81. The idea of an abstract extension which is limited, is a contradiction. Limit takes from extension generality; and generality destroys the limit. There can, therefore, be no abstract idea of limited extension; but when we form an idea of extension in the abstract, we conceive it as unlimited, and the imagination attempting to follow the understanding, pictures to itself an indefinite space.

82. Summing up this doctrine, and deducing its inevitable consequences, we may say:

I. That space is nothing else than the extension of bodies.

II. That the idea of space is the idea of extension.

III. That the different parts conceived in space are the ideas of particular extensions, from which we have not taken their limits.

IV. That the idea of infinite space is the idea of extension in general, abstracted from all limit.

V. That indefinite space arises necessarily from the imagination, which destroys the limit in attempting to follow the generalizing march of the understanding.

VI. That where there is no body there is no space.

VII. That what is called distance is only the interposition of a body.

VIII. That if every intermediate body be taken away, distance ceases; there is then contiguity, and, consequently, absolute contact.

IX. That if there were only two bodies in existence, it would be metaphysically impossible for them to be distant from each other.

X. That all vacuum, of whatever kind, or however obtained, is absolutely impossible.

83. These are the consequences which follow from the principle explained in this chapter.

If the reader ask me what I think of them and of the principle on which they are based, I frankly confess that, although the principle seems true and the conclusions legitimate, still the strangeness of some of them, and yet more so with regard to others which I shall point out as we come to them, makes me suspect that there is some error concealed in the principle, or else the reasoning which deduces these consequences contains some defect which is not easy to discover. I do not put forth a settled opinion, so much as a series of conjectures, with the arguments in their favor. The reader may see by this what sense I attach to the word demonstration, when in the sequel he sees it often employed in treating of the deduction of certain consequences which are exceedingly strange, although, in my opinion, deserving a careful attention. I say this not only to explain what is passing in my own mind, but also to warn the reader against too great confidence on these points, whatever may be the opinion which he adopts. Before commencing these investigations on space, I remarked that the arguments on both sides seemed equally conclusive; which shows that the human reason has reached its bounds, and makes us suspect that this investigation is beyond the sphere to which the mind is restricted by a primary condition of its nature.

However this may be, let us continue to conjecture; and although we cannot pass beyond certain limits, let us exercise the understanding by examining them in their full extent. Thus, if we were placed on a very elevated ground with deep precipices on all sides, we should take pleasure in walking around the circumference, and gazing upon the immense depth under our feet.

I shall now proceed to deduce other results, and to solve as far as possible the difficulties which arise, making some applications, the immense importance of which produces uncertainty and causes fear.

CHAPTER XIII.

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 which it 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 on ad 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 know that 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 the a priori demonstration 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, if we 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, outside of 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 this a 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.

CHAPTER XIV.

ANOTHER IMPORTANT CONSEQUENCE

89. I now proceed to deduce the last consequence of the principle explained above. It is of the greatest importance, and seems to deserve the careful attention of all those who unite their metaphysical and physical studies.

The existence of universal gravitation may be demonstrated a priori.

Universal gravitation is a law of nature by which some bodies are directed to others. [We abstract here the manner.] This direction is metaphysically necessary, if we suppose that there is no distance where there is no body. For, if this be so, two bodies cannot exist separated. The law of contiguity is a metaphysical necessity, and therefore the incessant approaching of some bodies to others is a continual obedience to this necessity.

The velocity with which they approach must be in the ratio of the velocity with which the medium departs. The limit of the velocity of this motion is the relation of space with an indivisible instant, such as we might suppose if God should suddenly annihilate the intervening body.

As the solid masses which revolve above our heads would in this case be submerged in a fluid, supposing this fluid to be of such nature as easily to change its place, it follows that the stars must be subject to the law of approximation, because the medium which separates them is continually retiring in various directions. If we suppose this fluid to be immovable, the metaphysical necessity of this approximation ceases.

90. This theory seems to lead to the explanation of the mechanism of the universe, by simple geometrical laws, and destroys what some have called occult properties, and others forces.

Although it is easy to explain by metaphysical and geometrical ideas, the fact of gravitation, or the mere tendency of bodies mutually to approach, it is still very difficult to determine by this order of ideas the conditions which govern gravitation.

91. If the motion of approximation depended only on the intervening body, inequality of these bodies would produce unequal motions. It is impossible to calculate the degree of this inequality in bodies which are not subject to our observation.

92. Besides this difficulty there is another still greater, which is, that bodies which move in a medium have no fixed direction, but vary their motions with the variations of the medium.

If the gravitation of the body A towards the body B, depends only on the motion of the retiring medium, the gravitation will not be in the right line AB, but will follow the undulations described by the medium. This is contrary to experience.

93. From these considerations, it follows that even though the gravitation naturally arises from the position of the bodies, still this necessity would not produce the order which exists, if its results were not subject to certain laws. And, therefore, the phenomena of nature, although founded on a necessity, would still, admitting the existence and position of bodies, be contingent in all that relates to the application of this necessity.

94. Going still deeper into this matter, we find that the tendency to approximation, although necessary, is not sufficient either to produce motion or to preserve it.

Whenever one body moves, it is always necessary that another should follow it, in order to preserve the contiguity; but, there being no vacuum, there is no reason why any body should move, and consequently, no cause of motion.

Therefore, geometrical ideas are not sufficient to explain the origin of motion, but we must look for its cause elsewhere. Contiguity being a metaphysical necessity, if the body A moves in any direction, the contiguous bodies B and C must also move; but if the contiguity already existed, there is no reason why the body A should begin to move, nor, consequently, why the bodies B and C should follow its motion.

At any instant whatever, if we suppose motion, we must suppose contiguity; for the state of the question supposes this condition always present, as being metaphysically necessary. There is then no reason why the motion should at any time be prolonged; for the bodies being at every instant contiguous there is no reason for its continuation. The motion of the body A draws with it the body B; B draws C, and so on. Now, if the motion of the body B has no other origin than its contiguity to A, the motion of C has no other origin than its contiguity to B. The cause of the motion is only not to interrupt the contiguity; this contiguity always existing as is absolutely necessary, there is no reason why the motion should begin, or after it has begun, why it should continue.

95. The laws of nature cannot then be explained by geometrical and metaphysical ideas, although we suppose approximation to be an intrinsical necessity of bodies. Under any supposition it is necessary to seek out of matter a superior cause which impresses, regulates, and continues motion.

CHAPTER XV.

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 and West. 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 as above or below; 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.