CHAPTER VII.
SPACE. – NOTHING
42. It may have been remarked in the preceding chapters that the idea of extension is always united with that of space, and when we endeavor to determine the real nature of the former, we encounter the questions which relate to the latter. It is not possible to explain one, while the other remains in obscurity. It is for this reason that I have concluded to examine carefully the questions concerning space under its ideal as well as under its real aspect; since only in this manner is it possible to determine clearly the nature of extension.
43. Space is one of those profound mysteries which the natural order presents to man's weak understanding. The deeper he examines it the more obscure he finds it; the mind is buried in the darkness which we imagine to exist beyond the bounds of the finite, in the abyss of immensity. We know not if what we behold is an illusion or a reality. For a moment we seem to have found the truth, and then we discover that we have stretched our arms to embrace a shadow. We form arguments which in any other matter would be conclusive, but are not so here, because they are in direct contradiction to others equally conclusive. We seem to have reached the limit which the Creator has put to our investigations; and in endeavoring to pass beyond it, our strength fails, for we find ourselves out of the element which is natural to our life.
When certain philosophers pass rapidly over the questions relating to space, and flatter themselves with explaining them in a few words, we can assure them that either they have not meditated much upon the difficulty which these questions involve, or else they have not understood them. It was not so that Descartes, Malebranche, Newton, or Leibnitz proceeded.
To descend this bottomless abyss is not to lose time in useless discussion; even though we should not find what we seek, we obtain a most precious result, for we reach the limits assigned to our intellect. It is well to know what may be known and what cannot; for from this knowledge philosophy draws high and valuable considerations. Moreover, though we have small hope of success, we cannot pass over without examining an idea that is so closely connected with all our knowledge of corporeal objects, that is to say, extension. There must be a motive of investigation since all philosophers have investigated it, and who can say that after long ages of efforts the truth is not perhaps reserved as the reward of constancy?
44. What then is space? Is it something real or only an idea? If an idea is there any object in the external world which corresponds to it? Is it a pure illusion? And is the word space without meaning?
If we do not know what space is, let us at least fix the meaning of the word, and thus determine in some measure the state of the question. By space we understand the extension in which we imagine bodies to be placed, or the capacity to contain them to which we attribute none of their qualities except extension.
Let us suppose a glass to be hermetically sealed, and the interior to remain empty by the annihilation of what it contained; this cavity or capacity which in our way of understanding it may be occupied by a body is a part of space. Let us imagine the world to be an immense receptacle in which all bodies are contained; let us suddenly make it empty and we have a cavity equal in space to the universe. If we imagine beyond the limits of the world a capacity to contain other bodies, we have an unlimited or imaginary space.
Space appears to us at first sight, if not infinite, at least indefinite. For in whatever part we conceive a body to be placed, we also conceive the possibility of its moving, describing any class of lines, or taking any kind of direction and departing indefinitely from its first position. Therefore we imagine no limit to this capacity, to these dimensions. Therefore space appears to us as indefinite.
45. Is space a pure nothing? Some philosophers maintain that abstracted from the surface of bodies, and considered as a mere interval, it is a pure nothing. At the same time they admit that it is only owing to space that two bodies are really distant from each other, and add that if we suppose the whole world, with the exception of one body only, to be reduced to nothing, this body could move and change its place. I am confident that this opinion involves irreconcilable contradictions. To say extension-nothing is a contradiction in terms, and the opinion of these philosophers is reduced to this expression.
46. If every thing in a room be reduced to nothing, it seems impossible for the walls to remain distant from each other; for the idea of distance implies a medium between the two objects; and nothing, being nothing, cannot be the medium required. If the interval is nothing, there is no distance. To attribute properties to nothing, is to destroy all ideas, – to affirm that a thing may be and not be at the same time, – and consequently to overthrow the foundation of human knowledge.
47. To say that if the contents were annihilated, a negative space would remain, is only to play with words without touching the difficulty to be solved. This negative space is either something or nothing; if it is something, the opinion we are opposing is false; if it is nothing, the difficulty remains the same.
48. But, it may be said, although nothing remains between the surfaces, they still retain the capacity of containing something. To this I reply, that this capacity is not in the surfaces themselves, but in their distance from each other; for if it were in the surfaces, they would still preserve it, no matter how they may be placed, which is absurd. We have not therefore advanced a single step. We must explain what this capacity, or this distance, is; and this is still untouched.
49. Perhaps it may be said that annihilating all that is contained between the surfaces, does not destroy the volume which they form, and the idea of this volume implies the idea of capacity. But I reply, that the idea of volume involves that of distance, and there is no distance if this distance is a pure nothing.
50. In our efforts to surmount these difficulties, another seemingly specious solution offers, but if we examine it we shall find it as weak as the others.
Distance, it might be said, is a mere negation of contact, but negation is a pure nothing; therefore this nothing is what we seek. I say this solution is as weak as the others; for, if distance is only the negation of contact, all distances must be equal, because negation cannot be greater or less. The negation of contact is the same whether the surfaces are a million leagues or only the millionth part of an inch distant from each other. This negation, therefore, explains nothing, and the difficulty still remains.
51. Not only is the idea of distance not explained by the idea of contact, but on the contrary, the idea of contact can only be explained by the idea of distance. Contiguity is explained by immediate union of two surfaces; we say that they touch each other because there is nothing between them, or there is no distance. The idea of contact does not involve the qualities which relate to the senses, nor the action which one body may exercise upon another which touches it, as impulse or compression. Contiguity is a negative, and purely geometrical, idea, and implies only the negation of distance. Contiguity cannot be greater or less; it is all that it can be when there is a true negation of distance. Two objects may be more or less distant, but they cannot touch more or less, with respect to the same parts. There may be contact of more points, but not more contact of the same points.
52. If we attribute distance and capacity to space, the argument in favor of its reality becomes still stronger. Let us suppose an empty sphere two feet in diameter. Within there is only space; if space is nothing there is nothing in it.
Is motion possible in this empty sphere? It does not seem that there can be any doubt of this. There is a movable body, an extension greater than the extension of the body, and a distance to be passed over. We may add to this, that if motion were not possible, it would not be possible to make the sphere empty, or after making it empty, to fill it. Neither emptying nor filling the sphere can be done without motion of bodies in the interior of the sphere, and motion of a body in another body is only possible in space, because bodies are impenetrable, and also because, when the sphere is filled after it is empty, the body which enters does not meet another body; and when the sphere is made empty, the body which passes out, moves over the space which it abandons, and in which nothing remains after it has passed out.
Therefore, supposing the sphere empty, there may be motion in it. But if the space contained in the sphere is a pure nothing, the motion also is nothing, and consequently does not exist. Motion can neither exist nor be perceived without a distance passed over. If, therefore, the distance is nothing, there is no motion. If we say that the body has passed over half of the diameter, or one foot, what does this mean? If the space is nothing, it can mean nothing. I see no reply which can be made to these arguments, which are all based on the axiom, that nothing has no properties.
53. However great may be the difficulties opposed to the reality of space, they are not so great as those which are brought against the opinion, which, while granting extension to space, still regards it as a pure nothing. The former, as we shall soon see, are produced by certain inaccuracies in our way of conceiving things, rather than by arguments founded on the nature of things; whilst those objections which we have brought against the opinion denying the reality of space, are founded on the ideas which are the basis of all our knowledge, and on this evident proposition: nothing has no properties. If this proposition is not admitted as an established axiom, the principle of contradiction falls, and all human knowledge is destroyed. For, it would be a plain contradiction, if nothing could have any properties or parts; if any thing could be affirmed of nothing, or could be moved in nothing; if a science like geometry could be founded upon nothing; or if all the calculations which are made on nature are referred to nothing.
CHAPTER VIII.
DESCARTES AND LEIBNITZ ON SPACE
54. If space is something, what is it? Here is the difficulty. To overthrow the opinion of our adversaries was easy, but to maintain our position is more difficult.
Can we say that space is only the extension of bodies; that conceived in the abstract it gives us the idea of what we call pure space; and that the different points and positions are mere modifications of extension?
It is easy to see that if space is the extension of bodies, where there is no body there can be no space, and consequently vacuum is impossible. This consequence is unavoidable.
This has been the opinion of celebrated philosophers like Descartes and Leibnitz; but I cannot understand why they both gave the universe an indefinite extension. It is true that by this means they avoid the difficulty of the space which we imagine beyond the limits of the universe; since, if the universe is not limited, there can be nothing beyond its limits, and therefore, whatever we can imagine, must be within the universe. But our object is not to avoid difficulties, but to solve them; and it argues nothing for the soundness of our opinion that it escapes difficulties.
55. According to Descartes, the essence of body is in extension, and as we necessarily conceive extension in space, it follows that space, body, and extension, are three essentially identical things. Vacuum, as it is generally conceived, that is, an extension without a body, is then a contradiction; for it is a body, because it is extension, and it is not a body, because we suppose that there is no body.
Descartes accepts all the consequences of this doctrine. He does not admit the supposition that if God should annihilate all the matter contained in a vessel, this vessel could still retain its form.
"We shall observe," he says, "in opposition to this serious error, that there is no necessary connection between the vessel and the body which fills it; but such is the invincible necessity of the relation between the concave figure of the vessel and the extension contained in this concavity, that it is not more difficult to imagine a mountain without a valley, than to conceive this concavity without the extension contained in it, or this extension without a thing extended. Nothing, as we have often said, cannot be extended. Therefore, if any one should ask, what would happen if God should destroy the matter contained in a vessel, without replacing it, we must say that the sides of the vessel would come so closely together as to touch each other. Two bodies must touch each other, when there is nothing between them. It would be a contradiction to assert that these two bodies were separated; that is to say, that there was a distance between them, if this distance were nothing, or did not exist. Distance is a property of extension, and cannot exist without extension."41
56. If Descartes had gone no farther than to maintain that space, because it contains real distances, cannot be a mere nothing, his reasoning would seem conclusive. But when he adds that space is body, because space is extension, and extension constitutes the essence of body, he asserts what he does not prove.
Because we cannot imagine or conceive a body without extension, it only follows that extension is a property of bodies without which we cannot conceive them, – not that it is their essence. To be able to say this, it would be necessary for us to have the idea of body as we have that of extension, in order that we might see if they are identical. But all that we know of bodies is derived through the senses; we are not able to penetrate into their more intimate nature.
Whence arises the inseparability of the ideas of body and extension? It arises from the idea which we have of bodies being a confused idea, since we conceive it to be a substance in certain relations to ourselves, and causing in us the impressions which we call sensations. But since the basis of sensations is extension, as we have demonstrated in a former chapter, this is the only medium by which we are placed in relation with bodies. When we suppress this basis, by abstracting it, we retain nothing of body beyond a general idea of being or substance without any thing to characterize it, or to distinguish it from others. We find all this in the order of our ideas, but we cannot infer from this that bodies have no other reality than extension.
57. The same reasoning destroys the opinion of indefinite or infinite extension. Descartes, explaining his doctrine on the idea of extension, says: "We shall also know that this world, or the extended matter which composes the universe, is without limits; for, no matter how far off we place these limits, we can imagine spaces indefinitely extended beyond them; and we not only imagine these spaces, but we conceive them as really existing such as we imagine them, and containing an indefinitely extended body, as the idea of extension which we conceive in every space is the true idea which we ought to form of a body."42
In this passage, besides the error in relation to the essence of bodies, there is a gratuitous transition from a purely ideal or rather, imaginary order, to the real order. It is certain that wherever I may imagine the limits of the universe, if I consider them as an immense arch surrounding it, I still imagine new immensities of space beyond this arch; but to conclude that the reality is as I imagine it, does not seem conformed to the rules of good logic. If it is as clear as Descartes supposes, if it is not only an imagination, but a conception founded on clear and distinct ideas, how happens it that so many philosophers see in all this only a play of the imagination?
58. Leibnitz thinks that space is "a relation, an order, not only between things existing, but also between possible things as if they existed."43 He also believes vacuum impossible, but not for the reason which Descartes gives. These are his words:
"Philalethes.– Those who take matter and extension for the same thing, pretend that the sides of a hollow empty body would touch each other. But the space which is between the two bodies is enough to prevent their mutual contact.
"Theophilus.– I am of your opinion; for, although I do not admit a vacuum, I distinguish matter from extension, and concede that although there were a vacuum in a sphere, the opposite poles would not on that account unite. But I do not believe this is a case which the divine perfection would permit."44
59. Leibnitz seems to me to commit what logicians call petitio principii, or, "begging the question." He says that in the case supposed, the sides would not touch each other, because the space between them would prevent it; but this is what he had to prove, – the real existence of this space. This reality is what Descartes denies.
60. If we compare the opinions of Descartes and Leibnitz, we shall see that both agree in denying to space a reality distinct from bodies, but basing their denial on very different reasons. Descartes places the essence of body in extension; where there is extension there is body; where there is space there is extension; consequently, there neither is nor can be a vacuum. Leibnitz does not believe an empty capacity intrinsically absurd, and that he does not admit it is solely because, in his conception, it is repugnant to the divine perfection. The two illustrious philosophers started from very different principles, but arrived at the same conclusion. Descartes rests upon metaphysical reasons, founded on the essence of things. Leibnitz bases his opinion on the absolute essence of things only in its relations with the divine perfection. Empty capacity is a contradiction in the opinion of Leibnitz, only inasmuch as it is opposed to optimism.
61. It is very remarkable that three so distinguished philosophers as Aristotle, Descartes, and Leibnitz, should agree in denying the existence of this capacity which is called space, considered as a being distinct from bodies, and with the possibility of existing by itself. The difference of their opinions only proves that at the bottom of the question there is a difficulty more serious than some ideologists believe, who explain the idea of space and its generation with the same ease as though they were treating of the simplest matters.
CHAPTER IX.
OPINION OF THOSE WHO ATTRIBUTE TO SPACE A NATURE DISTINCT FROM BODIES
62. The preceding considerations seem to me to establish beyond any question, that space and nothing are contradictory terms. If space is a capacity with dimensions that can be really measured, it has real properties, and therefore is distinct from a pure nothing. We have the idea of space, on it is based a certain and evident science, that of geometry; this idea is also necessary for the conception of motion. A pure nothing cannot be the object which corresponds to this idea.
Is space something distinct from the extension of bodies? It is objected to the opinion which maintains this, that space must be either body or spirit, and if not body it must be spirit, which is absurd, since that which is essentially composed of parts, as space is, cannot be a spirit, which is a simple being.
There are strong arguments against the opinion which attributes to space a nature distinct from bodies, but I do not attach much weight to the above objection; for it is only necessary to deny the disjunctive proposition and the whole argument falls to the ground. How can it be proved that there is no medium between body and spirit? We know the essence of neither body nor spirit, and shall we arrogate to ourselves the right to assert that there is nothing in the universe which is not comprised under one of two extremes, the nature of which we know not.
63. It may be replied, that there is no medium between the simple and the composite, any more than between yes and no; and therefore there is no medium between body which is composite, and spirit which is simple. I concede that there is no medium between the simple and the composite, and that whatever exists is one or the other; but I deny that whatever is composite is body, and whatever is simple is spirit.
These two propositions: every composite is a body, and: every body is composite, are not identical. There may, therefore, be composites that are not bodies. Composition, or the possession of parts, is a property of bodies, but does not constitute their essence, or, at least, we do not know that it does. If it were so, we should be obliged to embrace the opinion of Descartes, that extension constitutes the essence of bodies. How do we know that there may not be things which have parts, and yet are not bodies?
64. Even the state of the question makes us suppose space to be a substance, that is, a being subsisting by itself without requiring another being in which to exist. The difficulty once overcome on this supposition, it is solved in its most essential and inaccessible point, and therefore in all others. If we suppose space to be distinct from bodies, and at the same time a true reality, we must consider it as a substance, as it exists in itself without any other being in which it inheres.
65. I said that a simple being is not necessarily a spirit. To explain this, I need only observe, that to say every spirit is simple, is not the same as to say every simple being is a spirit. Simplicity is a necessary attribute of a spirit, but does not constitute its essence. The idea of simplicity expresses only the negation of parts, and the essence of spirit cannot consist in a negation.
66. The argument of those who object to this opinion which attributes to space a nature distinct from bodies, making it an extended substance, that it must also be infinite, is equally inconclusive. For even on this hypothesis, there is no reason why a limit may not be assigned to space. What is there beyond this limit? Nothing. We may, it is true, conceive a vague extension, but imagination is not reality. We also imagine an epoch prior to the Creation; if, then, imagination were an argument in favor of the infinity of the world, it would also be an argument for its eternity.
The arguments with which I have fought against the opinion that space is a pure nothing, are not founded on our imaginations, but on the impossibility of nothing being extended, or having any properties. This is the principal argument which I have used against those who, while they hold space to be a pure nothing, maintain the possibility of the conception or existence of the properties which they attribute to space.