EXTENSION AND SPACE.
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EXTENSION INSEPARABLE FROM THE IDEA OF BODY.
1. Having seen that among the objects of our sensations, extension alone has any external existence for us as any thing more than a principle of causality, let us now try to understand what extension is.
The idea of extension seems to be inseparable from that of body; at least, I am unable to conceive a body without extension. Take away extension, and the parts disappear, and with them all that has relation with our senses; there is no longer an object, or, if the object remains, it is something altogether different from what is contained in the idea of body. Imagine an apple, for instance, from which you suddenly take away extension. What will remain of it?
I am not now going to examine whether Descartes is right when he says, that the essence of body consists in extension; all that I here assert is that a body cannot be conceived without extension. I do not affirm the identity of two things, but only the inseparability of two ideas in our mind. It is not an opinion, but a fact asserted by consciousness, which is now under discussion.
Abstracting extension, I can conceive, it is true, a substance, or, to speak more generally, a being; but, then, there is no idea of body, unless we confound this idea with, that of substance or of being, in general.
2. All our notions of bodies are obtained through the senses, but without extension no sensation is possible; for without it there can be no color, no sound, no touch, no smell, and no taste; therefore, without extension there remains only something of which we have no idea, a vague notion which cannot enable us to distinguish one object from another, a pure abstraction, and nothing more.
3. To solve the difficulties which attend the separation of the two ideas of extension and of body, it is necessary to determine the essence of body. When we can distinguish the essence of a body from its extension, the difficulty will be overcome, but not until then.
4. In order to understand the reason of this inseparability, it is necessary to remember what was said before, that extension is the basis of all other sensations; it is the substratum which is confounded with none, depends on none of them in particular, yet is an indispensable condition of them all.
I look at an apple, and examine the mutual relations of the sensations which it produces.
It is evident that though I abstract the smell, I do not thereby destroy any of the other sensations which it causes. Though it lose its odor, it is still extended, colored, it has a taste, and may produce a sound. I may also, in like manner, abstract its taste, its color, and all that relates to the sight, but I have still an object which is tangible, and consequently extended, figured, and possessed of all its other properties which affect the touch.
If instead of abstracting what relates to the sight, I abstract what belongs immediately to the touch, I may do this without destroying the other sensations; for I can still see the apple, its extension, form, and color.
I may even go farther, and strip the apple of all its sensible qualities, of its taste, smell, color, hardness, and whatever the senses can perceive, still there remains extension, not indeed sensible, but conceivable. Extension exists abstracted from its visibility, since it exists for the blind man: abstracted from its tangibility, since it exists for the sight; abstracted from odor, taste, and sound, since it exists for those who are deprived of these sensations, so long as they have sight or touch.
5. Here a difficulty arises. There seems to be a mistake in what we have said of the existence of extension abstracted from other sensations; for, although in making this abstraction we conceive ourselves to be deprived of these sensations, still we retain the imagination of them; thus, when I strip the apple of all light and color, it is still extended; but that is because I still imagine a color, or, if I make a strong effort to destroy the color, it appears to me like a black object, on a ground of greater or less darkness, distinct from the apple. Does not this prove that there is an illusion in such abstractions, and that there is no complete abstraction, since the reality which we abstract is succeeded by the imagination of the same qualities, or of others which supply their place, so as to make the extension perceptible?
This objection is specious, and it would be difficult to give a satisfactory answer if the existence of men deprived of sight did not instantly dissipate it. No such imagination is possible in the case of a blind man, for him there is no color, no shade, no light, no darkness, nor anything which relates to sight, and still he conceives extension.
6. But at least, some one will answer, it must be confessed that the idea of extension is necessarily dependent on the sensations of touch; blind men also possess this sense, and by it they acquire the idea of extension. Therefore the idea of extension is inseparable from the sensations of touch. This argument is no better than the other; for, although we may acquire the idea of extension by the sense of touch, and this sense is all that is required to produce it, it is not true that this idea can only be acquired by touch. I have already proved that sight is sufficient of itself alone to produce the idea of the three dimensions which constitute a solid or extension in its full complement. But here I do not need the idea of a solid, that of a surface is sufficient; the extension of a surface is inseparable from sight. There is no sight without color, or light of some kind or other, and this cannot even be imagined without a surface.
I have another argument. Geometricians, doubtless, conceive extension, and yet they abstract all its relations to sight or touch; therefore, there is no necessary connection between them.
In any object submitted to the sight, what quality relating to the touch is necessary in order to produce the idea of extension? If we examine it closely, we shall find that there is none. Let us take a liquid; is its fluidity the necessary quality? No; for when congealed extension remains. Is it heat or cold? No; for without destroying its extension we may change its temperature as much as we please, no alteration is perceptible. Whatever quality relative to touch we may take, we shall find that it may be varied, modified, or entirely destroyed, without visibly affecting the extension.
It often happens that we have a clear and definite idea of the extension of an object without knowing any thing of its qualities in relation to touch. I see an object at a distance, I distinguish its color and its form, but I know not of what material it is, whether it is of marble, or wood, or wax, nor whether this material is hard or soft, moist or dry, warm or cold. I do not even know if it is tangible, as in the case of figures formed by vapors which are imperceptible to the touch.
7. Without extension there can be neither sight, nor touch, nor any other sensation. As to taste, it is clear that it requires touch, and cannot exist without it. Our assertion is less clear with regard to sound and smell; for, although we cannot separate these sensations from the idea of extension as they always involve this idea in one way or another, we do not know how it would be with a man who was deprived of all the other senses, and retained only those of smelling and hearing. But without speculating on this hypothesis, it is enough to know:
I. That nothing which is not extended can act upon our organs, unless by means wholly unknown to us, and which would give no idea of what we understand by body.
II. That even supposing the sensations of smelling and hearing to be possible without the idea of extension, they would in that case be only simple phenomena of our being, and would not place us in communication with the external world, as we now perceive it; because, if we should not know that they proceeded from another cause, we could have no more consciousness of them than that which we have of the me; and if we should know it, this cause would be represented to us only as an agent influencing us, and not by any means as a being having any thing similar to what we understand by body.
III. That in such a case we should have no idea of our own organization, nor of the universe; for it is clear that every thing being reduced to mere internal phenomena, and their relation to the agents producing them, and the idea of extension wanting, neither the universe nor our own body would be to us what they now are. What would the universe,—what would our body be without extension?
IV. That for the present we limit ourselves to the demonstration of the dependence which in the present system, of things, all sensations have in relation to extension; and this demonstration holds good, even though we suppose the man who possesses only the sense of smelling or that of hearing not to form any idea of extension, and not to need it in order to experience its sensations.
V. That even on this supposition, the proposition before established, that the idea of extension is independent of the other sensations, still remains unassailed.
VI. That the truth which we are principally endeavoring to demonstrate, that for us the idea of extension is inseparable from that of body, also stands firm.
8. This inseparability is so certain, that theologians explaining the august mystery of the Eucharist, distinguish in the extension of bodies the relations of the parts to each other, and their relation to place, in ordine ad se, et in ordine ad locum; and they say that the sacred body of our Lord Jesus Christ is in this august Sacrament, by extension in ordine ad se, though not by extension in ordine ad locum. This proves that the theologians saw that it is not possible for man to lose all idea of extension, without at the same time losing all idea of body; and thus they invented this ingenious distinction, of which I shall speak at greater length in another place.
CHAPTER II.
EXTENSION NOT PERCEPTIBLE AS THE DIRECT AND IMMEDIATE OBJECT OF SENSATIONS.
9. Extension has the remarkable peculiarity of being perceived by different senses. As regards sight and touch this is evident; it is also true as far as concerns the other senses. We perceive taste in different parts of the palate, and we refer sound and smell to distinct points in space, and this involves the idea of extension.
But what is more strange is, that although extension is the indispensable basis of all sensations and therefore perceived by all the senses, it is, in itself, and separated from every other quality, imperceptible to them all. The eye perceives only light, and the ear sound, the palate taste, the smell odor, and the object of touch is that which is warm or cold, moist or dry, solid or liquid, etc. None of these objects is extension, none in particular is necessary for the perception of extension; for we constantly find it separated from each of these qualities, and yet it is still perceptible. No one in particular is necessary for the perceptibility of extension, but some one is indispensable; for, unless accompanied by some one of them, it is imperceptible to the senses.
Hence, extension is a necessary condition of our sensations, but is not itself perceived by the senses. Still it is not therefore unknown, and this brings me to some other reflections which take us out of the phenomenal into the transcendental order, and give rise to very serious and difficult questions, which have hitherto been insolvable, and it is to be feared must ever remain so.
10. We have seen that extension in itself is not the direct object of sensation. What, then, is it? What is its nature?
There are two things which may be considered in the idea of extension: that which it is in us, and that which it represents to us; or, in other words, its relation to the subject, and its relation to the object. The first being subject to immediate observation, inasmuch as it exists within us, is difficult but not impossible to explain. The second is more difficult, and almost impossible to explain, because it is a very abstract and transcendental idea, and also requires a series of arguments, the thread of which may be broken without the one who reasons perceiving it.
11. Extension in us is not a sensation, but an idea. Sometimes we imagine it under a sensible form, confounding it with a determinate object; at other times we picture it to ourselves as a vague obscurity in which bodies are placed; but these are only fictions of the imagination. A man born blind can have none of these internal representations, and yet he forms a very good conception of extension. We ourselves in thinking of extension abstract all these forms under which we imagine it.
Two different sensations, those of sight and touch, produce the same idea of extension. This is conclusive proof that extension is rather intelligible than sensible.
Whatever may be the relation of extension to sensation, we cannot deny that it is an idea if we reflect that it is the foundation of the whole science of geometry. Thus, although we form various images of extension, they are only the particular forms with which the mind clothes the idea, if we may use the expression, according to the circumstances of the case. That which is fundamental and essential in the idea, is of a different and higher order, and has nothing in common with the applications which the mind makes in order to explain and apply it. This idea includes dimensions, but not determined or applied; they are mere conceptions which represent nothing in particular.
12. The idea of extension is a primitive fact of our mind. It is not produced by sensations, but precedes them, if not in time, at least in the order of being. There is no ground for asserting that the idea of extension exists in the mind prior to the first impression of the senses, but unless extension serves as their basis these impressions are inconceivable. Whether this idea is innate or developed, or produced in the mind by the impressions, there can be no doubt that it is distinct from them, necessary to them, and independent of any one of them in particular.
It may be that when these impressions are first received extension may not be known as a separate idea; but it is certain that it is afterwards separated and stripped of the corporeal form, and spiritualized, and that this phenomenon may be occasioned but not caused by the sensation.
In sight, abstracting extension, there is color, but we cannot discover in it any thing from which we can produce so fruitful an idea as that of extension. Even at first we see that the color itself is not perceptible without extension, and so far from extension being produced by color, it is on the contrary an indispensable condition without which color cannot be perceived.
Colors as the objects of sensation are only individual phenomena, which have no connection with one another nor with the general idea of extension. What has been said of them will equally apply to all the impressions of touch.
CHAPTER III.
SCIENTIFIC FRUITFULNESS OF THE IDEA OF EXTENSION.
13. In order to understand the superiority of the idea of extension over mere sensations; or rather, in order to understand that there is a true idea of extension considered in itself, and that there is no such idea of the direct and immediate objects of sensation, I wish to call attention to the fact that among all the objects of the senses, extension alone gives origin to a science.
This is a very important fact;—to explain it as it deserves, I shall establish the following propositions:
FIRST PROPOSITION.
Extension is the basis of geometry.
SECOND PROPOSITION.
Not only is extension the basis of geometry, but all that we know of the nature of bodies may be reduced to the manifestations, applications, and modifications of extension, with the addition of the ideas of number and time.
THIRD PROPOSITION.
Whatever we know of sensations that deserves the name of science is included in the modifications of extension.
FOURTH PROPOSITION.
We can form no fixed idea of corporeal objects, nor make any observation on the sensible world, unless we are guided by the rule of extension.
These four propositions are nothing more than the enunciation of certain facts, the mere exposition of which is a sufficient demonstration.
14. Extension is the basis of geometry. This is evident, since geometry treats only of dimensions, and the idea of dimension is essential to extension.
When geometry treats of figures, it is still extension which it is treating of; for figures are only extension with certain limitations. The quadrilateral contains two triangles. To distinguish them, it is only necessary to draw their limit, which is the diagonal. The idea of figure is merely the idea of limited extension, and the figure is of this or that kind according to the nature of its limits. Consequently, the idea of figure is nothing new superadded to extension; but merely its application.
Moreover, limit or termination is not a positive idea; it is a pure negation. If I have extension and wish to form all the figures possible, I need not conceive any thing new, but only abstract what I have already; I do not add, but take away. Thus in the quadrilateral I obtain the conception of the triangle by abstracting one of the two equal parts into which it is divided by the diagonal. In the same manner I deduce the quadrilateral from a pentagon by abstracting the triangle formed by a line drawn from one of its angles to either of the opposite angles. These observations apply to all geometrical figures.
The idea of extension is like an immense ground on which we have only to draw limits in order to obtain whatever we want.
It does not follow from this that the understanding cannot proceed by addition or the synthetic method; for, just as the subtraction of one of the parts of the quadrilateral formed a triangle, so also the addition of two triangles with an equal side will produce a quadrilateral. And in the same way points produce lines, lines surfaces, and surfaces solids. In all these cases the idea of figure is that of limited extension, since the quantities which constitute it are merely extension with certain limitations.
15. An observation here presents itself to my mind, which I think must throw great light upon the question which we are now discussing. If we compare the two methods by which the idea of figure is obtained; the synthetic, or that of composition or addition, and the analytic, or that of subtraction or limitation, we shall find that the second is more natural than the other; because that which the analytic method produces is permanent in the figure and essential to it, whilst the synthetic only seems to constitute it, and as soon as it is thus constituted the marks of its formation are obliterated.
An example will make this clearer. In order to conceive a rectangle I have only to limit indefinite space by four lines in a rectangular position; that is, to affirm a part, and deny the rest. The lines are nothing in themselves, and represent only the limit beyond which the space included in the rectangle cannot pass. To abstract this limitation or denial of all that is not contained in the surface of the rectangle, would be to destroy the rectangle. Therefore, the denial in which this method consists is always permanent, the manner of the production of the idea is inseparable from the idea itself.
But if, on the other hand, I proceed to form the rectangle by addition or by joining the hypotheneuse of two right-angle triangles, the ideas of the two component parts are not necessary to the idea of the rectangle after its formation. I can conceive the rectangle even abstracting the diagonal.
Thus, then, it is demonstrated that the idea of extension is the only basis of geometry, and that this idea is an immense field on which, by means of limitation or abstraction, we can obtain all the figures which form the object of geometry. Figures are only extension limited, a positive extension accompanied by a negation, and consequently whatever is positive in geometry is extension.
16. We cannot doubt that, whatever we know of the nature of bodies, may be reduced to certain modifications or properties of extension, if we observe that the entire object of the natural sciences is the knowledge of the motion or of the different relations of things in space, which is nothing more than the knowledge of the different kinds of extension.
Statics is occupied in determining the laws of the equilibrium of bodies, but in what way? Does it penetrate into the nature of the causes? No; it only determines the conditions to which the phenomenon is subject, and the only ideas which enter into these conditions are the direction of the force, that is to say, a line in space, and the velocity, which is the relation of space to time.
The idea of time is the only idea which is here joined with that of extension. In another place I shall prove that time, separated from things, is nothing, and consequently, although this idea is here joined to that of extension, it does not interfere with the truth of what I have established. In statics, all that relates to other sensations is counted as nothing; in order to solve the problems of the composition and decomposition of forces, we abstract all color, smell, and other sensible qualities of bodies in motion. What has been said of statics applies equally to dynamics, hydrostatics, hydraulics, astronomy, and to all sciences which regard motion.
17. Here an objection may be made. That with the ideas of time and space, we seem to combine another which is distinct from them, and necessary, in order to complete the idea of motion, and this is the idea of a body moved. It is not time, nor is it space, for space is not moved, therefore it is distinct from them.
To this I reply, first, that I am speaking of extension, and not of space alone, which it is important to remember, for what I shall afterwards say; and secondly, that science regards the thing moved as a point, and this is sufficient for all its purposes. Thus in the systems of forces there is a point of application for each of the component forces, and another for the resultant. This point is not regarded as having any properties, but is in relation to motion what the centre is in relation to a circle. Every thing is related to it, yet it is nothing in itself, except inasmuch as it occupies a definite position in space. It may change according to the quantity and direction of the forces, it may run over or describe a line in space with greater or less velocity, and the line may be of this or that class, and accompanied by various conditions. If a body be impelled by two forces, B and C, acting upon a point A, science considers in the body only the point through which the resultant of the forces B and C passes, and abstracts all the other points of the body which, being joined to the point A, move with it.
18. When I say that the natural sciences go no farther than the consideration of extension, I only mean to exclude the other sensations, but not ideas; for it is clear that the ideas of time and number are combined with the idea of extension. This is so true in mechanics, in this sense at least, that all its theorems and problems are reduced to geometrical expressions, and even the idea of time is expressed by lines.
In every force there are three things to be considered: the direction, point of application, and intensity. The direction is represented by a line, and the point of application by a point in space. The intensity is represented only in the effect which it can produce, and this is expressed by a line, the length of which expresses the intensity of the force. The effect of the intensity which is represented by a line includes the time also; for the measure of a motion cannot be determined until we know its velocity, which is merely the relation of space to time. Therefore, although the idea of time is combined with that of extension, the result is expressed by lines, that is, by extension.
19. There is another circumstance still which shows the fruitfulness of the idea of extension. It is that in the expression of the laws of nature, it reaches cases which are beyond the idea of number. If we suppose two equal rectangular forces, AB and AC, acting on the point A, the resultant will be AR. Now, if we consider AR to be the hypotheneuse of a right-angled triangle, AR2 = AB2 + AC2, extracting the square root AR = v(AB2 + AC2). If we suppose each of the component forces equal to 1, AR = v(12 + 12) = v2, a value which can neither be expressed in whole numbers nor in fractions, but which is represented by the hypotheneuse.
20. In the physical sciences, such words as force, cause, agent, etc., are frequently used, but the ideas which these terms express are a part of science only inasmuch as they are represented by effects. This is not because true philosophy confounds the cause with the effect, but as physical science regards only the phenomenon in all that relates to the cause, it limits itself to the abstract idea of causality, which presents nothing determinate, and consequently is not the object of its scientific labors. The system of universal attraction has immortalized the name of Newton, and he begins by confessing his ignorance of the cause of the effect which he explains. When we go beyond the phenomena and the calculations to which they give rise, we enter the field of metaphysics.
21. The natural sciences consider certain qualities of bodies which have no relation to extension, as, for example, heat and light, and this might seem to be a refutation of what we have said of extension. Still this objection disappears when we examine in what manner science takes note of these qualities, and instead of overthrowing our thesis, the result will strengthen, extend, and explain it.
Heat is not measured by the sensation which it produces in us. If we enter a room where the temperature is very high, we experience a strong sensation of heat, which gradually grows weaker, while the temperature remains the same. If we reach our hand to a friend we experience a sensation of heat or cold, in proportion as his hand is warmer or colder than our own.
Heat and cold are measured, not in themselves, nor in relation to our sensations, but in the effect which they produce. These effects are included in the modification of extension; for the thermometer marks the temperature by a greater or less elevation of the mercury in a line. Its degrees are expressed by parts of a line, on which they are marked.
I know that what is measured is distinct from extension; but, its measurement is only possible by relation to extension, and by attending to effects which are modifications of extension. Thus, the temperature at which water boils is 212°, and this is discovered by the motion of the water, and has relation to extension. So, also, the rarefaction and condensation of bodies are modifications of extension, since these states consist in the occupation of greater or less space, or in the increase or diminution of their dimensions.
22. All that science teaches us of light and colors relates to the different directions and combinations of the rays of light. Our observation goes no farther than sensation. We know that we can combine the rays in different manners, and direct them, so as to modify our sensation, but this is nothing more than the scientific knowledge of extension in the medium which we make use of, and of the sensation experienced in consequence. All beyond this is entirely unknown.
23. We may say the same of all other sensations, that of touch included. What is that quality of bodies which we call hardness? the resistance which we encounter when we touch them? But abstracting sensation, which only produces the consciousness of itself, what do we find? Impenetrability. And what do we understand by impenetrability? The impossibility of two bodies occupying the same space at the same time. Here, then, we meet with extension. If, by hardness, we mean the cohesion of molecules, in what does cohesion consist? In the juxtaposition of parts in such manner that they cannot, without difficulty, be separated. But, to be separated, is to be made to occupy a place different from that which was before occupied. Here, too, we find the idea of extension.
Of sound we know nothing scientifically, except as relates to extension and motion. The musical scale is expressed by a series of fractional numbers representing the vibrations of the air.
24. These examples demonstrate the third of the above propositions, that whatever we know of sensations that deserves the name of science, is included in the modifications of extension.
25. It is the same with the fourth proposition, that without the idea of extension, we can have no fixed idea of any thing corporeal, no fixed rule in relation to phenomena, but are like blind men. If, for an instant, we abstract the idea of extension, it is impossible for us to take a step in advance. The examples already adduced in order to demonstrate the second proposition, render further explanation here unnecessary.
26. Although extension is essentially composed of parts, there is in it something fixed, unalterable, and, in some manner, simple. There may be more or less extension, but not different kinds. One right line may be longer or shorter than another, but its length is not of a different species. One surface may be larger than another, a solid of a certain kind greater than another of the same kind, but not in a different manner.
When I say that in the idea of extension objectively considered there is a certain sort of simplicity, I do not mean that there is any thing entirely simple; for I have just said that its object is essentially composite. Neither do I abstract its essential elements, which are the three dimensions, nor any idea which it involves, as its limitability, or capacity to be limited in various ways. All I wish to show is that in all the different figures these fundamental notions are sufficient, that they are never modified, but always present the same thing to the mind.
Let us compare a right line with a curve. A right line is a direction which is always constant; the curve a direction which is always varied. A direction always varied is a collection of right directions infinitely small. Therefore, the circumference of a circle is considered as a polygon of an infinite number of sides. The curve is therefore formed by the variety of directions reduced to infinitesimal values. This theory which explains the difference of the right line and the curve, is evidently applicable to surfaces and solids.
Let us compare a quadrilateral with a pentagon; all that the second has which the first has not is one side more in perimeter, and in area the space contained in the triangle formed by a line drawn from one of its angles to either of the opposite angles. The lines are of the same kind, the surfaces differ only in the ways in which they terminate. But termination is the same as limitation. Therefore, all that is essential to the idea of extension, that is, direction and limitability, remain always the same and unchangeable.
This intrinsical constancy is indispensable to science. That which is mutable, may be the object of perception, but not of scientific perception.
REALITY OF EXTENSION.
27. We now come to more difficult questions. Is extension any thing in itself, abstracted from the idea of it? If any thing, what is it? Is it identified with bodies, or is it confounded with space?
I have proved[39] that extension exists outside of ourselves, that it is not an illusion of the senses; and this solves the first question, whether extension is any thing.
Whatever may be its nature or our ignorance on this point, there is in reality something which corresponds to our idea of extension. Whoever denies this truth must be content to deny every thing except the consciousness of himself, if indeed he does not experience doubts even of this too. Whatever idealists may assert, there is not, nor ever was a man who in his sound judgment seriously doubted the existence of an external world. This conviction is for man a necessity against which it is vain to contend.
This external world is for us inseparable from that which is represented by the idea of extension. It either does not exist, or else it is extended. If we could be persuaded that it is not extended, it would not be difficult to convince us that it does not exist. For my part, I find it just as difficult to imagine the world without extension as without existence, and if I could be made to believe its extension an illusion, I should easily believe its existence also an illusion.
28. It is to be observed that although we confess our ignorance of the internal nature of extension, it is still necessary to admit that we know something of it; its dimensions, namely, and what serves as the basis of geometry. The difficulty is not in knowing what extension is geometrically considered, but what it is in reality. We know the geometrical essence, but what we want to ascertain is, whether this essence realized is something which is confounded with some other real thing, or is only a quality which we know without knowing the being to which it belongs. Without this distinction we should deny the basis of geometry; for, it is evident that if we should not know the essence of extension in the aforesaid manner, we could not be sure that we are not building in the air when we raise upon the idea of extension the whole science of geometry.
29. Thus then under this aspect, we are certain that extension exists outside of us, and that there are true dimensions. This idea is a necessary consequence of the idea of the external world, as we said before. The dimensions in the external world must be subject to the same principles as those which we conceive, or the very idea which we have formed of the external world is reversed. I do not mean by this that a real circle may be a geometrical circle, but only that what is true of the second must be true of the first also, in proportion as it is constructed with greater or less exactness. Beyond what can be formed by the most perfect and exact instruments, I can conceive, without passing from the order of reality, a circle or any other figure, as near as I please to the geometrical idea. The sharpest instrument can never mark an indivisible point, nor draw a line without breadth; but this surface, on which the point is marked, on the line drawn, being infinitely divisible, I can conceive a case in which the reality will come infinitely near to the geometrical idea.
30. Astronomy and all the physical sciences rest on the supposition that real extension is subject to the same principles as ideal extension; and that experience comes closer to theory in proportion as the conditions of the second are more exactly fulfilled in the first. The art of constructing mathematical instruments, which has been brought in our day to a surprising perfection, regards the ideal as the type of the real order; and progress in the latter is the approximation to the models of the former.
Theory directs the operations of practice, and these in their turn confirm by the result the foresight of theory. Therefore, extension exists not only in the ideal order, but also in the real; and it is something, independently of our ideas; and geometry, that vast representation of a world of lines and figures, has a real object in nature.
How far the real corresponds with the ideal, we shall examine in the next chapter.
CHAPTER V.
GEOMETRICAL EXACTNESS REALIZED IN NATURE.
31. The disagreement which we discover between the phenomena and the geometrical theory makes us apt to think that reality is rough and coarse, and that purity and exactness are found only in our ideas. This is a mistaken opinion caused by want of reflection. The reality is as geometrical as our ideas; the phenomenon realizes the idea in all its purity and vigor. Be not startled by this seeming paradox; for it will soon appear to you a very true, reasonable, and well-grounded proposition.
We shall first prove that the ideas which are the elements of geometry have their objects in the real world, and that these objects are subject to precisely the same conditions as the ideas. This proved, it clearly follows that geometry in all its strictness exists as well in the real as in the ideal order.
32. Let us begin with a point. In the ideal order, a point is an invisible thing, it is the limit of a line and its generating element, and it occupies a determinate position in space. It is the limit of a line; for when we take away its length, we have a point remaining which we are forced to regard as the limit of the line unless we destroy it entirely so as to have nothing left. The more the line is shortened the nearer it approaches to a point, yet can never be identified with it until its length is wholly suppressed. The point is the generating element of the line; for we form the idea of lineal dimension by considering a point in motion. The occupation of a determinate position in space is another indispensable condition of the idea of a point, if we wish to use it in geometrical figures. The centre of a circle is a point in itself indivisible, it fills no space; but in order that it be of any use as centre, we must be able to refer all the radii to it, and this is impossible unless it occupy a determinate position equidistant from all points of the circumference. As a general rule, geometry acts upon dimensions, and these dimensions require points in which they commence, points through which they pass, and points in which they end, and by which distances, inclinations, and all that relates to the position of lines and planes, are measured. Nothing of all this can be conceived unless the point, although not extended, occupies a determinate position in space.
33. Does there exist in nature anything which corresponds to the geometrical point, and unites all its conditions with as great exactness as science in its purest idealism can desire? I believe there does.
Philosophers have adopted different opinions as to the divisibility of matter. Some maintain that there are unextended points in which the division ends, and that all composite bodies are formed of these. Others assert that it is not possible to arrive at simple elements, but the division may continue ad infinitum continually approaching the limit of composition, but never reaching it. The first of these opinions is equivalent to the admission of geometrical points realized in nature; the second, though apparently less favorable to this realization, must come to it at last.
Unextended molecules are the realization of the geometrical point, in all its exactness. They are the limit of dimension, because division ends with them. They are the generative elements of dimension, because they form extension. They occupy a determinate position in space, because bodies with all their conditions and determinations in space are formed of them. Therefore, from this opinion, held by eminent philosophers like Leibnitz and Boscowich, it follows that the geometrical point exists in nature in all the purity and exactness of the scientific order.
The opinion which denies the existence of unextended points, admits, as it necessarily must admit, infinite divisibility. Extension has parts, and therefore is divisible; these parts, in their turn, are either extended or not extended; if unextended, the supposition fails, and the opinion of unextended points is admitted; if extended, they are divisible, and we must either come at last to unextended points, or continue the division ad infinitum.
I remarked above that, although less favorable to the real existence of geometrical points, this opinion as well as the other does acknowledge their realization. The parts into which the composite is divided are not created by the division, but exist before the division, and without them the division would be impossible. They do not exist because they may be divided, but they may be divided because they exist. This opinion therefore, does not expressly admit the existence of unextended points, but it admits the possibility of eternally coming nearer to them, and this not only in the ideal, but also in the real order; because the divisibility is not affirmed of the ideas, but of the matter itself.
Although our experience of division is limited, divisibility itself is unlimited. A being endowed with greater powers than we possess, might carry the division further than we are able to do. Our ability to divide is limited, but God, by his infinite power, can push the division ad infinitum, and His infinite intelligence sees in an instant all the parts into which the composite may be divided.
Omitting the difficulties which attend an opinion which seems to suppose the existence of what it denies, I will ask if geometry can require more rigorous exactness than is found in the points to which infinite power can come, if we suppose it to exercise its eternal action in dividing the composite; or, in other words, can there be any more strictly geometrical points than those seen by an infinite intelligence in an infinitely divisible being? This not only satisfies our imagination and our ideas of exactness, but goes even beyond. Experience teaches us that to imagine an unextended point is not impossible; and to think it in the purely intellectual order, is only to conceive the possibility of this infinite divisibility, and to be suddenly placed at the last limit,—a limit which must still be far distant from that to which, not abstraction, but the sight of infinite intelligence can reach.
If the geometrical point exists, the geometrical line also exists; for it is only a series of unextended points; or, if we are unwilling to acknowledge these, a series of extremes to which division infinitely continued at last arrives. A series of geometrical lines forms a surface; and a union of surfaces forms a solid, the ideal order agreeing with reality in its formation as in its nature.
34. This theory of the realization of geometry extends equally to all the natural sciences. It is an error to say, for example, that the reality does not correspond to the theories of mechanics. It should rather be said that it is not the reality that is at fault, but the means of experimenting; the blame should not be imputed to the reality, but rather to the limitation of our experience.
The centre of gravity in a body, is the point where all the forces of gravitation in the body unite. Mechanics supposes this point to be indivisible, and in accordance with this supposition, establishes and demonstrates its theorems, and solves its problems. Here stops the mechanician, and the machinist begins, who can never discover the strict centre of gravity supposed in the theory. Experience disagrees with the principles, and we ought to correct the former by adhering to that which is determined by the latter. Is this because the centre of gravity does not exist in nature with all the exactness which science supposes? No; the centre exists, but the means of finding it are wanting. Nature goes as far as science; neither remains behind; but our means of experience are unable to keep up with them.
The mechanician determines the indivisible point in which the centre of gravity is situated, supposing the surface without thickness, lines without breadth, and the length divided at a determinate point of space, which has no extension. Nature entirely fulfills these conditions. The point exists, and the reality should not be blamed for the limitation of our experience. The point exists in either of the hypotheses mentioned above. The first, which favors unextended points, admits the existence of the centre of gravity in all its scientific purity. The other is not so decided, but it says to us: "Do you see this molecule, this little globe of infinitesimal diameter, the smallness of which the imagination cannot represent? Make it still smaller, by dividing it for all eternity, in decreasing geometrical progression, and you will always be coming nearer the centre of gravity without ever reaching it. Nature will never fail; the limit will ever retire from you; but you will know you are approaching it. Within this molecule is what you seek. Continue to advance, you will never reach it,—but what you want is there." In this case I do not see that the reality falls short of scientific exactness; no mechanical theory imagined or conceived can go farther.
35. These reflections place beyond all doubt that geometry with all its exactness, and theories in all their rigor, exist in nature. If we could follow it in our experience, we should find the real conformed to the ideal order, and we should discover that when experience is opposed to theory, it is not the latter which is wrong, but the limitation of our means makes us lay aside the conditions imposed by the theory. The machinist who constructs a system of indented wheels finds himself obliged to correct the rules of theory, on account of friction, and other circumstances, proceeding from the material which he employs. If he could see with a glance the bosom of nature, he would discover in the friction itself a new system of infinitesimal gearing which would confirm with wonderful exactness those very rules which a rude experience represents to him as opposed to reality.
36. If the universe is admirable in its masses of gigantic immensity, it is not less so in its smallest parts. We are placed between two infinities. Man in his weakness, unable to reach either one or the other, must content himself with feeling them, hoping that a new existence in another world will clear up the secrets which are now veiled in impenetrable darkness.
REMARKS ON EXTENSION.
37. If extension is something as we have proved; what is it?
We find extension in bodies and also in space because in both we find that which constitutes its essence, which is dimension. Is the extension of bodies the same as the extension of space?
I see and hold in my hand a pen: it is certainly extended. It moves, and its extension moves with it. The space in which its motion is executed remains immovable. At the instant A the extension of the pen occupies the point A'; at the moment B the same extension of the pen occupies the part B' of space which is distinct from the part A'; therefore neither the part A' of space nor the part B' is identified with the extension of the body.
This seems to have all the force of a demonstration; but to make it more clear and more general, I will put it into the form of a syllogism. Things which are separated or may be separated are distinct; but the extension of bodies may be separated from any part of space; therefore the extension of bodies and the extension of space are distinct. I said that this reasoning seems to have all the force of a demonstration, but it is nevertheless subject to serious difficulties. These difficulties cannot be understood without a profound analysis of the idea of space, and therefore I shall reserve my opinion until this has been treated of in the following chapters.
38. Is the extension of a body the body itself? I cannot conceive a body without extension, but this does not prove that extension is the same thing as the body. My soul has acquired a knowledge of the body by means of the senses. These senses have awakened in me the idea of extension; but they have told me nothing of the intrinsic nature of the body perceived.
In those beings which we call bodies we find the power of producing in us impressions very distinct from that of extension. From two bodies of equal extension we receive very different impressions, therefore there is in them something besides extension. If extension was their only quality, this being equal, the effect would be the same; but experience teaches us that it is not so.
Moreover we conceive extension in pure space where there is no body. The idea of body implies the idea of mobility, while space is immovable. It implies the power of producing impressions; the extension of space has not of itself this power.
Therefore the simple idea of extension does not include even in our cognitions the whole idea of a body. We do not know in what the essence of body consists; but we know that in the idea which we have of it there is something more than extension.
39. When it is said that a body is inconceivable without extension it is not meant that extension is the constitutive notion of the essence of body. This essence is unknown to us, and therefore we cannot know what does or does not belong to it. The true meaning of this inseparability of the two ideas of extension and body is this: As we have no knowledge a priori of bodies, but whatever we know of them, their existence included, we derive through the senses, all that we think or imagine concerning them must presuppose that which is the basis of our sensations. This basis, as we have already seen, is extension; without it there is no sensation, and consequently without it a body ceases to exist for us, or is reduced to a being which we cannot distinguish from others.
I will explain my ideas. If I strip bodies of extension and leave them only the nature of a being which causes the impressions which I receive; this being is the same, so far as I am concerned, as a spirit which should produce the same impressions. I see this paper, and it causes in me the impression of a white surface. There is no doubt that God could produce in my mind the same sensation without the existence of any body. Then supposing that I knew that no external extended object corresponded to my sensation, which was caused by a being acting upon me, it is evident that there would be two distinct things in my mind. First, the phenomenon of sensation, which under all hypotheses is the same; and secondly, the idea of the being which produced it, which is only the idea of a being distinct from myself, acting upon me, which in relation to the external world, would involve two ideas; those of distinction and causality.
I now take from the paper extension, and what remains? The same as before. 1. An internal phenomenon, made known by consciousness. 2. The idea of a being the cause of this phenomenon.
I do not know whether this must always be a body; but I know that the idea of a body, as I understand it, includes something more than this. I know that being is not in relation to myself distinguishable from other beings, and that if there is any thing in its nature to distinguish it from them, it is something unknown to me.[40]
40. This is the sense in which I say that we cannot separate the idea of extension from the body. But from this it must not be inferred that the things themselves are identified; perhaps, even, a more profound knowledge of matter would show us that instead of being identical, they are entirely distinct. We have seen that it is so with their ideas, and this is a sign that it is so in reality.
41. We have few ideas as clear as that of extension geometrically considered; every attempt to explain it is useless; we know it more perfectly by mere intuition than whole volumes could make it known to us. It is so clear an idea, that on it is founded a whole science, the most extensive and evident which we possess, that of geometry. Therefore there is reason to believe that we know the true essence of extension, since we know its necessary properties, and even base a whole science on this knowledge. Yet we do not discover in this idea, either impenetrability or any of the properties of bodies; but rather on the contrary, we find a capacity indifferent to them all. We conceive extension penetrable as easily as impenetrable, empty or full, white or green, with properties by which it can be placed in relation with our organs, as easily as without them. We can conceive extension in a body acting on another body, or in pure space; in the sun which enlightens and warms the world, or in the vague dimensions of an empty immensity.
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.
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.
OPINION OF THOSE WHO HOLD SPACE TO BE THE IMMENSITY OF GOD.
67. Overwhelmed by these difficulties, and unable to reconcile the reality which space offers us with nothing, or to conceive in any thing created the immobility, infinity, and perpetuity which we imagine in space, some philosophers have put forth the opinion that space is the immensity of God. At first sight this seems an extravagant absurdity, but if we wish fairly to prove the falsity of this opinion, we must do justice not only to the right intention of those who have defended it, and the sound explanations which they brought to their assistance, but also to the reasons which forced them to this extremity, and which, though certainly not weighty or solid, are far from being so contemptible as one may imagine.
68. The argument in favor of this opinion may be put in the following form. Space is something. Before God created the world space existed. It is not possible to conceive bodies as existing without space in which they are extended. Before they exist, we conceive this capacity in which they may be placed, as already existing. Therefore, space is eternal. There is no motion without space; and in the first instant of the creation bodies could move and be moved. Though we suppose only one body in the world, it could be moved; and this motion could be infinitely continued. Therefore space is infinite. Annihilate now this body also, and the extension in which it moved will remain; in it new bodies, new worlds may be created. Therefore space is indestructible. But an eternal, infinite, and indestructible being cannot be created. Therefore, space is uncreated. Therefore it is God himself. But it must be God inasmuch as we conceive him in relation to extension; and, therefore, space is the immensity of God. Immensity is the attribute by which God is in every part; it is an attribute which relates to extension. Space is, therefore, the immensity of God. Only by adopting this theory can we reasonably admit that space is eternal, infinite, and indestructible.
69. The objection to this opinion is that it destroys the simplicity of God. If space is a property of God, it is God; for, whatever is in God, is God. Therefore, as space is essentially extended, God too must be extended.
Clarke saw the force of this argument; he was made to feel it by the arguments of his adversary, Leibnitz; but he answers it very weakly. He says that space has parts, but they are not separable. But, however this may be, it is certain that space has parts. True, in the idea of space we distinguish parts without separating them; but we really conceive them in it, and we cannot conceive space without them. Besides, if we should admit this theory, what would become of the proofs of the immateriality of the soul? If the infinite wisdom is extended, why may not the human soul with much more reason be so?
Carried away by his favorite idea, Clarke went so far as to write what we should not have expected from such a man, that: "In questions of this nature, when we speak of parts, we mean parts that are separable, composite, and disunited like those of matter, which for this reason is always a compound and never a simple substance. Matter is not one substance, but a composition of substances. This is why, in my opinion, matter is incapable of thinking. This incapacity does not proceed from extension, but from the parts being distinct substances, disunited, and independent of each other."[45] This explanation tends to destroy the simplicity of thinking beings; for by simplicity has always been understood the absolute wanting of all parts and not the absence of this or that kind of parts. Inseparability does not destroy the existence of parts; it merely asserts the force of cohesion.
70. It is also to be feared that this doctrine opens the door to pantheism. It was even objected to Clarke that it made God the soul of the world, and although he defended himself from this charge, there still remains an objection which was not proposed to him, and which is a very serious one. If we say that God is space, or that space is a property of God, what hinders our saying that God is the world, or that the world is a property of God? The world is extended; but so is space. If God and space are not contradictory ideas in the same being, why are God and the universe contradictory? Clarke says that bodies are composed of different substances, that they are not one substance; but it is certain that all we know of bodies is that they are extended, and that they cause certain impressions in us. Since, then, extension is not repugnant to God, and much less so the causality of impressions, there can be no reason against saying that what Clarke calls distinct substances, are only the parts, or, if he prefers it, the properties of the infinite substance. Newton went so far as to say that space was the sensorium of God, and even Clarke maintained against Leibnitz that Newton's expression might bear a sound interpretation, as it was intended only as a comparison. But Leibnitz insists so strongly on this charge that it is plain that he had very great objections to this word.
71. Whatever tends to confound God with nature, or to place him in constant communication with it, otherwise than by pure acts of intellect and will, places us on a very slippery declivity, where we can hardly help being precipitated to the bottom, and at this bottom is pantheism, which is but a phasis of atheism.(30)
CHAPTER XI.
FENELON'S OPINION.
72. Clarke's opinion is very similar to that of Fenelon, who in his Treatise on the existence and attributes of God, explains immensity in a very surprising manner. He says: "After considering the eternity and immutability of God, which are the same thing, I ought to examine his immensity. Since he is by himself, he is sovereignly, and since he is sovereignly, he has all being in himself. Since he has all being in himself, he has without doubt extension; extension is a manner of being, of which I have an idea. I have already seen that my ideas upon the essence of things, are real degrees of being, which actually exist in God, and are possible out of him, because he can produce them. Therefore, extension is in him; he can produce it outside of himself, only because it is contained in the fulness of his being."
To a certain extent the words of Fenelon may be explained in a sense which most theologians would not reject. They distinguish two classes of perfections; those which involve no imperfection; such as wisdom, holiness, and justice; and those which involve imperfection, as, for example, all which belong to bodies, extension, form, etc. The former, which are also called perfections simpliciter, are in God formaliter; that is to say, just as they are, because their nature involves no kind of imperfection, and, therefore, in God, they do not diminish nor tarnish his infinite perfection. Those of the second class, which are called perfections secundum quid, are in God not formaliter; for the imperfection which they involve is repugnant to his infinite perfection, but virtualiter or eminenter; that is to say, that all the perfection, all the being which they contain is in God, who is infinite perfection, infinite being; and God can produce them exteriorly by his creative omnipotence. But inasmuch as they pre-exist in an infinite being, they are freed from all limitation and imperfection, and identified with the infinite essence, and have a mode of being far superior to what they are in reality. This is expressed by the term eminenter.
Among these perfections secundum quid, extension has always been numbered.
73. If the illustrious Archbishop of Cambrai had held to this sense, we should have nothing to say in relation to his doctrine, but the words which follow seem to show that he inclined to the opinion of those who maintain that space is the immensity of God.
"Whence, then," he adds, "is it that I do not call him extended and corporeal? It is because there is an extreme difference, as I have already remarked, between attributing to God all that is positive in extension, and attributing to him extension with a limit or negation. He that places extension without limits changes extension into immensity; he who places extension with limits, makes a corporeal nature." From these words it might be believed that Fenelon did not distinguish the two modes of being of extension as theologians do; but he gives to God all that is positive in extension, though he gives it to him without limit. From this it would seem to follow that God is really extended, although his extension is infinite. With all the respect due to the illustrious shade of one of the greatest ornaments of the Catholic Church, and one of the greatest men of modern times, I must say that such an opinion does not seem to me to be sustainable. A God really extended though with an infinite extension is not God. That which is extended is essentially composite; God is essentially simple. Therefore, God and extension are contradictory.
74. But let us hear the illustrious prelate continue the explanation and defence of his opinion. He says: "From the moment that you place no limit to extension, you take from it figure, divisibility, motion, and impenetrability;—figure, because this is only a mode of limiting by surfaces;—divisibility, because, as we have seen, that which is infinite cannot be diminished, therefore, it cannot be divided, and consequently, it is not composite and divisible;—motion, because, if you suppose a whole, which has no parts nor limits, it cannot move beyond its place, because there can be no place beyond the true infinite; neither can it change the arrangement and situation of its parts, because it has no parts of which it is composed;—impenetrability, in fine, because impenetrability can only be conceived by conceiving two limited bodies, one of which is not the other, and cannot occupy the same space as the other. There are no two such bodies in infinite and indivisible extension; therefore there is no impenetrability in this extension. These principles established, it follows that all that is positive in extension is in God, although God has no figure, is not movable, divisible, or impenetrable, and consequently is not palpable, nor measurable."
From this passage it is very evident that Fenelon was far from imagining a composite God, a God with parts. He expressly denies it more than once in these few lines. Not less was to be looked for from his deep penetration and the purity of his doctrines; but, although this saves the rectitude of his intention, it does not satisfy philosophical exactness. For my part, I honestly confess that if extension is to be taken in its true sense, I cannot conceive how taking away its limits destroys its parts. On the contrary, I should rather say that an infinite extension would have infinite parts. If it is infinite it will have no figure; because figure involves a limit; but if it be true extension, it is a sort of immense field on which all imaginable figures may be traced. It will have no essential figure of its own, but it will be the recipient of all figures, the inexhaustible sea from which they all arise. That which is traced in it, will be in it; the points which terminate the figures must be in it. Is not this to have parts, composition? Infinite extension could have no figure, not because it has no parts, or is simple, but because it has infinite parts, because its composition is infinite.
I agree that an infinite extension would not be divisible, if by dividing, is meant separating; because in that immense fulness everything would be in its position with infinite firmness. So also we imagine space, the place of all motion, with its parts immovable, the field of all separation, with its parts inseparable; but we are treating of division, not of separation. If there is true extension, it is divisible; we conceive space with its parts inseparable, but still divisible; for we measure them, count them, and it is by relation to them that we form an idea of the size, distance, and motion of bodies.
74. Such clear and conclusive reflections could not fail to present themselves to the mind of the illustrious philosopher; but he seems to have preferred inconsequence or obscurity of language to the fatal corollaries of his first proposition. He said plainly and without any restriction, that all that is positive in extension, except the limit, is in God. He had asserted that extension with limits is corporeal, and that to change extension into immensity it was only necessary to take away its limits. He consequently attributed to God a true, although infinite, extension, and then wishing to explain and strengthen his doctrine he tells us that this extension has no parts. What is extension without parts? Who can conceive it? Does not extension necessarily imply an order of things of which some are outside of others. It has been always so understood. To speak of an extension without parts is to speak of an extension improperly so called. When speaking of such extension it is not enough to say it has no limits, it should be added that it is of an entirely different nature, that the word extension is used in another sense. Fenelon seemed to know this, when, notwithstanding the obscurity of his former expressions, elevated on the wings of his religion and his genius, he says: "God is in no place, as in no time; for his absolute and infinite being has no relation to place or time, which are but limits and restrictions of being. To ask if he is beyond the universe, if he exceeds its extremities in length, breadth, and depth, is as absurd a question as to ask if he was before the world, and if he will still be when the world is no more. As there is neither past nor future in God, so there is neither hither nor thither. As his absolute permanence excludes all measure of succession, so also his immensity excludes all measure of extension. He has not been, he will not be, but he is. In the same manner, to speak properly, he is not here, he is not there, he is not beyond such a limit, but he is, absolutely. All expressions which place him in relation to any term, or fix him in a certain place, are improper and unbecoming. Where then is he? He is. He is in such a manner that we must not ask where. That which only half is, or with limits, is a certain thing in such a way that it is nothing else. But God is not any particular and restricted thing. He is all; he is being; or better and more simply, he is. For the fewer words we use, the more we say. He is. Beware of adding any thing to this."
76. While reading these magnificent words, I am carried away by the elevation and grandeur of his ideas of God and of his immensity, and I forget the objections to the first proposition, which, if not false or inexact, is not, to say the least, expressed with all the clearness that could be desired. Still, I do not hesitate to maintain that his opinion coincides with Clarke's; although the illustrious writer, Christian, and poet, seem to merit a pardon for the philosopher.
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.
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.
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.
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.
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 motion intrinsically impossible, or is it not? If it is impossible, there is no reason why we should be afraid to say that God cannot produce it: 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 the phenomena 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.
OBSERVATIONS ON KANT'S OPINION.
104. We have already shown that extension considered in us, is something more than a mere sensation, that it is a true idea, the basis of some sensations, and at the same time a pure idea. As far as it relates to sensations, it is the foundation of our sensitive faculties; and in so far as it is an idea, it is the root of geometry. This is an important distinction, and we shall find it useful to enable us rightly to appreciate the value of Kant's opinion of space.
105. All our sensations are, either more or less, connected with extension; although if we consider sensation a priori by itself, and independently of all habit, it would seem as though only the sensations of sight and touch were necessarily connected with an extended object. It does not seem to me that the loss of these two senses would necessarily involve the privation of the impressions of hearing or smelling, or, perhaps, even of taste; for although it is true that the sensations of touch, such as hardness or softness, etc., are always united with the sensations of the palate; it is equally certain that those sensations are wholly distinct from the sensation of taste, and we have no reason for asserting that they cannot be separated from it.
106. Extension, considered in us or in its intuition, may be regarded as a necessary condition of our sensitive faculties. Kant saw this, but he exaggerated it when he denied the objective reality of space, asserting that space is only a subjective condition a priori without which we cannot receive impressions, the form of phenomena, that is, of appearances, but nothing in reality. I have already said that space, as distinguished from bodies, is nothing, but the object of the idea of space is the extension of bodies; or, rather, this extension is the foundation from which we deduce the general idea of space, and is contained in this idea.
107. To say, as Kant does, that space is the form under which the phenomena are presented to us, and that it is a necessary subjective condition of their perception, is equivalent to saying that the phenomena which are presented as extended, require that the mind should be capable of perceiving extension. This is very true, but it throws no light on the nature of the idea of space, either in itself or in its object. "Space," says Kant, "is no empirical conception which is derived from external experience. For in order that certain sensations may be referred to something out of me, that is, to something in another part of space than that in which I am, and in order that I may conceive them as outside of and near one another, and, consequently, not only as separated, but also as occupying separate places, the conception of space must be placed as the foundation. Therefore, the conception of space cannot be obtained by experience from the relations of the external phenomenon, but this external experience itself is possible only by this conception."[48]
There is a great confusion of ideas here. What are the conditions which are necessary to the phenomenon of the sensation of the extended? We are not here treating of the appreciation of dimensions, but merely of extension as represented or conceived. I do not see how this phenomenon requires any thing a prior, except the sensitive faculty which, in fact, exists a prior, that is to say, is a primitive fact of our soul in its relations to the organization of the body which is united to it, and of the other bodies which surround it. Under certain conditions of our organization, and of the bodies which affect it, the soul receives the impressions of sight or touch, and with them the impression of extension. This extension is not presented to the mind in the abstract, or as separated from the other sensation which accompany it, but as united with them. The mind does not reflect, then, upon the position of the objects, but it has an intuition of the arrangement of the parts. So long as the fact is confined to mere sensation, it is common to the learned and the unlearned, to the old and the young, and even to all animals. This requires nothing a prior except the sensitive faculty, which simply means that a being, in order to perceive, must have the faculty of perceiving, and should hardly deserve to be announced as a discovery of philosophy.
109. There is no such discovery in Kant's doctrine of space, for on the one side he asserts a well known fact, that the intuition of space is a necessary subjective condition, without which it is impossible for us to perceive things, one outside of another; and on the other side he falls into idealism, inasmuch as he denies this extension all reality, and regards things and their position in space as pure phenomena, or mere appearances. The fact which he asserts is true at bottom; for it is, in fact, impossible to perceive things as distinct among themselves, and as outside of us, without the intuition of space; but, at the same time, it is not accurately expressed, for the intuition of space is this perception itself; and, consequently, he ought to have said that they are identical, not that one is an indispensable condition of the other.
110. Prior to the impressions, there is no such intuition, and if we regard it as a pure intuition and separated from intellectual conception, we can only conceive it as accompanied by some representation of one of the five senses. Let us imagine a pure space without any of these representations, without even that mysterious vagueness which we imagine in the most distant regions of the universe. The imagination finds no object; the intuition ceases; there remains only the purely intellectual conceptions which we form of extension, the ideas of an order of possible beings, and the assertion or denial of this order, according to our opinion of the reality or non-reality of space.
111. It is evident that a series of pure sensations cannot produce a general idea. Science requires some other foundation. The phenomena leave traces of the sensible object in the memory, and are so connected with each other, that the representation of one cannot be repeated without exciting the representation of the other, but they produce no general result which could serve as the basis of geometry. A dog sees a man stoop, and make a certain motion, and is immediately struck with a stone, which causes in him a sensation of pain; when the dog sees another man perform the motion, he runs away; because the sensations of the motions are connected in his memory with the sensation of pain, and his natural instinct of avoiding pain inspires him to fly.
112. When these sensations are produced in an intelligent being, they excite other internal phenomena, distinct from the mere sensitive intuition. Whether general ideas already exist in our mind, or are formed by the aid of sensation, it is certain that they are developed in the presence of sensation. Thus, in the present case we not only have the sensitive intuition of extension, but we also perceive something which is common to all extended objects. Extension ceases to be a particular object, and becomes a general form applicable to all extended things. There is then a perception of extension in itself, although there is no intuition of the extended; we then begin to reflect upon the idea and analyze it, and deduce from it those principles, which are the fruitful germs from the infinite development of which is produced the tree of science called geometry.
113. This transition from the sensation to the idea, from the contingent to the necessary, from the particular fact to the general science, presents important considerations on the origin and nature of ideas, and the high character of the human mind.
Kant seems to have confounded the imagination of space with the idea of space, and notwithstanding his attempts at analysis, he is not so profound as he thinks, when he considers space as the receptacle of phenomena. This a very common idea, and all that Kant has done is to destroy its objectiveness, making space a purely subjective condition. According to this philosopher, the world is the sum of the appearances which are presented to our mind; and just as we imagine in the external world an unlimited receptacle which contains every thing, but is distinct from what it contains, so he has placed space within us as a preliminary condition, as a form of the phenomena, as a capacity in which we may distribute and classify them.
114. In this he confounds, I say, the vague imagination with the idea. The limit between the two is strongly marked. When we see an object we have the sensation and intuition of extension. The space perceived or sensed is, in this case, the extension itself perceived. We imagine a multitude of extended objects, and a capacity which contains them all. We imagine this capacity as the immensity of the ethereal regions, a boundless abyss, a dark region beyond the limits of creation. So far there is no idea, there is only an imagination arising from the fact that when we begin to see bodies we do not see the air which surrounds them, and the transparency of the air permits us to see distant objects, and thus from our infancy we are accustomed to imagine an empty capacity in which all bodies are placed, but which is distinct from them.
But this is not the idea of space; it is only an imagination of it, a sort of rude, sensible idea, probably common to man and the beasts. The true idea, and the only one deserving the name, is that which our mind possesses when it conceives extension in itself, without any mixture of sensation, and which is, as it were, the seed of the whole science of geometry.
115. It should be observed that the word representation as applied to purely intellectual ideas must be taken in a purely metaphorical sense, unless we eliminate from its meaning all that relates to the sensible order. We know objects by ideas, but they are not represented to us. Representation, properly speaking, occurs only in the imagination which necessarily relates to sensible things. If I demonstrate the properties of a triangle, it is clear that I must know the triangle, that I must have an idea of it; but this idea is not the natural representation which is presented to me like a figure in a painting. All the world, even irrational animals have this representation, yet we cannot say that brutes have the idea of a triangle. This representation has no degrees of perfection, but is equally perfect in all. Any one who imagines three lines with an area enclosed, possesses the representation of a triangle with as much perfection as Archimedes; but the same cannot be said of the idea of a triangle, which is evidently susceptible of various degrees of perfection.
116. The representation of a triangle is always limited to a certain size and figure. When we imagine a triangle, it is always with such or such extension and with greater or smaller angles. The imagination representing an obtuse angled triangle sees something very different from an acute or right angled triangle. But the idea of the triangle in itself is not subject to any particular size or figure; it extends to all triangular figures of every size. The general idea of triangle abstracts necessarily all species of triangles, whilst the representation of a triangle is necessarily the representation of a triangle of a determinate species. Therefore the representation and the idea are very different, even in relation to sensible objects.
117. It is the same with space. Its representation is not its idea. The representation is always presented to us as something determinate, with a clearness like that of the air illuminated by the sun, or a blackness like the darkness of night. There is nothing of this sort in the idea, or when we reason upon extension and distances.
The idea of space is one; its representations are many. The idea is common to the blind man and to him who sees. For both it is equally the basis of geometry, but the representation is very different in these two. The latter represents space as a confused reproduction of the sensations of sight; the blind man can only represent it as a confused repetition of the sensations of touch.
The representation of space is only indefinite, and even this progressively. The imagination runs over one space after another, but it cannot at once represent a space without limits; it can no more do this than the sight can take in an endless object. The imagination is a sort of interior sight, it reaches a certain point, but there it finds a limit. It can, it is true, pass beyond this limit, and expand still farther, but only successively, and always with the condition of encountering a new limit. Space is not represented as infinite, but as indefinite, that is to say, that after a given limit there is always more space, but we can never advance so far as to imagine an infinite totality. It is the contrary with the idea; we conceive instantaneously what is meant by infinite space, we dispute on its possibility or impossibility, we distinguish it perfectly from indefinite space, we ask if it has in reality limits or not, calling it in the first case finite, in the latter infinite. We see in the word indefinite the impossibility of finding limits, but at the same time we distinguish between the existence of these limits, and finding them. All this shows that the idea is very different from the representation.
To regard space as a mere condition of sensibility is to confound the two aspects under which extension should be considered, as the basis of sensations, and as idea; as the field of all sensible representations, and as the origin of geometry. I have often insisted on this distinction, and shall never weary of repeating it; because it is the line which divides the sensible from the purely intellectual order, and sensations from ideas.
CHAPTER XVII.
INABILITY OF KANT'S DOCTRINE TO SOLVE THE PROBLEM OF THE POSSIBILITY OF EXPERIENCE.
118. I think that Kant's Transcendental Æsthetics, or theory of sensibility, is not sufficiently transcendental. It is too much confined to the empirical part, and does not rise to the height which we should expect from the title. The problem of the possibility of experience which Kant proposed to solve, either is not at all touched by his doctrine, or else it is solved in a strictly idealist sense. It leaves the problem untouched, if we consider only what relates to observation; for he only repeats what we already knew in establishing the fact of the exteriority of things; it solves the problem in a strictly idealist sense, inasmuch as these things are only considered as phenomena or appearances.
119. A purely subjective space either does not explain the problems of the external world, or it denies them in denying all reality. What progress has philosophy made by affirming that space is a purely subjective condition? Before Kant, did we, perchance, not know that we had perception of external phenomena? The difficulty was not in the existence of this perception attested by consciousness; but in its value to prove the existence of an external world, in relation with it. The difficulty was in the objective, not the subjective part of the perception.
120. To say that the perception is nothing more than a condition of the subject, is to cut the knot instead of untying it. It does not explain the manner of the possibility of experience, but denies this possibility.
What is experience if there is only the subject? There will be the phenomenon or appearance of objectiveness, but nature is then only a mere appearance, and there is nothing in reality which corresponds to our experimental perceptions. We then have experience reduced to the perception of appearances; and as even this purely phenomenal experience is only possible by virtue of a purely subjective condition, the intuition of space; all experience remains purely subjective, and we find ourselves holding the system of Fichte, admitting the me as the primitive fact, the development of which constitutes the universe. Thus the system of Fichte follows from Kant's doctrine; the former has only carried out the principles of his master.
121. In order to make the connection between the two doctrines still clearer, we shall make some further reflections on Kant's system. If space is something purely subjective, a condition of the sensibility and of the possibility of experience, it follows that the mind instead of receiving any thing from the object, creates whatever is in the object, or rather, whatever we consider as in it. Things in themselves are not extended; extension is only a form with which the mind clothes them. In the same manner, they are not colored, sonorous, tasteful, or odorous, except inasmuch as we transfer to them that which is in ourselves alone. Every thing being reduced to mere appearances, there is in the external world not even the principle of causality of subjective extension; the mind gives it to objects, does not receive it from them. These objects are pure phenomena; and, consequently, the soul only sees what it contains in itself, it knows no other world than that which is its own creation. Thus, we see the real world spring from the me; or, rather, the real world is only the ideal creation of the mind. On this supposition, the laws of nature are only the laws of our own mind, and instead of seeking for the types of our ideas in nature, we ought to regard our ideas as the generative principle of all that exists, or seems to exist; and the laws of the universe are merely the subjective condition of the me applied to phenomena.
122. Some of the disciples of Kant show no fear of his idealist tendencies; in fact they accept them without any hesitation, as may be seen by the comparisons which they use in explaining his doctrine. If a seal be applied to a piece of soft wax, it will leave its impression on the wax; if we suppose the seal to be capable of perception, it would see its mark on the wax, and attribute to the object what it had itself given it. If a vase full of water were capable of perception, it would attribute to the water the form, which in reality is only the form of the vase itself, and is communicated from it to the water. In a similar manner the mind constructs the external world, giving to it its impression and form, and then believing it has received from the external world what it has itself communicated to it.
123. Still we must confess that Kant, in the second edition of his Critic of Pure Reason, rejects these conclusions, and expressly combats idealism. There is no necessity of examining how far the second edition contradicts the first: it is sufficient for me to inform the reader that this contradiction exists, and that in the first edition there are expressions which so plainly lead to idealism, that it is impossible not to be surprised on finding the same author in the second edition of his work strongly opposing the idealist system. I have pointed out the consequences of the doctrine; if the author understood it in a different sense from that which his words expressed, this is merely a personal, not a philosophical question.(31)
CHAPTER XVIII.
THE PROBLEM OF SENSIBLE EXPERIENCE.
124. The great problem of philosophy does not consist in the explanation of the possibility of experience; but in establishing the reason of the consciousness of experience, as experience. Experience in itself is a fact of our soul attested by consciousness, but to know that this fact is a fact of experience, is something very different from mere experience; for, by knowing this, we pass from the subjective to the objective, referring to the external world what we experience within us.
We refer objects to different points of space, and regard them as outside of, and distinct from, each other: to say that the instinct by which we so regard them is a condition of the subject and of sensible experience is to establish a sterile fact. The difficulty is in knowing why we have this instinct; why the representation of an extension is in our soul; and why this subjective extension in a simple being should be presented to our perception as the image of something external and really extended.
125. Transcendental esthetics may determine the following problems:
I. To explain what is the subjective representation of extension, abstracted from all that is objective.
II. Why this representation is found in our soul.
III. Why a simple being contains in itself the representation of multiplicity, and an unextended being the representation of extension.
IV. Why and how we pass from ideal to real extension.
V. To determine how far we may apply to extension what is true of the other sensations, which are considered as phenomena of our soul, having no external object like them, and no other correspondence with the external world than the relation of effects to their cause.
126. What is the subjective representation of extension, abstracted from all that is objective? It is a fact of our soul; no further explanation is possible; he that has it, knows what it is; he that has it not, does not, except intelligences of a higher order, which know what this representation is, without experiencing it as we do.
127. I do not pretend that it is possible to explain why the representation of extension is found in our soul; we might as well ask why we are intelligent and sensible beings. The only reason a priori which we can give, is that God has so created us. This representation may be found in us, and it is so found, for we experience it; but this internal experience is the limit of philosophy; immediate observation can go no farther back. Reason raises us to the knowledge of a cause which created us, but not to a phenomenon which is the source of the phenomena of experience.
128. Why a simple being contains in itself the representation of multiplicity, and an unextended being the representation of extension, is the problem of intelligence, which, because it is intelligence, is one and simple, and capable of perceiving multiplicity and composition.
129. We pass from ideal to real extension by a natural and irresistible impulse, which is confirmed by the assent of reason. This has been demonstrated in the first book, and also in the second when treating of the objectiveness of sensations.
130. Of the five problems the last remains. We must determine how far we may apply to extension what is true of the other sensations, which are considered as phenomena of our soul, having no external object like them, and no other correspondence with the external world than the relation of effects to their cause.
131. The solution of this problem settles the question for or against the idealists. If we may apply to extension what is true of the other sensations, idealism triumphs, and the real world, if it exists, is a being which has no resemblance to the world which we think.
I have proved in treating of sensations[49] that extension is something real, and independent of our sensations, and I have shown[50] that it represents multiplicity and continuity. This is sufficient to overthrow idealism, and also to explain, to a certain extent, what extension consists in; but as the idea of space, which is closely connected with extension, had not then been examined, it was not possible for us to rise above the order of phenomena and regard extension under a transcendental aspect, examining it in itself, abstracted from all its relations with the world of appearances. This is what I propose to do in the following chapters.
132. We come now to a more cragged path; we have to distinguish the reality from appearance; our understanding, which is always accompanied by sensible representations, must now depart from them, and place itself in opposition to a condition to which it is naturally subjected in the exercise of its functions.
CHAPTER XIX.
EXTENSION ABSTRACTED FROM PHENOMENA.
133. That which is extended is not one being only; it is a collection of beings. Extension necessarily contains parts, some outside of, and consequently distinct from, others. Their union is not identity; for, the very fact that they are united, supposes them distinct, since any thing is not united with itself.
It would seem from this that extension in itself and distinguished from the things extended, is nothing; to imagine extension as a being whose real nature can be investigated is to resign one's self to be the sport of one's fancy.
Extension is not identified in particular with any one of the beings which compose it, but it is the result of their union. This is equally true whether we consider extension composed of unextended points, or of points that are extended but infinitely divisible. If we suppose the points unextended, it is evident that they are not extension, because extended and unextended are contradictory. Neither are these points identified with extension, if we suppose them extended; for extension implies a whole, and a whole cannot be identified with any of its parts. If a line be four feet long, there cannot be identity between the whole line and one of its parts a foot long. We may suppose these parts, instead of a foot, to be only an inch in length, and we may divide them ad infinitum, but we shall never find any of these parts equal to any of its subdivisions. Therefore, extension is not identical with any of the particular beings which compose it.
134. The idea of multiplicity being involved in the idea of extension, it would seem that extension ought to be considered, not as a being in itself, but as the result of a union of many beings. This result is what we call continuity. We have already seen[51] that multiplicity is not sufficient to constitute extension. It enters into the idea of number, and yet number does not represent any thing extended. We also conceive a union of acts, faculties, activities, substances, and beings of various classes, without conceiving extension, and yet multiplicity is a part of all these conceptions.
135. Therefore continuity is necessary, in order to complete the idea of extension. What, then, is continuity? It is the position of parts outside of, but joined to other parts. But what is the meaning of the terms, outside of, and joined to? Inside and outside, joined and separated, imply extension, they presuppose that which is to be explained; the thing to be defined enters into the definition in the same sense in which it is to be defined. Exactly; for, to explain the continuity of extension is the same as to show the meaning of the terms inside and outside, joined and separated.
136. We must not forget this observation, unless we wish to accept the explanations which are found in almost all the books on the subject. To define extension by the words inside and outside, is not to add any thing, under a philosophic aspect; it is merely to express the same thing in different words. Without doubt this language would be the simplest, if all we wanted was to establish the phenomenon only, but philosophy will not be satisfied with it. It is a practical, not a speculative, explanation. The same may be said of the definition of extension by space or places. What is extension?—the occupation of place:—but, what is a place?—a portion of space terminated by certain surfaces:—what is space?—the extension in which bodies are placed, or the capacity to receive them. But even admitting the existence of space as something absolute, what is the capacity of bodies to fill space? Who does not see that this is to define a thing by itself, a vicious circle? The extension of space is explained by the capacity of receiving; the extension of bodies by the capacity of filling. The idea of extension remains untouched; it is not defined, it is merely expressed in different words, but which mean the same thing.
To suppose the existence of space as something absolute, does not help the question, and is, besides, an entirely gratuitous supposition. To take the extension of space as a term by relation to which we may explain the extension of bodies, is to suppose that to be found which we are looking for.
We run into the same error if we try to explain the words inside and outside, by referring them to distinct points in space, we should define a thing by itself; for, we have the same difficulty with respect to space to determine the meaning of inside and outside, joined and separated, and contiguous and distant. If we presuppose the extension of space as something absolute, and try to explain other extensions by relation to this, we only make the illusion more complete. We have to explain extension in itself, the extension of space must be explained as well as the rest; to presuppose it is to assume the question already solved, not to solve it.
137. Extension in relation to its dimensions seems to be independent of the thing extended in the same place. An extension may remain absolutely fixed with the same dimensions, notwithstanding the change of place of the thing extended. If we suppose a series of objects to pass over a fixed visual field, the things extended vary incessantly, but the extension remains the same. If we suppose a very large object to pass before a window, it changes continually; for the part which we see at the instant A is not the part which we see at the instant B, but the extension has not varied in its dimensions. This regards surfaces only, but the same doctrine may be applied to solids. A space may be successively filled with a variety of objects, but its capacity remains the same. There is no identity between the object and the extension which contains it; for any number of objects of the same size may occupy the same place; neither is the air, or any surrounding object, identified with the extension; for these, too, may change without affecting the extension in which the object is contained.
138. Though the dimensions remain fixed while the objects vary, it does not follow that extension is purely subjective, even though we suppose that the objects which vary cannot be distinguished. If the contrary were maintained, the change of the dimensions would prove them to be objective; and the argument might be retorted against our adversaries. That the dimensions are fixed shows that different objects may produce similar impressions; and therefore we can form an idea of a determinate dimension or figure, without reference to the particular object to which it does, or may correspond. No one will deny that we have the representation of dimensions, without necessarily referring them to any thing in particular; but what we wish to determine is, whether these dimensions exist in reality, and what is their nature, independently of their relations to us.
139. If we admit that continuity has no external object either in pure space or in bodies, what becomes of the corporeal world? It is indeed to a collection of beings which in one way or another, and in a certain order, act upon our being.
The difficulties against the realization of phenomenal continuity are not destroyed by appealing to the necessities of the corporeal organization of sensible beings. If any one should ask how external beings can act upon us, and affect our organs, if they have not in them the continuity with which they are presented to us; such a one would show that he does not understand the state of the question. For it is evident that if we should take from the external world all real continuity, leaving only the phenomenal, we should at the same time take it from our own organization, which is but a part of the universe. There is here a mutual relation and sort of parallelism of phenomena and realities which mutually complete and explain each other. If the universe is a collection of beings acting upon us in a certain order, our organization is another collection of beings, receiving their influence in the same order. Either both are inexplicable, or else the explanation of one involves the explanation of the other. If that order is fixed and constant, and its correspondence remains the same, nothing is changed, no matter what hypothesis is assumed in order to explain the phenomenon.
140. The object of our searches here, is the reality subject to the condition of explaining the phenomenon, and not contradicting the order of our ideas.
It might be objected to those who take from the external world the phenomenal or apparent qualities of continuity, that they destroy geometry, which is based on the idea of phenomenal continuity. But this objection cannot stand; for it supposes the idea of geometry to be phenomenal, whereas it is transcendental. We have already shown that the idea of extension is not a sensation, but a pure idea, and that the imaginary representations by which it is made sensible are not the idea, but only the forms with which the idea is clothed.
141. All phenomenal extension is presented to us with a certain magnitude; geometry abstracts all magnitude. Its theorems and problems relate to figures in general abstracted absolutely from their size, and when the size is taken into consideration it is only in so far as relative. Of two triangles of equal bases that which has greater altitude has the greater surface. Here the word greater relates to size, it is true; but to a relative, not to any absolute size; the question is not of the magnitudes themselves, but of their relation. Consequently, the theorem is equally true whether the triangles are immense, or infinitely small. Therefore, geometry abstracts absolutely all magnitudes considered as phenomena, and makes use of them only in order to assist the intellectual perception by the sensible representation.
142. This is an important truth, and I shall explain it further when combating Condillac's system in the treatise on ideas, where I shall show that even the ideas which we have of bodies neither are, nor can be, a transformed sensation. According to these principles, geometry is a science which makes its pure ideas sensible by a phenomenal representation. This representation is necessary so long as geometry is a human science, and man is subject to phenomena; but geometry in itself and in all its purity has no need of such representations.
143. In order that this doctrine may seem less strange, and may be more readily accepted, I will ask, whether pure spirits possess the science of geometry? We must answer in the affirmative; for, otherwise we should be forced to conclude that God, the author of the universe and greatest of geometricians, does not know geometry. Does God, then, have these representations, by the aid of which we imagine extension? No; these representations are a sort of continuation of sensibility which God has not; they are the exercise of the internal sense, which is not found in God. St. Thomas calls them phantasmata, and says they are not found in God, or in pure spirits, nor even in the soul separated from the body. Therefore, the science of geometry is possible, and does really exist without sensible representations, and, consequently, we may distinguish two extensions, the one phenomenal, and the other real, without thereby destroying either the phenomenon or the reality, so long as we admit the correspondence between them; so long as we do not break the thread which unites our being with those around us; so long as the conditions of our being harmonize with those of the external world.(32)
CHAPTER XX.
ARE THERE ABSOLUTE MAGNITUDES?
144. The preceding doctrine will seem much more probable if we reflect that all purely intellectual perceptions of extension may be reduced to the knowledge of order and relation. There is nothing absolute in the eyes of science, not even of mathematical science. The absolute, in relation to extension, is an ignorant fancy which the observation of the phenomena is sufficient to dissipate.
In the order of appearances there are no absolute magnitudes; all are relations. We can not even form an idea of a magnitude, unless with reference to another which serves for a measure. The absolute is found only in number, and never in extension; a magnitude is absolute, not in itself, but only by being numbered. A surface two feet square, presents two distinct ideas; the number of its parts, and the kind of parts. The number is a fixed idea, but the kind is purely relative. I will try to make this clearer.
145. When I speak of a surface four feet square, the number four is a simple, fixed, and unchangeable idea; but I can explain a square foot only by relations. If I am asked what is a square foot, I can answer only by comparison with a square rod or a square inch; but if I am again asked what is a square rod or a square inch, I am again forced to recur to other measures which are greater or smaller; I can nowhere find a fixed magnitude.
146. If there were some fixed measure it might be some dimension of the body, my hand, or foot, or arm. But who does not see that the dimensions of my body are not a universal measure, and that the hands, or feet, or arms, of all men are not equal? And even in the same individual they are subject to a thousand changes more or less perceptible. Shall we take for our fixed measure the radius of the earth, or of a heavenly body? But one has no claim to preference before the other. Every one knows that astronomers take sometimes the radius of the earth, and sometimes the radius of its orbit as the unity of measure. If we suppose these radii to be greater or smaller, can we not equally in either case take them as the measure? They are preferred because they do not change.
But even astronomers regard these magnitudes as purely relative, and at one time consider them infinitely large, at another infinitely small, according to the point of view from which they look at them. The radius of the earth's orbit is considered infinite in comparison with a small inequality on the earth's surface, and infinitely small when compared with the distance of the fixed stars.
We can form no idea of these measures except by comparison with those in constant use. What idea should we have of the magnitude of the radius of the earth if we did not know how many million measures it is equal to? What idea should we have in turn of these measures if we had nothing constant to which we could refer them?
147. There is something absolute in magnitudes, it may be objected; for a foot is a certain length which we both see and touch, and cannot be greater or smaller; the surface of a square yard is in like manner something definite which we see and which we touch; and the same may be applied to solids. There is no necessity of going farther to find that which is so clearly presented to us in sensible intuition. This objection supposes that there is something fixed and constant in intuition; this is false. I appeal to experience.
It is probable that men see the same magnitudes very differently according to the disposition of their eyes. No one is ignorant that this happens when the objects are at a distance; for, then, one sees clearly what another cannot even distinguish; to one it is a surface, while to another it is not even so much as a point. We all know what a great variety there is in the size of objects when looked at through differently graduated glasses. From all this we conclude that there is nothing fixed in phenomenal magnitude; but that every thing is subject to continual changes.
When we look through a microscope objects which were before invisible, take large dimensions; and as the microscope may be infinitely perfected, it is not absurd to suppose that there are animals to whom what is invisible to us appears larger than the whole earth. The construction of the eye may also be considered in an inverse sense, and as infinite perfection is also possible in this case, it is possible that magnitudes which to us are immense may be invisible to other beings. To this eye of colossal vision the terrestrial globe would perhaps be an imperceptible atom. This is no more than what happens by the interposition of distance; immense masses in the firmament seem to us to be only small specks of light.
148. It must now be very evident that there is nothing absolute in magnitudes of sight; but that all is relative, and that objects appear to us greater or less, according to habit, the construction of our organs, and other circumstances. The variety of appearances is in accordance with philosophy; since no necessary relation can be discovered between the size of the organ and the object. What connection is there between a narrow surface like the retina of our eye and the immense surfaces which are painted on it?
149. From sight we may pass to touch, but we find no reason of the fixity of phenomenal magnitude. The sense of touch gives us the ideas of magnitudes by relation to the time it takes to pass over them, and to the velocity of our motion. The ideas of time and velocity are also relative; they refer to the space passed over. When we measure velocity we say that it is the space divided by the time; in measuring time we say that it is the space divided by the velocity; and we measure space by multiplying the velocity by the time. All these ideas are correlative, and are measured by each other, and by their mutual relations. This shows that these ideas have nothing absolute; their whole character is that of a relation which is incomplete, or rather does not exist, if one of the terms is wanting.
150. We shall find it equally impossible to determine these measures by the impressions which the motion causes in us. If for example we propose to measure the degree of velocity, by the agitation which we feel in our body, we shall find that the measure varies with the agitation, but this agitation depends on the degree of force exerted, and still more on the strength of the subject. Thus a little child is obliged to run till he is almost out of breath, to keep up with his father who is walking fast.
The impossibility of any fixed measure by means of impressions will be still more apparent if we compare the motion of a horse with the motion of a microscopic animal. The distance which a horse would pass over almost without any sensible motion, would require the microscopic animal to display its whole activity, and run perhaps a whole day. The horse would scarce believe he had changed his place, whereas the poor animalcule would at night be overcome by fatigue like one who has travelled a long journey. Compare now the motion of the horse with the motion of those fabulous giants who piled up mountains to scale the heavens; a single step of one of those giants would be a long distance for the horse to travel.
151. Art seems to be in accordance with science on this point. In art, size is nothing, the only thing which is regarded is the proportion or relation. A skilful miniature represents a person as clearly as a painting the size of life. The same principle is applied to all the objects embraced by art, the artistic thought never refers directly to the size; proportion, the relative is all that is attended to; the absolute counts for nothing. We see the system of relations transferred to the order of appearances, inasmuch as they affect the faculties susceptible of pleasure; reason is thus admirably harmonized with sentiment, in the same manner as we have found intellect harmonized with the senses.
CHAPTER XXI.
PURE INTELLIGIBILITY OF THE EXTENDED WORLD.
152. Objects in themselves do not change their nature, by the variety of appearances which they produce in us. A polygon turning with rapidity has the appearance of a circle; the stars appear like small points; and considering the various classes of objects, we may observe that there is a great variety of appearances depending on circumstances. The nature of a being does not consist in what it appears, but in what it is. Suppose there were no sensitive being in the world, the present order of sensibility would disappear; for without sensitive beings there would be no representations. What would the world be in that case? This is a great problem of metaphysics.
153. A pure spirit,—the existence of which we must always suppose; for, though all finite beings were annihilated, there would still remain the infinite being which is God,—a pure spirit would know the extended world just as it is in itself, and would not have the sensible representations either external or internal, which we have. This is certain, unless we mean to attribute imagination and sensibility to pure spirits, and even to God himself.
On this supposition I ask, what would a pure spirit know of the external world? or, to speak more properly, since the existence of such a spirit is certain and its intelligence infinite, what does this spirit know of the external world?
154. That which this spirit knows of the world is the world, because he cannot be deceived. But this spirit does not know the world under any sensible form. Therefore the world may be known without any of the forms of sensibility, and consequently may be the object of a pure intelligence.
There is no difficulty on this point in what regards sensations. It is only necessary that we should say that the pure spirit knows perfectly the principle of causality which resides in the object, and produces the impressions which we experience. There is no need of attributing to the intelligent spirit any sensation of the thing understood.
This question is more difficult when we come to explain what relates to extension. For, if we say that the spirit only knows the principle of causality of the subjective representation of the extended, it follows that there is no true extension in the objects, because the spirit sees all that there is, and if the spirit does not see it, it is because it is not. We fall into Berkeley's idealism; an external world without extension is not the world of common sense, but the world of the idealists. If, on the other hand, we say that this pure spirit does know extension, we seem to attribute to the spirit sensible representation; because the extension represented seems to involve sensible representation. What is an extension with lines, surfaces, and figures? And these objects, as we understand them, are sensible; if, however, they be taken in another sense, the extension of the world will be of another nature, it will be something of which we have no idea; and here again we fall into idealism.
155. To solve this difficulty, which is really a serious one, it is necessary to recollect the distinction on which I insisted so earnestly between extension as sensation and extension as idea. The former can become subjective only in a sensible being; the second may be, and is, subjective in a purely intellectual being. Extension as sensation is something subjective, it is an appearance; its object exists in reality, but without including in its essence any thing more than is necessary in order to produce the sensation. Extension as idea is also subjective; but it has a real object which corresponds to it, and satisfies all the conditions of the idea.
156. Does not this theory seem to establish two geometries? We must distinguish. The scientific and the pure ideal geometry will remain the same, save the difference of the intelligences which possess it. But notwithstanding this difference, what is true in one is true in the other. Empirical geometry as the representative part of geometry will be different: we have the idea only of our own.
157. In fact we observe two parts in geometry even in ourselves; the one purely scientific, the other of sensible representation. The former includes the connection of ideas; the latter the images and particular cases by means of which we make the ideas sensible: the first is the ground; the second is the form. But although the two are different, we cannot separate them entirely: we cannot have the geometrical idea without the sensible representation, we understand it only per conversionem ad phantasmata, as say the scholastics. Thus the two orders of geometry, the sensible and the intellectual, though different, are always joined in us; whether because the pure geometrical idea arises from the sensible, or is excited by it, or because this is perhaps a necessary primitive condition imposed on our mind by its union with the body.
158. This shows how the pure geometry may be separated from the sensible, and how it may exist in pure intellectual beings, without any of the forms which represent the geometrical idea in sensible beings.
159. But what becomes of extension in itself and stripped of all sensible form? When we speak of extension stripped of all sensible form, we do not mean to deprive it of its capacity to be perceived by the senses, we merely abstract the relations of this capacity to sensible beings. Extension is then reduced, not to an imaginary space, nor to an eternal and infinite being, but to an order of beings, to the sum of their constant relations subject to necessary laws. What then are these relations? I know not. But I know that they exist and that these necessary laws exist. That they exist in reality I know by experience, which gives testimony of their existence; that they are possible, I know on the authority of my ideas, the connection of which forces my assent to their intrinsical evidence.
160. That this evidence touches but one aspect of the object, is true; that there are many things in the object which we do not know, is likewise true; but this only proves that our science is incomplete, not that it is illusory or false.
161. It is difficult for us to conceive the pure intelligibility of the sensible world, both because our ideas are always accompanied by representations of the imagination, and because we try to explain it by simple addition and subtraction of parts, as though all the problems of the universe could be reduced to expressions of lines, surfaces, and solids. Geometry plays an important part in all that regards the appreciation of the phenomena of nature; but when we want to penetrate to the essence of things, we must lay aside geometry and take up metaphysics.
There is no more seductive philosophy than that which reduces the world to motions and figures, but at the same time there is none more superficial. A slight reflection on the reality of things shows the insufficiency of such a system. For, though the imagination be satisfied with it, the understanding is not, and it takes a noble revenge on its unfaithful companion, when, forcing the imagination to fix itself upon objects, the understanding sinks it in an ocean of darkness and contradiction. Those who laugh at the forms, the acts, the forces, and other such expressions used with more or less exactness in different schools, ought to reflect that even in the physical world there is something more than is perceived by the senses; and that even sensible phenomena cannot be explained by mere sensible representations. Physical science is not complete until it calls to its aid metaphysics.
The best proof of this will be found in the next chapter, where we shall see the imagination entangled in its own representations.
INFINITE DIVISIBILITY.
162. The divisibility of matter is a question that torments philosophers. Matter is divisible because it is extended, and there is no extension without parts. These parts are extended or are not: if they are, they are again divisible; if they are not, they are simple, and in the division of matter we must come to unextended points.
This last consequence can be avoided only by recourse to the infinite divisibility of matter, and even this is a means of escaping the difficulty rather than a true solution. I intimated elsewhere[52] that infinite divisibility seems to suppose the very thing which it denies. Division does not make the parts, it supposes them; that which is simple cannot be divided; therefore, the parts which may be divided pre-exist in the infinitely divisible composition.
Let us imagine God to exert his infinite power in dividing, will he exhaust divisibility? If you say no, you seem to place limits to his omnipotence; if you say yes, we shall have arrived at simple points, as otherwise the divisibility would not be exhausted.
Even supposing that God does not make this division, his infinite intelligence certainly sees all the parts into which the composite is divisible; these parts must be simple, or else the infinite intelligence would not see the limit of divisibility. If you answer that this limit does not exist, and therefore cannot be seen, I reply that we must then admit an infinite number of parts in each portion of matter; there would, in this case, be no limit of divisibility, because the number of parts would be inexhaustible; but this infinite number would be seen by the infinite intelligence, as it is, and all these parts would be known as they are. The difficulty still remains; these parts are simple or composite; if simple, the opinion which we are opposing does, at least, admit unextended points; if composite, the same argument may be repeated; they are again divisible. We shall then have a new infinite number in each one of the parts of the first infinite number; but as this series of infinities must be always known to the infinite intelligence, we must come to simple points, or else say that the infinite intelligence does not know all that there is in matter.
It does not mend the matter to say that the parts are not actual but only possible. In the first place, possible parts are existing parts, because, if the parts are not real, there must be real simplicity, and consequently, indivisibility. Secondly, if they are possible, they may be made to exist by the intervention of an infinite power; and then what are these parts? they are either extended or unextended, and the matter returns to where it was before.
163. Some say that a mathematical quantity, or a body mathematically considered, is infinitely divisible, but that natural bodies are not, because their natural form requires a determinate quantity. This is the explanation which was given in the schools; but it is very clear that there is no ground for affirming that these natural bodies require a certain quantity, beyond which division is impossible. This cannot be proved either a prior nor a posteriori: not a priori, because we do not know the essence of bodies, and cannot say that there is a point where the natural form requires the limit of divisibility; neither can it be proved a posteriori, because the means of observation at our disposal are so coarse, that it is impossible for us to reach the last limit of division and discover a part which cannot be divided. Besides, when we reach this quantity beyond which division cannot go, we have a true quantity, by the supposition; if it is quantity it is extended; if it is extended it has parts; if it has parts it is divisible. Therefore there is no reason for saying that there is any natural form which limits division.
164. The distinction between a natural and a mathematical body is not admissible in what relates to division. This is a result of the nature of extension, which is real in natural bodies, and ideal in mathematical. That the parts in natural bodies are not actual but possible, may be understood in two ways; it may mean that they are not actually separated; or, that they are not distinct. That they are not separated has no bearing on the question; for division may be conceived without separating the parts. But, if they are not distinct, the division is impossible; for it cannot even be conceived where the things are not distinct.
165. This distinction seems to have originated in the attempt to avoid the necessity of admitting infinite divisibility in natural bodies. But the difficulty still remaining with regard to mathematical bodies, the philosophical mystery still subsists. It consists in this, that no limit can be assigned to division so long as there is any thing extended; and, on the other hand, if, in order to assign this limit, we come to simple points, then it is impossible to reconstitute extension. The difficulty arises from the very nature of extended things, whether realized or only conceived; the real order escapes none of the difficulties of the ideal. If ideal extension cannot be constituted out of unextended points, neither can real extension; if ideal extension has no limit to its divisibility until we come to simple points, the same is also true of real extension; for in both it is a result of the essence of extension, and inseparable from it.
UNEXTENDED POINTS.
166. There are two strong arguments against the existence of unextended points: the first is, that we must suppose them infinite in number, for otherwise it does not seem possible to arrive at the simple, starting from the extended: the second is, that even supposing them infinite in number they are incapable of producing extension. These arguments are so powerful as to excuse all the aberrations of the contrary opinion, which, however strange they may seem, are not more strange than the simple forming extension, and the smallest portion of matter containing an infinite number of parts.
167. It does not seem possible to arrive at unextended points unless by an infinite division. The unextended is zero in the order of extension, and in order to arrive at zero by a decreasing geometrical progression it must be continued ad infinitum. Mathematical calculation presents a sensible image of this. When two parts are united they must have a side where they touch, and another where they are not in contact. If we separate the interior side from the exterior we have two new sides, one which touches and another which does not. Continuing the division the same thing happens again; we must, therefore, pass through an infinite series in order to arrive at the unextended, which is equivalent to saying that we shall never arrive there. To continue the division ad infinitum we must suppose infinite parts, and consequently the existence of an actual infinite number. From the moment that we suppose this infinite number to exist it seems to become finite, since we already see a limit to the division, and also other numbers greater than it. Let us suppose that this infinite number of parts is found in a cubic inch; there are numbers which are greater than this which we suppose infinite; a cubic foot, for example, will contain 1,728 times the infinite number of parts contained in the cubic inch.
Thus the opinion of unextended points seeking to avoid infinite division, runs into it; just as its adversaries trying to escape from unextended points are forced to acknowledge their existence. The imagination loses itself and the understanding is confused.
168. The other objection is not less unanswerable. Suppose we have arrived at unextended points, how shall we reconstitute extension? The unextended has no dimensions; therefore, no matter how many unextended points we may take, we can never form extension with them. Let us imagine two points to be united, as neither of them alone occupies any place, neither will they both together. We cannot say that they penetrate each other; for penetration cannot exist without extension. We must admit that these parts being zero in the order of extension, their sum can never give extension, no matter how many of them we may add together.
169. It is certain that a sum of zeros can give only zero for the result, but mathematicians admit that there are certain expressions equal to zero, which multiplied by an infinite quantity will give a finite quantity for the product. 0 + 0 + 0 + 0 + N × 0 = 0; but if we take 0/M = 0, and multiply it by the expression M/0 = 0, we shall have (0/M) × (M/0) = (0 × M)/(M × 0) = 0/0 which is equal to any finite quantity, which we may express by A. This is shown by the principles of elementary algebra only; if we pass to the transcendental we have dz/dx = o/o = B; B expressing the differential coefficient which may be equal to a finite value. Can these mathematical doctrines serve to explain the generation of the extended from unextended points? I think not.
It is evident that, multiplication being only addition shortened, if an infinite addition of zeros can give only zero; multiplication can give no other result, although the other factor be infinite. Why then do mathematical results say the contrary? This contradiction is not true, but only apparent. In the multiplication of the infinitesimal by the infinite we may obtain a finite quantity for product, because the infinitesimal is not regarded as a true zero, but as a quantity less than all imaginable quantities, but still it is something. If this condition were wanting, all the operations would be absurd, because they would turn upon a pure nothing. Shall we therefore say that the equation, dz/dx = o/o, is only approximate? No; for it expresses the relation of the limit of the decrement, which is equal to B only when the differentials are equal to zero. But as geometricians only consider the limit in itself, they pass over all the intervals of the decrement, and place themselves at once at the point of true exactness. Why then operate on these quantities? Because the operations are a sort of algebraic language, and mark the course that has been followed in the calculations, and recall the connection of the limit with the quantity to which it refers.
170. Unity which is not number produces number; why then cannot points without extension produce extension? There is a great disparity between the two cases. The unextended, as such, involves only the negative idea of extension; but in unity, although number is denied, this negation does not constitute its nature. No one ever defined unity to be the negation of number, yet we always define the unextended to be that which has no extension. Unity is any being taken in general, without considering its divisibility; number is a collection of unities; therefore the idea of number involves the idea of unity, of an undivided being, number being nothing more than the repetition of this unity. It belongs to the essence of all number that it can be resolved into unity; it contains unity in a determinate manner. But the extended can not be resolved into the unextended, unless by proceeding ad infinitum, or else by some process of decomposition which we know nothing of.
A CONJECTURE ON THE TRANSCENDENTAL NOTION OF EXTENSION.
171. The arguments for or against unextended points, for or against the infinite divisibility of matter seem equally conclusive. The understanding is afraid that it has met with contradictory demonstrations; it thinks it discovers absurdities in infinite divisibility, and absurdities in limiting it; absurdities in denying unextended points, and absurdities in admitting them. It is invincible attacking an opinion, but its strength is turned into weakness as soon as it attempts to establish or defend any thing of its own. Yet reason can never contradict itself; two contradictory demonstrations would be the contradiction of reason, and would produce its ruin; the contradiction can, therefore, only be apparent. But who shall flatter himself that he can untie the knot? Excessive confidence on this point is a sure proof that one has not understood the true state of the question, and such vanity would be punished by the conviction of ignorance. With all these reserves I now proceed to make a few observations on this mysterious subject.
172. I am inclined to believe that in all investigations on the first elements of matter, there is an error which renders any result impossible. You wish to know whether extension may be produced from unextended points, and the method which you employ consists in imagining them already approached, and then trying to see if any part of space can be filled by them. This seems to me like trying to make a denial correspond to an affirmation. The unextended point represents nothing determinate to us except the denial of extension; when, therefore, we ask if this point joined with others like it can occupy space, we ask if the unextended can be extended. Our imagination makes us presuppose extension in the very act in which we wish to examine its primitive generation. Space, such as we conceive it, is a true extension; and, as has been shown, is the idea of extension in general; to imagine, therefore, that the unextended can fill space, is to change non-extension into extension. It is true that this is precisely what is required, and in this consists the whole difficulty; but the error is in attempting to solve it by a juxtaposition which makes these points both unextended and extended, an evident contradiction.
173. In order to know how extension is generated, it would be necessary to free ourselves from all sensible representations, and from all ideas which are in the least degree affected by the phenomenon, and to contemplate it with an eye as simple, a look as penetrating, as that of a pure spirit. It would be necessary to take from all geometrical ideas all phenomenal forms, all representations of the imagination, and present them to the imagination purified from all mixture with the sensible order. It would be necessary to know how far extension, real continuity, agrees with the phenomenal. It would, in fine, be necessary to eliminate from the object perceived, all that relates to the subject which perceives it.
174. In extension, as we have already seen, there are two things to be considered; multiplicity, and continuity. As to the first, there is no objection to supposing that it may be the result of unextended points, since number results from various units whether they are simple or composite. But the difficulty is with regard to continuity, which sensible intuition clearly presents to us as the basis of the representations of the imagination, but the nature of which is a puzzle to the understanding. It may perhaps be said that continuity, abstracted from the sensible representation, and considered only in the transcendental order, is, in its reality and as it appears to a pure spirit, nothing more than the constant relation of many beings, which are of a nature to produce in a sensitive being the phenomenon of representation, and to be perceived in the intuition which we call the representation of space.
According to this hypothesis extension in the external world is real, not only as a principle of causality of our impressions, but also as an object subject to the necessary relations which we conceive.
175. But, then, it will be asked, is the external world such as we imagine it? To this we must answer, in accordance with what we have said when treating of sensations, that it is necessary to take from sensations all that is subjective, and which by an innocent illustration we look upon as objective; we may then say that extension really exists outside of us and independent of our sensations; considered in itself, it exists free from all sensible representation, and in the same manner in which a pure spirit may perceive it.
176. We see no objection which can reasonably be made to this theory which affirms the reality of the corporeal world, at the same time that it settles the difficulties of idealism. To give my opinion in a few words, I say: That extension in itself, exists such as God knows it, and in the cognition of God there is no mixture of any of the sensible representations which always accompany man's perception. That which is positive in extension is multiplicity, together with a certain constant order; continuity is nothing more than this constant order, in so far as sensibly represented in us, it is a purely subjective phenomenon which does not at all affect the reality.
177. We may even assign a reason why sensible intuition has been given to us. Our soul is united to an organized body,—that is to say, a collection of beings bound together by constant relation to each other and to the other bodies of the universe. In order that the harmony might not be interrupted, and that the soul which presides over this organization might rightly exercise its functions, there was need of a continued representation of this collection of the relations of our own and other bodies. This representation must be simultaneous and independent of intellectual combinations; for otherwise the animal faculties could not be exercised with the promptness and perseverance which the satisfaction of the necessities of life demands. Therefore it is that all sensible beings, even those which have not reason, have been endowed with this intuition of extension or space: which is like an unlimited field on which the different parts of the universe are represented.
HARMONY OF THE REAL, PHENOMENAL, AND IDEAL ORDERS.
178. We may consider two natures in the external world, the one real, the other phenomenal; the first is particular and absolute, the second is relative to the being which perceives the phenomenon; by the first the world is, by the second it appears. A pure intellectual being knows the world as it is; a sensitive being experiences it as it appears. We can discover this duality in ourselves; in so far as we are sensitive beings, we experience the phenomenon, but in so far as intelligent, although we do not know the reality, we attempt to reach it by reasoning and conjecture.
179. The external world in its real nature, abstracted from the phenomenal, is not an illusion. Its existence is known to us not by phenomena only, but by principles of pure intelligence which are superior to all that is individual and contingent. These principles, based on the data of experience,—that is, on sensations the existence of which we know from consciousness, assure us that the objectiveness of sensations, or the reality of the external world, is a truth.
180. This distinction between the essential and the accidental, and between the absolute and the relative, was admitted in the schools. Extension was considered not as the essence, but as an accident of bodies; the relations of bodies to our senses are not founded immediately on their essence, but on their accidents. Matter and substantial form united constitute the essence of bodies; the matter receiving the form, and the form actuating the matter. Neither the matter nor the substantial form can be immediately perceived by the senses, because this perception requires the determination of figure and other accidents distinct from the essence of body.
Therefore the scholastics distinguished sensible objects into three classes; particular, common, and accidental, proprium, commune, et per accidens. The particular is that which appears immediately to the senses, and is only perceived by one of them, as color, sound, taste, and smell. The common is that which is perceived by more than one sense, as figure, which is the object of sight and of touch. The accidental is that which is not directly perceived by any of the senses, but is hidden under sensible qualities, by means of which it is discovered, as are substances. The sensible per accidens is connected with sensible qualities; but they do not present it to the understanding as an image presents the original, but as a sign the signified. Hence they did not consider the sensible per accidens as proceeding from the species and reducing the sensitive faculty to act: it was intelligible rather than sensible.
181. In the corporeal universe considered in its essence, there is no necessity of supposing any thing resembling the sensible representation, but we must suppose the object to correspond to the idea; for otherwise we should have to admit that geometrical truths may be contradicted by experience.
182. Although extension is an order of beings of which we cannot form a perfect conception, because we cannot purify our ideas from all sensible form, still this order must correspond to our ideas, and even to our sensible representations, so far as is necessary to prove the truth of the ideas.
It is evident that although the phenomenal order is distinct from the real, it depends on it, and is connected with it by constant laws. If we suppose that there is no parallel between the reality and the phenomenon, and that the reality has not all the conditions necessary to satisfy the demands of the phenomenon, there can be no reason why the phenomena should be subject to constant laws, and why experience should not suffer continual confusion. Without a fixed and constant correspondence between the reality and the appearance, the world becomes a chaos to us, and all regular and constant experience becomes impossible.
183. Let us examine this at greater length. One of the elementary propositions of geometry says: "When two straight lines intersect each other, the opposite or vertical angles, which they form, are equal." In order to demonstrate this, I must have the internal intuition of two lines intersecting each other. But the geometrical proposition is not confined to any particular intuition, but embraces all that can be imagined, without any limit to their number, or any determination as to the measure of the angles, the length of the lines, or their position in space.
Here the pure idea extends to an infinity of cases, whereas the sensible intuition represents them only one at a time, and isolated if represented successively. The understanding is not limited to the affirmation of this relation between the ideas, but applies it to the reality, and says: Whenever the conditions of this ideal order are realized, that which I see in my ideas is true in reality, and the relation expressed will be more or less exact in proportion to the exactness of the realization of the conditions; the more delicate the real lines are, that is, the more they approach the condition of right lines, the nearer will the relation of the two angles approach to perfect equality. This conviction is founded on the principle of contradiction, which would be false if the proposition were not true; and it is confirmed by experience, so far as it touches the conditions of the ideal order.
184. What is there in reality which corresponds to this proposition? An existing or real line is an order of beings; two lines which intersect each other are two orders of beings with a determinate relation; the angle is the result of this relation, or, rather, it is the relation itself; the equality of the opposite angle is the correspondence of these relations in the ratio of equality by the continuation of the same order in another sense. These relations between the orders and the beings, and the correspondence of these orders to each other, is what corresponds in reality to the pure geometrical idea, or to the idea separated from all sensible representation. Since the relations of the idea have their corresponding objects in the relations of the reality, geometry exists not only in the ideal order, but also in the real. Since the phenomenon or sensible representation is subject to the same conditions as the idea, because the order of phenomena presents certain relations of the same nature as the relations of the idea and the fact; the idea, the phenomenon, and the reality agree, and it is explained why the intellectual order is confirmed by experience, and experience receives with confidence the direction it gives.
185. This harmony must have a cause; we must look for a principle which is the sufficient reason of this wonderful agreement between things so distinct. Here new problems arise which overwhelm the understanding, but at the same time expand and invigorate it by the grandeur of the spectacle presented to its view, and the immensity of the field opened to its investigations.
CHARACTER OF THE RELATIONS OF THE REAL ORDER TO THE PHENOMENAL.
186. Is the agreement of the idea, the phenomenon, and the reality necessary, is it founded on the essence of things, or has it been freely established by the will of the Creator?
If the world had no other reality than that expressed by the sensible representation, if the appearances were an exact copy of the essence of things, we should have to say that this agreement is unalterable, that things are what they appear, and that if we suppose them to exist, it is absolutely necessary that they should be just what they appear; for nothing can be in contradiction with its constitutive notion. That which now is extended, would be necessarily extended, and could not but be extended in the same manner in which it appears to us, and under the same conditions; the relation of bodies to each other would be necessarily subject to the same phenomenal laws, and all which does not come under this order would be a contradiction, and beyond the limit of omnipotence.
187. Bodies are presented to us in the sensible intuition with a determinate magnitude, and in a certain fixed relation which we calculate by comparison with an immovable extension, such as we imagine space. By magnitude, bodies occupy a certain space, determinate, though changeable by motion; by the relation of magnitudes they occupy a greater or smaller place, and mutually exclude each other; this exclusion is called impenetrability. The question to be examined here is, whether the determination of magnitudes, and their relation in respect to the occupation of place, are things absolutely necessary, so that their alteration involves a contradiction, or not. I answer that they are not.
188. Relation to place considered as a portion of pure space, means nothing; for I have already shown that this space is only an abstraction of our understanding, and that in itself it has no reality,—it is nothing. Therefore the relation to it must be nothing also, because the relation is destroyed if one of the terms is nothing. Therefore, the relations of bodies to place can only be the relations of bodies to one another.
189. This is the principal thing to be noticed in this question. The understanding gets confused when it begins by supposing space an absolute nature with necessary relation to all bodies. We must remember the doctrine of the chapters,[53] where we explained how the idea of space is generated in us, what object corresponds to this idea in reality, and how; and we shall easily perceive that the absolute and essential relations which we think we discover between bodies and a vacant and real capacity, are illusions of our imagination, in consequence of our not sufficiently purifying the ideal order by separating from it all sensible impressions. We cannot understand so much as the meaning of these questions, if we do not make an attempt at this separation as far as is possible to our nature. If this is done, then the questions proposed in the following chapters will appear very philosophical, and their solution will seem probable, if not true; but they must seem absurd, if we confound the pure intellectual order with the sensible. We cannot admit the idealism which destroys the real world; but the empiricism which annihilates the ideal order, is equally objectionable. If we cannot rise above the sensible representations, let us renounce philosophy, give up thinking, and confine ourselves to sensation.
WHETHER EVERY THING MUST BE IN SOME PLACE.
190. Is it necessary that whatever exists should be in some place? This question may seem strange, but it is profoundly philosophical. To be is not the same as to be in a place. To be, whether taken substantively as signifying to exist, or copulatively, as expressing the relation of the predicate to the subject, does not involve the idea of being in a place. The relation of an object to place is not necessary to it; for it is not contained in the notion of object. It is something added to the object, whether it is given to the object with more or less foundation by ourselves, or the object has it in reality by communication from some other.
The imagination can represent nothing which does not occupy a place, but the understanding may conceive things that are not situated in any place. When we reflect on the essence of objects, what position does our mind give them? The intellectual act is always accompanied by sensible representations, which sometimes assist it, and sometimes embarrass and confuse it; but in either case the act of the understanding is always distinct from these representations.
191. There is no reason for saying that every thing must occupy a place. The imagination cannot see how any thing can exist otherwise, but the understanding finds no absurdity in it, and it is in accordance with the principles of philosophy. If place considered in itself is only a part of space terminated by a surface, and space abstracted from bodies is nothing, the relation to place or to points in space must be nothing. We must have bodies in order to have a term of the relation; therefore, if we suppose a being which has no relation to bodies, it is not necessary that it should be in any place.
192. The relation of a being to bodies may be of three kinds: that of commensuration, as is the relation of lines, surfaces, and solids to each other; that of generation, as we conceive the line generated by the point; and that of action in general, as we conceive the relation of pure spirits to matter. The first cannot exist if the object has no dimensions; for then it cannot be measured; the second can exist only in unextended or infinitesimal points, from which extension is generated; therefore these two relations can only exist between bodies, or their generative elements. Therefore, nothing which is not a body or an element of body, can occupy place under either of these aspects. As to the third relation, that of action of a cause upon a body, it may be found in all agents capable of acting upon matter; but it is evident that the position which results from this, is something very different from that which we conceive in bodies or their elements; it is something of a wholly distinct order, and belongs rather to the pure idea of causality than to the intuition of space.
193. We can conceive a being which is not a body, nor an element of body, and which does not exercise any action on bodies; in this case, this being has none of the three relations of which we have spoken, consequently it is not in any place, and to say that it is here, or that it is there, that it is near or distant, would be using words without meaning.
194. Viewed from the point of this doctrine, the following questions are easy to answer:
Where must a pure spirit be which has no relation of causality nor influence of any kind upon the corporeal world? Nowhere. The answer will not seem strange to one who understands that the question is absurd. In the case supposed, there is no where, for this involves a relation and there are no relations here.
Where would the pure spirits be if the world did not exist? Nowhere, unless we have a mind to say they would be in themselves. But, the word to be does not mean the position of which we are speaking here, but only the existence of the spirit, or its identity with itself.
Where was God before the world was created? He was, but he was not in any place; for he has no parts.
195. I wish here to expose an error of Kant. This philosopher believed that space was conceived by us as a condition of all existence in general, and on this he founded one of his arguments that space was a purely subjective form. In the second edition of his Critic of pure Reason, explaining the subjectiveness of space, he seems to hold, that we do not even conceive things in the pure intellectual order, without referring them to space. He observes that in natural theology, when treating of things which cannot be the object of intuition either for us or for themselves, we are very careful not to attribute to this intuition or manner of perception time and space, which are the conditions of human intuition. "But," he adds, "by what right do we proceed thus, when time and space have already been established as the forms of things in themselves, and conditions of their existence a prior, subsisting still after all else has been annihilated by thought? As conditions of all existence in general, they must be the conditions of the existence of God. If we do not make space and time the objective forms of all things, it only remains for us to make them the subjective forms of our mode of intuition, as well internal as external." Kant is right in saying that space and time ought not to be considered as real forms, not susceptible of annihilation, and therefore necessary and eternal; but I do not see the necessity of the disjunctive by which he asserts that if we do not make space and time the objective forms of all things, we must make them the subjective forms, and that, otherwise, we should make space and time conditions of the existence of God.
196. We regard space as an actual condition of things, which occupy place, but not of all things. We conceive existence in pure spirits without the necessity of any relation to place, and, consequently, independent of all position in space.
On this point, as on all relating to the pure intellectual order, we find in the theologians doctrines which are highly important, and deserve to be consulted by all who wish to go deeply into philosophical questions. The author of the Critic of Pure Reason would have found there some observations which would have cleared up the difficulties which embarrassed him. He would have found how incorrect it is to say that space is a condition of the existence of all things, in the beautiful as well as profound theory by which many of the scholastics explain the presence of God in the corporeal world, and the presence of the angels in different places, their motion from one point to another without passing through the intermediate points, and the manner in which the soul is wholly in the whole body and in every part of the body. In these works, unfortunately so little consulted, the German philosopher would have learned that the presence of a spirit in a place is something different from the presence of a body, and has no relation to the intuition of space, whether regarded as the basis of sensible representations or as a geometrical idea.
197. St. Thomas[54] asks if God is in all things, and answers that he is. In proving this assertion he does not consider the necessity of every thing being in some place, but on the contrary seems rather to forget the idea of space, and regards only causality.
"As God," he says, "is being itself by his essence, created being must be his effect, as to burn is the effect of fire. But God causes this effect in things not only when they begin to be, but as long as they are preserved in being; thus the light is caused in the air by the sun as long as air remains illuminated. As long therefore as things retain their being, God is necessarily present to them, according to the manner in which they have their being. But being is that which is most internal, and most closely inherent in every thing because it is the form of all that is in it, God therefore is in all things internally."
To be situated in space is to be contained in it; so, at least, we conceive whatever we consider situated in space. St. Thomas rejects this meaning as applied to spiritual beings, and says, that although corporeal beings are contained in things, spiritual beings on the contrary contain the things in which they are.
In the second article he asks whether God is in all places (ubique); and, he says, that as God is in all things, giving them being and the power of acting, so he is in all places giving them being and capacity (virtutem locativam). He states as an objection that incorporeal things are not in any place, and answers in the following philosophical words: "Incorporeal things are not in place by the contact of measurable quantity, like bodies; but by the contact of activity (virtutis)." Then explaining how the indivisible can be in different places, he says: "The indivisible is of two kinds; first, it is the limit of the continued, as a point in permanent things, and a moment in successive things. The indivisible in permanent things, cannot be in different parts of place or in different places, because it has a determinate position; and in the same manner the indivisible in action or in motion cannot be in different parts of time, because it has a determinate order in action or motion. But there is another indivisible which is beyond all kind of continuation, and in this sense incorporeal substances, as God, the angels, and the soul, are called indivisible. The indivisible in this manner, is not applied to the continued as any thing which belongs to it, but only as reaching it by its activity; therefore as its activity may extend to one or many, to the small or to the great, it may be in one place or in many places, in a small place or in a great place."
What can be clearer, relatively to the intuition of space, than that when any thing is in a place it cannot be out of that place? But the holy Doctor, rising above sensible representations, boldly maintains that God may be whole in the whole, and in every part of the whole, as the soul is whole in every part of the body. And why? Because what is called totality in corporeal things relates to quantity, but the totality of incorporeal things relates to essence, and cannot be measured by quantity, and is not confined to any place.
In the Treatise on the Angels,[55] he says that the expression to be in place is used equivocally (oequivoce),[56] when applied to angels and bodies. Bodies are in place by the contact of measurable quantity, but angels by virtual quantity, that is to say, by the action which they may exercise upon a body. We cannot, therefore, say that an angel has a position in the continued (quod habeat situm in continuo). In the Treatise on the Soul[57] he maintains that the soul is whole in every part of the body. He distinguishes the totality of essence from the totality of quantity, and makes use of an argument similar to that which he used with respect to the angels. The more we reflect on this doctrine the more profound it appears; those who have made light of it, have shown that they never penetrated beyond the surface in all that concerns the relations of spiritual to corporeal things. It is generally dangerous to laugh at opinions held by great men; for if they are not certain, they have, at least, powerful arguments in their favor. Nothing is more contrary to sensible representations than the possibility of any thing being in different places at the same time, but we shall find nothing more in conformity with the principles of sound philosophy than this possibility, after we have profoundly analyzed the relations of extension with unextended things, and discovered the difference between the position of quantity and the position of causality.
198. From these doctrines it may be concluded, that to be in space is not a general condition of all existences, even according to the manner of existences; for we can conceive existences without relation to any place. Many have confounded imagination with understanding on this point, and believed that what is impossible for the former is equally so for the latter. It is certain that we can imagine nothing without referring it to points of space, and even in purely intellectual objects there is always a sensible representation, but the understanding regards these representations as false and does not conform to them. As imagination is a sort of continuation of sensibility, or an internal sense, and the basis of sensations is extension; it is impossible for us to exercise this internal sense, without the presence of space, which, as we have shown, is only the idea of extension in general. Position in space is consequently a general condition of all things, as perceived by the senses, but not as perceived by the intellect.
CONTINGENCY OF CORPOREAL RELATIONS.
199. Position in place is the relation of a body to other bodies. Is this relation necessary? I distinguish: conditionally, yes; essentially, no. God has established this relation, and therefore it is necessary; but God might have ordered it otherwise, and can even now change it, without varying the essence of things.
If we admit, as we must, a correspondence between the subjective and the objective, or between the appearance and the reality, we cannot deny that the relations of bodies are constant, and this constancy must proceed from some necessity. But that the existing order is subject to fixed laws, does not prove that these laws have their root in the essence of things, in such a manner that, supposing the existence of objects, their relations could not have been very different from what they actually are.
200. In order to assert that the existing order of the universe is intrinsically necessary, we must know the essence of things; but this is not possible for us, because objects are not immediately present to our understanding, and we see them only under one aspect, that which places them in relation with our sensitive faculties. The best proof of our ignorance of the essence of bodies is the great division of opinion on this subject. Some maintain that the essence of bodies is extension or dimensions; and others that extension is merely an accident, not only distinct, but even separable from corporeal substance.
The great obscurity in which the investigation of the constitutive elements of bodies is involved, proves that their essence is unknown to us, and that we know nothing of them except their relation to our sensibility.
201. It is not necessary that the aspect under which being is presented to us should contain its whole nature. To say that bodies contain nothing besides what we perceive in them, is to make our faculties the type of things in themselves, a ridiculous pretension in a being which finds its activity limited at every step and is almost always passive in its relations to bodies, and which, in order to exercise its faculties externally, is forced to submit to the laws of the external world, or else to encounter obstacles which are absolutely insurmountable.
If we are ignorant of the essence of bodies we can have no certain knowledge of what is intrinsically necessary in them; with the exception of composition, which even the sensible order presents to us, and which we cannot take from bodies without seeming to run into a contradiction. Simplicity and composition in the same object are incompatible and contradictory.
202. Hence, in all that pertains to the relations of bodies we must abstain from judging absolutely, and speak only conditionally. We may say: "This happens now; this must happen according to the order now established;" but we cannot say: "This happens, and it is absolutely necessary that it should happen." The transition from the first proposition to the second, implies the knowledge of what no man can know, that the aspect under which the external world is presented to us is the image of its essence.
203. One of the greatest errors of Descartes was, that he did not make sufficient account of this difference: he placed the essence of bodies in dimensions, which is to confound the real world with the phenomenal, and to take one aspect of things for their nature. It is true that whatever affects us has extension, and that extension is the basis of the relations of our sensibility with the external world; but it does not follow that the essence of this world is nothing more than what is presented to us in its dimensions. We might as well say that the essence of man is the lines which mark his form.
204. The different aspects under which the external world is presented to our senses, ought to prevent us from confounding what is absolute in it with what is relative. A man deprived of one sense would not reason well if he should conclude that the world has no other aspects than those which he perceives. What do we know of the manner in which objects are presented to pure spirits, or of the many other phases which they might offer to our sensibility?
Let us then leave nature its secrets; and let us not limit omnipotence by saying, that the order of the world is so intrinsically necessary that its present relations cannot be changed without contradiction. When we examine the possibility of a new order of relations between the beings which we call bodies, let us not settle the question too quickly, taking for our only type of the possible the vain impotence of our faculties. What should we think of a blind man who should laugh at those who see, if he heard them speak of the relations of objects as seen? Yet we present the same spectacle to a pure spirit when we talk of the impossibility of an order different from what our senses perceive.
205. The principles of physical science are in great part conditional; for they are true only on the supposition of the reality of the data furnished by experience. If position and relation to place are not essential to bodies, distance and motion are conditional facts true only under certain suppositions. All the natural sciences, as we have seen, are reduced to the calculation of extension and motion; they do not reach the essence of things, but are limited to one aspect, that presented by experience. In these sciences there is consequently nothing strictly absolute; in this respect, they are far below metaphysics, which knows things that are absolutely necessary. A further explanation of this doctrine is required, and will be given in the following chapters.
SOLUTION OF TWO DIFFICULTIES.
206. Must not the theory which supposes the relations of bodies to be variable, put an end to all the natural sciences? Can there be science without a necessary object? and can there be a necessity which is compatible with variability?
The natural sciences have two parts: one physical, and the other geometrical. The first supposes the data furnished by experience; the second forms its calculations relative to these data. Change the relations of external beings, and the data will be different, you will have a new experience producing a new physical science: the calculation will be the same, only new results will be obtained from the new data. The difficulty thus disappears. All the physical sciences are based on observation, all their combinations are made from data furnished by experience; therefore the physical sciences are not wholly absolute, but they have a part which is conditional. The theory of universal gravitation is developed as a body of geometrical science, but it starts from the data furnished by experience. Destroy these data and from a body of physical science it becomes a body of pure geometry. In mechanics, the problems of the composition and decomposition of forces have a physical signification, inasmuch as they presuppose the data of experience; suppress these data and there remains only a composition of lines which mean nothing when we call them forces. Therefore mechanics is only a system of geometrical applications.
207. Here another difficulty arises which is apparently more serious than the other. If the relations of bodies are not essential, but are subject to variation; if our calculations upon them are not founded upon data which are intrinsically necessary, it seems that geometry is destroyed, or limited in such a way to the ideal order, that it cannot be sure that on descending to the field of experience it will not find that false which it regarded as true, and that true which it reputed false. For example, the distances of bodies are calculated by considerations of geometry: if the relation of distance is variable, and a body may be in many places at the same time, geometry turns out false. Such a supposition is no more than the application of the foregoing theory; for, if the relations are variable, this variation may affect distance, which is only a relation. I said this difficulty was more serious than the other, because it leaves the field of experience, and attacks the order of our ideas, an order which we must hold to be indestructible, unless we wish to give up our reason. What would become of our reason if geometry were contradicted by the reality? what would become of an order of ideas in contradiction to facts? Still I repeat that the force of this difficulty is only apparent, and if analyzed will be found of no more weight than the objection which we have already answered.
A body which is a hundred yards distant from another, cannot be only one yard distant; geometry would be opposed to it. But if the relations of bodies are variable this proposition can mean nothing with respect to the reality. Therefore geometry is false. I admit the consequence; but the principle on which it is based involves a supposition contrary to my theory. If you alter or destroy the relations of bodies, you destroy distance, which is a relation, consequently you cannot have a distance of one hundred yards, nor of one yard, nor any distance at all, and if there is no distance there is no contradiction. If, then, you ask how great is the distance between them, your question is absurd; for it supposes a distance, whereas there is no distance at all.
208. This solution rests on a fundamental principle which we ought never to lose sight of. Geometrical truth is true in reality when the conditions of geometry exist in reality; if these conditions do not exist, there is no real geometry. There is nothing strange in this: in fact, the same occurs in the purely ideal order; even there, geometry rests on certain postulates, without which it is impossible. Two triangles with the same base and altitude are equivalent to each other. This is a true proposition, but only on the supposition that there are those orders of points which are called lines, and that the lines form angles, and are united at three points. If these relations are not presupposed, the geometrical theorem has no meaning.
209. Geometry in itself, or in the purely ideal order, is founded on the principle of contradiction. The truth of this principle being absolutely necessary, that of geometry is equally so. But the principle of contradiction, like all purely ideal principles, abstracts existence, and is applied to nothing in practice, unless we suppose some fact to support it. Yes and no at the same time are impossible; but the principle determines nothing for or against either of the extremes. It only affirms that one excludes the other; if we suppose yes, it excludes no, and if we suppose no, it excludes yes; that is to say, it always needs a condition, a datum which only experience can furnish.
It is the same with geometry. All its theorems and problems refer to the ideal field within us, where there are certain conditions which lead to certain results, by virtue of the principle of contradiction: whenever the conditions exist, the results are true; but if the former fail the latter are false. Ideal sciences consider the connection of conclusions with principles in the order of possibility, but take no note of facts. If the connection is admitted the science is true.
CHAPTER XXX.
PASSIVE SENSIBILITY.
210. Active sensibility, or the faculty of perceiving by the senses, has been a subject of great dispute among philosophers. Passive sensibility, or the capacity of an object to be perceived, is a question of not less interest.
Can every thing which exists be perceived by the senses?
Before answering this question, let us remember that to be perceived by the senses may be understood in two ways: First, it may mean, to cause an impression in a sensitive being; and secondly, to be the immediate object of sensible intuition. The first is true of every being capable of producing the impression; the second is true only of those beings which unite the conditions which the intuition supposes.
211. To produce an impression is simply to cause; and causality is not repugnant to simple beings. There is, therefore, no absurdity in supposing that pure spirits can produce sensible impressions: were it otherwise God could not act upon our soul, causing an impression in it, without the mediation of bodies. This causality cannot be called passive sensibility; the being which has it is not perceived by the senses. The relation of the sensation to the being which produces it would be only that of an effect to its cause.
212. To be the immediate object of sensible intuition, is to be presented to this intuition as an original to the copy. Under this view, only the extended can be perceived by the senses; that is to say, multiplicity combined with continuity is an absolutely necessary condition of our sensitive faculties in relation to external objects.
213. In this manner, it is a manifest contradiction to say that the simple can be sensible. Instinct and reason force us to suppose a real object of sensible intuition. This intuition is referred to the object as to something essentially composite, belonging to the order which we call continuity. If we make this object simple, it ceases to be sensible; and we both affirm and deny its sensible objectiveness. It is a contradiction to suppose a faculty in act, and at the same time to deprive it of the conditions to which its action is necessarily subject.
214. It may be said, that there is no necessity of transferring to the object the conditions of the subject, and therefore a simple object may be presented to the senses. But this is to elude the question at issue. For, either the sensible intuition is referred to the object, or it is not; if it is, the object cannot be simple; if it is not, we fall into idealism, which we have so often combated in the course of this work.
215. If you answer, that our soul, which is simple, has the representation of the composite, I reply, that the objective representation is not the same thing as the subjective perception of the composite; nor the presentation of the object as multiple the same thing as the perception of the multiple. Our soul perceives the multiple, and for this reason must itself be one, or it could not perceive that which is multiple. So much for the subjective; as to the objective, we must remark, that our sensible representations do not always proceed from real objects; but they always refer to objects which are at least possible; that is to say, the intuition is never entirely void; and when it has no object in reality, it finds one in possibility.
216. The external world, as involving multiplicity, or a collection of many beings, and as susceptible of this order which we call continuity, may be the object of sensible intuition, as we experience in reality. But this passive sensibility is not intrinsically necessary to it: I mean that God could so have disposed the collection of beings constituting the universe as not to be sensible. This is based on the variability of the relations of bodies; for, it is evident that if these relations did not exist, or were not subject to the conditions required by sensible representation, this representation would be impossible, and the world not sensible.
217. Experience confirms this conclusion which is obtained from transcendental philosophy. We find a slight alteration continually changing sensible bodies into insensible, and making sensible those that were insensible. The condensation of the air makes it visible; and its rarefaction invisible. A liquid body is tangible, but it ceases to be so when converted into vapor. The same variety which is caused by the alteration of the object may also proceed from a modification of the organ. A proof of this is found in what happens to the sight when aided by certain instruments. If, then, these transitions from sensible to insensible are now possible, without infringement of the fundamental laws of the relations of bodies, why could there not be a radical change in these relations which should make bodies wholly insensible?
218. By the variation of the relations of the beings which compose the corporeal universe, the sensible might become insensible; and, on the other hand, there are many insensible beings which by a different arrangement might be made sensible. To a certain extent we have something besides idle conjectures on this matter: facts speak; in proportion as the field of experience is expanded, new phenomena are discovered; thus magnetic attraction, electricity, and galvanism, have been added to experimental science.
In these phenomena there are agents at work which are not perceptible to the senses; why may they not be disposed in such way as to be perceived like other bodies? Where is the limit of these agents? We know not; but reasoning from analogy we may believe that there are many others whose existence is not known to us.
The perfection of a sensitive organ by means of instruments, is an arrangement by which we vary the ordinary system of the relations of our body to those around us. This perfectibility is indefinite, and the farther we advance, the greater do we find its extension. It is therefore probable, that in the universe there are many beings which are imperceptible to our senses, but which a modification of our organs, or a change of some of the laws of nature would render sensible. What a vast field of bold conjectures and sublime meditations!
POSSIBILITY OF A GREATER SPHERE IN ACTIVE SENSIBILITY.
219. Having treated of passive sensibility in the order of possibles, a similar question naturally arises with respect to the active sensibility of beings subject to different conditions from those of our soul while united to the body.
I speak only of possibility, for, limited to what experience teaches us, we know not what may be in the sphere of beings with which we have no communication. Whatever we know of them is by divine revelation; and the object of revelation is not to teach us philosophy, but virtue.
220. To examine how far active sensibility is possible in an order different from that of our experience, not only raises curious and interesting questions, but it also gives an opportunity to explain by new reflections, the nature of this phenomenon in its relations to bodily organization. There is a special reason why we should seek to investigate this question. It consists in the interest inspired by every thing which relates to a state of existence into which we must soon enter. Short are the moments allotted to man to dwell in this world. We all hasten with astonishing rapidity to the final instant when the fragile organization which envelops our mortal spirit shall dissolve, and crumble into dust,—when the being which feels, thinks, and wills within us, shall pass to a new state, and be separated from the bodily organization. What will then be its faculties? This is a question which we cannot be indifferent to; for it concerns us, and the state of our future existence.
221. If we are asked whether a pure spirit is capable of sensible perception, we must answer negatively; because we are treating of active sensibility, which is not possible without the mediation of a body. I believe that some explanation of the question may be given. But we must first of all determine the meaning of the words. Sometimes we understand by a pure spirit, one which is not united to a body; but, more strictly speaking, the term is confined to a spirit which neither is united to a body, nor destined to this union. Thus the human soul is a spirit, but not a pure spirit; for it is either actually united to a body or is destined to this union.
It might appear at first sight that as we are limiting ourselves to the sphere of possibility, there is no difference between the two acceptations of the term; for, if it is not essentially repugnant to the soul when separated from the body, to have sensible intuition, it will not be so to other spirits. The parity is not certain; still, for the present, when speaking of pure spirits in general, I shall include souls separated from bodies.
222. What do we understand by sensing? This word may mean two things. It may mean the receiving of an impression by means of bodily organs; or it may mean simply the experiencing of the impression, independently of the bodily organ. For example: I see an object. Here is the affection called seeing, and the mechanism by which the object transmits light to the retina, and a certain impression to the brain. These are two very different things; the first is a fact of my mind; the second a modification of my body.
223. If by sensing is meant the receiving of the impression of a bodily organ, it is clear that a spirit which has no body cannot sense; but if by it is meant only the subjective affection abstracted from the medium by which it is produced or communicated, then the question is different, and the existence or non-existence of bodies cannot affect its answer either affirmatively or negatively.
224. The question then becomes this: Can a pure spirit have the various affections and representations which we call sensible?
Simplicity is not opposed to the sensitive faculty. Our soul senses, and still it is simple. The body aids it in the exercise of the sensitive faculties; but this aid is instrumental, not, however, in such a manner that the soul senses by the body, as an action is performed by means of the instrument. That which senses is the soul itself, and the instrumental action of the body consists in providing certain conditions from which sensation follows, by a physical or occasional influx. Therefore, the simplicity of a pure spirit is no argument against the sensitive faculties. Such an argument would prove too much; consequently, it proves nothing.
225. Hence there would be no intrinsical repugnance in God communicating to a pure spirit sensitive faculties; whether representative like those which place us in relation with the corporeal world, or purely subjective, like those of pleasure or pain.
226. Although in the present order these functions depend on certain conditions to which bodies are subject, considered in themselves, inasmuch as they are a modification of the soul, they have no essential relation to the corporeal world. It would therefore seem contrary to the principles of sound philosophy to say, that the soul separated from the body could not experience affections similar to those it has in this life. If this is not repugnant to the soul in its separate existence, why should it be so to other spirits?
The sensitive faculties are a sort of inferior order of perception. We see them in beings united to bodies, but they are not exercised immediately by a bodily organ. So far from contradicting simplicity, they require it; and therefore we have seen[58] that matter is incapable of sensation. Many grave philosophers are of opinion that the causality of bodies with respect to sensations, is only occasional. This opinion is founded on the difficulty of explaining how a composite being can produce affections of any kind in a simple being. Instead of a repugnance between simplicity and the sensitive faculties, there is, on the contrary, a necessary connection. No composite being can be sensitive.
227. Perhaps it may now be thought that there is no longer any doubt of the possibility of sensation independently of the bodily organs; and that to hold the contrary, it would be necessary to maintain that God can not produce immediately that which he produces by means of second causes. The observations which we have made may seem to have exhausted the matter, but if we reflect on it, we shall find that we have scarce entered on it.
It must not be forgotten that we are examining the possibility of sensitive faculties, in relation to one attribute only, that of simplicity. This greatly limits the question, as it leaves it to be solved under one aspect only. Simplicity is a negative property. When we say that any thing is simple, we deny that it has parts, but we affirm none of its properties; we say what it is not, not what it is. Therefore, in maintaining that sensitive faculties are not repugnant to a pure spirit, we ought to restrict the proposition; we should express our meaning more exactly, if instead of saying "sensitive faculties are not repugnant to a pure spirit," we should say, "sensitive faculties are not repugnant to the simplicity of a pure spirit."
228. This last observation seems to me to present the question in its true point of view. Any other expression of it seems only to confuse ideas and raise problems which we have not sufficient data to solve. In fact, how do we know but what the repugnance which does not exist between sensibility and simplicity, may exist between sensibility and some attribute which we know nothing about? This argument is not valid for the human soul, because we already know that the soul is capable of sensing; but it is valid for other spirits, whose essence is unknown to us, and the character of whose perceptive faculties experience has not discovered to us.
229. One of the distinctive marks of sensitive perception is the reference to individual objects, not in what concerns their essence, but inasmuch as they are arranged in a certain order, the variations of which do not affect their internal nature. Extension itself, which both instinct and reflection teach us to regard as objective, is rather a result of the relations of the beings which form the composite extended object, than those beings themselves. The sensitive faculties are the lowest grade in the order of perception. Their sole function is to make known to their possessor a certain arrangement of external objects, but they teach him nothing concerning the nature of those objects. Pure spirits are a grade higher in the scale of perceptive beings, and one of the characteristics of intelligence is, that it penetrates to the inward nature of things. Therefore it might easily happen that the sensible faculties are repugnant to intelligences of a higher order than ours, not by reason of their simplicity, but on account of the different manner of their perception.
230. Reasoning by analogy from what takes place within ourselves, we are confirmed in this opinion. Sensible representations are often powerful auxiliaries to purely intellectual perception; but they just as often embarrass and confuse it. In meditating on very abstract matters sensible representations are a hinderance to the understanding, from which we should be glad to free ourselves. Every one has experienced this to be so. They are like shadows which come between the eye of the intellect and the object: the necessity of continually removing them delays and weakens our perception. Thus, we propose, for example, to think of causality. No sensible representation should find place in this idea in the abstract, yet in spite of all our efforts the representation haunts us. At one time it is the word causality, written or spoken; at another, the image of a man doing something, or of any other agent. The sensible representation is always in our way, and we cannot free ourselves from its presence. The understanding is forced to repeat continually to itself, "This is not the idea of causality; it is only an image, a comparison, an expression;" in order to defend itself against illusions, which would make it confound the particular with the universal, the contingent with the necessary, the phenomenal with the real.
231. We must conclude from this that a repugnance of sensitive faculties to the nature of a pure spirit, might proceed from the character of its intelligence, which by reason of its perfection rejects the duality of perception which exists in us. The object of the understanding is the essence of the thing understood, quidditas, as the scholastics called it. Sensible representations tell us nothing of this essence. They offer only one aspect of things, and even this is limited to the perception of extension; for as regards the other sensations, they are a subjective fact which instinct and reason teach us to attribute to external causes, rather than a perception of the real disposition of things.
232. This suggests another observation which supports the conjecture that the elevation of intelligence above a certain degree makes it incompatible with sensitive faculties. Sensations would tell us nothing even of this aspect and disposition of things if they did not have extension for their basis. To what should we reduce the corporeal world if we supposed it unextended? Since extension, as we have shown,[59] although the basis of some sensations, is not the direct and immediate object of sensation; that which in the sensitive faculties makes us perceive something of the reality of objects, is not strictly sensible. Therefore, if it is the character of intellectual perception to know the reality of the object, the more elevated an intelligence is the farther it will be from sensation, and there may be a subject in which intellectual faculties are incompatible with sensitive faculties.
233. We shall better understand the force of this observation by casting a glance at the scale of beings, and noting the difference in them in proportion to their perfection. The isolation of a being is a mark of its imperfection. The lowest idea of an object is that which we form when we conceive it absolutely limited to existence, completely inert, without either internal or external activity. A stone has existence and a determinate form; it is what it was made, and nothing more; it preserves the form which was given to it, but it has no activity to communicate with other beings, no consciousness of what it is; in all its relations it is passive; it receives but cannot give.
234. In proportion as beings rise in the scale of perfection, this isolation ceases; active properties are combined with the passive; such we conceive to be the corporeal agents, which, although they do not reach the category of living beings, take an active part in the production of phenomena in the laboratory of nature. In these beings we find besides what they are, what they can do; their relations with other beings are many and varied; their existence is not confined to the circle of their own existence; but it expands and is communicated in some way to others.
235. In organized beings we find a more expansive nature. Their life is a continual expansion. The living being extends in a measure beyond the limits of its own existence; for it bears within it the germs of its reproduction. Its existence is not for itself alone, but for others also. It is only an imperceptible link in the great chain of nature; but the vibrations of this link are felt in the remotest confines of the universe.
236. Life is still more extended when it becomes sensation. The sensitive being contains in himself, as it were, the universe. By the consciousness of its affections, it places itself in new relations with all that acts upon it. Perception is immanent, that is to say, it remains in the subject, but with the subjective is combined the objective, by which the universe is reflected on a point. Being does not then exist in itself alone, it becomes in some manner other things. There is a profound truth in the expression of the scholastics: "That which knows is the thing known." There is a certain order in sensations; they are more perfect in proportion as they are less subjective; the most noble are those which place us in communication with objects considered in themselves,—those which are not limited to the experience of what the objects cause in us, but include the knowledge of what the objects are.
237. Extension is the basis of the objectiveness of sensations, but it is not the direct and immediate object of sensation. Although extension teaches us something of the reality of beings as regards a certain arrangement of them among themselves, it is not so much the object of a sensitive faculty as of intelligence. Here sensation ceases and science commences. Science is not satisfied with what the objects appear. It penetrates to the reality; the understanding does not stop with the subjective, but passes to the objective, and when it cannot reach the reality, it wanders in the regions of possibility.
238. Thus we see that the perfection of beings is in proportion to their expansion. Accordingly as they are more perfect, they go farther out of their own sphere, and exercise a more extended activity. Hence the highest degree of perception is the least subjective; the lowest is sensation, which is limited to the experience of the sentient subject. Intelligence which is the highest degree, abstracts experience, and gives its whole attention to reality, its proper object.
239. If we could know the intimate nature of pure spirits, perhaps we should find that the sensitive faculties are altogether incompatible with the elevation of their intelligence, and that the analogy founded on the nature of our perceptions has no value when applied to a more perfect order of intelligence. However this may be, we must admit that the question would have been solved in a very incomplete way, if we had limited it to the single aspect of simplicity. These observations on the nature of intelligence ought to make us very cautious in affirming to be possible, what we should perhaps see to be impossible, if our knowledge of the nature of things were greater.
240. So far we have spoken only of the intrinsical possibility; what shall we say of the reality? This is a question of fact which can only be solved on data which our experience is unable to furnish, as we are not in immediate communication either with souls separated from bodies, or with pure spirits.
241. If we wish to look for an argument to prove that pure spirits and souls after they are separated from bodies, have no sensitive faculties, we shall find it in the consideration of the end to which these faculties are destined, better than by attempting to discover the essence of things. The body, to which the soul is united in this life, is an organization subject to the general laws of the corporeal universe. In order that the soul may rightly exercise its functions, it must be in constant communication with its own body and the bodies around it; it must have sensible intuition of the relations of bodies; it must be notified by pain of any disorder which occurs in its body, and guided by the sentiment of pleasure as by an instinct which, directed and moderated by reason, may point out to it what is profitable or necessary. When the soul is no longer united to the body, there is no reason why it should have these affections, as it does not require to be directed in its acts. As this applies equally to pure spirits, we may form a conjecture as to the cause of the difference which there must be between the state of our soul in this life, and that of spiritual beings which are not united to bodies.
This argument, deduced from the final cause, is not to be considered as a proof; at best it is only a conjecture: for we do not know how far the soul in its separate existence, or pure spirits, may be in relation with bodies; and consequently, we do not know whether these sensible affections would be useful or necessary for ends of which we have no conception. And even supposing that neither the soul nor pure spirits have any relations with bodies, we are far from sure that sensible affections would be useless to them. On the contrary, so far as we can form an opinion on the subject, it seems that to take from the soul its imagination and sensation, would be to deprive it of two of its most beautiful faculties; for they not only assist the understanding, but are often a strong motive of its acts.
242. It is difficult for us to form an idea of pleasure or pain, without sensible affections. In the purely intellectual will, we conceive only willing and not willing, acts of a most simple relation, which do not have for us the same meaning as a pleasant or unpleasant affection. We often wish a thing in which we experience pain; and as often find pleasure in what we do not wish. Therefore to wish and not to wish do not imply pleasure and displeasure, but are independent of these affections and may exist in opposition to them.
243. It might be said that the cause of this discord is in the disagreement of the sensitive with the intellectual faculties. This is true, but it proves nothing against what I have been saying. The purely intellectual will, in opposition with the sensible affections, does not involve pleasure or exclude pain. The will triumphs, it is true, but it does so by virtue of its freedom. Its triumph is like that of a master obliged to exact obedience by severe punishment, who experiences pain at the very time when he is obtaining the execution of his commands. Who can tell, then, whether the will, after this life, will be accompanied by affections similar to those which it now has, but purified from the grossness of the body which weighs down the soul? I see no intrinsical impossibility in it. If questions of philosophy could be solved by sentiment, I should not hesitate to express my opinion that this fair and noble union of faculties which we call the heart, does not go down to the grave, but flies with the soul to the regions of immortality.
244. As to the imagination,—that mysterious faculty which not only gives life to the real world, but possesses an inexhaustible activity in creating new worlds of its own, displaying before the eyes of the soul rich and splendid panoramas; why should it desert the soul on its separation from the body? Why may not the harmony of nature be perceived in a similar manner hereafter? Let us not advance opinions on secrets of which we are ignorant, but, at the same time, let us beware of setting bounds to the omnipotence of God. Sound philosophy should not multiply opinions beyond measure; but neither should it circumscribe within the limits of human reason the sphere of possibility.
POSSIBILITY OF THE PENETRATION OF BODIES.
245. The more we meditate on the corporeal world, the more we discover the contingency of many of its relations, and the consequent necessity of recourse to a higher cause which has established them. Even those properties which seem most absolute cease to appear so when submitted to the examination of reason. What more necessary than impenetrability? Yet from the moment it is carefully analyzed, it becomes reduced to a fact of experience not founded on the nature of things, which consequently may exist or cease to exist without any contradiction.
246. Impenetrability is that property of bodies by which two or more cannot be in the same place at the same time. For those who do not make pure space a reality independent of bodies this definition has no meaning; for if place like pure space is nothing, to speak of the same place abstracted from bodies, is to speak of nothing. In that case, impenetrability can only be a certain relation either of bodies or of ideas.
247. Above all, we must distinguish the real order from the purely ideal. We may consider two kinds of impenetrability; physical impenetrability, and geometrical impenetrability. The physical is that which we see in nature; the geometrical that which is found in our ideas. Two balls of metal cannot be in the same place: this is physical impenetrability. The ideas of the two balls present two extensions which mutually exclude each other in the sensible representation: this is geometrical impenetrability. If we imagine two balls which perfectly coincide, they are no longer two, but only one; and if we imagine one ball to occupy a part of the other, we have a new figure, or, rather, one is considered as a portion of the other, and is consequently contained in the idea of the other, as a small ball inside of a larger ball. On either supposition the balls are regarded as penetrating each other in whole or in part; but by penetration is here meant only that there are certain parts in one, considered as pure space, which the other, also considered as pure space, occupies. Geometrical impenetrability exists only when the two objects are supposed to be separated, and only inasmuch as they are separated; in which case impenetrability is absolutely necessary, because penetration would be to confound what is by the supposition separated, and would imply separation and non-separation, which are contradictory. Therefore, geometrical impenetrability is no argument in favor of physical impenetrability; for the former exists only in case it is presupposed or required under pain of contradiction. The same would occur in reality; for if we suppose two bodies separated, they cannot be in the same place whilst they are separated, without a manifest contradiction. On this point, therefore, the ideal teaches us nothing as to the real.
248. Can penetration exist in reality? Can one ball of metal, for example, enter another ball of metal, as we make one geometrical ball enter another? We are not treating of the regular order of things which is repugnant to such suppositions, but of the essence of things. On this supposition, I maintain that there is no contradiction in making bodies penetrable, and that an analysis of this matter proves that the impenetrability of bodies is not essential.
We have seen that the idea of place as pure space is an abstraction. It is therefore an entirely imaginary supposition on which we give to every body a certain extension to fill a certain place, necessarily, and in such a manner that it is impossible for it to admit another body into the same place at the same time. The position of bodies in general is the sum of their relations; the particular extension of each body is only the sum of the relations of its parts among themselves, until we come by an infinite division to unextended or infinitesimal points.
The sum of the relations of indivisible or infinitesimal beings constitutes what we call extension and space, and all that is contained in the vast field of sensible representation. Who can assure us that these relations are not variable? Is our experience, perhaps, the limit of the nature of things? Evidently not. The universe was not planned after our experience, but our experience is obtained from the universe. To say that it contains, and can contain only what our experience sees in it, is to make the me the type of the universe; to affirm that its laws are derived from us, that they are emanations from our being. Foolish pride of an imperceptible atom, which appears for an instant on the great theatre of nature, and goes out like a spark of fire; foolish pride for a spirit which, despite its great idea of its own importance, feels that it is unable to withdraw itself from these laws and phenomena, which it pretends to consider as its own creation!
A TRIUMPH OF RELIGION IN THE FIELD OF PHILOSOPHY.
249. There are two things in extended objects: multiplicity and continuity. The first is absolutely necessary to extension; it supposes distinct parts, and that which is distinct cannot be identical without evident contradiction. The continuity represented in the sensible impression is not essential to extension, because it is only the result of a union of relations inseparable in the present order of sensibility, but not absolutely necessary in the order of reality. Transcendental philosophy rising above sensible representations, and leaving phenomena to enter on the contemplation of beings in themselves, nowhere discovers the necessity of these relations, and is obliged to consider them as simple facts which might cease to be without any contradiction. In this manner the correspondence of the phenomenon with the reality is saved, and the internal world harmonized with the external, but the subjective conditions of the former are not all transferred to the latter in such a way as to make what is necessary for our representations, absolutely necessary in itself.
250. Arrived at this point of transcendental philosophy, the mind beholds new worlds unfolded to its view. We rejoice to say that this discovers to us a new proof of the divinity of the Catholic religion, and teaches us to distrust that proud philosophy which finds a contradiction in every thing which it cannot understand.
251. There is a mystery which the Church celebrates with august ceremonies, and the Christian adores with faith and with love. The unbeliever sees the holy Tabernacle, and exclaims, in the pride of his ignorance: "Here is a monument of superstition; here man adores an absurdity."
As the present is a work of philosophy, not of theology, I might pass over without answering the objections of infidelity, but the occasion seems so well suited for the solution of some difficulties brought by light and superficial thinkers, that I am unwilling to pass them in silence. The nature of the work requires me to be brief in this discussion, though the subject is too important to be entirely omitted; the more so, as Catholic writers on philosophy have given their explanations on these points in what they considered the most seasonable place, and most frequently when treating of extension.
252. That the mystery of the Eucharist is a supernatural fact incomprehensible to man, and inexplicable by human words, is confessed by Catholics and acknowledged by the Church. We cannot, therefore, give a philosophical reason to explain this secret; no one was ever so vain as to attempt it. We can only examine whether the mystery is absurd and intrinsically contradictory; for if it were, it would not be a truth but an error, because divine omnipotence does not extend to what is absurd. The question is, whether the fact, although beyond the laws of nature, is intrinsically possible; for then it belongs to the field of criticism. If the incredulous man admits God, he must admit his omnipotence; the discussion must then be, not whether God can perform this miracle, but whether he has performed it.
253. The objections brought against the Eucharist may be reduced to the following: a body exists without the conditions to which other bodies are subject; it produces none of the sensible impressions which we receive from other bodies; and is in many places at the same time. To answer these objections, let us first determine our ideas.
254. The doctrines explained in the theory of sensations in this volume, show how false it is to say that the Eucharist is impossible. Under the sacred species is a body which does not affect our senses; here is a miracle, but not an impossible thing. I have shown that there is no necessary relation between bodies and our sensibility. The connection which now exists cannot be explained by any intrinsical property of spirits and bodies; we must, therefore, recur to a higher cause which freely established these relations. The same cause can suspend them. From this point of view the question becomes this: Can the power of God make a body which shall not produce the phenomena of sensibility, and suspend the laws which he was free to establish? Thus presented, the question cannot bear two answers. It must be answered in the affirmative, or the omnipotence of God is denied.
255. Those who attempt to show the impossibility of our dogma, must prove the following propositions:
I. Passive sensibility is so essential to bodies that they cannot lose it without destroying the principle of contradiction.
II. The relations of our organs [to] objects are intrinsically immutable.
III. The transmission of the impressions of the organ to the sensitive faculties of the soul is equally essential, and can fail under no supposition.
If they do not prove the truth of these three propositions, all the objections founded on the phenomena of sensibility fall to the ground. If one only is not proved, all the objections are solved; for it is evident that the phenomena of sensibility may be altered by three causes:
I. By the absence of the dispositions necessary to the body, that it may be the object of sensibility.
II. By the interruption of the ordinary relations between our organs and the body.
III. By the failure of the transmission of the impressions of the organ to the sensitive faculties.
Consequently, if one of the first propositions is false, the doubter is reduced to silence.
256. Whoever should attempt to prove these three propositions, not only would fail, but the attempt would prove his ignorance of the phenomena of sensibility, and that his philosophy on this point is the notions of the vulgar. It is not necessary to be a philosopher, it is sufficient to have acquired a very slight knowledge of philosophy to see that such an attempt would suppose a complete ignorance of the history of philosophy. At any rate, I need not insist on this point; for I have treated these questions at length in the last two books of this volume.
257. The solution there given ought to suffice to answer satisfactorily the objection founded on the particular state of a body without the conditions of extension which we find in others. From the moment that we suppose the correspondence of a body with our senses to be suspended, as these are the only means by which we are informed of what passes in the external world, it is impossible for us to affirm that there is any absurdity in that of which we have no experience. We perceive extension only by sensation, therefore we can say nothing in relation to the extension of an object of which we have no sensation. But although this answer should cut short all objections, I shall not confine myself to this alone.
258. What is extension? In reality it is the sum of the relations of the beings which compose the extended object. These relations, as I have proved, are not intrinsically necessary: therefore God can alter them. Thus this question comes to the same point as the preceding: can the power of God suspend, alter, or entirely take away relations which are not intrinsically necessary? Evidently it can. The difficulty then is not as to what could have been, but as to what is. Again we find ourselves out of the field of philosophy in that of facts, or the examination of the motives of credibility.
259. The other objection founded on the impossibility of body being in several places at the same time, though in appearance more difficult, amounts to the same as the former. To be in a place, as we now understand it, is to have a particular extension, with the ordinary form and relations with respect to the extension of other bodies. If we suppose a body with extension subject to other conditions, without the ordinary relation to the extension of other bodies, we destroy the supposition on which we base the impossibility of a body being at the same time in several places. Therefore, as we have proved that the omnipotence of God can alter and even take away these relations, there is no contradiction in admitting the destruction of the results which proceed from these relations.
260. This is why the distinction of the scholastics between two classes of extension: in ordine ad se, et in ordine ad locum, or quantitative and sacramental extension, though to the eyes of a superficial philosophy it might appear to be an empty subtlety, invented for the purpose of avoiding the difficulty, is nevertheless a profound observation, confirmed by the analysis of the reality and the phenomenon in the sensible order. I do not mean by this to say that when this distinction was made in the schools, they understood perfectly all the truth and philosophical nicety which it involves; nor that the distinction was always accompanied by the critical analysis which belongs to it. At present I abstract the merit of the men and regard only the thing. The less philosophical intelligence we suppose in those who used the distinction, the more admirable appears that religion which inspires its defenders with fruitful thoughts which the ages to come might unfold. The philosophical schools disputed warmly on extension, on accidents, and on the sensitive faculties: the Catholic dogma taught a truth which was contrary to all appearances, it stimulated them to examine more profoundly the distance of the phenomenon from the reality, the difference between the contingent and the necessary; the mystery which the Church taught introduced into philosophy questions which without it would probably never have occurred to man's understanding.
261. Bacon expressed a profound truth when he said that a little philosophy carried its possessor from religion, and a great deal of philosophy leads him to it. A careful study of the objections brought against Christianity, lays bare a truth confirmed by the history of eighteen centuries; the most weighty objections against Catholicity, instead of proving any thing against it, involve a proof which confirms it. The secret for discovering this proof, is to go to the bottom of the objection, and examine it under all its aspects. Original sin is a mystery, but it explains the whole world; the Incarnation is a mystery, but it explains the traditions of the human race; faith is full of mysteries, but it satisfies one of the greatest necessities of reason; the history of the creation is a mystery, but this mystery clears up chaos, throws light on the world, and is the key to the history of mankind; all Christianity is a collection of mysteries, but these mysteries are connected by a secret union with all that is profound, grand, sublime, or beautiful in heaven or earth; they are connected with the individual, with the family, with society, with God, with the understanding, with the heart, with languages, sciences, and art. The investigator who rejects religion and even seeks means to oppose it, finds it at the entrance as at the outlet of the mysterious ways of life; at the cradle of the infant as in the shadow of the tomb; in time as in eternity; explaining every thing by a word; listening unmoved to the wanderings of ignorance and the sarcasms of unbelief, patiently awaiting till the course of ages shall acknowledge its truth, which existed before all ages.
CONCLUSION AND SUMMING UP.
262. Before passing to another subject, let us fix our attention for a few moments on the nature and origin of the idea of extension. We shall thus collect the fruit of the preceding investigations, and prepare the way for those which follow.
The scientific fruitfulness of this idea to our mind proves how distant sensible impressions are from intellectual perception. We cannot know whether this idea existed in our mind before the sensible impression; if it did exist we were not conscious of it, and in this respect it is affirming a gratuitous proposition to say that it is an innate idea. What we can safely say, is, that there are two distinct orders of internal phenomena, that sensation could not have produced the idea, that this idea is immeasurably superior to the external impression, or even the internal sensitive intuition, and that if it did not already exist in the mind, it was not produced by sensation as an effect is produced by its cause.
263. Here we make an important transition from the order of sensations, to the order of ideas, and discover in our mind a new class of facts. It matters little whether these facts exist before the impression, or result from its presence. In the first case, we see in the mind a deposit of germs which need only the warmth of life in order to be developed; in the second, we find in the mind a fertility which produces these germs. In either case we find a being of a privileged nature, a sublime being which by a single leap rises above the region of matter, and awakened by the external impression, arises to a new life which this world cannot contain.
264. In this sense there are innate ideas; ideas which sensation could not have produced. In this sense all general and necessary ideas are innate; for sensation could not produce them. Sensation is never any thing more than a phenomenon, a particular and contingent fact, and consequently incapable of producing general ideas, or the ideas of the necessary relations of being. Sight, or the imaginary representation of a triangle, is a contingent phenomenon which tells us nothing of the necessary relations of the sides and angles to each other. In order to perceive these relations, this necessity, something else is required. This something else, call it innate ideas, force, fecundity, or activity of the mind, or any thing you please, exists, and could not have been produced by sensation, but belongs to a higher order distinct from sensible phenomena.
265. After such long investigations of the phenomena of sensation, we at last find an idea; it is the idea of extension, the foundation of all the mathematical sciences and of their application to the laws of nature.
The human mind, in all its relations with the material world, seems to have one great idea, that of extension, which, modified in infinite ways, is the origin of all the sciences which relate to matter. The whole material world rests on this idea, and all knowledge of material objects proceeds from it. It is a pure idea in its necessary relations and in its necessary branches. It is a light given to the lord of creation that he may know and admire the prodigies of nature.
266. We find the same wonderful simplicity amidst so complicated a multiplicity in another order of ideas. Hence we infer that the whole edifice of the sciences and all human knowledge are founded on a small number of ideas, perhaps on two alone. These ideas are not sensible representations, they are the objects of pure intuitions; they cannot be decomposed, but they may be applied to an infinite variety of things; they are not explained by words, as a union including various conceptions; by them a mind acts on another mind, not to teach it any thing, but to make it concentrate its activity in order to note what it contains within itself, and learn, in a certain measure, what it already knows.
Try to explain extension, the idea by which we perceive this order which we cannot express in words, but on which we found sensible experience and geometrical science, and you can find no expression. Will you define it to be "parts outside of parts?" But what are parts, and what does outside mean, if you have not the idea of extension? Take any extended thing, make your mind concentrate itself and exercise its activity in generalization. Is this triangle a quadrilateral? No. Are they both extended? Yes. Is this surface a solid? No. Are they both extended? Yes. Are all triangles different from quadrilaterals? Yes. Have all surfaces and solids extension? Yes. How do you pass from one fact to all the facts of the same kind, from the contingent to the necessary? Have you explained what extension is? No. Have you shown what there is common to all these different things? No. All that you have done then is to arouse the activity of your mind, and to make it direct its attention to the general idea of extension, and the mind applies this idea to various things which are different, yet have something in common, it applies the different modifications of this idea to various things which have something in common, and finds them different. You have not taught the truths of geometry to the mind, but have awakened them in it, whether they already existed in it, or the mind had the faculty of producing them.
267. Let us now collect the result of the investigations we have made. I do not give an equal value to all the propositions which follow. I have explained my opinion of each in its proper place, but I consider it well to sum them all up here in order to assist the understanding and help the memory.
I. There is immediate certainty of our relations with beings distinct from us.
II. There is certainty of the existence of an external world.
III. The external world in relation to us, is only an extended being which affects us, and is subject to constant laws which we may determine.
IV. We have the idea of extension.
V. The idea of extension is excited by sensations, but it is not confounded with them.
VI. The idea of extension is the basis of all our cognitions of bodies.
VII. The idea of extension should not be confounded with the imaginary representation of extension.
VIII. An extended space which is nothing real, is an absurdity.
IX. Space is nothing real distinguished from the extension of bodies.
X. Where there are no bodies, there are no distances.
XI. Motion is the change of the positions of bodies among themselves.
XII. There is not and cannot be vacuum of any kind.
XIII. The idea of space is the idea of extension in the abstract.
XIV. The imagination of an unlimited space is only an attempt of the imagination to follow the understanding in the abstraction of extension. It also arises from our habit of seeing through transparent mediums, and moving in fluids whose resistance is not perceptible.
XV. As all that we know of bodies is, that they are extended and affect us, whatever has these two conditions is to us a body.
XVI. But as we do not know the essence of bodies, we do not know whether a body can exist without extension.
XVII. Neither do we know what modifications the extension of one body may be subject to, with respect to others.
XVIII. The elements of which bodies are composed are unknown to us.
XIX. The approximation of some bodies to others, and the gravitation which results from it, seem to be the necessary effect of their present relations.
XX. The necessity of approximation does not suffice to explain the laws of motion, or their beginning, or their continuation.
XXI. The idea of space is not an absolutely necessary condition of sensation.
XXII. The idea of extension has a real objectiveness.
XXIII. The transition from the subjective to the objective in relation to extension is a primitive fact of our nature.
XXIV. Therefore bodily phenomena have a real existence outside of us.
XXV. Therefore a real certainty, scientific as well as phenomenal, arises from the testimony of the senses.
XXVI. Reason justifies the instinct of nature when it examines the relation of subjectiveness with objectiveness in sensations.
XXVII. Geometry considers extension in the abstract; but with the certainty that when the principle exists in the real order, the consequences cannot fail to be produced, and that the consequences will be more or less exact in proportion as the principle is more or less exactly realized.
XXVIII. Notwithstanding our certainty of the existence of the external world we do not know its essence.
XXIX. We do not know what this world is when seen by a pure spirit.
XXX. Sensible intuition, to which our geometry relates, does not constitute the essence of scientific knowledge, and may be separated from it.
XXXI. A change in the relations of corporeal beings among themselves, and with our sensitive faculties, is not intrinsically impossible.
