Fundamental Philosophy, Vol. 2 (of 2)

164. Although we have the conception of infinite extension, it is impossible for us to imagine it.

165. No extrinsic or intrinsic repugnance can be discovered in the existence of infinite extension.

166. We cannot know by purely philosophical means whether the extension of the universe is infinite or finite.

167. Although an absolutely infinite number may be indeterminately conceived, it is not susceptible of any arithmetical or geometrical expression: no series of what mathematicians call infinite expresses an absolutely infinite number.

168. The intrinsic impossibility of an actual infinite number may be demonstrated from the intrinsic repugnance of the co-existence of certain things which may be numbered.

169. The idea of the absolutely infinite real being cannot be indeterminate: it necessarily involves positive and formal perfections.

170. All that does not imply a contradiction must be affirmed of the infinite being. That which is absurd is not a perfection.

171. Analyzing indeterminate and intuitive ideas, we find that all the reality contained in them is affirmed of God.

172. The absolutely infinite being must be intelligent.

173. Intelligence is a perfection which does not imply contradiction.

174. Will and liberty must also be found in the absolutely infinite being.

175. The indeterminate idea of the infinite is favored by the combination of the ideas of being and not-being.

176. The idea of an absolutely infinite being consists in the idea of a union of all being that involves no contradiction.

177. The indeterminate idea of a real infinite being, or of God, is formed from the idea of an absolutely infinite being, combined with the intuitive ideas of intelligence, will, liberty, causality, and all others that can be conceived without imperfection, in any infinite degree.

BOOK NINTH.

ON SUBSTANCE

CHAPTER I.

NAME AND GENERAL IDEA OF SUBSTANCE

1. What is substance? Have we a clear and distinct idea of it? The disputes of philosophers concerning the idea of substance and the continual applications which we make of it, prove two things: first, that the idea of substance exists; and secondly, that its clearness and distinctness are not all that could be desired. A mere name, containing no idea, could not so strongly draw the attention of all philosophers, nor be used so generally, even in ordinary language; a clear and distinct idea could not give occasion to so much dispute.

2. The importance of this idea may be seen in the results to which philosophers are led, according to the way in which they explain it. The entire system of Spinosa is founded on wrong definition of substance.

3. In the present question as in many others, it does not seem to be the shortest way to begin with a definition, unless the thing defined is only a name: to define a thing is to explain it, and we cannot explain it if we are ignorant of what it is, and we are ignorant, or are supposed to be ignorant of this, when we enter on investigations in order to ascertain what it is. If philosophers, at the beginning of their treatises, would not say, substance is this, but only, this is what I understand by substance, they would escape a number of difficulties.

4. After defining the name of substance, and making a clear and distinct idea correspond to it, it is still necessary to show how far the idea represents objects really existing, or, whether it belongs to the class of ideas expressing only the relation of different ideas, without our having any means of ascertaining whether this relation is found in the positive world or not; that is to say, whether the idea of substance is only the work of our understanding, a mere result of the combination of certain ideas, or is furnished us by experience itself. I shall try not to fall into any of these faults; I know not, however, whether I can escape them. For this purpose, I shall first analyze the word, with respect to its etymological sense, and then examine the various meanings which have been given to it. The analysis of words is very useful for the analysis of ideas: words often contain a great deal of truth, which we lose by not attending to their common meaning.

5. The word substance, substantia, implies something which is under, substat, which is the subject on which other things are placed; just as its correlative, accident or modification, expresses something which happens to the subject, accidit; something which modifies it, which is in it, as a mode of being, modus.

6. By substance we seem to understand something constant in the midst of variation, something which, although it is in various ways successively, according to the variety of modifications which affect it, remains constant and identical under different transformations. When we say that the substance has received any new modification, although we understand by this that the substance is, in a new mode, we do not mean that it is different in itself, that it has lost its internal primitive being, and taken a new being; but we only consider this change as external, and as leaving untouched a certain base, which is what we call substance.

If it were not so, if we did not conceive something constant and identical under modifications, we could not distinguish substance from its modifications. The modification passes from not-being to being, and from being to not-being; now it is, and now it resigns its post to another and very different modification. But the substance is the same under different modifications; it does not pass from not-being to being with the succession of its modifications. From the moment that we attribute to substance the instability which belongs to its modifications, it ceases to be distinguishable from them.

Ordinary language confirms this truth. When there is a variation of modifications we say that the substance changes, that is, we conceive something which existed before the change, and exists after it. We say that a modification has entirely disappeared; we do not say this of the substance, but only that it is, or is presented to us, in a different manner. We therefore conceive something which remains constant and identical under different modifications: the subject in which these changes occur, this something which does not disappear with the disappearance of the modifications, which is not changed internally with these changes, we call substance, substantia, substratum.

CHAPTER II.

APPLICATION OF THE IDEA OF SUBSTANCE TO CORPOREAL OBJECTS

7. Let us apply the ideas contained in that of substance to a corporeal object: this will help explain these ideas, and perhaps suggest others.

The paper on which I am writing is susceptible of various modifications: I may write on it a thousand different things, in various characters, and in different colors; I may fold it in various ways, and give it an infinite variety of positions in relation to the objects around it, and I may move it in all imaginable directions. Under this infinity of changes there is something constant, something which does not change. There are many new things, but there is one which is not new, which is always the same. There is one which suffers these changes, but retains something which does not change. If I make the paper blue and then red, that which is now red is the same that was blue, and before that white, and to this which is constant all those changes are referred. If a white paper is shown me, and then another paper that is blue, and then one that is red, it is clear that it is not the same as though I gave all these transformations to the same paper. The impression which the color produces in me remains the same; in what, then, does the difference consist? The difference is, that in the one case there is something permanent, which has passed through successive changes; in the other case this something is not the same, but is another and different thing. In the one case there are different modifications; in the other there are different substances.

8. Let us go deeper into the matter. If we only received the successive impressions without any means of referring them to the same object, to connect them in a common point, we should find no difference between the two cases of which we have been speaking. If a piece of white paper be placed before us, and, after turning our eyes aside for a moment, we find a blue paper in the same place, with the same dimensions, and after again turning our eyes aside we find a red paper: it is clear that it would be impossible for us to distinguish, by the mere succession of the visual impressions, whether the same paper has been differently colored in succession, or different papers have been substituted for the first. But if we keep our eyes on the place where the paper is, we see whether the paper is colored or changed. In the first case, the appearance of the new color will continue with the same sensation of the paper, unmoved, the transformation is made without our losing sight of it, and the paper receives the continued succession of its motions and positions under the hand of the one who colors it. We are then sure that the paper is the same, because there has been a continuity of sensation, or rather a connection of the different colors with a third, resulting from the situation of the paper and its motions, and from all that by which we know what is common to the first and the second. But if there is no new coloring of the paper, but a substitution of a differently colored paper, we see that the first paper is taken away; the whole order of the sensation is interrupted, and new sensations are presented. These last have no connection with the first; there is, consequently, for us a different thing.

9. This shows how the idea of substance with respect to bodies is generated in us, or, to speak more properly, how we apply the idea of substance to bodies. When we discover a link which unites the different sensations in one point, we call that in which they are united, substance. And as we meet in nature with many of these points which are independent of one another, we naturally say there are many corporeal substances.

10. When we perceive an impression we never call it a substance, if we refer it to an object, or consider it as objective: for the object is not, of itself alone, capable of connecting various sensations. We receive the sensations of red, and not only ordinary people, but even philosophers, when not philosophizing, make the color objective, and consider the red, not as a simple sensation, but as an external quality. No one would call this quality by itself a substance; for it is not capable, of itself alone, of connecting other impressions or qualities. If there is a change of color the red disappears, and the new impression is connected in the order of time with the sensation of the red, but does not reside in it. If there is a change of form, although the red continues, we do not conceive this color as the necessary link between the two forms, because we know that the continuance of the red is indifferent to the variety of form, which may be changed with or without the continuance of this color.

As in general we have experienced that no sensation is necessarily connected with another, and that among sensations connected at a common point, some disappear without the rest disappearing, we infer that none of them is a necessary link; and therefore, although we make them objective, we do not give them the character of a substance, of any thing remaining identical through changes, of which it is, as it were, the recipient.

11. There is a property in bodies which is necessary to all sensations, or at least, to the two principal sensations of sight and touch. This property is extension, which, whether considered subjectively or objectively, we regard as a recipient of all sensations. We neither see nor imagine the white or black; we neither touch nor imagine the hard or the soft, the warm or the cold, without the extension in which the whiteness or blackness, the hardness or softness, the warmth or the cold reside. Thus extension might perhaps merit the honor of substance, if it were not subject to another condition, which deprives it of this title.

Although when we conceive extension in general, in the abstract, considering it as a mere continuity, we absolutely abstract it from all form; when we have need of an applied extension as the recipient of sensations, it is impossible to find it without a determinate form and figure. We do not see a color simply, but we see it in a circular, triangular, or other extension. These forms are confounded with extension itself as its applications; and do not serve as a link for other sensations. Sometimes, it is true, the same figure receives different colors, different positions, different degrees of heat or cold, etc., but the contrary also sometimes occurs, and with the same color, and the same degree of heat or cold, with the same continuance of the other sensations, the object changes its form; just as a red circle may become a green circle, a red object may become circular, and afterwards triangular. In the first case, the circular figure is the link connecting the sensations of the colors; in the second, the color is the link connecting the figures.

12. Having deprived extension of the honor of substance, as well as all other sensations, in so far as objective; we may observe that all these variations in the objects are successive, and the sensations are connected with each other. Thus the same circle may take different colors; and the same color different figures; the colors may be again changed, and the first reproduced, the figure remaining the same; or the first figure may be reproduced, the colors remaining the same. We conclude that under this variety there is something constant, that under this multiplicity there is something which is one; that under this succession of being and not-being there is something permanent; and this which is constant, one, and permanent, the recipient of these changes, the point outside of us which connects them, and enables us to conceive them connected, – this is what we call substance.

CHAPTER III.

DEFINITION OF CORPOREAL SUBSTANCE

13. What is the permanent subject of transformations in the sensible order? Is it a pure illusion? Is it a reality? What reality can it be? Does it not seem rather an abstraction? A thing which is no color, but lends itself all colors; which is none of the qualities which we experience, but the subject and cause of them all; which is no form, but accommodates itself to all forms; which is not pure extension, because this is an abstraction, and it is something which serves as the ground of other things; a corporeal object which, in itself, can affect none of the senses; what is it? Is it what the Aristotelians call an occult quality, a mysterious, and fantastic being, a mere illusion? Let us examine it by the light of experience.

14. Let us take a piece of wax and without letting it go out of our hands paint it different colors successively, subject it to different degrees of temperature, softening it by warming, and then cooling it; let us give it different forms, of a globe, a cylinder, a parallelopipedon, a table, a vase, or a statue; do all these changes take place in the same thing? Yes. Is this thing not a color, or a figure, or a degree of temperature? No; because all these qualities were and ceased to be whilst the thing remained the same. How do I know that the thing remained the same? Because there was a continuity of sensation in the eye fixed upon the object; in the touch which, although it felt the modifications of warm and cold, hard and soft, experienced also an uninterrupted sensation of an object, which remained constantly in the hand, and the weight of which was continuously felt. Therefore there is something there which is not the modifications, but is that which is modified, something common to them all, which receives and connects them, outside of me and within me.

15. Examining one conception of this permanent something, we find that, after abstracting its qualities, we have:

I. The idea of being. We say the thing, the something, the subject, etc., we therefore speak of a being, of a quality. Without the reality there is nothing; and nothing cannot be the subject of modifications, or the link connecting impressions.

II. The idea of being, which we here find, is not pure, it is not being alone. The qualities exist, are beings, and still we do not confound them with the subject.

III. That which accompanies the idea of being is the idea of permanence amidst succession, and the relation of this permanence as the point of connection, the immovable centre in the midst of succession.

16. If, therefore, we wished to define substance, we could only say that it is a permanent being in which occur the changes which are presented to us in the sensible phenomena. Our knowledge is all reduced to this; all that we can add beside, is only hypothesis or conjecture. In vain you ask me, what is this being? Give me the intuition of the essence of corporeal things, and I will tell you; but while I know them only by their effects, that is, the impressions which they produce in me, I cannot answer you. I know that it is something; I know its relation to its forms; I know that the forms are in the subject, and are not the subject; but here is the limit of my knowledge. The object corresponding to the idea composed of a permanent being and its relation to various forms is what I call corporeal substance.

17. Since the substance changes its accidents, remaining the same itself, it follows that its existence is independent of the accidents. Abstracting, for the present, whether it can or cannot exist without any, I only affirm that none in particular is necessary to it. Here we must take note of the difference between substance in itself, and in the medium by which it is manifested to us, and placed in active or passive communication with us. The accidents are this medium; they are the transitory forms it puts on. How can we know the existence of bodies, except by sensations? The object of sensation is not substance in its inner nature, but only its qualities as affecting us.

CHAPTER IV.

RELATION OF CORPOREAL SUBSTANCE TO ITS ACCIDENTS

18. In the idea of corporeal substance the idea of permanence is perfectly included, the idea of unity only imperfectly. The unity which we conceive in every corporeal substance is a factitious unity; since that which is constant is not one but an aggregate of many, as is proved by the divisibility of matter; out of every corporeal substance we may make many which will have the same right as the first to be called substances. A piece of wood is a substance; but we may slit it into several pieces which will be equally substances. These pieces, joined together, formed what are called one substance; but it is clear that this unity was very imperfect, and was rather a union than a unity, and that if we consider it as one, it was in relation to the unity of effect which it produced in us, by the connection which it gave to our sensations and to the phenomena which resulted from it.

19. Hence, every corporeal substance involves multiplicity, or combination of the elements which compose it. Experience informs us that this combination is not permanent; there is, consequently, no corporeal substance which does not imply at least one modification, namely, the arrangement of its parts. Abstracting the changes which this modification may undergo, it can never be confounded with the substance: although the bodies might be presented constantly to our senses with the same arrangement of the parts, the permanent being would be in the parts, not in their arrangement. The latter is something external which is added to the thing existing; there can be no union and combination without parts which are united and combined.

20. A difference which we observe between the substance and its modifications is, that the substance is independent of the modifications, but the modifications are not independent of the substance. The substance, while remaining the same, changes its accidents, but an accident cannot change its substance and remain the same. The same block may receive different figures successively; but a figure, numerically the same, cannot pass from one block to another. Two blocks may have a similar or a different figure, whether cubic, spherical, or pyramidal, and one may take the figure of the other; but in that case, the figures are not identical, but similar, they are specifically but not numerically the same.

21. If I am asked how I know that there is only similarity and not numerical identity in the figures which bodies take successively, that there is no permanence in the figures which change their subject, and consequently that the same figure cannot pass from one substance to another, in the same manner that the same substance passes from one figure to another; I shall not find it difficult to prove what I assert.

There is no one who does not see what an extravagant thing it would be for a cubic figure to leave a body and pass to another. What is this figure separated from the body? How is it preserved during the transition? Why is it not exactly the same in both, but presented with slight modifications? Has it undergone a modification in its passage from one body to another? Then there would be a modification of a modification, and the figure in itself abstracted from all body, would be a kind of substance of a secondary order, permanent under modifications. These are but absurd dreams in which that is applied to the concrete which belongs to the idea only in the abstract. This transition of the forms would suppose their separate existence, and thus we might have all kinds of abstract figures, cubes, spheres, circles, triangles, etc., subsisting in themselves without application to any thing figured.

22. A still stricter demonstration of this truth is possible. If we suppose a figure, numerically the same, to pass from one body to another; the block A, which loses the cubic form, transmits it to the body B. Now, this individual form cannot be in both at the same time. Suppose that after the cubic form has left the block A, we turn it back before it has touched the body B, evidently it will not be the same in both: therefore the body B has not acquired the same, but only a similar form. It is also evident that in order to give the cubic form, we need not take it from another; therefore, the form of one is not individually that of the other; otherwise we should have to say that it is and is not, that it is preserved and ceases to exist at the same time.

23. The term transmission or communication of motion, which is so much used in physical science, expresses something real so long as limited to the phenomenon which is under calculation; but it would be an absurdity, if it meant that the same motion which was in one body has passed to another. The sum of the quantities of motion is the same in elastic bodies after impact as before it; the velocity being divided between them, and the one gaining what the other loses. This is proved by calculation, and confirmed by experience. But it is evident that one body does not impart the same individual velocity which it contained to the other body; for not only can the velocity not be separated from the body and pass from one subject to another; but it cannot even be conceived except as a relation, the idea of which includes the ideas of a body moved, of space, and of time. It is true that Q representing the quantity of the motion before impact, the value of Q remains the same after impact; but this only expresses the phenomenon in relation to its effects, as subject to calculation; not that the velocity in the second member of the equation is composed of the parts of the first. Let A and B represent two bodies, the individual masses of which are expressed by these two letters; and V, v their respective velocities before impact. The quantity of motion will be Q = A × V + B × v. After impact there will be a new velocity which we may call w, and the quantity of motion will be Q = A × w + B × u. Mathematically speaking, the value of Q will be the same; but this only means that if the results of the motion be expressed in lines or numbers, we shall have the same after impact as before it; it does not and cannot mean that in the velocity u, considered as united to the subject, there is a portion of velocity which has been detached from V to be joined to v.