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.
24. Hence, we do not conceive the accidents of bodies as possible without a subject in which they are inherent; and that substances are not inherent in another being, but are conceived and really exist without this inherence. A figure cannot exist without a thing figured, but the thing figured may still exist, through all other things are destroyed. The analysis of the nature of substance shows that its existence supposes the existence of another being which produced it; but relation between them is that of cause and effect, not of inherence, or that of the subject and its modification.
25. These last observations explain another mark of corporeal substances. In the third chapter of this book we found the three characteristics of being, the relation of the permanent to the variable, and the subject of the variations; we now find a fourth, which is a negation, non-inherence in another. This negative characteristic is included in the positive one, permanent subject of variations; for it is clear that in conceiving a subject permanent amid variations we do not include inherence, but rather deny it, at least implicitly. Non-inherence supposes something positive, something on which is founded the denial of the necessity of being inherent. What is this something? We know not. We know that it exists, but its explanation is beyond our reach. It is probably inexplicable without the intuition of the essence of things;—an intuition which we have not.
[CHAPTER V.]
CONSIDERATIONS ON CORPOREAL SUBSTANCE IN ITSELF.
26. The idea of substance, such as we have thus far explained it, implies a relation to accidents in general. The idea we are now examining is not that of an indeterminate substance, but of corporeal substance; and it must be confessed that it is difficult to conceive a particular corporeal substance without any accident. If I take from the paper, on which I am writing, its figure, extension, and all that relates to my senses, what is there left for me to conceive something particular and determinate, something which is not the idea of being in general, but of this being in particular? It is clear that, in order that the object may not disappear altogether, and losing its individuality be confounded in the universal idea, I must reserve something by which I can say this: that is to say, that which is here, or which has affected me in this or that manner, or has been the subject of such or such modifications. I consider at least its position with respect to other bodies, or its causality in relation to the effects which it has produced in me, or its nature as the subject of determinate accidents. Just as the idea of finite substance in general involves relation to certain accidents in general, the idea of a particular substance involves relation to particular accidents.
27. We find this relation in our mode of conceiving corporeal substance; we cannot assert that it is involved in the nature of the substance. This nature is unknown to us, and when we attempt to examine it, we pass to another question, that of the essence of bodies.