§342I also doubt, with M. Bayle, whether pain be necessary in order to warn men of peril. But this writer goes too far (Reply to the Questions of a Provincial, vol. II, ch. 77, p. 104): he seems to think that a feeling of pleasure could have the same effect, and that, in order to prevent a child from going too near the fire, God could give him ideas of pleasure in proportion to the distance he kept from it. This expedient does not appear very practicable with regard to all evils, unless a miracle were involved. It is more natural that what if it were too near would cause an evil should cause some foreboding of evil when it is a little less near. Yet I admit that it is possible such a foreboding will be something less than pain, and usually this is the case. Thus it indeed appears that pain is not necessary for causing one to shun present peril; it is wont rather to serve as a penalty for having actually plunged into evil, and a warning against [331] further lapse. There are also many painful evils the avoidance whereof rests not with us. As a dissolution of the continuity of our body is a consequence of many accidents that may happen to us, it was natural that this imperfection of the body should be represented by some sense of imperfection in the soul. Nevertheless I would not guarantee that there were no animals in the universe whose structure was cunning enough to cause a sense of indifference as accompaniment to this dissolution of continuity, as for instance when a gangrenous limb is cut off; or even a sense of pleasure, as if one were only scratching oneself. For the imperfection that attends the dissolution of the body might lead to the sense of a greater perfection, which was suspended or checked by the continuity which is now broken: and in this respect the body would be as it were a prison.

§343There is also nothing to preclude the existence in the universe of animals resembling that one which Cyrano de Bergerac encountered in the sun. The body of this animal being a sort of fluid composed of innumerable small animals, that were capable of ranging themselves in accordance with the desires of the great animal, by this means it transformed itself in a moment, just as it pleased; and the dissolution of continuity caused it no more hurt than the stroke of an oar can cause to the sea. But, after all, these animals are not men, they are not in our globe or in our present century; and God's plan ensured that there should not be lacking here on earth a rational animal clothed in flesh and bones, whose structure involves susceptibility to pain.

§344But M. Bayle further opposes this on another principle, one which I have already mentioned. It seems that he thinks the ideas which the soul conceives in relation to the feelings of the body are arbitrary. Thus God might have caused the dissolution of continuity to give us pleasure. He even maintains that the laws of motion are entirely arbitrary. 'I would wish to know', he says (vol. III, ch. 166, p. 1080), 'whether God established by an act of his freedom of indifference general laws on the communication of movements, and the particular laws on the union of the human soul with an organic body? In this case, he could have established quite different laws, and adopted a system whose results involved neither moral evil nor physical evil. But if the answer is given that God was constrained by supreme wisdom to establish the laws that he has established, there we have neither more nor less than the Fatum of [332] the Stoics. Wisdom will have marked out a way for God, the abandonment whereof will have been as impossible to him as his own self-destruction.' This objection has been sufficiently overthrown: it is only a moral necessity; and it is always a happy necessity to be bound to act in accordance with the rules of perfect wisdom.

§345Moreover, it appears to me that the reason for the belief held by many that the laws of motion are arbitrary comes from the fact that few people have properly examined them. It is known now that M. Descartes was much mistaken in his statement of them. I have proved conclusively that conservation of the same quantity of motion cannot occur, but I consider that the same quantity of force is conserved, whether absolute or directive and respective, whether total or partial. My principles, which carry this subject as far as it can go, have not yet been published in full; but I have communicated them to friends competent to judge of them, who have approved them, and have converted some other persons of acknowledged erudition and ability. I discovered at the same time that the laws of motion actually existing in Nature, and confirmed by experiments, are not in reality absolutely demonstrable, as a geometrical proposition would be; but neither is it necessary that they be so. They do not spring entirely from the principle of necessity, but rather from the principle of perfection and order; they are an effect of the choice and the wisdom of God. I can demonstrate these laws in divers ways, but must always assume something that is not of an absolutely geometrical necessity. Thus these admirable laws are wonderful evidence of an intelligent and free being, as opposed to the system of absolute and brute necessity, advocated by Strato or Spinoza.

§346I have found that one may account for these laws by assuming that the effect is always equal in force to its cause, or, which amounts to the same thing, that the same force is conserved always: but this axiom of higher philosophy cannot be demonstrated geometrically. One may again apply other principles of like nature, for instance the principle that action is always equal to reaction, one which assumes in things a distaste for external change, and cannot be derived either from extension or impenetrability; and that other principle, that a simple movement has the same properties as those which might belong to a compound movement such as would produce [333] the same phenomena of locomotion. These assumptions are very plausible, and are successful as an explanation of the laws of motion: nothing is so appropriate, all the more since they are in accord with each other. But there is to be found in them no absolute necessity, such as may compel us to admit them, in the way one is compelled to admit the rules of logic, of arithmetic and geometry.

§347It seems, when one considers the indifference of matter to motion and to rest, that the largest body at rest could be carried along without any resistance by the smallest body in motion, in which case there would be action without reaction and an effect greater than its cause. There is also no necessity to say of the motion of a ball which runs freely on an even, horizontal plane, with a certain degree of speed, termed A, that this motion must have the properties of that motion which it would have if it were going with lesser speed in a boat, itself moving in the same direction with the residue of the speed, to ensure that the ball, seen from the bank, advance with the same degree A. For, although the same appearance of speed and of direction results through this medium of the boat, it is not because it is the same thing. Nevertheless it happens that the effects of the collision of the balls in the boat, the motion in each one separately combined with that of the boat giving the appearance of that which goes on outside the boat, also give the appearance of the effects that these same balls colliding would have outside the boat. All that is admirable, but one does not see its absolute necessity. A movement on the two sides of the right-angled triangle composes a movement on the hypotenuse; but it does not follow that a ball moving on the hypotenuse must produce the effect of two balls of its own size moving on the two sides: yet that is true. Nothing is so appropriate as this result, and God has chosen the laws that produce it: but one sees no geometrical necessity therein. Yet it is this very lack of necessity which enhances the beauty of the laws that God has chosen, wherein divers admirable axioms exist in conjunction, and it is impossible for one to say which of them is the primary.

§348I have also shown that therein is observed that excellent law of continuity, which I have perhaps been the first to state, and which is a kind of touchstone whose test the rules of M. Descartes, of Father Fabry, Father Pardies, Father de Malebranche and others cannot pass. In virtue of this law, one must be able to regard rest as a movement vanishing [334] after having continually diminished, and likewise equality as an inequality that vanishes also, as would happen through the continual diminution of the greater of two unequal bodies, while the smaller retains its size. As a consequence of this consideration, the general rule for unequal bodies, or bodies in motion, must apply also to equal bodies or to bodies one of which is at rest, as to a particular case of the rule. This does result in the true laws of motion, and does not result in certain laws invented by M. Descartes and by some other men of talent, which already on that score alone prove to be ill-concerted, so that one may predict that experiment will not favour them.