345. Moreover, 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.
346. I 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 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.
347. It 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.
348. I 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 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.
349. These considerations make it plain that the laws of Nature regulating movements are neither entirely necessary nor entirely arbitrary. The middle course to be taken is that they are a choice of the most perfect wisdom. And this great example of the laws of motion shows with the utmost clarity how much difference there is between these three cases, to wit, firstly an absolute necessity, metaphysical or geometrical, which may be called blind, and which does not depend upon any but efficient causes; in the second place, a moral necessity, which comes from the free choice of wisdom in relation to final causes; and finally in the third place, something absolutely arbitrary, depending upon an indifference of equipoise, which is imagined, but which cannot exist, where there is no sufficient reason either in the efficient or in the final cause. Consequently one must conclude how mistaken it is to confuse either that which is absolutely necessary with that which is determined by the reason of the best, or the freedom that is determined by reason with a vague indifference.
350. This also settles M. Bayle's difficulty, for he fears that, if God is always determinate, Nature could dispense with him and bring about that same effect which is attributed to him, through the necessity of the order of things. That would be true if the laws of motion for instance, and all the rest, had their source in a geometrical necessity of efficient causes; but in the last analysis one is obliged to resort to something depending upon final causes and upon what is fitting. This also utterly destroys the most plausible reasoning of the Naturalists. Dr. Johann Joachim Becher, a German physician, well known for his books on chemistry, had composed a prayer which looked like getting him into trouble. It
began: 'O sancta mater natura, aeterne rerum ordo'. And it ended by saying that this Nature must forgive him his errors, since she herself was their cause. But the nature of things, if taken as without intelligence and without choice, has in it nothing sufficiently determinant. Herr Becher did not sufficiently take into account that the Author of things (natura naturans) must be good and wise, and that we can be evil without complicity on his part in our acts of wickedness. When a wicked man exists, God must have found in the region of possibles the idea of such a man forming part of that sequence of things, the choice of which was demanded by the greatest perfection of the universe, and in which errors and sins are not only punished but even repaired to greater advantage, so that they contribute to the greatest good.
351. M. Bayle, however, has extended the free choice of God a little too far. Speaking of the Peripatetic Strato (Reply to the Questions of a Provincial, vol. III, ch. 180, p. 1239), who asserted that everything had been brought forth by the necessity of a nature devoid of intelligence, he maintains that this philosopher, on being asked why a tree has not the power to form bones and veins, might have asked in his turn: Why has matter precisely three dimensions? why should not two have sufficed for it? why has it not four? 'If one had answered that there can be neither more nor less than three dimensions he would have demanded the cause of this impossibility.' These words lead one to believe that M. Bayle suspected that the number of the dimensions of matter depended upon God's choice, even as it depended upon him to cause or not to cause trees to produce animals. Indeed, how do we know whether there are not planetary globes or earths situated in some more remote place in the universe where the fable of the Barnacle-geese of Scotland (birds that were said to be born of trees) proves true, and even whether there are not countries where one could say: