The Law Of Continuity

³⁴⁷ Matter is indifferent to motion and to rest.

The largest body at rest could be carried along without any resistance by the smallest body in motion In such a case, there would be:

• action without reaction and
• an effect greater than its cause.

Assume:

1. Ball A rolls freely on a nonmoving, even, horizontal plane with speed A.
2. Ball B rolls slower at speed B but is on a moving plane at speed C that makes the ball travel at speed A when viewed from outside that plane

The moving plane makes Ball B move like Ball A. But this moving plane is not the same as the moving ball.

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 am first to state the excellent law of continuity.

It is a kind of touchstone whose test the rules of Descartes, of Father Fabry, Father Pardies, Father de Malebranche and others cannot pass.

It says that:

• rest is a movement that disappears after having been continually reduced
• equality is an inequality that disappears also through the continual reduction of the greater of two unequal bodies, while the smaller retains its size.

This leads to 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 results in the true laws of motion. It does not result in certain laws invented by Descartes and others.

Their laws were ill-concerted, not proven by experiments.

³⁴⁹ This means 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. This creates 3 different causes of movements:

1. From an absolute blind necessity

This is metaphysical or geometrical. This does depends only on efficient causes.

2. From a moral necessity

This comes from the free choice of wisdom in relation to final causes

3. Something absolutely arbitrary

This depends on 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.

This vague indifference confuses the movement which is absolutely necessary with that which is determined by moral necessity.

³⁵⁰ This also settles M. Bayle’s difficulty.

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 was a German physician, well known for his books on chemistry.

He wrote a prayer saying that 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 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:

… populos umbrosa creavit

Fraxinus, et foeta viridis puer excidit alno?

But with the dimensions of matter it is not thus: the ternary number is determined for it not by the reason of the best, but by a geometrical necessity, because the geometricians have been able to prove that there are only three straight lines perpendicular to one another which can intersect at one and the same point. [336]Nothing more appropriate could have been chosen to show the difference there is between the moral necessity that accounts for the choice of wisdom and the brute necessity of Strato and the adherents of Spinoza, who deny to God understanding and will, than a consideration of the difference existing between the reason for the laws of motion and the reason for the ternary number of the dimensions: for the first lies in the choice of the best and the second in a geometrical and blind necessity.