The law of continuity

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.

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 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 vanishing after having continually diminished
• equality is an inequality that vanishes 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 by some other men of talent. 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 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 was a German physician, well known for his books on chemistry.

He had composed a prayer which looked like getting him into trouble. It [335]began: ‘O sancta mater natura, aeterne rerum ordo’.

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:

… 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.

352. Having spoken of the laws of bodies, that is, of the rules of motion, let us come to the laws of the union between body and soul, where M. Bayle believes that he finds again some vague indifference, something absolutely arbitrary. Here is the way he speaks of it in his Reply (vol. II, ch. 84, p. 163): ‘It is a puzzling question whether bodies have some natural property of doing harm or good to man’s soul. If one answers yes, one plunges into an insane labyrinth: for, as man’s soul is an immaterial substance, one will be bound to say that the local movement of certain bodies is an efficient cause of the thoughts in a mind, a statement contrary to the most obvious notions that philosophy imparts to us. If one answers no, one will be constrained to admit that the influence of our organs upon our thoughts depends neither upon the internal qualities of matter, nor upon the laws of motion, but upon an arbitrary institution of the creator. One must then admit that it depended altogether upon God’s freedom to combine particular thoughts of our soul with particular modifications of our body, even when he had once established all the laws for the action of bodies one upon another. Whence it results that there is in the universe no portion of matter which by its proximity can harm us, save when God wills it; and consequently, that the earth is as capable as any other place of being the abode of the happy man…. In short it is evident that there is no need, in order to prevent the wrong choices of freedom, to transport man outside the earth. God could do on earth with regard to all the acts of the will what he does in respect of the good works of the predestined when he settles their outcome, whether by efficacious or by sufficient grace: and that grace, without in any way impairing freedom, is always followed by the assent of the soul. It would be as easy for him on earth as in heaven to bring about the determination of our souls to a good choice.’

353. I agree with M. Bayle that God could have so ordered [337]bodies and souls on this globe of earth, whether by ways of nature or by extraordinary graces, that it would have been a perpetual paradise and a foretaste of the celestial state of the blessed. There is no reason why there should not be worlds happier than ours; but God had good reasons for willing that ours should be such as it is. Nevertheless, in order to prove that a better state would have been possible here, M. Bayle had no need to resort to the system of occasional causes: it abounds in miracles and in hypotheses for which their very originators confess there is no justification; and these are two defects such as will most of all estrange a system from true philosophy. It is a cause for surprise, in the first place, that M. Bayle did not bethink himself of the System of Pre-established Harmony which he had examined before, and which for this matter was so opportune. But as in this system all is connected and harmonious, all following from reasons and nothing being left incomplete or exposed to the rash discretion of perfect indifference, it seems that it was not pleasing to M. Bayle: for he was here somewhat biassed in favour of such indifference, which, notwithstanding, he contested so strongly on other occasions. He was much given to passing from one extreme to the other, not with an ill intention or against his own conviction, but because there was as yet nothing settled in his mind on the question concerned. He contented himself with whatever suited him for frustrating the opponent he had in mind, his aim being only to perplex philosophers, and show the weakness of our reason; and never, in my opinion, did either Arcesilaus or Carneades argue for and against with more eloquence and more wit. But, after all, one must not doubt for the sake of doubting: doubts must serve us as a gangway to the truth. That is what I often said to the late Abbé Foucher, a few specimens of whose work prove that he designed to do with regard to the Academicians what Lipsius and Scioppius had done for the Stoics, and M. Gassendi for Epicurus, and what M. Dacier has so well begun for Plato. It must not be possible for us to offer true philosophers such a reproach as that implied in the celebrated Casaubon’s answer to those who, in showing him the hall of the Sorbonne, told him that debate had been carried on there for some centuries. What conclusions have been reached? he said to them.

354. M. Bayle goes on (p. 166): ‘It is true that since the laws of motion were instituted in such forms as we see now in the world, it is an inevitable necessity that a hammer striking a nut should [338]break it, and that a stone falling on a man’s foot should cause some bruise or some derangement of its parts. But that is all that can follow the action of this stone upon the human body. If you want it in addition to cause a feeling of pain, then one must assume the institution of a code other than that one which regulates the action and reaction of bodies one upon another; one must, I say, have recourse to the particular system of the laws of union between the soul and certain bodies. Now as this system is not of necessity connected with the other, the indifference of God does not cease in relation to the one immediately upon his choice of the other. He therefore combined these two systems with a complete freedom, like two things which did not follow naturally the one from the other. Thus it is by an arbitrary institution he has ordained that wounds in the body should cause pain in the soul which is united to this body. It therefore only rested with him to have chosen another system of union between soul and body: he was therefore able to choose one in accordance wherewith wounds only evoke the idea of the remedy and an intense but agreeable desire to apply it. He was able to arrange that all bodies which were on the point of breaking a man’s head or piercing his heart should evoke a lively sense of danger, and that this sense should cause the body to remove itself promptly out of reach of the blow. All that would have come to pass without miracles, since there would have been general laws on this subject. The system which we know by experience teaches us that the determination of the movement of certain bodies changes in pursuance of our desires. It was therefore possible for a combination to be effected between our desires and the movement of certain bodies, whereby the nutritive juices were so modified that the good arrangement of our organs was never affected.’

355. It is evident that M. Bayle believes that everything accomplished through general laws is accomplished without miracles. But I have shown sufficiently that if the law is not founded on reasons and does not serve to explain the event through the nature of things, it can only be put into execution by a miracle. If, for example, God had ordained that bodies must have a circular motion, he would have needed perpetual miracles, or the ministry of angels, to put this order into execution: for that is contrary to the nature of motion, whereby the body naturally abandons the circular line to continue in the tangent straight line if nothing [339]holds it back. Therefore it is not enough for God to ordain simply that a wound should excite an agreeable sensation: natural means must be found for that purpose. The real means whereby God causes the soul to be conscious of what happens in the body have their origin in the nature of the soul, which represents the bodies, and is so made beforehand that the representations which are to spring up one from another within it, by a natural sequence of thoughts, correspond to the changes in the body.

356. The representation has a natural relation to that which is to be represented. If God should have the round shape of a body represented by the idea of a square, that would be an unsuitable representation: for there would be angles or projections in the representation, while all would be even and smooth in the original. The representation often suppresses something in the objects when it is imperfect; but it can add nothing: that would render it, not more than perfect, but false. Moreover, the suppression is never complete in our perceptions, and there is in the representation, confused as it is, more than we see there. Thus there is reason for supposing that the ideas of heat, cold, colours, etc., also only represent the small movements carried out in the organs, when one is conscious of these qualities, although the multiplicity and the diminutive character of these movements prevents their clear representation. Almost in the same way it happens that we do not distinguish the blue and the yellow which play their part in the representation as well as in the composition of the green, when the microscope shows that what appears to be green is composed of yellow and blue parts.

357. It is true that the same thing may be represented in different ways; but there must always be an exact relation between the representation and the thing, and consequently between the different representations of one and the same thing. The projections in perspective of the conic sections of the circle show that one and the same circle may be represented by an ellipse, a parabola and a hyperbola, and even by another circle, a straight line and a point. Nothing appears so different nor so dissimilar as these figures; and yet there is an exact relation between each point and every other point. Thus one must allow that each soul represents the universe to itself according to its point of view, and through a relation which is peculiar to it; but a perfect harmony always subsists therein. God, if he wished to effect representation [340]of the dissolution of continuity of the body by an agreeable sensation in the soul, would not have neglected to ensure that this very dissolution should serve some perfection in the body, by giving it some new relief, as when one is freed of some burden or loosed from some bond. But organic bodies of such kinds, although possible, do not exist upon our globe, which doubtless lacks innumerable inventions that God may have put to use elsewhere. Nevertheless it is enough that, due allowance being made for the place our world holds in the universe, nothing can be done for it better than what God does. He makes the best possible use of the laws of nature which he has established and (as M. Regis also acknowledged in the same passage) ’the laws that God has established in nature are the most excellent it is possible to conceive’.

358. I will add to that the remark from the Journal des Savants of the 16th March 1705, which M. Bayle has inserted in chapter 162 of the Reply to the Questions of a Provincial (vol. III, p. 1030). The matter in question is the extract from a very ingenious modern book on the Origin of Evil, to which I have already referred here. It is stated: ’that the general solution in respect of physical evil which this book gives is that the universe must be regarded as a work composed of various pieces which form a whole; that, according to the laws established in nature, some parts cannot be better unless others become worse, whence would result a system less perfect as a whole. This principle’, the writer goes on, ‘is good; but if nothing is added to it, it does not appear sufficient. Why has God established laws that give rise to so many difficulties? philosophers who are somewhat precise will say. Could he not have established others of a kind not subject to any defects? And to cut the matter short, how comes it that he has prescribed laws for himself? Why does he not act without general laws, in accordance with all his power and all his goodness? The writer has not carried the difficulty as far as that. By disentangling his ideas one might indeed possibly find means of solving the difficulty, but there is no development of the subject in his work.’

359. I suppose that the gifted author of this extract, when he thought the difficulty could be solved, had in mind something akin to my principles on this matter. If he had vouchsafed to declare himself in this passage, he would to all appearance have replied, like M. Regis, that the laws God established were the most excellent that could be established. He would have acknowledged, [341]at the same time, that God could not have refrained from establishing laws and following rules, because laws and rules are what makes order and beauty; that to act without rules would be to act without reason; and that because God called into action all his goodness the exercise of his omnipotence was consistent with the laws of wisdom, to secure as much good as was possible of attainment. Finally, he would have said, the existence of certain particular disadvantages which strike us is a sure indication that the best plan did not permit of their avoidance, and that they assist in the achievement of the total good, an argument wherewith M. Bayle in more than one place expresses agreement.