Delphi Collected Works of René Descartes

by René Descartes

  There is no one who does not believe that this same rule is observed in the old world with respect to size, shape, rest, and a thousand other like things. But from it the philosophers have exempted motion, which is, however, the thing I most expressly desire to include in it. Do not think thereby that I intend to contradict them. The motion of which they speak is so very different from that which I conceive that it can easily happen that what is true of the one is not true of the other.

  They themselves avow that the nature of their motion is very little known.32 To render it in some way intelligible, they have still not been able to explain it more clearly than in these terms: motus est actus entis in potentia, prout in potentia est,33 which terms are for me so obscure that I am constrained to leave them here in their language, because I cannot interpret them. (And, in fact, the words, “motion is the act of a being in potency, insofar as it is in potency,” are no clearer for being in [English].) On the contrary, the nature of the motion of which I mean to speak here is so easy to know that mathematicians themselves, who among all men studied most to conceive very distinctly the things they were considering, judged it simpler and more intelligible than their surfaces and their lines. So it appears from the fact that they explained the line by the motion of a point, and the surface by that of a line.

  The philosophers also suppose several motions that they think can be accomplished without any body’s changing place, such as those they call motus ad formam, motus ad calorem, motus ad quantitatem (“motion to form,” “motion to heat,” “motion to quantity”), and myriad others. As for me, I conceive of none except that which is easier to conceive of than the lines of mathematicians: the motion by which bodies pass from one place to another and successively occupy all the spaces in between.

  Beyond that, the philosophers attribute to the least of these motions a being much more solid and real than they do to rest, which they say is nothing but the privation of motion. As for me, I conceive of rest as being a quality also, which should be attributed to matter while it remains in one place, just as motion is a quality attributed to it while it is changing place.34

  Finally, the motion of which they speak is of such a strange nature that, whereas all other things have as a goal their perfection and strive only to preserve themselves, it has no other end and no other goal than rest. Contrary to all the laws of nature, it strives on its own to destroy itself. By contrast, the motion I suppose follows the same laws of nature as do generally all the dispositions and all the qualities found in matter, as well those which the scholars call modos et entia rationis cum fundamento in re (modes and beings of thought with foundation in the thing) as qualitates reales (their real qualities), in which I frankly confess I can find no more reality than in the others.

  I suppose as a second rule that, when one of these bodies pushes another, it cannot give the other any motion except by losing as much of its own at the same time; nor can it take away from the other body’s motion unless its own is increased by as much. This rule, joined to the preceding, agrees quite well with all experiences in which we see one body begin or cease to move because it is pushed or stopped by some other. For, having supposed the preceding rule, we are free from the difficulty in which the scholars find themselves when they want to explain why a stone continues to move for some time after being out of the hand of him who threw it. For one should ask instead, why does it not continue to move always? Yet the reason is easy to give. For who is there who can deny that the air in which it is moving offers it some resistance? One hears it whistle when it divides the air; and, if one moves in the air a fan or some other very light and very extended body, one will even be able to feel by the weight of one’s hand that the air is impeding its motion, far from continuing it, as some have wanted to say. If, however, one fails to explain the effect of the air’s resistance according to our second rule, and if one thinks that the more a body can resist the more it is capable of stopping the motion of others (as one can perhaps be persuaded at first), one will in turn have a great deal of trouble explaining why the motion of this stone is weakened more in colliding with a soft body of middling resistance than it is when it collides with a harder one that resists it more. Or also why, as soon as it has made a little effort against the latter, it spontaneously turns on its heels rather than stopping or interrupting the motion it has. Whereas, supposing this rule, there is no difficulty at all in this. For it teaches us that the motion of a body is not retarded by collision with another in proportion to how much the latter resists it, but only in proportion to how much the latter’s resistance is surmounted, and to the extent that, in obeying the law, it receives into itself the force of motion that the former surrenders.35

  Now, even though in most of the motions we see in the true world we cannot perceive that the bodies that begin or cease to move are pushed or stopped by some others, we do not thereby have reason to judge that these two rules are not being observed exactly. For it is certain that those bodies can often receive their agitation from the two elements of air and fire, which are always found among them without being perceptible (as has just been said), or even from the grosser air, which also cannot be perceived. And they can transfer the agitation, sometimes to that grosser air and sometimes to the whole mass of the earth; dispersed therein, it also cannot be perceived.

  But, even if all that our senses have ever experienced in the true world seemed manifestly contrary to what is contained in these two rules, the reasoning that has taught them to me seems to me so strong that I would not cease to believe myself obliged to suppose them in the new world I am describing to you. For what more firm and solid foundation could one find to establish a truth (even if one wanted to choose it at will) than to take the very firmity and immutability that is in God?36

  Now it is the case that those two rules manifestly follow from this alone: that God is immutable and that, acting always in the same way, He always produces the same effect. For, supposing that He placed a certain quantity of motions in all matter in general at the first instant He created it, one must either avow that He always conserves as many of them there or not believe that He always acts in the same way. Supposing in addition that, from that first instant, the diverse parts of matter, in which these motions are found unequally dispersed began to retain them or to transfer them from one to another according as they had the force to do, one must of necessity think that He causes them always to continue the same thing. And that is what those two rules contain.

  I will add as a third rule that, when a body is moving, even if its motion most often takes place along a curved line and (as has been said above) can never take place along any line that is not in some way circular, nevertheless each of its individual parts tends always to continue its motion along a straight line. And thus their action, i.e. the inclination they have to move, is different from their motion.

  For example, if a wheel is made to turn on its axle, even though its parts go around (because, being linked to one another, they cannot do otherwise), nevertheless their inclination is to go straight ahead, as appears clearly if perchance one of them is detached from the others. For, as soon as it is free, its motion ceases to be circular and continues in a straight line.

  By the same token, when one whirls a stone in a sling, not only does it go straight out as soon as it leaves the sling, but in addition, throughout the time it is in the sling, it presses against the middle of the sling and causes the cord to stretch. It clearly shows thereby that it always has an inclination to go in a straight line and that it goes around only under constraint.

  This rule rests on the same foundation as the two others and depends only on God’s conserving everything by a continuous action and, consequently, on His conserving it not as it may have been some time earlier but precisely as it is at the same instant that He conserves it. Now it is the case that, of all motions, only the straight is entirely simple; its whole nature is understood in an instant. For, to conceive of it, it suffices to think that a body is i
n the act of moving in a certain direction, and that is the case in each instant that might be determined during the time that it is moving. By contrast, to conceive of circular motion, or of any other possible motion, one must consider at least two of its instants, or rather two of its parts, and the relation between them.37

  But, so that the philosophers (or rather the sophists) do not find occasion here to exercise their superfluous subtleties, note that I do not thereby say that rectilinear motion can take place in an instant; but only that all that is required to produce it is found in bodies in each instant that might be determined while they are moving, and not all that is required to produce circular motion.

  For example, suppose a stone is moving in a sling along the circle marked AB and you consider it precisely as it is at the instant it arrives at point A: you will readily find that it is in the act of moving38 (for it does not stop there) and of moving in a certain direction (that is, toward C), for it is in that direction that its action is directed in that instant. But you can find nothing there that makes its motion circular. Thus, supposing that the stone then begins to leave tile sling and that God continues to preserve it as it is at that moment, it is certain that He will not preserve it with the inclination to go circularly along the line AB, but with the inclination to go straight ahead toward point C.

  According to this rule, then, one must say that God alone is the author of all the motions in the world, insofar as they exist and insofar as they are straight, but that it is the diverse dispositions of matter that render the motions irregular and curved. So the theologians teach us that God is also the author of all our actions, insofar as they exist and insofar as they have some goodness, but that it is the diverse dispositions of our wills that can render those actions evil.

  I could set out here many additional rules for determining in detail when and how and by how much the motion of each body can be diverted and increased or decreased by colliding with others, something that comprises summarily all the effects of nature.39 But I shall be content with showing you that, besides the three laws that I have explained, I wish to suppose no others but those that most certainly follow from the eternal truths on which the mathematicians are wont to support their most certain and most evident demonstrations; the truths, I say, according to which God Himself has taught us He disposed all things in number, weight, and measure.40 The knowledge of those laws is so natural to our souls that we cannot but judge them infallible when we conceive them distinctly, nor doubt that, if God had created many worlds, the laws would be as true in all of them as in this one. Thus, those who can examine sufficiently the consequences of these truths and of our rules will be able to know effects by their causes and (to explain myself in the language of the School) will be able to have demonstrations a priori of everything that can be produced in that new world.

  And so there will be no exception that impedes this, we will add, if you wish, to our suppositions that God will never mark any miracle in the new world and that the intelligences, or the rational souls, which we might hereafter suppose to be there, will in no way disturb the ordinary course of nature.

  Nonetheless, in consequence of this, I do not promise you to set out here exact demonstrations of all the things I will say. It will be enough for me to open to you the path by which you will be able to find them yourselves, whenever you take the trouble to look for them. Most minds lose interest when one makes things too easy for them. And to compose here a setting that pleases you, I must employ shadow as well as bright colors. Thus I will be content to pursue the description I have begun, as if having no other design than to tell you a fable.

  CHAPTER EIGHT On the Formation of the Sun and the Stars of the New World

  Whatever inequality and confusion we might suppose God put among the parts of matter at the beginning, the parts must, according to the laws He imposed on nature, thereafter almost all have been reduced to one size and to one middling motion and thus have taken the form of the second element as I described it above. For to consider this matter in the state in which it could have been before God began to move it, one should imagine it as the hardest and most solid body in the world. And, since one could not push any part of such a body without pushing or pulling all the other parts by the same means, so one must imagine that the action or the force of moving or dividing, which had first been placed in some of the parts of matter, spread out and distributed itself in all the others in the same instant, as equally as it could.

  It is true that this equality could not be totally perfect. First, because there is no void at all in the new world, it was impossible for all the parts of matter to move in a straight line. Rather, all of them being just about equal and as easily divertible, they all had to unite in some circular motions. And yet, because we suppose that God first moved them diversely, we should not imagine that they all came together to turn about a single center, but about many different ones, which we may imagine to be diversely situated with respect to one another.

  Consequently, one can conclude that they had to be naturally less agitated or smaller, or both, toward the places nearest to these centers than toward those farthest away. For, all of them having an inclination to continue their motion in a straight line, it is certain that the strongest (i.e. the largest among those equally agitated and the most agitated among those equally large) had to describe the greatest circles, i.e. the circles most approaching a straight line. As for the matter contained in between three or more of these circles, it could have been at first much less divided and less agitated than all the other. What is more, in as much as we suppose that at the beginning God placed every sort of inequality among the parts of this matter, we must imagine that there were then all sorts of sizes and shapes, and dispositions to move or not to move, in all ways and in all directions.

  But that does not prevent them from having afterwards been rendered almost all fairly equal, principally those that remained an equal distance from the centers about which they were turning. For, since some could not move without the others’ moving, the more agitated had to communicate some of their motion to those that were less so, and the larger had to break and divide in order to be able to pass through the same places as those that preceded them, or in order to rise higher. Thus, in a short time all the parts were arranged in order, so that each was more or less distant from the center about which it had taken its course, according as it was more or less large and agitated in comparison with the others. Indeed, in as much as size always resists speed of motion, one must imagine that the parts more distant from each center were those which, being a bit smaller than the ones nearer the center, were thereby much more agitated.41

  Exactly the same holds for their shapes. Even if we were to suppose that there were at the beginning all sorts of shapes and that they had for the most part many angles and many sides, like the pieces that fly off from a stone when it is broken, it is certain that afterward, in moving and hurtling themselves against one another, they little by little had to break the small points of their angles and dull the square edges of their sides, until they had almost all been rendered round, just as grains of sand and pebbles do when they roll with the water of a river. Thus there cannot now be any notable difference among those parts that are rather close, nor indeed even among those that are quite distant, except that they can move a bit more quickly one than another and be a bit larger or a bit smaller, and that does not prevent one’s attributing the same form to all of them.

  Only one must except some which, having been from the beginning much larger than the others, could not be so easily divided or which, having had very irregular and impeding shapes, joined together severally rather than breaking up and rounding off. Thus, they have retained the form of the third element and have served to compose the planets and the comets, as I shall tell you below.

  It is necessary to note in addition that the matter that came out from around the parts of the second element, to the extent that they broke and dulled the small points of their
angles in rounding off, necessarily had to acquire a much faster motion than theirs and along with it a facility for dividing and changing shape at every moment to accommodate itself to the shape of the places where it is. Thus, it took the form of the first element.

  I say that it had to acquire a much faster motion than theirs, and the reason is clear. For, having to go off to the side through very narrow passages and out of the small spaces left between the parts of the second element as they proceeded to collide head-on with one another, it had much more of a path than they to traverse in the same time.

  It is also necessary to note that what there is of that first element beyond what is needed to fill the small intervals that the parts of the second (which are round) necessarily leave around them must draw back toward the centers about which those parts turn, because [the parts of the second] occupy all the other, more distant places. At those centers, the remaining first element must compose perfectly liquid and subtle round bodies which, incessantly turning much faster than, and in the same direction as, the parts of the second element surrounding them, have the force to increase the agitation of those parts to which they are closest and even (in moving from the center toward the circumference) to push the parts in all directions, just as they push one another. This takes place by an action that I must soon explain as exactly as I can. For I tell you here in advance that it is this action that we shall take to be light, as also we shall take one of those round bodies composed purely of the matter of the first element to be the sun, and the others to be the fixed stars, of the new world I am describing to you; and we shall take the matter of the second element turning about them to be the heavens.