£56 CORRESPONDENCE.
indestructible but it always knows itself and con- tinues to exist with self-consciousness. Regarding its origin, it can be said that God produced it only when this animated body, which was in the seed, determined itself to assume human form. This brute soul, which formerly animated this body before the transformation, is annihilated when the reasoning soul takes its place; or if God changes the one into the other by giving to the former a new perfection by means of an extraordinary intervention, this is a particular in regard to which I have not sufficient light.
I do not know whether the body, when the soul or substantial part is put aside, can be called.a sub- stance. It might very well bé a machine, an aggre- gation of several substances, of such sort that if I were asked what I should say regarding the forma cadaverits or regarding a block of marble, I should say that they might perhaps be units by aggre- gation, like a pile of stones, but that they are not substances. The same may be said of the sun, of the earth, of machines; and with the exception of man, there is no body, of which I can be sure that it is a substance rather than an aggregate of several substances or perhaps a phenomenon. It seems to me, however, certain, that if there are corporeal sub- stances, man is not the only one, and it appears probable that beasts have souls although they lack consciousness.
Finally, although I grant that the consideration of forms or souls is useless in special physics, it ts, nevertheless, important in metaphysics. Just as geometers pay no attention to the composition of the continuum, and physicists do not ask whether LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 157 one ball pushes another or whether it is God who does this.
It would be unworthy of a philosopher to admit these souls or forms without reason, but without them it is not possible to understand how bodies are substances.
XIV Letbniz to Arnauld.
Hanover, Nov. 28-Dec. 8, 1586. Monsieur: As I have found something very extraordinary in the frankness and in the sincerity with which you accepted certain arguments which I employed, I cannot avoid recognizing it and wondering at it. I was quite confident that the argument, based upon the general nature of propositions, would make some impression upon your mind, but I confess: at the same time that there are few people able to enjoy truths so abstract whose cogency, perhaps, no one else would have been able to see so easily. I should like to be instructed by your meditations regarding the possibilities of things. They would certainly be profound and important, inasmuch as they would have to deal with those possibilities in a manner that might be worthy of God. But this will be at your convenience. As regards the two diff- culties which you have found in my letter, the one regarding the hypothesis of the concomitance or of the agreement of substances among themselves, the other regarding the nature of the forms of corporeal substances, I grant that the difficulties are consider- able, and if I were able to meet them entirely I 158 CORRESPONDENCE, 158 CORRESPONDENCE, should think myself able to decipher the greatest secrets of universal nature. But est aliquid prodire Lenus.
As regards the first I find that you have yourself sufficiently explained the obscurity that you found in my statement concerning the hypothesis of con- comitance, for, when the soul has a feeling of pain at the same time that the arm is injured, I think it is as you say, M., that the soul forms for itself this pain, which is a natural consequence of its condition or of its concept. And it is surprising that St. Augustine, as you have remarked, seems to have recognized the same thing, when he said that the pain which the soul has in these accidents is noth- ing else than a grief which accompanies the ill con- dition of the body. In fact, this great man has very stable and profound thoughts. But it will be asked, how does the soul know this 111 condition of the body? I reply that it is not by any impression or action of the body upon the soul but because the nature of every substance carries a general expres- sion of the whole universe and because the nature of the soul bears more particularly a_ distincter expression of that which happens immediately to its body. This is why it is natural for it to notice and to recognize the accidents of its body by its own accidents. The same is true with regard to the body when it accommodates itself to the thoughts of the soul, and when I wish to raise my arm it is exactly at the very moment when everything is ready in the body for this effect; in such a way that the body moves in virtue of its own laws; while tt happens, by the wonderful though unfailing agree- ment of things among themselves, that these laws LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 159 work together exactly at the moment that the will is so inclined. God had regard to this in advance when he formed his resolve in regard to this sequence of all the things in the universe. All of this is only the consequence of the concept of an individual substance, which involves all its phenomena in such a way that nothing can happen to its substance that does not come from its own being, conformably, however, to that which happens to another, although the one may act freely and the other without choice. This agreement is one of the best proofs that can be given of the necessity of a substance which shall be the sovereign cause of everything.
I should like to be able to explain as clearly and decisively the other question with regard to the substantial forms. The first difficulty which you point out, M., is that our souls and our. bodies are two substances really distinct; therefore, it seems that one is not the substantial form of the other. I reply that in my opinion our body by itself, leaving out of question the soul, the physical body, can be called one substance only by a misuse of terms, just as a machine or a pile of stones might be called one although they are beings only by accu- mulation. The regular or irregular arrangement does not constitute a substantial unity. Aside from this, the last Lateran council declares that the soul is veritably the substantial form of our body.
Regarding the second difficulty I agree that the substantial form of our body is indivisible and this seems also to be the opinion of St. Thomas. I agree, also, that every substantial form, or, indeed, every substance is indestructible and also ingener- able, which latter was also the opinion of Albertus 160 CORRESPONDENCE.
Magnus and among the ancients of the author of the book called De diaeta, usually attributed to Hippoc- rates. They can come into being therefore only. by an act of creation. I ama good deal inclined to believe that all the births of unreasoning animals, which do not deserve a new act of creation, are only transformations of another animal already living, but at times invisible. Consider for example, the changes which happen to a silk-worm and other Irke creatures, where nature has disclosed its secrets in certain instances while it conceals them in others. Thus, brute souls would have all been created from the very beginning of the world, in accordance with that fertility of seeds mentioned in Genesis, but the reasoning soul 1s created only at the time of the formation of its body, being entirely different from the others souls which we know because it is cap- able of reflection and imitates on a small scale the divine nature.
Thirdly, I think that a block of marble is, per- haps, only a mass of stones and thus cannot be taken as a single substance but as an assembly of many. For, supposing there are two stones, (for example, the diamond of the Grand Duke and that of the Great Mogul), the same collective name could be put for both of them, and we could say that it is a pair of diamonds, although they are very far apart; but, we should not say that these two dia- monds compose one substance. Matters of greater or less in this case would make no difference. They might be brought nearer together, even to touch- ing. Yet they would not be substantially one, and if, after they had touched they were joined together by some other body, constructed to prevent their LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 166 separation—for instance, if they were set in the same ring—all this would make only what ts called aunity by accident, for it is as by accident that they are subjected to the same motion. I hold, therefore, that a block of marble is no more a thoroughly single substance than would be the water in a pond with all the fish included, even when all the water and all the fish were frozen; or any more than a flock of sheep, even when the sheep were tied together so that they could only walk in step and so that one could not be touched without pro- ducing acry from all. There is as much difference between a substance and such a being, as there is between a man and a community—say a people, an army, a society or college, which are moral beings, yet they have an imaginary something and depend upon the fiction of our minds. Substantial unity calls for a thoroughly indivisible being, naturally indestructible since its concept involves all that must happen to it. This characteristic cannot be found either in forms or in motions, both of which involve something imaginary as I] could demon- strate. It can be found, however, in a soul or a substantial form, such as is the one called the me. These latter are the only thoroughly real beings as the ancients recognized and, above all, Plato, who showed very clearly that matter alone does not: suffice for forming a substance. Now, the me- above mentioned or whatever corresponds to it, in each individual substance can neither be made nor destroyed by the bringing together or the separa- tion of the parts. Such juxtapositions are wholly apart from the constitution of a substance. I can- not tell exactly whether there are other true cor- 162 CORRESPONDENCE, poreal substances beside those which have life. But souls serve to give us a certain knowledge of others at least by analogy.
All this can contribute to clear up the fourth dif- ficulty, for, without bothering with what the School- men have called formam corporettatis, 1 assign sub- stantial forms to all corporeal substances that are more than mechanically united.
But fifthly, if I. am asked in particular what I should say of the sun, the earth, the moon, of the trees, and of similar bodies, and even of the beasts, I am not able to say surely whether they are ani- mated, or at least whether they are substances, or whether they are merely machines or aggregations of several substances, but I am able to say that if there are no corporeal substances such as I claim, it follows that bodies are only true phenomena like the rainbow. For a continuum is not only divis- ible to infinity, but every particle of matter is actually divided into other parts as different among themselves as were the two diamonds above men- tioned. And since this could always be continued, we should never reach anything of which we could say, here is really a being, unless there were found animated machines whose soul or sub- stantial form constituted the substantial unity inde- pendently of the external union of contact. And if there are no substantial forms, it follows that with the exception of men there is nothing substantial in the visible world.
Sixthly, since the conception of an individual substance in general, which I have given, is as clear as is the conception of truth, the conception of cor- poreal substance will be clear also, and consequently LEIBNIZ. ARNAULD., HESSEN-RHEINFELS. 163 that of substantial forms. If, however, this should not be so, we should be obliged to admit a good many things whose knowledge is not so clear and distinct. I hold that the conception of extension ts much less clear and distinct; witness the remark- able difficulties found in the composition of the con- tinuum. And it can, indeed, be said that there is no definite and precise form in the body because of the actual subdivision of the parts. With infinite sub- division the body would be doubtless imaginary and a mere appearance, if there was only the material and its modificatioas. Nevertheless, it is useless to make mention of the unity, the concept, or the substantial forms of bodies when it is a question of explaining the particular phenomena of nature, just as it is use- less for Geometers to examine the difficulties of the continuum when they are at work in solving some problem. These things are nevertheless important and worthy of consideration in their place; all the phenomena of the body can be explained mechanic- ally or by the corpuscular philosophy in accor- dance with certain assumed mechanical principles without troubling oneself as to whether there are souls or not. Inthe ultimate analysis of the prin- ciples of physics and mechanics, however, it is found that these assumed principles cannot be explained solely by the modifications of extension, and the very nature of force calls for something else. Finally, in the seventh place I remember that M.
Cordemoy, in his treatise on the distinction between the body and the soul, in order to save the substan- tial unity in the body, feels himself obliged to assume atoms or indivisible extended bodies, so as to have something permanent to constitute a simple 164 CORRESPONDENCE, being; but you rightly concluded, M., that I did not share this opinion. It appears that M. Cordemoy made an approach to the truth, but he did not yet see in what the true notion of a substance consisted and this latter is the key for most important knowl- edge. The atom, which consists of only an imagined mass with an infinite duration, an idea which I hold conforms no more to the divine wisdom than does a vacuum, cannot contain in itself. all its past and future states and much less those of the whole universe.
I come to your observations upon my objection to the Cartesian principle regarding the quantity of motion;.and,1,grant, M.,,that.the, acceleration. of, a body comes from the impulse of some invisible fluid and that it is like a ship which the wind causes to go at first very slowly and then faster; my demon- stration, however, is independent of any hypothesis. Without troubling myself at present as to how the body has acquired the velocity which it has, I accept it such as it is, and I say that a body weigh- ing one pound, which has a velocity of two degrees, has twice as much force as a body weighing two. pounds which has a velocity of one degree, because it can raise the same weight twice as high. I hold that in distributing the motion between bodies which come into contact, regard must be had, not to. the «quantity.0of motion, as, 1s the.case. in. the Cartesian principle, but to the quantity of the force; otherwise, we should obtain perpetual motion in mechanics. For example, suppose that in a square LM a body A goes along the diagonal 1A 2A to strike two equal bodies B and C at the same moment in such a way that at the moment of con: LEIBNIZ. ARNAULD. HESSEN-RHEINFELS, 165 tact the three centers of these three spheres are found in an isosceles right triangle, the whole being in a horizontal plane. Suppose now that the body A remains at rest after the contact in the place 2A, and imparts all its force to the bodies Band C. In this case B would go from 1B to 2B, having the velocity and direction 1B2B, and C from IC to 2C, with the velocity and direction 1C2C. That is to Say, sil Aotakes one second of time to pass with uniform motion from 1A to 2A before contact, then in. one second after contact B 1B will pass to 2B, and C to 2C. The question is, what is the length 6b Bb2 Bort 72:C,. which represent the 14 velocity. I say that it will be equal. to AL or AM sides of the square LM, for the bodies, being supposed equal, the forces would be only as the height from which the body would have to descend in order to acquire these velocities, that is to say, as the squares of the velocities. Now, the squares of 1B2B and 1C2C taken. together are equal ‘ito the square 1A2A. Hence, there is as much force after as before the contact. But we see that the quantity of motion has been augmented; for, since the bodies are equal, the quantity of motion can be estimated by their velocities. Now, before the contact this was the velocity 1A2A but after the contact it is. the velocity 1B2B plus the velocity 1C2C; 1B2B plus 4B x Q he C2 LS ee @Qeuwnanenwe M cere w= eo weeveweawse= 166 CORRESPONDENCE.
1C2C, however, ts greater than 1A2A; it must needs be, therefore, that, according to M. Descartes, in order to maintain the same amount of motion the body B would go from 1B only to £, or from 1C only to x, insuch a way that 1B or 1Cx shall each be equal to half 1A2A. In this way, however, there will be as much force lost as the two squares of 1B8 and of 1Cx, taken together are less than the square 1A2A. And, on the other hand, I will show that by another means force can be gained through the con- tact. For, since according to M. Descartes, the body A with the velocity and direction 1A2A gives by hypothesis to the bodies at rest B and C velocities and directions 1BB and 1Cx« so that it may come to rest in their place, reciprocally if these bodies shculd return and come in contact with the body A resting at 2A with the velocities and direc- tions B1B and «IC and should come to rest after the contact, they would make A move with the velocity and direction 2A1A. In this way, however, per- petual motion would be inevitably attained for, sup- posing that the body B, weighing one pound with the velocity 81B could rise to the height of one foot, and C the same, there would be before the shock a force capable of lifting two pounds to the height of one foot, or one pound the height of two feet, but, after the contact of 1B and 1C with 2A the body A weighing one pound and having a double velocity (that is to say, the velocity of 2A1A, double the velocity of B1B or of «1C), could lift one pound to the height of four feet, for the height to which the bodies can rise by virtue of their velocities is as the squares of their velocities. If, therefore, double the force can be gained, perpetual motion is completely LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 167 discovered, or it 1s possible that force should be gained or lost, and principles are not well-based when such consequences can be derived from them.
I found in Descartes’ letters what you mentioned to me—namely, that he had tried to avoid the con- sideration of velocities in formulating the reasons for moving forces and had taken into account only the heights. If he had remembered this when he wrote his principles of physics perhaps he would have avoided the errors into which he has fallen with respect to the laws of nature, but he happens to have avoided the consideration of velocity there where he might have retained it, and to have retained it in the case where it could produce errors. For, with regard to the power which I call dead (as when a body makes its first effort to descend before it has acquired any impetus from the continuance of the motion), and with regard to the case when two bodies are in equilibrium (for then, the first efforts which the one exercises on the other are always dead), it happens that the velocities are as the dis- tances; when, however, we consider the absolute force of bodies which have a certain impetuosity (and this is necessary for establishing the laws of motion), the calculation should be made from the cause or from the effect, that is to say, according to the height to which it can rise by virtue of this velocity, or according to the height from which it must descend in order to acquire this velocity. If we should attempt to employ the velecity, we should gain or lose a great deal of force without any reason for it. In place of the height we might suppose a spring or any other cause or effect, and the result 168 CORRESPONDENCE.
would always be the same; viz., proportional to the squares of the velocities.
I find in The News of the Republic of Letters for the month of September, of this year, that someone named Abbé D. C., of Paris, whom I do not know, has replied to my objection. The trouble is that he seems not sufficiently to have thought over the difficulty. While pretending to contradict me vehemently he grants me more than I wish and he limits the Cartesian principle to the single case of isochronous powers as he calls them, as in the five usual forms of machinery, and this is entirely against Descartes’ intention. Besides this, he thinks that the reason why in the case which I pro- posed one of the bodies has quite as much force as the other although it has a smaller quantity of motion, is the result of this body’s having fallen for a longer period since it has come from a greater height. If this made anydifference, the Cartesian principle which he wishes to defend would be ruined by that very fact. This reason, however, is not valid, for the two bodies can descend from those different heights in the same time, according to the inclination which is given to the planes along which they must descend; and my objection would still be entirely valid. I hope, therefore, that my objec- tion may be examined by a Cartesian who shall be a Geometer and well versed in these matters.
Finally, M., as I honor you infinitely and am very much interested in whatever concerns you I will be delighted to learn from time to time of the state of your health and of the works which you have in hand; whose value I am proud to be able to recog- nize. I am, with a passionate zeal, LEIBNIZ. ARNAULD. HESSEN-RHEINFELS., 169 XV Letbnis to Count Ernst von Hessen-Rhetinfels. {Taken from my letter of November, 1686.]
I take the liberty, Monseigneur, to beg your Serene Highness to have the enclosed sent to M. Arnaud, and, as it treats of matters far from the external senses and dependent upon pure intellection, which are not agreeable to and most frequently are looked down upon by persons who are, nevertheless, active and successful in the affairs of the world, I will say here something in favor of these meditations; not because I am so fatuous as to wish your Serene High- ness to amuse himself with them (this would be as unreasonable as to wish that the general of an army should apply himself to algebra, however important this science may be to any one who is concerned with mathematics), but so that your Serene High- ness may better estimate the purpose and the use of such thoughts that might appear unworthy of taking up a man’s time; especially since all a man’s moments ought to be so precious to him. As these matters are usually treated by the Schoolmen, they are only disputations and distinctions and plays upon words; but there are veins of gold among these barren rocks. I think in fact that thought is the principal and perpetual function of the soul. We shall always think, but we shall not always live here; this is why whatever renders us more capable of thinking about most perfect objects and in the most perfect way is what naturally contributes to our per- fection. Nevertheless, the present state of our life compels us to a great number of confused thoughts 17° CORRESPONDENCE.
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which do not add to our perfection, such is the knowledge of customs, of genealogies, of languages, and even all historical knowledge of facts, whether civil or natural; these are useful for us in avoiding dangers and in taking care of the bodies and of the men whom we have around us, but they do not enlighten the mind. The knowledge of routes is useful to a traveller while he is on his journey, but whatever has a greater relation to the duties that lie before him 7a patria is more important for him. Now we are destined to live some day a spiritual life, where substances separated from matter will occupy us much more than do the bodies.
Here are a few examples taken from the arts, which will enable us to distinguish between that which enlightens the mind and that which only leads it along as a blind man might be led. If a workman knows by experience or by hearsay that when the diameter is seven feet the circumference of the circle ts a little less than twenty-two feet, or if a gun- ner knows by hearsay, or because he has frequently measured it, that bodies are thrown the farthest at an angle of 45 degrees, the knowledge is confused and is that of an artisan; it does very well for earn- ing a living and for performing services to others, but the knowledge which enlightens the mind is that which is distinct, or which gives the causes or rea- sons involved, as when Archimedes gave the demon- stration for the first rule and Galileo for the second. In a word, it is only knowledge of the reasons in themselves or of the necessary eternal truths, above all of those which are the most comprehensive and which have the most relation to the sovereign being, that are able to make us more perfect. This knowl- LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 371 edge alone is good in itself; all the rest 1s mercenary, and should be learned only when necessary and to serve the needs of this life, and so that this life may be in a better position to contribute afterwards to the perfection of the mind when one’s subsistence has been provided for. But the intemperance of men, and what is called the care de pane lucrando, and often also vanity, lead us to forget the lord for the valet and the end for the means. This, accord- ing to the poet is ‘“‘to lose the reasons for living while trying to live.’’ Very much asa miser pre- fers gold to his health, while gold is only for pro- curing the commodities of life. Now, since that which perfects the mind (leaving aside the light of grace), ts the demonstrative knowledge of the great- est truths through their causes or reasons, it must be granted that metaphysics or natural theology which treats of immaterial substances and particularly of God and of the soul, is the most important of all. One cannot go very far in this without inquiring into the true conception of substance, which I, in my preceding letter to M. Arnaud explained in such a manner that he himself who is so exact and who was at first repelled by it, accepted it.
_ Finally, these meditations furnish surprising con- sequences which are, nevertheless, of wonderful use in freeing men from doubts regarding the relation of God to created things, his fore-knowledge and fore- ordination and the union of the soul with the body, the origin of evil and other things of this nature. I say nothing here of the great applications that these principles have in the humanities, but at least I am able to say that nothing lifts our minds more to the knowledge and to the love of God, however much 172 CORRESPONDENCE.
nature may help us in this. I confess that all these speculations are of no service without grace and that God gives grace to people who have never dreamed of these meditations, but God wishes also that we should not omit anything on our part and that each one of us according to his vocation and according to the time, should make use of the per- fections which God has given to human nature. And since he has created us only that we may know and love him, we cannot work enough toward this nor can we make a better use of our time and of our energy except when we are occupied elsewhere for the public and for the welfare of others.
XVI Arnauld to Letbhnizc.
March 4th, 1687.
It has been a long time, M., since I received your letter, but I have been so busy since then that I have not been able to reply to it earlier.