J.am not able to let this occasion pass without speaking to you in regard to certain of my medita- tions since | had the honor of seeing you. Among other things I have made quite a number of investi- gations into jurisprudence and it seems to me that something permanent and useful might be estab- lished, quite as much for the sake of having ascer- tained laws, of which there is a great lack in Germany and perhaps aiso in France, as also for the establish- ment of short and good forms of procedure. For this purpose it 1s not sufficient to be strict with cegard to the terms or the established days and other conditions, as is the case with the laws com- pied under the code of Louis; for to suffer a good cause to be lost because of formalities, is in juris- prudence a remedy comparable to that of a sur- geon who is continually cutting off arms and legs They say that the King ts having work done for the reform of chicanery, and I think that some- thing of importance might be done along this line.
I have also. been) interested in ithe subject,of mines, because of those which we have in our coun- LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 139 try; and I have frequently visited them by command of the Prince. I think I have made several dis- coveries in regard to the formation, not so much of the metals as of those forms in which the metals are found and of certain bodies among which they lie. For example, I have shown the manner of the for- mation of slate.
Besides this I have gathered together memoirs and titles concerning the history of Brunswick, and recently I read a document regarding the boundaries of the Hildesheim bishopric of the canonized Em- peror Henry II., where I was surprised to find these words, ‘‘for the safety of his royal wife and child.’’ This seemed to me to be quite contrary to the accepted opinion which would have us believe that he maintained a state of virginity toward his wife, St. Cunigunde.
Besides this I have diverted myself frequently with abstract thoughts in metaphysics and geometry. I have discovered a new method of tangents, which I have had printed in the Journal of Leipsic. You know, that Hudde and later De Sluse developed this matter quite far, but there were two things lacking. The one was that when the unknown term or indeterminate was expressed in fractions and irra- tionals, these had to be eliminated in order to use their methods, which made the calculation assume an extent and an elaborateness very awkward and often unmanageable; while my method is not encum- bered at all with fractions or irrationals. This is why the English have made so much of it. The other fault of the method of tangents is that it does not apply to the lines which Descartes calls mechan- ica] and which I prefer to call transcendental; while 140 CORRESPONDENCE.
my method applies to them just the same, and I can calculate the tangent of the cycloid or of any other line. I claim also to give in general the means of reducing these lines to calculation, and I hold that they must be received into geometry, whatever M. Descartes may say. My reason its that there are analytical problems which are of no degree or whose degree is required; ¢. ¢., to cut an angle in the incommensurable ratio of one straight line to another straight line. This problem is neither in plane geom- metry nor in solid nor in super-solid geometry, it is, nevertheless, a problem, and for this reason I call it transcendental. Such is also this problem: Solve the following equation: <*+2%=30, where the un- known term « is found also in the exponent and the degree also of an equation is required. It ts easy to find here that x 1s equal to 3 for 3°+3 or 27+3 makes 30. But it is not always so easy to solve it, above all when the exponent is not ‘a rational number; and we must have recourse to lines or loci which are appropriate to the purpose and which therefore must be admitted into geometry. Now I show that the lines which Descartes would exclude from geometry depend upon equations which transcend algebraic degrees but are yet not beyond analysis, nor geometry. I therefore call the lines, which M. Descartes accepts, algebraic because they are of a certain degree in an algebraic equation. The others I call transcendental. These I reduee to calculations, and their construction I show either through points or through motion; and, 1f I might venture to say, I claim to advance analysis thereby ultra Flerculis columnas.
Regarding the subject of metaphysics I claim to LEIBNIZ, ARNAULD. HESSEN-RHEINFELS. I4t advance by geometrical demonstrations, positing only two primary truths; to wit, in the first place, the principle of contradiction, (for if two contradic- tories could be true at the same time all reasoning would be useless); and secondly, the principle that nothing 1s without reason, or that every truth has its proof a priori, drawn from the meaning of the terms, although we have not always the power to attain this analysis. I reduce all mechanics to a single metaphysical proposition and I have several important propositions in geometric form regarding causes and effects, and the same regarding simili- tude by my definition of which I easily demonstrate several truths which Euclid proves in a roundabout way.
In addition I cannot approve the custom of those who have recourse to their ideas, when they are at the end of their proofs, and who abuse the principle that every clear and distinct conception is good. For I hold that we must possess the criteria of dis- tinct knowledge And seeing that we often think without ideas, employing in place of the ideas in question, characters whose signification we wrongly suppose ourselves to know, and thus form impos- sible chimeras, therefore I hold that the criterion of a true idea is that its possibility can be proved, whether @ priort in conceiving its cause or reason, or @ posterior’ when experience enables us to know that it is actually found in nature. This is why I consider definitions to be real when it is known that the defined is possible; otherwise they are only nominal and cannot be trusted; for if by chance the thing defined implies contradictions, two contradic- tories can be deduced from the same definition. It 142 CORRESPONDENCE, is for this reason that you had good cause to insist against Father Malebranche that a distinction must be made between true and false ideas, and that too much confidence must not be placed in the imagina- tion under the pretext of a clear and distinct intel- lection.
I know no one who ts better able than yourself to examine this class of thoughts, particularly those whose consequences ‘ead into theology; few people having the necessary penetration and the broad enlightenment which is called for; and few people having that fairness which you have now dis: played toward me. I therefore pray God to lengthen your life and not to deprive us too soon of an ally whose like wi!l not be easily found again.
I am yeurs, sincerely, Monsieur, XI Arnauld to Leibniz.
I thought, M., that I might make use of the lib- erty which you gave me to take my time in reply- ing to your kindness; and therefore I have put it off, until 1 had completed a work which I had com- menced. I have been a gainer in doing you justice, for there was never anything more honorable or more gracious than the manner in which you received my excuses. So much was not called for to make me resolve to acknowledge in good faith that I am satisfied with the manner in which you have explained what was startling to me at first, regerding the concept of the individual nature.
LEIBNIZ. ARMNWAULD. HESSEN-RHEINFELS. 143 For no man of honor should have any difficulty in accepting a truth as soon as it is made known to him. I have been above all struck by this argu- ment, that in every affirmative true proposition, necessary or contingent, universal or singular, the concept of the attributes is comprised in some way in that of the subject. Predtcatum tnest subjecto.
There remains for me only the difficulty in regard to the possibility of things and in regard to this way of conceiving of God as though he had chosen the universe, which he created, out of an infinity of other possible universes which he saw at the same time and which he did not choose to create. But as this has nothing to do properly with the concept of the individual nature, and as I should have to meditate at too great length in order to make clear what I think about it or rather what I find to object to in the thoughts of others, because they do not seem to me to do justice to God’s power, you will permit me to pass over this subject.
1 would prefer to ask you to clear up two things which I find in your last letter. They seem to me important, but I do not understand them very well.
The first is as to what you mean by ‘“‘the hypoth- esis of the concomitance and of the agreement of substances among themselves.’’ You claim that by this means, that which happens in the union of the soul and the body and in the action or the passion of a mind with respect to any other created thing, can be explained. I cannot understand what you say in explaining this thought, which, according to you, agrees neither with those who think that the soul acts physically upon the body and the body 144 CORRESPONDENCE.
‘upon the soul, nor with those who think that God alone is the physical cause of these effects, and that the soul and the body are only the occasional causes. You say, “‘God created the soul in sucha way that for the ordinary events it has no need of ‘these changes, and that which happens to the soul arises from its own being without its having to agree with the body in what results, any more than the body does with the soul. Each one follows its Jaws. The one acting with freedom and the other without choice, they fit in together, one with another, in the same phenomenon.’’ Examples will enable you to make your thought clearer: some one wounds my arm. With regard to my body, this is only a bodily motion but my soul at once has a feeling of pain which it would not have if this had not happened to my arm. The question is, what is the cause of this pain? You deny that my body has acted upon my soul, and that God, on the occasion of this which happened to my arm, immediately produced in my soul the feeling of pain. It must be, therefore, that you think that it is the soul which has formed this feeling in itself and this must be what you mean when you say that, ““What hap- pens in the soul on the occasioning of the body arises from its own being.’’ St. Augustine was of this opinion because he thought that bodily pain was nothing else than the grief which the soul had when its body was ill-affected. But what reply can be made to those who object that the soul must therefore have known that its body was ill-affected before it could become sorrowful, while in fact it seems to be the pain which informs the sou! that the body is injured.
LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 145 Let us take another example where the body has some movement on the occasioning of the soul. If I wish to take off my hat, I lift my arm to my head This movement of my arm upward is not at all in line with the ordinary laws of motion. What then is its cause? It is because the spirits, having entered. into certain nerves, have stimulated them. But these spirits have not been through their own power determined to enter into these nerves. They had not given to themselves the movements which cause them to enter into these nerves. What has given it to them then? Is it God, who has done it on the occasion of my wishing to lift my arm? This is what the partisans of occasional causes say. It seems that you do not approve of their position. It must, therefore, be our soul itself, but this again it seems that you will not grant, for this would be to act physically upon the body; and you appear to deny that.a substance can act physically upon another..._ The second thing upon which I should like to be enlightened is your statement, ‘‘In order that the body or matter should not be a simple phenomenon, like a rainbow, nor a being brought together by acci- dent or by an accumulation, like a pile of stones, it must not consist merely in extension, and there must needs be something which Is called the sub- stantial form and which corresponds in some sort to what is called the soul.’’ There are a good many things to ask upon this point.: Ist. Our body and our soul are two substances really distinct. Now, if we put into the body a substantial form aside from this extension, we can- not imagine how there should be two distinct 146 CORRESPONDENCE.
substances, we cannot see therefore that this sub- stantial form has any relation to what we call our soul.
2nd. This substantial form of the body must be either extended and divisible or not-extended and indivisible. If we should say the latter, it would seem to be as indestructible as is our soul; and if we should say the former, it would seem that nothing would be gained toward making the body a unum per se, any more than if it consisted only in exten- sion. For it is the divisibility of extension into an infinity of parts which presents the difficulty of conceiving itasaunit. This substantial form there- fore would not remedy this difficulty at all so long as it also is divisible like extension itself.
3rd. Is it the substantial form of a block of mar- ble which makes it one? If this is so, what becomes of that substantial form when it ceases to become one, after it has been cut in two? Is it annihilated, or does it become two? The first is inconceivable, if this substantial form is not a mere manner of being, but is a substance; and it cannot be said that it is a manner of being or a mode, because then the substance, of which this form would be the mode, would be an extension. This apparently is not your. thought. And if this substantial form should. be- come two instead of one, why would not the same be said of the extended alone without this substan- tial form?
4th. Do you give to extension a general sub- stantial form such as has been admitted by certain Schoolmen who have called it formam corporettacs? Or do you wish that there should be as many differ- ent substantial forms as there are different bodies: LEIBNIZ. ARNAULD., HESSEN-RHEINFELS. 147 and are these different in kind when the bodies are different in kind?
sth. In what do you put the unity which is attributed to the earth, to the sun, or to the moon, when we say that there is only one earth which we inhabit, one sun which lightens us, only one moon which turns about the earth in so many days? Do you think that this earth, for example, made up of so many heterogeneous parts must necessarily have a substantial form which is appropriate to it and which gives to it this unity? It does not seem that you believe this. I should say the same thing of a tree, of a horse, and still further I would instance mixtures; for example, milk is composed of the serum, of the cream, and of the portion which hard- ens. Are there here three substantial forms, or is there only one?
6th. Finally, it will be said that it is not worthy of a philosopher to admit entities of which there are no clear distinct ideas; and there are no such clear and distinct ideas of these substantial forms. And furthermore even, you do not let them be proved by their effects, since you acknowledge that it is by a corpuscular philosophy that all the particular phenomenon of nature should be explained, and that there is no advantage in bringing up these forms.
7th. The Cartesians in order to find unity in bodies have denied that matter was divisible to infinity and they have held that indivisible atoms must be accepted; but I think that you do not share their opinion.
I have examined your little brochure and I find it very subtle, but take care lest the Cartesians should reply that it brings nothing up against their position.
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because you posit something which they think false —namely, that a stone, in descending, gives to its own self this greater velocity which it acquires as it descends. They will say that this acceleration comes from the corpuscles, which, in rising, cause everything that they find in their way to descend and impart to them a part of the motion which they had; and therefore there is no cause for surprise if the body B, four times the weight of A, has more motion when it has fallen one foot than the body A when it has fallen four feet, because the corpuscles which have pressed upon B have communicated to it a motion proportioned to its mass and those which have pressed upon A, in proportion to its mass. I do not assure you that this reply will be valid, but I think at least that you ought to see if there be anything init. I shall be very glad to know what the Cartesians have said to your brochure.
I do not know whether you have examined what M. Descartes says in his letters in regard to the gen- eral principle of mechanics. It seems to me that when he wishes to show why the same force can lift by means of a machine twice or four times as much as what it can lift without a machine, he declares that he has not taken into consideration the velocity. My recollection about it, however, is very confused, for I have gone into those things only from time to time and at odd moments, and it is more than twenty years since I have seen any of those books.
I do not wish you, M., to turn away from any of your occupations however important, in order to reply to the two objections which I have brought forward. You may do as you please about them and at your leisure.
LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 149 I should like very much to know if you have not given the finishing touches to the two machines which you invented while at Paris. The one in the province of arithmetic seemed to be much more perfect than that of M. Pascal, and the other was an absolutely correct watch.
I am yours devotedly, XII Count Ernst von Hessen-Rheinfels to Leibniz.
Rheinfels, 21/31, Oct., 1686. Monsieur: I enclose herewith a letter from M. Arnauld, which, by some carelessness of mine, has been here over two weeks. On account of occupation in other business 1 have not read it, and besides such matters are too remote and speculative for me. I send you also four other writings that you may be interested in, and remain, Yours very affectionately, E.
XIII Draft of the letter of Nov. 28-Dec. 8 to Arnauld.
The hypothesis of concomitance is a consequence of the conception which I have of substance, for, in my opinion, the individual concept of a substance involves all that will ever happen to it, and it is in this that complete beings differ from those which are not complete. Now, since the soul is an indi- vidual substance it must be that its concept, idea, 150 CORRESPONDENCE, essence or nature involves all that will happen to it, and God, who sees it perfectly, sees there what it will do or endure forever and all the thoughts which it will have. Therefore, since our tdeas are only the consequences of the nature of the soul and are born in it by virtue of its concept, it is useless to ask regarding the influence of another particular sub- stance upon it. This aside from the fact that this influence would be absolutely inexplicable. It is true that certain thoughts come to us when there are certain bodily movements and that certain bodily movements take place when we have certain thoughts, but this is because each substance ex- presses the whole universe in its fashion and this expression of the universe which brings about a movement in the body is perhaps a pain in regard to the soul. It is customary to attribute the action to that substance whose expression is more distinct and which ts called the cause, just as when a body is swimming in water there are an infinity of move- ments of the particles of water in such a way that the place which the body leaves may always be filled up in the shortest way. This is why we say that this body is the cause of the motion, because by its means we can explain clearly what happens. But if we examine the physics and the reality of the motion, it 1s quite as easy to suppose that the body is in repose and that all the rest is in motion conform- ably to this hypothesis, since every movement in itself is only relative, that is to say, is a change of position which cannot be assigned to any one thing with mathematical precision; but the change is attributed to that body by means of which the whole is most clearly explained. In fact, if we take ail LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. I§t phenomena, great or small, there is only one single hypothesis which serves to explain everything clearly. We can therefore say, that, although this body is not an efficient physical cause of these effects, its idea is at least, so to speak, the final cause of them, or, if you prefer, a model cause* of them in the understanding of God; because, if we wish to ask what reality there is in motion we may imagine that God desires expressly to produce all the changes of position in the universe exactly the same as that ship was producing them while going through the water. Is it not true that it happens exactly in the same way, for it is not possible to assign any real difference? If we speak with meta- physical precision there is no more reason for say- ing that the ship presses upon the water in order to make that large number of circular movements because of which the water takes the place of the ship, than to say that the water itself exerts pressure to make all these circles and that it therefore causes the ship to move conformably. Unless we say, how- ever, that God expressly desired to produce sucha great number of movements so well fitted together, we do not give any real cause for it, and as it is not reasonable to have recourse to divine activity for explaining a particular detail, we have recourse to the ship, notwithstanding the fact that, in the last analysis, the agreement of all the phenomena of different substances comes about only because they are productions of the same cause, that Is to say, of God. Therefore, each individual substance ex- presses the resolves which God made in regard to the whole universe. It is therefore for the same *Cause exemplaire in the original.
152 CORRESPONDENCE.
reason that pain is attributed to changes in the body, because thus we reach something distinct and this is enough for us to produce the phenomena or to prevent them. In order not to advance anything that is unnecessary, however, I say that we only think, and also that we produce only thoughts, and that the phenomena are only thoughts. As, how- ever, all our thoughts are not effective and do not serve to produce for us others of a certain nature, and since it is impossible for us to work out the mystery of the universal connection between phenomena, we must pay attention by means of experience to those which have produced thoughts before, and this is the way the senses do and this is what is called external action, outside of us.
The hypothesis of the concomitance or of the agreement of substances among themselves, follows from what I have said regarding each individual substance: that it involves, forever, all the acci- dents that will happen to it and that it expresses the whole universe in its manner. Thus whatever is expressed in the body by a movement or by a change of position, is perhaps expressed in the soul by asense of pain. Since pains are only thoughts, we must not be surprised if they are the conse- quences of a substance whose nature it is to think. If it happens constantly that certain thoughts are joined to certain movements, this is because God has. created from.the very start all substances in such a way that in the sequence, all their phenomena shall correspond without any need for a mutual physical influence. This latter does not even appear explicable. Perhaps M. Descartes would rather have accepted this concomitance than the LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 153 hypothesis of occasional causes, for so far as I know, he has never expressed himself upon the matter. I am_ pleasantly surprised, M., that St. Augustine, as you say, already held some such view, when he maintained that pain is nothing else than the grief which the soul has when its body ts ill dis- posed. This great man surely thought far into things. The soul, however, feels that its body is ill disposed, not through an influence of the body upon the soul, nor by a particular intervention of God who carries the information, but because it is the nature of the soul to express whatever happens in the body, having been created from the start in such a way that the sequence of its thoughts will agree with the sequence of the movements. Thesame can be said of the motion of my hand upward. It will be asked what it is that influences the spirits to enter into the nerves of a certain material; I reply that it is as much the impressions made by the objects, in virtue of the ordinary laws of motion, as it is the dis- position of the spirits or even of the nerves. By the general inter-agreement of things, however, all these dispositions happen only when there ts at the same time in the soul the will to which we have been accustomed to attribute the operation. Thus, the souls change nothing in the ordering of the body nor do the bodies effect changes in the order- ing of the souls (and it is for this reason that forms should not be employed to explain the phenomena of nature). One soul changes nothing in the sequence of thought of another soul, and in general one par- ticular substance has no physical influence upon another; such influence would besides be useless since each substance is a complete being which 154 CORRESPONDENCE.
suffices of itself to determine by virtue of its own nature all that must happen to it. Nevertheless, one has good reason to say that my will is the cause of this movement of my arm and that an interrup- tion inthe continuity of the matter of my body ts the cause of the pain, for the one expresses distinctly what the other expresses more confusedly and the action should be attributed to the substance whose expression is most distinct. The same can be said practically where phenomena are produced. If it is not a physical cause, we can say that it is a final cause or better a model cause, that is to say, that the idea in the understanding of God has contributed to God’s resolve in regard to this particularity, when the determination regarding the universal sequence of things was being made.
The second difficulty is incomparably greater regarding the substantial forms and the souls of bodies, and I grant that I am not myself satisfied in regard to it. First of all, we must maintain that the bodies are substances and not merely true phenomena like the rainbow, but, on the other hand, even if this were granted, it might be inferred, I think, that the corporeal substance consists neither in extension nor in divisibility for it will be granted that two bodies distant from each other, for exam- ple, two triangles are not really one substance; sup- pose now that they come together to compose a square, does the mere contact make them one sub- stance? J do not think so. Now, every extended mass may be considered asa composite of two or of a thousand others, and the only extension there Is, is that by contact. Consequently, we shall never find a body of which we can say that it is really one LEIBNIZ. ARNAULD. HESSEN-RHEINFELS., 155 substance; it will always be an aggregate of several. Or rather, it will not be a real being, because the component parts are subject to the same difficulty, and we should never reach a real being, for the beings which result from an aggregation have only as much reality as there is in their ingredients. Whence it follows that the substance of a body, if it has one, must be indivisible; whether we call it soul or form makes no difference to me.
The general conception of individual substance, which seems to appeal to you, M., evidences the same thing, that extension is an attribute which can never constitute a complete being; no action can ever be derived from extension, and no change. It merely expresses a present state. Never does it express the future or the past state as the concep- tion of a substance should. When two triangles are joined, we cannot decide howthis union is made, for this might happen in several ways, and what- ever can have several causes is never a complete being.
Nevertheless, I acknowledge that it is very diffi- cult to answer several question which you have put, I think we must say that if bodies or substantial forms, for example, if the beasts have souls, then these souls are indivisible. This is also the opin- ion of St.Thomas. Are these souls therefore inde- structible? I think they are, unless it is possible that in accordance with the opinion of M. Leeuwen- hoeck every birth of an animal is only the transfor- mation of an animal already alive. There is ground, moreover, for thinking that death ts also another transformation. The soul of man, how- ever, is something more divine. It is not only £56 CORRESPONDENCE.