But the Cartesians, not sufficiently understanding the nature of forces, confounding motive force with motion, have seriously erred in determining the laws of motions. For although Descartes knew that the same force must be preserved in nature, and that a body, although he attributed a part of its force (namely, the derivative) to another, so retains a part that the sum of the forces remains the same, (yet), deceived by the example of equilibrium or dead force as I call it (which here does not enter into the reckoning, and of living force or of that which is now in question, it is only an infini tesimal part), (he) believed that force exists in a composite system (ralione composita) of masses and velocities, or that it is the same as that which he calls quantity of motion, by which term he under stands the product of the mass into the velocity (ex ductu massce in celeritatem), when, nevertheless, it has elsewhere been demonstrated by me a priori that forces exist in a composite system of simple masses and double velocities. I know that lately certain learned men, when at length they were compelled to admit against the Cartesians that the same quantity of motion is not preserved in nature, and considered this too alone as absolute force, concluded that this force also does not abide, and took refuge in the conserva tion alone of relative (respective^) force, but we have discovered that not in the conservation of absolute force even has nature been mindful of her own constancy and perfection. And the opinion of the Cartesians indeed, in which the quantity of motion is pre served, contradicts all the phenomena, (while) ours is wonderfully confirmed by experiments.
The Cartesians err, also, in this, because they think that changes occur by a leap (per saltum); as if, for example, a body at rest can in a moment pass over into a state of determined motion, or as if a body placed in motion can suddenly be brought back to rest, not by passing through the intermediate grades of velocity, because they have plainly not understood the use of elastic force in the concourse of bodies. Which, if it were absent, I confess that neither the law which I call the law of continuity would be observed in things, through which APPENDIX 705 APPENDIX 705 leaps are avoided, nor the law of equivalence by which absolute forces are conserved, nor other excellent inventions of nature's architect have place, by which the necessity of matter and the beauty of form are united. Moreover, the elastic force itself implanted in every body shows that there is in every body, also, internal motion and infinite (so to speak) primitive force, although in the impact itself, when circumstances demand, it is determined by derivative force. [For, as in an arch, any part whatever sustains the entire weight, or in a tense cord the traction, and any portion whatever of compressed air, has as much force as the weight of the air pressing upon it, so any corpuscle whatever, of the entire ambient (ambientis) mass is solicited to action by the conspiring force, and awaits nothing but an occasion for exer cising its power, as is shown by the example of gunpowder (pulveris pijrii) ].
There are many other things in which I have been obliged to de part from Descartes, but those which I have now brought forth relate chiefly to the principles themselves of corporeal substances, and, if you interpret them rightly, are capable of vindicating the ancient philos ophy of a healthier school, which I see deserted by many of the more recent scholars, even those well disposed towards it, where there was no need. The philosophy of Rev. Father Ptolemseus,1 a man very versed in the principles of the ancients and the moderns, whose remarkable teaching I examined myself, at Rome (from which philos ophy I promise myself very much), has not yet reached us.
In a note, Leibnitz has added: In addition, I am pleased to state, that although very many Cartesians boldly reject forms and forces in bodies, Descartes nevertheless spoke more moderately, and professed this only, that he found no reason for using them. I indeed admit that they should be rejected if of no use; but in this very thing I have shown that Descartes has erred. For not only in entelechies, or TW SwayuiKoJ, are placed the principles of mechanism, by which all things are regulated in bodies, but I have also shown in the " Acta Eruditorum," 2 when I was replying to the very celebrated man, John Christopher Sturm,3 who attacked, in his " Physica Eclectica," my in- 1 Giovanni Battista Tolomei, 1053-1726, was acquainted with all the Euro pean languages and had a very extensive knowledge of all the sciences of his time, and was reputed a profound theologian and skilful critic. Among his works was Philosophia mentis et sensuum, Romas, 1696, fol., Augusta; Vin- delicorum, 16(J8, fol. — TK.
2 Sept. 1698. The piece is the De ipsa natura, cf. Gerhardt, Leibniz, philos. Schrift., 4,504-516; Erdmann, 154-160; Jacques (in French), 1,455-468; Janet (in French), 2, 553-567; transl., Duncan, 112-126. Cf. also Gerhardt's Einlei- 3 Johann Christoph Sturm, 1635-1703, was, from 1669, Professor of Mathe matics and Physics at the University of Altdorf. His Physica Eclectica appeared at Nuremburg, 1697, 4to. While not celebrated for physical dis- 706 LEIBNITZ'S CRITIQUE OF LOCKE sufficiently understood doctrine, with irrefragable demonstration that, completeness being assumed, if there were nothing in matter but mass itself and arrangement of its parts, it would be impossible for any perceptible variation whatever to occur, since equivalences are substi tuted for limits, and by banishing conatus, or the force of tendency, to the future (the entelechies, that is, being removed), the state of things present at one moment cannot be distinguished from the state at any other moment. And I think Aristotle perceived this when he saw that, besides local motion, change is necessary in order to satisfy the phenomena. But changes, although in appearance manifold, just as qualities, are reduced in the last analysis to variation alone of forces. For all the qualities of bodies, that is, all their real stable accidents, except forms (that is, those which do not exist in transition, as motion, but are known as present, although referred to the future), are at length, when analysis is set up, reduced to forces. Further, when forces are removed, nothing real remains in motion itself, for from variation alone of arrangement it cannot be determined where the true motion or the cause of variation is.
VIII VIII LETTER OF LEIBNITZ TO BASNAGE DE BEAUVAL, EDITOR OF THE "HISTOIRE DES OUVRAGES DES SAVANTS," PRINTED IN THAT JOURNAL, JULY, 1698, Explanation of the difficulties which M. Bayle has found in the New System of the Union of the Soul and the Body I take the liberty, Sir, to send you this explanation of the diffi culties which M. Bayle has found in the hypothesis which I have proposed in order to explain the union of the soul and the body. Nothing is kinder than the manner which he has used towards me, and I consider myself honored by the objections he has placed in his excellent Dictionary, in the article Rorarius. Moreover, a mind as great and as profound as his cannot make them without instruct ing, and I shall try to profit by the light which he has shed upon coveries, he emphasized the method of experiment, and spread abroad a taste for experimenting. Germany is said to owe to him the introduction of the teaching of mathematics into the gymnasia and the common schools. — Tit.
1 Of. Gerhardt, Leibniz. philos. Schrift., 4, 517-524, cf. G.'sEinlcitung, ibid., 419; Erdmann, Leibnit. op. philos., 150-154; Jacques, (Euvres de Leibniz, 1, 481-487; Dutens, Leibnit. op. om., 2, Pt. I., 74-79.
APPENDIX 707 these matters in this part as well as in many other parts of his work. He does not reject what I had said of the conservation of the soul and also of the animal, but he does not yet appear satisfied with the manner in which I have claimed to explain the union and the inter course of the soul and the body in the " Journal des Savants " of June 27 and of July 4, 1695, and in the " Histoire des ouvrages des savants," Here are his words, which seem to indicate wherein he has found difficulty: "I cannot understand," he says, "the series of actions, internal and spontaneous, which would cause the soul of a dog to feel pain immediately after having felt joy, although it were alone in the universe." I reply that when I said that the soul, although only God and it should exist in the world, would feel all that it now feels, I only employed a fiction in supposing that which cannot happen naturally, in order to show that the feelings of the soul are only a consequence of that which is already in it. I know not whether the proof of incomprehensibility which M. Bayle finds in this series must be sought alone in that which he calls lower, or whether he wished to introduce it from this time by the example of the spontaneous pas sage from joy to pain; perhaps, by wishing to throw out a hint that this passage is contrary to the axiom which teaches us that a thing always continues in the state in which it is once if nothing occurs which obliges it to change, and that thus the animal having once joy will always have it if it is alone or if nothing external makes it pass to pain; in every case I agree with the axiom, and, further, I main tain that it is in my favor, as in fact it is one of my grounds. Is it not true that from this axiom we conclude, not only that a body at rest will always be at rest, but also that a body which is in motion will always preserve this motion or change, that is to say, the same velocity and the same direction, if nothing occurs to hinder it? Thus a thing does not remain only so long as it depends upon itself (d'elle) in the state in which it is; but also when this is a state of change, it continues to change, following always one and the same law. Now it is, according to my view, the nature of created substance to change continually according to a certain order which conducts it spontane ously (if I may avail myself of this word) through all the states which will happen to it, so that he who sees all, sees in its present state all its past and future states. And this law of order, which con stitutes the individuality of each particular substance, has an exact relation to that which happens in every substance and in the entire universe. Perhaps I do not make too bold a statement if I say that I can demonstrate all this, but at present the question is only of maintaining it as a possible hypothesis suitable for explaining the phenomena. Now in this way the law of the change of the substance of the animal bears it from joy to pain at the moment that a continu- 708 LEIBNITZ'S CRITIQUE OF LOCKE ous solution is made in its body, because the law of the indivisible substance of this animal is to represent what is done in its body in the way that we experience it, and also to represent in some fashion and in relation to this body all that is done in the world; the unities of substance being nothing else than different concentrations of the universe represented according to the different points of view which distinguish them.
M. Bayle continues: " I understand why a dog passes immediately from pleasure to pain when, being very hungry, and eating bread, we give him a blow with a stick." I do not know whether we understand it sufficiently. No one knows better than M. Bayle him self, that it is in this that the great difficulty consists of explaining why that which passes in the body produces a change in the soul, and that it is this which has forced the defenders of occasional causes to recur to the care which God must take to represent continually to the soul the changes which take place in the body; whilst I believe that it is the nature itself which God has given it to represent in virtue of its own laws what passes in the organs. He continues: " But that his soul is constructed in such a way that at the moment he is struck he would feel the pain, although we should not strike him, although he should continue to eat the bread undisturbed and unhindered, this is what I cannot understand." I do not remember, also, to have said it, and we could say it only by a metaphysical fiction, as when we suppose that God annihilates a body in order to produce a vacuum, both being equally contrary to the order of things. For since the nature of the soul was made at first in a manner suited to represent successively the changes of matter, the case we suppose cannot happen in the natural order. God could give to each substance its phenomena independent of those of others; but in this way he would have made, so to speak, as many worlds without connection as there are substances; almost, as we say, that when we dream we are in a world apart, and that we enter into the common world when we awake. It is not that the dreams are unrelated to the organs and the rest of the body, but that they are related in a manner less distinct. Let us continue with M. Bayle: "I find, also," says he, "the spontaneity of this soul very incompati ble with the feelings of pain, and, in general, with all the perceptions which are displeasing to it." This incomprehensibility would be cer tain, if spontaneous and voluntary were the same thing. Everything voluntary is spontaneous; but there are spontaneous actions which are without choice, and consequently are not voluntary. It does not depend upon the soul, always, to procure feelings which please it, since the feelings it will have depend upon those which it has had. M. Bayle proceeds: " Moreover, the reason why this clever man does not approve the APPENDIX 709 Cartesian system appears to me to be a false supposition: for it cannot be said that the system of occasional causes makes the action of God intervene by a miracle (Dc.um ex machina) in the reciprocal dependence of the body and soul; for, as God intervenes only according to general laws, he does not act there in an extraordinary way." It is not for this reason alone that I do not approve of the Cartesian system; and if you consider mine a little, you see clearly that I find in itself that which leads me to embrace it. Moreover, if the hypothesis of occa sional causes should not need miracle, it seems that mine would not cease to have other advantages. I have said that \ve may imagine three svstenis to explain the intercourse we find between the soul and the body; namely, first, the system of the influence of the one upon the other, which is that of the schools taken in the common sense, which I believe impossible, after the Cartesians; second, that of a perpetual overseer, who represents in the one that which takes place in the other, very much as if a man were charged with making two bad clocks always to agree, which of themselves would not be capable of agreeing, and this is the system of occasional causes; and third, that of the natural agreement of two substances such as would exist between two very accurate clocks; and I find this as possible as the system of the overseer, and more worthy of the author of these sub stances, clocks or automata. But let us see whether the system of occasional causes does not in reality suppose a perpetual miracle. They say here, no, because God would act according to this system only through general laws. I agree, but, in my opinion, that is not sufficient in order to remove the miracles: if God did it continually, they would not cease to be miracles, taking this word not popularly, as a thing rare and wonderful, but philosophically, as that which exceeds the forces of created beings. It is not sufficient to say that God has made a general law; for, besides the decree, there must also be a natural means of executing it; that is to say, what takes place must be capable of being explained by the nature which God gives to things. The laws of nature are not so arbitrary or so indifferent as many think. If God decreed, for example, that all bodies should have a tendency toward a circular line, and that the radii of the circles should be proportional to the size of the bodies, it would be necessary to say that there is a means of executing this decree by more simple laws, or rather, it would be necessary to admit that God will execute it miraculously, or at least by angels expressly charged with this care, very nearly like those who were sometimes given to the celestial spheres. It would be the same if some one said that God has given to the bodies natural and primitive gravities by which each should tend to the centre of its globe, without being pushed by other bodies; for in my opinion this system would need a perpetual miracle, or at least the assistance of the angels.
710 LEIBNITZ'S CRITIQUE OF LOCKE " Does the internal and active property communicated to the forms of bodies know the series of actions it is to produce? Not at all; for we know by experience that we are ignorant that we have in an hour such or such perceptions." I reply that this property, or rather this soul or form, does not know them distinctly, but that it feels them confusedly. There is in each substance traces of all which has hap pened to it and of all which will happen to it. But this infinite mul titude of perceptions hinders us in distinguishing them; as when I hear a great confused noise of a whole people, I do not distinguish one voice from another.
"It would be necessary, then, that the forms be directed by some external principle in the production of their acts; would not this be the Deus ex machina, just the same as in the system of occasional causes? " The preceding reply puts a stop to this inference. On the contrary, the present state of each substance is a natural result of its preceding state; but there is only one infinite intelligence therein which can see this result, for it envelops the universe in souls as well as in each portion of matter.
M. Bayle concludes with these words: "Finally, as he supposes with much reason that all souls are simple and indivisible, we cannot understand how they can be compared to a pendulum, that is to say, that by their original constitution they can diversify their operations, by availing themselves of the spontaneous activity which they would receive from their Creator. We conceive clearly that a simple being will always act uniformly, if no foreign cause turns it aside. If it were composed of many pieces, as a machine, it would act diversely, because the particular activity of each piece might change at every moment the course of that of the others; but in a single substance, where will you find the cause of the change of operation? " I find that this objection is worthy of M. Bayle, and that it belongs to those which most deserve to be cleared up. But I also think that if I had not provided for it at first, my system would not deserve to be ex amined. I have compared the soul to a pendulum only in regard to the regulated precision of its changes, which is indeed but imperfect in the best clocks, but which is perfect in the works of God; and we may say that the soul is an immaterial automaton of the most accurate kind. When it is said that a simple being will always act uniformly, there is a distinction to be made, if to act uniformly is to follow per petually one and the same law of order or of continuity, as in a cer tain rank or series of numbers, I admit that every simple being itself, and indeed every complex being acts uniformly; but if uniformly means likewise, I do not agree. To explain the difference of this sense by an example, a movement in a parabolic line is uniform in the first sense; but it is not so in the second, the portions of the para bolic line not being similar among themselves like those of the straight APPENDIX 711 lines. It is true, to mention it in passing, that a simple body left to itself describes only straight lines, if we speak only of the centre which represents the motion of this entire body; but when a simple and rigid body, having once received a turbination or circulation around its centre, retains it in the same sense and with the same velo city, it follows that a body left to itself may describe circular lines by its points distant from the centre, when the centre is at rest, and even certain quadratrices, when this centre is in motion, which have the ordinate composed of the straight line running through the centre, and of the right sine whose versed sine is the abscissa, the area being to the circumference as this straight line is to a given straight line. We must consider also that the soul, wholly simple as it is, has always a feeling composed of many perceptions at once, which fact effects as much for our purpose as if it were composed of pieces like a machine. For each preceding perception influences the following, conformably to a law of order which exists in perceptions as in move ments. Thus the majority of philosophers, for many centuries, who allow thoughts to souls and to angels, which they believe destitute of all body, to say nothing of the intelligences of Aristotle, admit a spontaneous change in a simple being. I add that since the percep tions which are found together in one and the same soul, at the same time, involve a multitude veritably infinite of minute indistinguishable feelings as the sequel must develop, we must not be astonished at the infinite variety of that which must result therefrom in time. All this is only a consequence of the representative nature of the soul, which must express what passes and indeed what will pass in its body, and in some fashion in all others, through the connection or correspon dence of all parts of the world. It would perhaps suffice to say that God, having made atoms corporeal, might also well have made them immaterial to represent the first; but we have thought it would be well to dwell upon it a little more.
For the rest, I have read with pleasure what M. Bayle says in the article Zeno. It might, perhaps, be perceived that what can be drawn therefrom agrees better with my system than with every other, for what there is of reality in extension and motion consists only in the ground of the order and the regulated series of phenomena and per ceptions. In like manner, as many academicians and sceptics as those who wish to reply to them, seem to be embarrassed principally only because they sought a greater reality in sensible things outside of us than that of the regulated phenomena. We conceive extension in conceiving an order in coexistences, but we must not conceive it any more than space, after the fashion of a substance. It is like time, which presents to the mind only an order in changes. And as for motion, what is real therein is the force or the power; that is to say, what there is in the present state which carries with itself a 712 LEIBNITZ'S CRITIQUE OF LOCKE change for the future. The rest is only phenomena and relations. The consideration of this system shows also that, when we enter into the heart of things, we iind more reason than we thought in the majority of the philosophic sects. The little substantial reality of the sensible things of the Sceptics; the reduction of all to harmonies or numbers, ideas, and perceptions of the Pythagoreans and Platon- ists; the one and also the all of Parmenides and of Plotinus without any Spinozism; the Stoic connection, compatible with the spontaneity of the others; the vital philosophy of the Kabbalists and Hermetics who put feeling above everything; the forms and entelechies of Aristotle and the Scholastics, and even the mechanical explanation of all particular phenomena, according to Democritus and the moderns, and so forth, find themselves reunited as in a centre of perspective, whence the object, obscured in regarding it from an entirely different point, shows its regularity and the agreement of its parts; we have failed through a sectarian spirit in limiting ourselves by the rejection of others. The formalist philosophers blame the material or cor- pusculary ones, and vice versa. We wrongly give limits to the division and subtilty as well as to the richness and beauty of nature when we posit atoms and the vacuum, when we imagine certain primary ele ments, such as the Cartesians, instead of veritable unities, and when we do not recognize the infinite in everything, and the exact expres sion of the greatest in the smallest, united to the tendency of each to develop itself in a perfect order, which is the most admirable and the most beautiful result of the sovereign principle, whose wisdom would leave nothing better to be desired by those who could under stand its economy.
IX FRAGMENT OF A LETTER TO AN UNKNOWN PERSON October 10, 1707 l [From the French] I think, then, I have good reasons for believing that all the differ ent classes of beings whose union forms the universe, exist in the ideas of God only as so many ordinates of the same curve, the union of which does not allow the placing of others between them, because that would indicate disorder and imperfection. Men are connected 1 Guhrauer, Leibnitz, Eine Biographic, Anmerkungen z. zw. Buche, pp. 31-33. Guhrauer says in the note which contains the Fragment here translated: "The Principle of Continuity, with which Leibnitz accomplishes so much in APPENDIX 713 with the animals, these with the plants, and these again with the fossils, which will be united in their turn with bodies which the senses and the imagination represent to us as perfectly dead and shapeless. Now since the law of continuity demands that when the essential determinations of a being approach those of another so that like wise accordingly all the properties of the first must gradually approach those of -the last, it is necessary that all the orders of natural beings form only one chain, in which the different classes, like so many links, connect so closely the one to the other, that it is impossible for the senses and the imagination to fix the precise point where any one begins or ends: all the species which border on or which occupy, so to speak, the regions of inflection and retrogression being obliged to be equivocal and endowed with characters which can refer to the neighboring species equally. Thus the existence of Zoophytes for example, or, as Buddeus1 calls them, Plant- Animals, is nowise mon strous, but it is indeed agreeable to the order of Nature that there are some. And such is the force of the principle of continuity with me that, not only should I not be astonished to learn that beings had