edged that he was ignorant of the author. I desire a judgment naturalism. He published Be admirandis naturse reginx deseque mortalium arcanls, lib. quat., Paris, 1616. His philosophical works, translated into French by Rousselot, appeared at Paris, 1841. Leibnitz, in a letter to Sebas tian Kortholt, March 15, 1713, says: " Apologiam Vanuini uoiidum vidi, nee magnopere dignam legi puto. Scripta ejus parvi moment! suut, sed homo ineptus, imo stultus comburi non merebatur, claudi jure poterat, ne alios inficeret" (Dutens, 5, 321).— TB.
1 Philip Jacob Spener, 1635-1705, was chief pastor of the Lutheran church at Frankfort-on-the-Main, from 1606-1080, first Court-chaplain at Dresden, 1086-1(591, and rector of St. Nicolas, in Berlin, with the title of " Consistorial- rath," from 1691. He directed the foundation of the University of Halle in 1691. Though, according to Ritschl, Gesch. d. Pietismus, 2, 163, Bonn, 1884, "himself not a Pietist," Spener has justly been called "the father of Pietism." He was a voluminous author. Two letters of Leibnitz to Spener are given by 2 Theophil Gottlieb Spitzel, or Spizel, 1639-1091, a German pastor and poly- historian, was deacon of St. James's church, Augsburg, in 1662 and pastor from 1082 to 1090. " As a theologian, in spite of his many-sided and universal sci entific interests, he remained well-nigh unfruitful." Leibnitz refers to the matter here alluded to again in his letter to Spizel, December 12-22, 1(5(59; cf. Dutens, 5, 343. The Confessio Naturse contra Atheistas first appeared as a J'ostscriptum in Theo. Spizelii de Atheismo eradicando ad Virum prsestantis- simum Dr. Antonium Reiserum Aityustanum, etc., Epistola...August.
3 Anton Reiser, 1628-1686, a learned and distinguished Lutheran theologian, was an earnest defender of evangelical truth. He published De ori(/ine, pro- ffrpssn ct incremento antitfieismi sen Atheisini, Augsburg, 1669, 8vo; Index MSIS. bibliothecsB Augmtanx, Augsburg, 1675, 4to. — TR.
650 LEIBNITZ'S CRITIQUE OF LOCKE concerning the reasoning itself of the demonstration. Nor do T seek praise, but criticism, since it is important to religion that it be not perfunctorily defended. Although meanwhile I seem to myself to have penetrated far more deeply into both. For neither the thoughts which I have thrown out since that time concerning perpetual creation in motion, nor the inmost nature of thinking being or mind, are brought together therein. 1 wrote you at one time about the society which certain Germans are starting. It will show its existence by a German paper published by the book seller Goezius with the title " Collegium Philadelphicum." But to me it seems a pleasant dream, like the society of the Red Cross. It is wonderful how great a dissension in Parnassus that Schurz- fleisch l who is with you excited. I very much wish to know what the great men with you by whom he hopes he will be advanced, think of this specimen. Boeder2 threatens that one from the court. The author of the " Itinerarium politicum " which is now appearing is without doubt Burgoldensis,3 that commentator on the " Instru- mentum pacis." I am astounded at the audacity of the man.
As for the rest, most illustrious sir, I have discoursed the more 1 Konrad Samuel Schurtzfleisch, 1G41-1708, was Professor of History at Wittenberg, and because of his great learning was given the nickname of a living library and a walking museum. While at Wittenberg he published, under the name of Eubulus Theosdatus Sarckmasius, a pamphlet, Judicia de novissimis prudentise civilis Scriptoribus, Leipzig, 1669, in which he freely ex pressed his opinion of the most celebrated German jurisconsults, and which aroused against him many adversaries. He continued the history of Sleidau 2 Johann Heinrich Boeder, 1611-1692, Professor of Eloquence at Strassburg and Upsala, and afterwards of History at Strassburg, was author of many commentaries on classical authors and of works of history, politics, criticism, morals, etc. Among them were: De jure Galilee in Lotharingiam, Strass burg, 1663; Ad Grotium de jure belli et pacis dissert., V., 1665. The Elector of Mayence appointed him "conseiller " in 1662, and the next year the Em peror Ferdinand III. bestowed on him the same title and made him Count Palatine. — TR.
3 Philippus Andrea Oldenburgerus, the anagram of which is Burgoldensis, a pupil of H. Conring, was Professor of Law and History at Geneva, where he died in 1678. He published a large number of valuable works, some of them under assumed names, among which are: Itinerarium Germanise Politicum, modernam prsecipuarum Aularum Imperil faciem reprsesentans, Cosmopoli (Geneva), 1668, 12mo; Limnseus enucleatus, an abstract of Limne, De jure imperil Romano-r/ermanici, Geneva, 1670, fol.; Nolitia Imperil, sive Discur- sns in Instrumentum Pacis Osnabrugo-Monasteriensis (this work under the name of Burgoldensis), Freistadt, 1669, 4to. Of the Itinerarium Germanise Politicum, Morhof, Polyhistoria, 2, 497, says: " in quo multa est rerum inep- tissimarum farrago, quibus nonnunquam immiscentur aliqua notatu non in- digna, sed lectore prudente opus est, qui cum judicio ilia legere posit." The freedom with which the author spoke of the political interests and vices of the German courts led to the interdiction of his book. It was, nevertheless, APPENDIX 651 APPENDIX 651 at length of this whole matter to you for this reason, because I had no more learned and equitable judge of these things. Since you have examined all the recesses of the ancients and do not despise the discoveries of the moderns when deserving, you alone of all can best examine this and also illustrate them. For you rightly judge, that although new opinions are brought forth and their truth most evidently shown, yet from the views publicly received we must scarcely ever depart, a thing which we should not strive for if the Scholastics had done it. Farewell, ornament of our country, and do not bring to an end (absolve) your noble thoughts (for many are both begun and at the same time perfected with rare felicity of mind), but produce them.
[From the Latin] The primary matter 2 of Aristotle is identical with the subtile matter of Descartes. Each is divisible to infinity. Each is per se lacking in form and motion, and each receives forms through motion. Each receives motion from mind. Each is formed into certain rings (gyros), and there is no more solidity in the vortices of Aristotle than of Descartes. Each has solidity from motion, because nothing drives it asunder, although Descartes himself has not assigned this cause of solidity. Each ring (gyrus) extends (propagat) the action im pressed through motion on account of the continuity of matter into another ring. For Aristotle also, no less than Descartes or Ilobbes, derives all particulars from the motion alone of universal rings. Whence Aristotle adds intelligences only to the principal rings, because from the impacts of these rings the actions of the others follow. In this Aristotle erred, because he made the earth the centre of the universe and of all gyrations. But he should be par- several times reprinted. In Pt. IV. of his Thesaurus rerum publicarum totius orbis, Geneva, 1675, 4 vols., 8vo, he repudiated the errors and condemned the reprehensible expressions which he had employed in the earlier work. Of the Discui-sus in Instrumentum Pads, Lenglet du Fresnoy remarks: "a bold and learned piece." — TR.
1 Gerhardt, Leibniz. philos. Schrift., 1, 259-GO. In his Einleitung, ibid., 251, G. says: " The fragment, n. I., which was written, perhaps, at the time of the composition of the Hypothesis phyxica (1071), contains a comparison of the metaphysics of Aristotle and Descartes, what Leibnitz borrowed from both, and what he has added of his own." — TR.
2 Upon a bit of paper without date and superscription, proceeding according to the handwriting from the earliest period. — Gerhardt' s Note. — TR.
652 LEIBNITZ'S CRITIQUE OF LOCKE doned for this, because philosophy was not yet sufficiently instructed by observations.
To these I now add, that primary matter if at rest is nothing. This also is a statement which certain Scholastics have obscurely made, that primary matter also has existence from form. Of this fact there is demonstration. Because whatever does not think, is nothing.
o o But that in which there is no variety also does not think. In like manner: If primary matter moves in one direction, that is, in parallel lines, it is at rest, and consequently is nothing. All things are full, because primary matter and space is the same thing. Therefore every motion is circular, either composed of circulars or at least returning into itself. Many circulations mutually hinder each other, or mutually lead into each other. Many circulations try to unite in one or all bodies tend to rest, that is, annihilation. If bodies are without mind, it is impossible for motion to have been eternal. x From universal conflicting circulations are produced particular bodies. Matter is actually divided into infinite parts. There are infinite creatures in any given body whatever. All bodies cohere among themselves. All are indeed forcibly separated (distrahuntur) from all, but not without resist ance. There are no atoms, or bodies whose parts are never forcibly separated. There are two principles by which motion is changed: compositions of efforts (conatuum), and compositions...[a word and two lines are in consequence of the destruction of the paper illegible. — GERHARDT].
Ill DEMONSTRATION AGAINST ATOMS TAKEN FROM THE CONTACT OF ATOMS2 [From the Latin] DEFINITION I. A thing is distinguished from other things in two ways, either through itself, or extrinsically. Through itself a thing is distinguished from another, when a method of distinguishing through the consideration alone of the thing is used, no operation or change being made in the thing. Extrinsically, when by external application something new is produced in the thing, which does not appear in 1 Over the words, " motum fuisse seternum," Leibnitz has written, " potest diminni sine fine," i.e. can be diminished without end. — Gerhardl's Note. — Tn.
2 Gerhardt, Leibniz, philos. Schrift., 7, 284-288; Stein, Leibniz, u. Spinoza, APPENDIX 653 another. Thus the sphere and the cube can be distinguished both by consideration and also by operation; by consideration, because in the sphere no angles are found, of which there are eight in the cube; by operation, as, if both are placed upon an inclined plane, the sphere will descend the plane by rolling, the cube by sliding.
AXIOM. Whatever is distinguishable extrinsically from another, is also distinguishable through itself.1 For example, let there be two coins from the same stamp (typo), one of true gold, the other of false, which may be easily distinguished extrinsically by the blow of the hammer. I say even before the blow, by an attentive consideration, differences in the composition itself of each would be detected by the naked or equipped eye, and although the keenness of vision could not reach thither, yet differ ences exist within and can be detected by some more acute creature (for example, by an angel).2 OBSERVATION. Certain bodies are mutually separated violently from each other.
CONCEDED HYPOTHESIS. Matter is uniform, or, motion and figure excepted, everywhere like itself.
DEFINITION II. An Atom is a body which cannot be broken.
POSTULATE. If there are atoms, we may assume them of any figure and size whatever and in any position whatever.
THEOREM.
It is impossible for all bodies to consist of atoms.
Let us assume (by the postul.) three atoms, A, B, C, of which A is cubical, but B and C are triangular prisms, composing the cube D, similar and equal to the former A. The cube D cannot (by the conceded hypothesis) be distinguished from the cube A. Therefore they cannot be distinguished extrinsically (by Axiom I.). If there fore other bodies strike against the cube D, they will be able either to separate the atoms B and C, or they will not be able. If able to separate them, then the same bodies striking in the same way against 1 On the margin of the Ms., Leibnitz has remarked: "Whatever is dis tinguishable in itself, is also distinguishable extrinsically. If two bodies are similar through a third similar body, they cannot be distinguished. If two bodies are similar, but mutually unequal per se, they can be distinguished, no third body even being assumed. Similar and equal bodies cannot be dis tinguished extrinsically, nay, rather, in any way, and so are one and the same." — Gerhardt's Note. — TR.
2 Stein here inserts in his text the following marginal gloss, wanting in Gerhardt's text: "Hie ostenditur ex hypothesi Atomistica sequi, quod novaj Atomi nasci possint, nee tamen iterum dissolvi contra naturae morem," i.e. Here it is shown to follow from the Atomistic hypothesis, that new atoms can be produced, but nevertheless cannot again be dissolved coutrary to the law of nature. — TR.
LEIBNITZ'S CRITIQUE OF LOCKE the cube A will be able violently to separate the same into parts, for otherwise A and B might be distinguished extrinsically (by Defin. I.), the contrary of which has been shown. But if the cube A is vio lently separated into parts, it certainly (by Defin. II.) will not be an atom, as was supposed. But if other bodies cannot again separate the cube D into component parts, it follows that the atom was not produced from non-atoms through contact. And the same principle Avill hold, whatever figure the atoms be assigned. Whence it follows that atoms which have once touched each other cannot again be violently separated. Now if all bodies are composed of atoms, bodies do not touch each other except through the atoms. Therefore they cannot be violently separated after contact, unless the atom of the one is violently separated from the atom of the other, which we have shown cannot be done. But bodies not be violently sepa rated...1 And so it is not true that all bodies are composed of atoms. Q. E. D.
SCHOLIUM TO THE DEMONSTRATION AGAINST ATOMS TAKEN FROM THE CONTACT OF ATOMS.
October 24, 1G90.
I do not see what reply can be made to this demonstration unless by a denial of the postulate. For we postulated that it be conceded us: If there are atoms, they can be assumed of any figure and size and in any position whatever. This alone seems possible to be said with any reason, atoms cannot be granted, the parts of which are connected only by a point or line. And so there cannot (for example) be an 1 More words illegible. — Gerhardt's Note. sentence. — TK.
Stein omits this incomplete APPENDIX 655 atom similar to one composed from two spheres touching each other. But if then atoms spherical or terminated by any other curved sur faces whatever are granted, they never touch each other save in a point, and so never compose a body similar to an atom. Here in some way I think a reply can be made, in the first place if the contact in the surface is the cause of stability, it follows that stability is greater when the surface is greater. Whence the atoms would not be equally stable. And so there would be a certain determinate force of violent separation by which stabilities could be measured. I do not see where we can find this force, if it is not in the motion of bodies, unless we advocate certain spiritual powers whose method of acting in bodies nevertheless cannot be known. But if the stability of all atoms is equal, it does not matter how great the contact is; even contact in a line, nay in a point, would suffice.
A second reply w7hich can be made is this: it has at least been demonstrated by us that bodies cannot be composed of atoms ter minated by plane sides. But besides the fact which can be doubted, whether indeed curvilinears properly called are granted, this excep tion does not seem in agreement with the reasons of things, that if composition from atoms is possible it must necessarily take place through bodies destitute of a plane surface.
The third reply is this: not only the atoms of plane surfaces but also of concave must be assumed (tollendas) from nature. Otherwise we shall be permitted to make atoms from the non-atom, as often as the concave surface of one atom happens to be applied to the convex surface of another, and that will happen until all the atoms of the concave surfaces shall be filled as far as can be done by the convex existing in nature. But this restriction also does not seem in har mony with the reasons of things. And in general, if any one denies that there are other atoms than the perfectly spherical, in order to escape the force of the demonstration, these things are devised which indeed are accommodated to the latter, but do not accord with the primal reasons and amplitude of nature. In brief: from the hypo thesis of atoms I can deduce absurdity, provided I am allowed to assign to the atoms size, figure, and motion as 1 will.1 1 On the margin of the Ms., Leibnitz has remarked: "Another argument could be set up, namely: If atoms could be granted, bodies similar and equal, and nevertheless different from each other, as would be two equal spheres, could be granted. If atoms were granted, no cause of reflection, which in fact must be taken from an elastic body (Elaterio), could be perceived, nor would the atoms striking each other leap apart, in turn, from each other. Further superficial contact is the cause of cohesion, two atoms coming together in sides or surfaces would not leap apart; thus, if the velocity of each approach is equal, the whole force would perish'." — Gcrhardt's Note. Stein has put this marginal gloss into the text, with a note stating that it is a marginal gloss.
656 LEIBNITZ'S CRITIQUE OF LOCKE APPENDIX TO THE DEMONSTRATION AGAINST ATOMS TAKEN FROM THE CONTACT OF ATOMS.
If any one denies that there can be atoms, the parts of which touch each other in a point only or line, and so requires contact in the sur face for cohesion, that he may avoid the force of our demonstration, that one will entangle himself in other new difficulties.
For if cohesion arises from superficial contact, a case can be seen in which an atom is unable to graze (radere) an atom; for where a part of the side of the atom. B coincides with a A 2 A iA part of the side of the atom -r4, they are not only unable to leap apart and also to separate — J violently, but even the one will not be able to slide upon the other, for they touch each other in the surface. Nay, rather, what is more FIG. 2. wonderful, the atom A coming by its own mo tion from the place VA into the place 2A so situated, that it is unable to proceed farther, because it grazes the atom B, is there arrested without any obstacle as if it were an en chanted object. Xor does it suffice to say that no such atoms are given, and that no others exist unless spherical or at least bounded by convex surfaces. For it suffices that atoms bounded by plain or concave sides are possible, if those bounded by convex sides are possible; and from the supposed possibility of these that which is absurd follows, whence it follows that convex atoms are not to be admitted.
But if any one because of these considerations now requires no longer superficial contact only, but also the rest of bodies tangent to each other for cohesion, lest forsooth one atom be kept from sliding upon another, that one is unable to bring forth proof of his opinion, nor does it appear why the nature and the force of the present state which is contact must depend upon a past state, so that forsooth the present contact causes cohesion, if it has remained for some consider able time in the same place, as if there were need of a certain habi tude, whence indeed it would follow that stability is increased by duration and that atoms newly produced are the more stable the longer they cohere, a fact which no one will surely easily affirm. But neither can the moment be assigned in which the cohesion of two atoms begins, because it is entirely perfect at once. And if it does not begin unless it has continued for some time, it will never begin, for it would itself be prior to itself. Moreover, all rest can be under stood as composed of two motions, so that if a body is moved at the same time by two moving bodies and so remains quiet accidentally, shall it then be understood also to adhere to the sides of another body APPENDIX 657 APPENDIX 657 which it grazes? And so whithersoever we are turned, we fall into awopa, which is not strange, because we assumed an hypothesis lack ing in reason, namely, that the highest stability is without an intelli gible cause.
But if any one thinks that atoms can be produced at least by the decree of God, we confess to him that God can make atoms, but a perpetual miracle would be needed to resist a forcible separation, since in a body itself a principle of perfect stability cannot be per ceived. God can perform whatever is possible, but it is not always possible to transfer his power to creatures, and to bring it to pass that they themselves can do per se what they accomplish through his own power alone.
IV ESSAY ON DYNAMICS ON THE LAWS OF MOTION, IN WHICH IT IS SHOWN THAT NOT THE SAME QUAN TITY OF MOTION IS PRESERVED, BUT THE SAME ABSOLUTE FORCE, OR RATHER THE SAME QUANTITY OF MOVING ACTION (L' ACTION MOTRICE)1 [From the French] The opinion that the same quantity of motion is preserved and abides in the concourse of bodies has reigned a long time, and passed as an incontestable axiom among modern philosophers. We under stand by the quantity of motion the product of the mass by the velocity, so that the mass of the body being as 2 and the velocity as 3, the quantity of motion of the body will be as 6. Thus if there were two concurrent bodies, multiplying the mass of each by its velocity and taking the sum of the products, it is maintained that this sum must be the same before and after the concourse.
We begin now to be disabused of this opinion, especially since it has been abandoned by some of its most ancient, most skilful, and most eminent defenders, and above all by the author himself of the " Search after Truth." 2 But in this case an inconvenience has arisen, namely, that we have been thrown too far into the other extreme, and do not recognize the conservation of anything absolute which might hold the place of the quantity of motion. But our mind looks for this, and it is for this reason that I remark that philosophers who do 1 Gerhardt, Leibniz, math. Schrift., II. 2 [Vol. 6], pp. 215-231. Published from the Ms. in the Royal Library at Hanover. Written, according to Ger hardt, probably about 1691, cf. op. cit., Einleitung, p. 14. — Tit.
658 LEIBNITZ'S CRITIQUE OF LOCKE not enter into the profound discussions of mathematicians have diffi culty in abandoning an axiom such as this of the quantity of con served motion without giving themselves another to which they may hold.
It is true that the mathematicians who a long time since established the rules of motion based on experiments have remarked that the same relative velocity is preserved between the concurrent bodies. For example, if one of the two is at rest, or if both are in motion, and proceed the one against the other, or in the same direction, there is a relative velocity, with which they approach or depart the one from the other; and we find that this relative velocity remains the same, so that the bodies depart after the impact with the velocity with which they were approaching before the impact. But this relative velocity can remain the same although the true velocities and absolute forces of the bodies change in an infinite number of ways, so that this conser vation does not concern that which is absolute in bodies.
I remark also another conservation, namely, that of the quantity of progress, but neither is this the conservation of that which is abso lute. I call progress the quantity of motion with which a body pro ceeds in a certain direction, so that if the body went in a contrary direction, this progress would be a negative quantity. Now if two or more bodies are concurrent, we take the progress from the direction whence proceeds their common centre of gravity, and if all these bodies proceed from the same direction, then we must take the sum of the progress of each for the total progress; and it is plain that in this case the total progress and the total quantity of motion of the bodies are the same thing. But if one of the bodies proceeded from a contrary direction, its progress in the direction in question would be negative and consequently must be subtracted from the others in order to have the total progress. Thus if there are only two bodies, one of which proceeds in the direction of the common centre, and the other in a contrary direction, from the quantity of motion of the first must be subtracted that of the second, and the remainder will be the total progress. Now it will be found that the total progress is con served, or that there is as much progress in the same direction before or after the impact. But it is also plain that this conservation does not correspond to that which is demanded of something absolute. For it may happen that the velocity, quantity of motion, and force of bodies being very considerable, their progress is null. This occurs when the two opposed bodies have their quantities of motion equal. In such case, according to the sense we have just given, there is 110 total progress at all.
Long since I corrected and rectified this doctrine of the conser vation of the Quantity of Motion, and put in its place the con servation of some other absolute thing; but as regards the precise APPENDIX 659 form iu w iiich this doctrine should be conceived,1 that is to say, the conservation of absolute force, it is true that commonly they do not appear to have entered sufficiently into my reasons nor to have appre hended the beauty of that which I have observed, as I remark in all that has been published in France or elsewhere on the laws of motion and mechanics, even after what I have written on Dynamics. But as some of the most profound mathematicians after many discussions have yielded to my opinion, I promise myself with time general ap proval. To return then to what I said of the conservation of absolute force, we must know that the origin of the error concerning the quan tity of motion arises from that which has taken it as force. We have been led, I think, naturally to believe that the same quantity of the total force abides before or after the impact of the bodies, and I have found this very true. Now the quantity of motion and force being taken as one and the same thing, we have concluded that the quan tity of motion is conserved. What has contributed the most to con found force with quantity of motion is the abuse of the static doc trine. For we find in statics that two bodies are in equilibrium when