O R G A N O N 5 (1968) LE 250e ANNIVERSAIRE DE LA MORT
DE G. W. LEIBNIZ
Dieter T urek (German Federal Republic)
THE CONCEPT OF MOTION IN LEIB N IZ’ EARLY PHILOSOPHY AND ITS INFLUENCE ON THE DEVELOPMENT
OF HIS PHILOSOPHICAL METHOD *
Compared w ith Leibniz’ m ature m etaphisical system , commonly called the th eo ry of Monads, his early philosophy has been paid relativ ely little attention to. For sim ilar reasons the stu dy of K a n t’s pre-critical w ri tings has been tem porarily neglected. The great original philosophical systems w hich K ant and Leibniz published at th e age of 57 and 40, re spectively, w ere regarded by both of them as th e m ain achievem ents of th e ir lives and as th eir philosophical legitim ations; and it is in fact these systems w hich have deeply influenced the developm ent of hum an thought. In th e ir eyes and in those of posterity the w orks th a t had been w ritten p rio r to th e conception of th e ir final philosophy w ere only of minor, if any, im portance. They w ere regarded as th e products of ju v e nile and im m ature minds. N evertheless, a closer exam ination of the early thought, especially in the case of Leibniz, is very rew arding. It can open up new ways of understanding his m atu re philosophy w hich the latter, if considered in itself, cannot o f f e r .1
An approach like this can rely for its justification upon one of Leibniz’ basic methodological principles w hich suggests th a t if a certain object or a set of objects are to be understood one has to go back to th eir origin and find out th e conditions w hich led to th e ir generation. 2 This principle proves successful also if applied to the philosophy of
* R eport read at th e Intern atio n al Leibnizian congress, H annover, Novem ber 1966.
1 Among th e studies of Leibniz which attem p t to show th e origin of his m atu re philosophy in his early w ritings the m ost valuable are: Willy Kabitz, Die Philo
sophie des jungen Leibniz, Heidelberg 1909; M artial G ueroult, D ynam ique et M eta physique Leibniziennes, P aris 1934; Joseph M oreau, L ’Univers Leibnizien, Lyon
1956; F riedrich K aulbach, Der philosophische B egriff der Bewegung, K oln-G raz 1965.
2 Cf. De Syn th esi et A nalysi universali seu A rte inveniendi et judicandi, in: G erhardt, Die Philosophischen Schriften von G ottfried W ilhelm Leibniz, Vol. 7, Hildesheim 1965, p. 292 (below quoted as: G erhardt).
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Leibniz. The exam ination of certain ideas and problem s to be found in his w ritings as early as 1671 casts a surprisingly new light on th e The ory of Monads. It is th e ultim ate aim of this paper to show one such pos sibility of understanding Leibniz’ la ter m etaphysics by an exam ination of his early thought. It attem pts to give some h ints a t th e system atical and the historical origin of th e Theory of Monads. This origin w ill be found to lie in Leibniz’ methodology, i.e. in a decisive sh ift from the purely deductive and m athem atical m ethod both in science and in p h i losophy in his early years to th e m ore inductive and em pirical m ethod of his la te r years. To illu strate this th e m ain p a rt of this paper is de dicated to an exam ination of Leibniz’ trea tm e n t of th e concept of mo tion in his early years prior to the conception of the Theory of Monads. In his discussion of the problem of motion, Leibniz from the very outset (since 1665 or 1666, i.e. since the end of his earliest, scholastic period) resolutely abandoned A ristotelianism and adopted the view of the new philosophy of n atu re of th e 16th and 17th centuries, according to w hich m otion is nothing b u t local motion, i.e. change of place o r si tuation. In exam ining Leibniz’ m ajor w ritings and le tters on th e phi losophy of n atu re from before 1670 one im m ediately realizes th a t from the v ery beginning he pays p a rticu lar atten tion to two problem s of motion—th a t of its n atu re and th a t of its origin. Nowadays those pro blems are considered as p a rt of the theory of the foundations of n atu ra l science; for Leibniz, however, they belonged to m etaphysics. Therefore we shall have to look upon Leibniz’ trea tm e n t of motion prim arily as a problem of contem porary m etaphysics. The term “m etaphysics of na tu re ” used in this paper is to be understood in this sense; it is m eant to be a philosophical foundation of n a tu ra l science, notably of physical motion and its laws.
F irst, let us tu rn to th e problem of the origin of motion. It derives logically from the principle of sufficient reason w hich can be found expressis verbis a t various places still before 1670. In the treatise Con- fessio Naturae contra Atheistas (1668) Leibniz expresses it this way: “Omnis enim affectionis Ratio vel ex re ipsa, vel ex aliquo extrinseco deducenda est.” 3 A pplying this principle to motion Leibniz arrives at the question: Does motion originate from physical bodies o r is it conveyed to them from w ithout? In order to answ er it he has first to enquire into th e n atu re of physical bodies, i.e. he has to look for the definition of a physical body. This definition renders the essence of an object and w ithout it we cannot tell w hich properties can be deduced from the object and w hich cannot. Leibniz is quite sure of having the tru e de finition of a physical body. According to this definition th e essence of bodies consists in extension (extensio) and im penetrability (im
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bilitas, antitypia). Extension is a pu rely geom etrical property. There fore it is only im penetrability w hich distinguishes m a tter from em pty- space, the corpus p h ysicum from th e corpus m athem aticum . U n fo rtun a tely, Leibniz is by no means clear about the n atu re of im penetrability. The term is not m uch m ore th an a m ere label for a whole set of unknow n properties (among them cohesion) and it is n o t u ntil the 1680’s th a t he finds a solution to the problem of m ateriality.
Does this definition of physical bodies contain or somehow give rise to motion as a universal pro p erty of th e physical world? One can, to be sure, deduce m agnitude and figure from it (if only as general p roper ties, not as this p articu lar m agnitude or this p articu lar figure); b u t the concept of motion is not contained in th e definition, nor can we de duce it in any conceivable w ay from it. Consequently, motion does not originate in the physical world; it comes from outside, i.e. from God. Leibniz explicitly refers to the A ristotelian doctrine of the prim e mov er.4 If this w orld w ere left to itself, motion would be non-existent; there w ould be nothing but homogeneous prim e m atter uniform ly di stributed throughout space.
Accordingly natu re, i.e. the physical world, is no independent realm , it has no substantiality as it has in D escartes. For Leibniz a substance is an e n tity w hich bears the origin of its activity in itself. All activity of physical bodies consisting in locomotion, a physical body in order to be a substance w ould have to have th e origin of its motions in itself. This is impossible, as it is brought out by its definition. Therefore, p h y sical bodies can be no substances. Only the soul or the m ind (mens) are substances. Bodies are accidental, th e y partake in a su bstantial being only insofar as their m ovem ent is continuously sustained by th e suprem e substance, i.e. by God. L et us now consider the second problem . Here, things are getting more difficult. Leibniz thinks he is sure about the origin of motion, b ut he is by no m eans sure about its nature. Is motion something real, is it som ething like an entity? Leibniz app aren tly a n swers in th e affirm ative when, in a long le tte r to his academic teacher Jacob Thomasius w ritten in 1669 he declares th a t th ere are only four kinds of real entities, nam ely space, m atter, m otion and s p ir it.5 In th e same letter, though, he expresses serious doubts w h eth er motion has any reality at all.6 W hat seems to him doubtful is, above all, its con tinuity, its being a perm anent im palpable flu x not to be fixated in any one m om ent and at any one place. One thing is, however, quite clear to him. If th ere should be anything real in motion it would have to be conceived as ultim ate p arts or elem ents to w hich motion finally can be reduced and out of w hich it could arise as a continuous process extended
4 F or exam ple in a le tter to Thomasius, G erhardt, vol. 1, p. 11.
5 G erhardt, vol. 1, p. 24. 6 G erhardt, vol. 1, p. 24.
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in tim e and space. For two reasons, th e n atu re of th e relation of these elem ents cannot be th a t of the quantitativ e relation of a p a rt to its whole. F irst, if we conceive a continuous process as consisting of ul tim ate p a rts w hich can be obtained by finite or infinite division, these ultim ate p a rts w ill still have to be spatially and tem porally extended— w hich is inconsistent w ith th e concept of an ultim ate p art. Next, it is inconceivable th a t by joining those u ltim ate discrete p arts together we shall ever be able to produce the tran sito ry and gliding character w hich is th e peculiar featu re of motion as a continuous process. In other words, we m ay become entangled in all th e philosophical paradoxes of con tinuity.
Leibniz had intensely studied the problem s of continuity and when, in 1671, he believed to have found th e ir solution he published his first m ajor w ork on n atu ra l science and its foundations, the Hypothesis Phy- sica Nova. Its second p art, th e Theoria M otus Abstracti, is dedicated to an analysis of the m athem atical concept of m o tio n .7 The solution of the problem of continuity offered in this treatise is th e theory of the “cona- tu s ”. This term m ay have been borrow ed from Hobbes, whom Leibniz then studied; in any case it is fam iliar in 17th cen tu ry mechanics. A co- natus is th e ultim ate inextended elem ent of motion w hich distinguishes motion from absolute rest and w hich cannot originate from rest. Conse quently, it is also th e elem ent of re ality in motion by w hich motion is distinguished from nothingness, i.e. absolute rest ju st as th e 1 is d istin guished from the 0. The n atu re of th e conatus is defined by Leibniz as a tendency tow ards m otion; not tow ards motion in general but always tow ards this p articu lar motion w ith this p articu lar velocity and this p articu lar direction w hich it tends to produce. We m ay say th a t motion is “concentrated” in the conatus or th a t it “rep resen ts” th e conatus, which in itself is inextended, in th e mode of spatial and tem poral extension.
The conatus of bodies in motion can either be added to or subtracted from one another. In th e form er case the body w ill move faster, in the la tte r it w ill move slowlier. If two or m ore conatus w ith differen t direc tions are merged, a new conatus w ith a new direction w ill arise. If, however, tw o conatus are directed p erpendicularly to each other, th ere are two possibilities. E ither th e stronger conatus conquers th e w eaker w ith th e effect th a t th e body possessing it continues its motion, if w ith dim inished speed, or th e two conatus are equally strong, in w hich case they com pensate each o th e r and their bodies come to a standstill. This does not mean, however, th a t the conatus have been extinguished. Being ultim ate re a l entities th ey cannot be destroyed b u t only be added, substracted o r compensated. L et us take, for instance, circular motion.
Motion in L eibniz’ Early Philosophy 1 1 7
Leibniz explains it by tw o conatus of equal stren g th being directed perpendicularly to one another; th ey act upon one another w ith o ut in te r ruption, th u s forcing a body to move in a circle. If one of th e conatus loses in pow er the course of the body in question is still a curve b u t no longer a circle. If a conatus ceases entirely th e body breaks free from the periph ery moving either tow ards the centre or along the tan gen t of the circle.
Yet, th ere is som ething unsatisfying about the conatus. It has no “life of its ow n” bu t has to be p erp etu ally preserved from w ithout, i.e. by God. It is a m etaphysical en tity unable to sustain itself beyond the present mom ent. Leibniz therefore calls a moving body in itself a “mo m entary sp irit” (m ens m omentanea) m eaning th a t it is no independent entity—no substance. This is necessarily so because Leibniz th ro u g h o u t the Theoria M otus Abstracti consistently sticks to his definition of phy sical bodies employed in his earliest w ritings. According to th a t de finition, as we have alread y seen, a body in motion w ill possess th ree essential qualities: a definite extension and a definite m ovem ent (i.e. conatus) as w ell as im penetrability. However, it possesses no inertia, elasticity or kinetic energy. Motion and the laws of motion, Leibniz thinks, are com pletely explicable from th e d ifferent kinds of th e com position of conatus. Thus, a physical body in motion does not basically d iffer from a m athem atical body. U nder these presuppositions th e only tru e theory of motion for Leibniz is ab stract kinem atics and this is w hat the Theoria M otus Abstracti is m ainly concerned w ith. Its purpose is a p urely geom etric deduction of all the possible “m ovements, figures, lines of m ovem ent and bodies”. It is in fact m ore th an a m ere kinem atics, it is an attem p t a t an ab stract physics constructed afte r th e model of th e Euclidean Elem enta, an am bitious project w hich Leibniz expresses in the following way: “Omnes possibles lineas, figuras, corpora et motus secundum omnes lineas Physice construere m eris m otibus rectis in te r se aequalibus, item m eris motibus curvis cujuscunque generis, adhibitis corporibus quibuscunque.” 8
This concept of motion w hich claims to produce som ething like a p h y sical w orld by geom etric m eans alone has b u t little to do w ith real, i.e. em pirical motion. A w orld created afte r the principles of the Theoria M otus Abstracti would look very d ifferen t from th e w orld as we know it. Leibniz thinks th a t this kinem atically constructible w orld resu lts inevitably from his presuppositions and is therefore a necessary one. The reason w hy em pirical reality is d iffere n t is unintelligible at th is point of the discussion and will become clear la te r on. In any case th ere arises a contradiction betw een th e results of m athem atical deduction on the one hand and the data of experience on th e other.
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This contradiction is best illu strated by a com parison of th e laws of elastic im pact, w hich Leibniz deduces in the Theoria M otus Abstracti, w ith those discovered by H uygens and W ren. There is some evidence th a t Leibniz has gone deeply into th e laws of th e cen trally directed elastic im pact w hich H uygens and W ren had published independently in 1669. In this paper we are essentially in terested in th e first two of these laws. The first m ay be rendered in this w ay: If an elastic body in m otion collides w ith another elastic body at rest and of equal m agni tude, th e n th e form er body w ill cease to move, the second w ill obtain a velocity equal to th a t of the first body before the im pact. The second law run s as follows: Two equal bodies move on th e same straig h t line in the sam e direction, the second body moving faster th an th e first; afte r the im pact, however, the first and slower body will move w ith th e very speed th e second one had before the im pact and vice versa, i.e. the velo cities w ill have been exchanged.
Leibniz adm its th a t these two laws are valid in th e case of th e em pirical im pact, b u t he denies th eir validity in the case of the im pact in the p u rely kinem atical sense. According to his abstract kinem atics, in the case of th e first of the two laws, the body at rest w ould offer no resistance at all to the body in motion im pinging on it, i.e. the la tte r body would continue its course in the same direction w ith undim inished speed. There would be no longer two b u t only one body afte r the im pact. For sim ilar reasons Leibniz also rejects th e second law of Huygens.
The exchange of velocities betw een th e tw o bodies as it is stipulated by tihej law of H uygens and as it is confirm ed by experience itself is impossible in th e Theoria M otus Abstracti. According to it th e tw o bo dies w ill not move aw ay from one another afte r the collision but, on the contrary, w ill form a single body moving at the original speed of th e faster body. According to Leibniz we can regard motion in two ways: from the point of view of pure reason on th e one hand, and from sense experience on the other. Should th ere arise any contradiction betw een th e resu lts of those two approaches, the rational point of view will necessarily prevail. In presenting the tru e theory of motion we have to ignore com pletely the point of view of experience. The Theoria Motus Abstracti has to be understood in the light of the exigences of pure reason. Sensuous experience is here regarded as a subordinate and u n re liable mode of knowledge w hich obscures and falsifies ra th e r th a n r e veals the tru e n atu re of motion. Experience and the results of Lei bniz’ m etaphysico-m athem atical presuppositions do not harm onize but contradict each other, a discrepancy w hich the theory of ab stract motion can n eith er even up no r gloss over.
How can we account for this striking contradiction betw een abstract and concrete motion, betw een the kinem atical laws of im pact and the em pirical laws of im pact? The reason is of both logical and m etaphysi
Motion in L eibniz’ Early Philosophy 119
cal nature. According to the principle of sufficient reason, as it was expressed in the Confessio, nothing m ay be attrib u ted to the essence of physical bodies which is not contained in th e ir definition. This definition consists of two qualities: extension and im penetrability. The th ird quality, movement, is produced by God, i.e. it is of su p ern atu ra l origin. Now a physical body w hich is defined in th is w ay and w hich is supposed to be in motion can by no means have those qualities w hich we consider (and so did Leibniz) to be essential to all em pirical bodies, nam ely inertia, elasticity, and kinetic energy (or w h at he called „living force”, vis viva), three qualities w ithout w hich th e em pirical laws of im pact are u n in telli gible. Now, u nder these conditions, i.e. presupposing his p u rely kine- m atical definition of bodies, Leibniz could not arriv e a t th e em pirical laws of motion, bu t had necessarily to end up w ith th e laws presented in the Theoria M otus Abstracti, which, as we have seen, flatly contra dict experience.
To account for this contradiction Leibniz has to draw a distinction betw een ab stract or ration al and concrete or em pirical motion. W hat makes him p refer ab stract motion as th e “tr u e ” motion to concrete motion as th e “ap p are n t” one is w hat we m ay call his unlim ited ratio nalism, and w hat makes him arrive at those “ration al” laws of motion instead of the em pirical laws of motion is th e deductive m ethod derived from his rationalist presuppositions as opposed to the em pirical or scien tific m ethod employed by Huygens.
It should be quite clear from the previous discussion th a t any w orld established according to th e abstract laws of motion w ould be a m ere chaos. If th ere were no inertia, perpetual motion would be th e result; if there w ere no elasticity and no kinetic energy, all m otion w ould gra dually cease, i.e. there would be no w orld, no m a tter organized accor ding to certain laws and principles. N atu re left to itself w ould be ruled by a blind m athem atical necessity, i.e. it would not be governed by reason, but by destructive absurdity. Q uite d ifferen t from that, ho wever, it is an organized system keeping up its order by certain in telli gible laws. To prevent the Theoria M otus Abstracti from becoming an em pty ab stract speculation Leibniz feels th a t he is bound to prove th at, in spite of an initial discrepancy, it is a valid theory in the long run, i.e. th a t it is confirm ed by experience. He has somehow to bridge the gap betw een pure reason and sensuous experience. This he attem p ts in th e first p a rt of the H ypothesis Physica Nova, the Theoria M otus Con- c r e ti.9 Tre purpose of th a t paper is in Leibniz’ own words “omnes mo tus sensibiles explicare”.
Now, still em ploying the deductive m ethod Leibniz cannot derive the em pirical laws of motion d irectly from the presuppositions of the
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Theoria M otus Abstracti. Therefore, an additional assum ption or p rin ciple is requ ired w hich can account for concrete motion. This additional assum ption m ay be called the principle of ratio n al order or, as it will be called la ter on by Leibniz, the principle of perfection.
A w orld ruled b y the blind geom etrical necessity of the composition of conatus, Leibniz argues, is not in accord w ith th e wisdom of God. God would not have created disorder b ut the best order imaginable. F u rth er on he w ould not have created a w orld th e order of w hich has to be preserved by his continuous interference. The w orld created by him is so perfect as to sustain its order independently. For these two reasons motion has to follow the em pirical laws discovered by Huygens, which m eans th a t all physical bodies possess inertia, elasticity, and energy.
There are thus two reasons w hy th e ab stract laws of motion cannot be valid for th e real world: experience w hich falsifies them and th e principle of order w hich gives an explanation for this. Now th e sole principle of order can only be the startin g point for the deduction of the em pirical laws of motion. In itself it is insufficient for the deduction proper.
W hat is required is a physical explanation w hich on th e one hand confirm s Leibniz’ concept of physical bodies but, on the other, explains w hy physical bodies nevertheless have inertia, elasticity, and energy.
Leibniz attem pts to m eet these requirem ents in the Theoria Motus Cqncreti w ith the hypothesis of the eth er penetratin g every particle of m atter. From the various degrees of penetration he hopes to explain all n atu ra l phenom ena and, among them, inertia, elasticity, and energy.
He explains elasticity by the circulation of th e ether penetrating the bodies according to their density. If two bodies moving in th e same direction along the same line w ith d ifferent velocities collide and ex change th e ir velocities (as it is laid down in th e second law of Huygens) nothing has actually happened to the body itself: only the ether pervad ing it has been tran sferred to the o th er body and vice versa.
In ertia is explained by the fact th a t bodies in reality are disconti nuous. They consist of sm all particles which, owing to an in n er move m ent brought about by the ether, are pressed against each o ther for th e body to be coherent. They will offer resistance th en to a body in motion im pinging on them , th a t is to say, th ey will oppose th e ir own conatus (apart from w hich th ere is nothing real in the bodies) w hereby a conatus of equal stren g th of th e im pinging body is com pensated. The larg er the num ber of th e particles of a resisting body th e g reater th e subtraction of the conatus of the im pinging body. It is in this way, then, th a t a body offers more or less resistance to the m odification of its state.
By this tim e Leibniz has not y et got acquainted w ith the concept of energy or of active force as a dynam ic category and the principle of its preservation. W hat he acknowledges is th a t bodies in motion can
Motion in L eibniz’ Early Philosophy 1 2 1 ex ert effects and th a t the sum total of these effects which, following Descartes, he calls “q u an tity of m otion” (quantitas m otus) obviously rem ains constant in a self-contained system . He assumes these effects to be proportional to th e sim ple velocities.
According to the Theoria M otus Concreti, th e sum total of m otions in the w orld should be constantly dim inishing, for the concept of conatus does not explain how a body can obtain a velocity w hich is g reater th a n its own before the im pact from another slow er body. And this necessarily is the1 case w hen th e sum to tal of motion before and afte r th e im pact rem ains constant as it is laid down in the second law of im pact by Huygens. Besides each curvilinear motion (w ith a curved course) w ould— —owing to reasons we have pointed out already—tu rn into a rectilin ear motion so th a t in th e end a state of all bodies moving in the sam e direc tion w ith the same homogeneous velocity w ould be reached; and this would m ean the end of all observable motion. The world, according to this theory, w ould gradu ally make for a state of absolute rest; this is a conclusion which, owing to the m etaphysical und theological conse quences it entails w ould be point-blank scandalous; the m ore so w hen we consider how vehem ently Leibniz w ill later on argue on this point against Newton. M oreover, this th eo ry contradicts th e principle of th e preservation of the q u an tity of motion in th e w orld established by Descartes and generally acknowledged. It is th erefo re incom patible w ith th e com m unis opinio. Therefore, in th e Theoria M otus Concreti, Leibniz attem pts to explain th e stab ility of th e sum to tal of effects by means of the eth er perp etually flowing a t the same velocity. O nly afte r a thorough exam ination of his position does Leibniz, some tim e later, conceive the idea of th e capability of bodies to produce fu tu re effects and, w ith th at, the introduction of th e concept of energy into m atter. Only then, together w ith the concept of energy, he finds the rig h t m ea sure of preservation.
Leibniz tries at first to in te rp re t positively th e fact th a t th e w orld of experience is in itself not explicable from the presuppositions of th e Theoria M otus Abstracti, i.e. th e concept of physical body and of m ath e m atical m otion alone. This is th e proof, he argues, th a t reality has n eith er existed eternally nor been brought fo rth accidentally, but th a t an u lti m ate and perfect being has brought about the creation of th e world. Thus, in th e Theoria M otus Concreti he persistently emphasizes th e wise and perfect order of things and, in th e p refatory note to th e Theoria M otus Abstracti he calls it th e most distinguished purpose of this w ork to dem onstrate th e “intrinsic n atu re of Thought, th e im m ortality of th e spiritual being and th e suprem e cause by apodictic proofs”. 10 Conside rations of such kind or analogous reflections could not, in th e long run,
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blind Leibniz to the decisive weakness of th e system of the H ypothesis Physica Nova, a weakness which consists in the insufficiency of its philosophical foundations to deduce physical reality in its most im po rtan t qualities. This is most obvious in th a t elasticity, inertia and preservation of motion (i.e. energy) are degraded into m ere appearance w ithout reality. By a trick of God they are brought into the w orld w here, to hum an experience endeavouring to explain the phenom ena of reality, th ey counterfeit qualities of bodies which these do not possess at all. Leibniz has to introduce an additional theological assumption in order to uphold his ab stract theory against the evidence of experience. The principal criticism of the later Leibniz is levelled against this issue of his early system, and it is exactly there th a t we find the decisive turning-point in his m etaphysics of nature. If em pirical motion and its laws w ere not deducible from the philosophic foundations of th e w orld of bodies as he at th a t tim e conceived them , but w ere explicable only by artificial additional hypotheses, then these very foundations had to be revised, a conclusion w hich became more and m ore obvious to Leibniz. The m etaphysical foundations of natu re had to contain th e sufficient conditions for the deduction of the w orld of experience and its order. The theory of abstract motion had disregarded experience; consequently, to come back to our exam ple, th e laws of elastic im pact could not be deduced from it. To p u t it in the words of Cassirer, “experience and reason”, i.e. experience and rationalist m etaphysics, “have not yet been brought into accord”. 11
The problem Leibniz found him self having to face then was a r e exam ination of the philosophical concept of bodies; a re-exam ination w hich had to take into account the results obtained by the discussion of the laws of elastic im pact. Thus, a threefold task arose for Leibniz.
F irst of all he had to abandon the principle obstinately m aintained throughout the Theoria M otus Abstracti th a t motion originates outside the physical world. All he had actually to do was to bring out certain im plications of th e concept of the conatus w hich his m etaphysi cal assum ptions had prevented him from drawing. As we have seen previously, th e conatus is supposed to be the u ltim ate elem ent of motion and a t the same time its ontological legitim ation, i.e. w hat is real in motion is the conatus and nothing else. A lthough it is dependent on God’s concourse for its preservation beyond th e infinitesim al m om ent of time it is an entity evidently not of the same n atu re as m atter o r space but som ething spiritual. Now, let us suppose th a t th e conatus gets rid of its dependency upon God’s concourse; let us suppose fu rth e r th a t it is not th e infinitesim al elem ent of actual motion b ut th e source of
11 E rnst Cassirer, L eibniz’ S ystem in seinen wissenschaftlichen Grundlagen, D arm stadt 1962, p. 502.
Motion in Leibniz’ Early Philosophy 1 2 3
motion, a lasting active potency w hich produces actual motion if not prevented. In this case the origin of motion w ould lie in physical bodies themselves. Bodies th en would contain w hat Leibniz calls an active, self- suficient and self-sustained tendency tow ards motion; in short: they would contain force. The essence of bodies, then, would no longer consist of extension and im penetrability alone, bu t first and forem ost of force.
This is a sim plified version of the reasoning by which Leibniz was led to a new concept of physical bodies. All bodies are endowed w ith an ac tive force or vis activa. There is no need any longer for God to produce and sustain motion constantly. N ature is a realm ruled by certain laws w hich it observes independently from any influence or concourse from w ithout. Active force in this sense is, of course, a m etaphysical en tity but it is th e foundation of physical phenom ena because it gives rise to w hat Leibniz calls “living force” (vis viva) and w h at nowadays is called kinetic energy.
The concept of force as the essence of physical bodies offers a satis factory solution to th e second crucial point, nam ely to the n atu re of elasticity. If there is in physical bodies a spontaneous active tendency or potentia th en it becomes intelligible w hy a body after colliding w ith another body reacts in tu rn upon th e latter, thus producing th e pheno menon of elasticity.
Finally, the problem of inertia receives its solution by an extension of the concept of force. If we acknowledge inertia as a constitutive p ro p erty of physical bodies—as we are bound to do, if we w an t to account for the em pirical laws of motion—then we have to look for a principle th a t explains w hy physical bodies offer a certain am ount of resistance to any kind of change of th eir present condition. Mass or inertia, as Lei bniz calls it taking up a term used by Kepler, comes in in both laws of im pact which we have discussed in this paper; w ithout it those laws are unintelligible.
The im portance of the problem of inertia for the philosophical d e velopm ent of Leibniz cannot be overestim ated. As he tells us repeatedly in his la ter years he was for a long time unable to give a satisfactory explanation of the fact th a t in the phenom ena of motion and im pact velocity evidently depended on a certain factor th e n atu re of w hich was unknow n to him. “Nam dicere m ateriam m otui resistere et totum ex A et B compositum nunc tardius mover! quam antea solum A, est aliquid asserere quod ex simplici n atu ra corporis et motus,... si in ea nihil aliud quam spatii im pletionem et m utationem intelligim us, duci non potest.” 12 Again, as in th e cases of energy and elasticity, Leibniz assu mes a m etaphysical principle underlying inertia w hich he calls “passive force” (uis passiva). S trictly speaking, force as th e essence of bodies has
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two d ifferen t aspects; it is active as the source of m otion and kinetic energy and passive as the source of mass or inertia. The active and passive forces together form w hat Leibniz calls a substance or, from about 1695 onw ards, a “m onad”. Monads are m etaphysical entities ca pable of producing motion and inertia.
This re-exam ination of th e concept of bodies required a re-exam ina tion of both his scientific and m etaphysical methods. P u rely deductive and m athem atical physics as it was presented in th e Theoria Motus Abstracti had been refu ted by experience. Science has to explain th e phenom ena of experience. Obviously the theory of abstract motion does not m eet this requirem ent. C onsequently science has to revise its method, i.e. its procedure has, at least in part, to be em pirical and inductive. The same applies m utatis m utandis to m etaphysics. The object of the m eta physics of natu re, as Leibniz understood it, is the philosophical founda tion of n atu ra l science. Now, if science is legitim ate only as a theory concerned w ith th e actual phenom ena of nature, m etaphysics is legiti m ate only as a theory concerned w ith the philosophical foundations of em pirical science. It has therefore also to revise its m ethod.
L eibniz’ new m etaphysics of natu re conceived in th e years betw een 1671 and 1685 and first laid down in the Discours de M étaphysique and in the lé tters to A rnauld in 1686 has an em pirical foundation, though not exclusively. The m ethod employed in its form ation resem bles th a t of n atu ra l science, i.e. it is em pirical and inductive, at least in part. In subscribing to a m axim consistently m aintained also by W hitehead, n a mely th a t m etaphysics has to explain w h at is contained in experience, Leibniz tacitly adopts th e fundam ental principle of the new science of the 16th and 17th centuries represented by the nam es of Bacon, Kepler, Gelileo, Boyle and Huygens. His new m etaphysics of n atu re m ay even be called an hypothesis, and th a t for the following reasons:
(1) According to Leibniz the task of a sound hypothesis m ust not be a rb itra ry fiction (a sense of the w ord employed by Newton in his proud dictum “hypotheses non fingo”) b u t a consistent explanation of n atu ral phenom ena.
(2) For Leibniz the procedure of an hypothesis has to be both induc tive and deductive; its validity is to be confirm ed in tw o ways, by de scending from the principles to phenom ena and by ascending again from phenom ena to the principles. This is one of the fundam ental rules of Leibniz’ theory of science.
(3) Finally, Leibniz dem ands th a t a sound hypothesis should be simple, clear and concise. The num ber of basic principles, assumptions or axioms should be as sm all as possible, but they should enable us to solve as m any p articu lar problems, i.e. phenom ena, as possible.13
13 For L eibniz’ concept of hypothesis see his le tte r to F abri, G erhardt, vol. 4, p. 247, also his le tte r to Conring, G erhardt, vol. 1, pp. 173—4.
Motion in Leibniz’ Early Philosophy 1 2 5
M etaphysics of n atu re intends to analyse and explain the d ata of experience by following the principle of sufficient reason. M etaphysics, therefore, has to establish the ultim ate and most general foundations of experience. W hereas a scientific hypothesis reduces th e p articu la r phe nomena to general ones—in th e case of the Theoria M otus Concreti to th e rotations of sun and earth and th e eth er—m etaphysics probes be neath the fundam ental concepts of science to discover its ultim ate p rin ciples.
Such principles appear to be the tru e foundations of n a tu re only after having been verified in the two ways of analysis and synthesis as describ ed above. M etaphysics of n atu re, fu rtherm o re, m ust be clear and simple. Here it becomes obvious th a t the a priori proposition of w orld order is one of th e prem ises of scientific as w ell as of m etaphysical hypotheses. The Theory of Monads as the new m etaphysics of n atu re derives from the inextricable connection of m etaphysics and experience, a connection w hich can be traced back to the influence of scientific hypothesis. This influence is evident from th e fact th a t Leibniz la ter on rep eatedly calls the Theory of Monads as w ell as th e P re-established H arm ony „hy potheses”. 14
O ur conclusions ought to be confirm ed by a close exam ination of one of th e m ajor docum ents of Leibniz’ m a tu re m etaphysics, nam ely the correspondence w ith th e D utch philosopher, scientist and m athem atician B urcher de Voider. In the le tters to de Voider the concept of a prim itive active and passive force underlying the phenom ena of motion and in e r tia and in h e ren t in all physical bodies, i.e. the concept of th e monad, emerges as a m etaphysical hypothesis w hich Leibniz believes to be the only possible satisfactory explanation of phenom ena. We cannot here discuss this correspondence in any detail, how ever in terestin g for our subject it m ay be. Only a very brief account of Leibniz’ m ain argum ent can be given. De Voider is w illing to accept L eibniz’ concept of m onad only on condition th a t Leibniz gives w h at de V oider calls an “a priori proof”. By this he clearly m eans a deduction w hich proceeds in th e same w ay as we can deduce from the concept of trian g le th a t th e sum to tal of its angles is equal to 180°. Leibniz persistently refuses to give th a t deduction by pointing to the fact th a t “everything m ust be deduced from phenom ena”, i.e. th a t the basic concepts of m etaphysics m ust be form ed w ith constant reference to experience.
That L eibniz’ famous m etaphysical system —th e Theory of Monads derives, at least in p art, from his philosophy of dynam ics has been re peatedly stressed by famous scholars such as H annequin, Cassirer, G ue- roult and others. But th ere seems to be little appreciation of th e fact
14 See Leibniz’ le tte r to de Voider, G erhardt, vol. 2, p. 241; his le tter to Lady Masham, G erhardt, vol. 3, p. 352; th e Systèm e Nouveau, G erhardt, vol. 4, p. 485.
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th a t it was a problem of method w hich made Leibniz abandon his early m etaphysics of nature. He is still w idely believed to be an arch -ratio n al ist w ho starte d from pre-conceived a priori assumptions and who m ainly
indulged in lofty speculations about the n atu re of God, of the soul and of reality in general. This commonplace characterization, if th e re is any tru th in it, m ay be tru e of the unlim ited apriorism of his early philo sophy b u t tends to overlook th e strong cu rren t of scientific empiricism in his la ter m etaphysics.
