SOURCE: "On Leibniz's Metaphysics," translated by R. Allison Ryan, in Leibniz: A Collection of Critical Essays, edited by Harry G. Frankfurt, Anchor Books, 1972, pp. 19-45.

In the preface to La Logique de Leibniz, we asserted that Leibniz's metaphysics rests entirely on his logic. This thesis is confirmed implicitly in our book and is evident from the texts we had occasion to cite there. Nevertheless, since it is contrary to the classical interpretations and to current opinion, it will be useful to establish it explicitly and in detail. Moreover, although it appears to us to be sufficiently proven by the texts which are already known, we are now able to confirm it by adducing some unpublished documents of unusual value and importance. The most interesting and most significant is a short work of four pages in which Leibniz himself has given a succinct account of his entire metaphysics in deducing it from the Principle of Reason. We cited its essential propositions in our preface and in the course of our book. We [now] want to make the new material available….¹

This fragment is unfortunately not dated. But, by comparing it to short works and letters of known date, we can conjecture with high probability that it was written about 1686 when Leibniz completed the principles and the essential theses of his system, first in the Discours de métaphysique and then in his Lettres à Arnauld.² In fact, the preceding passage does not contain a single proposition which is not already to be found in one of these works. It is none the less original and valuable, however, in virtue of the order and connection which it establishes among all those known propositions.

In the first place, it formulates precisely the famous principle of reason, of which the classical expression nihil est sine ratione is, according to Leibniz, only a popular formula borrowed from common sense.³ In its exact sense, this principle means that in every true proposition the predicate is contained in the subject; therefore, that every truth can be demonstrated a priori by the simple analysis of its terms. In a word, that every truth is analytic. This may seem paradoxical and even shocking to us who have read Kant. But it seemed entirely natural and evident to Leibniz's contemporaries who, like him, were trained in the Aristotelian and scholastic tradition. And the proof of this is that Arnauld, who was extremely averse to admitting certain consequences of this principle (in particular, the major thesis that "the individual notion of each person contains definitively all that will ever happen to him"), never dreamed of expressing any reservation or doubt about it. On the contrary, he accepted it without qualification and without discussion.⁴

Why is this principle called the "principle of reason" (of determining reason at first and, later, of sufficient reason)? It is because it means, in brief, that one can give the reason for every truth, that is, demonstrate it by analysis. Thus it was originally called "the principle of giving the reason" (principium reddendae rationis).⁵ This must not lead one to confuse it with the principle of identity; it is precisely its reciprocal. The principle of identity states: every identity (analytic) proposition is true. The principle of reason affirms, on the contrary: every true proposition is an identity (analytic). Its effect is to subordinate all truths to the principle of identity. One might call it the principle of universal intelligibility, or, if one may venture this barbarism, of universal demonstrability.

This is the source of the metaphysical import of the principle, which Leibniz recognized and utilized at an early date.⁶ We know how he derived from it the principle of indiscernibles and that other principle, really equivalent to the preceding one, that "there are no purely extrinsic characteristics [dénominations]";⁷ then, step by step, the notion of the monad (though not the name), which includes not only all its past, present, and future states, but also all the successive states of the universe of which it is a mirror or rather a perspective; further, the pre-established harmony, which necessarily results from the fact that the monads interact only apparently (physically) and not really (metaphysically); finally, the ideality of space and time and hence of movement and of bodies, which are reduced to mere "true phenomena," and the immortality not only of souls, but of all substances.⁸

In a word, it is the entire Monadology which Leibniz thus progressively derives from the principle of reason and which he presents in rational order and in proper perspective. Actually, the Monadology takes as its point of departure this same notion of the monad which is here the conclusion of a long deduction; it reverses the logical construction of the system in a sense and makes the pyramid rest on its peak. In order to convince oneself that the order followed by the Monadology is really the inverse of the order that is both logical and genetic, it suffices to notice that one cannot at all see how the principle of reason would follow from the definition of the monad, whereas one understands perfectly how the concept of the monad derives from the principle of reason.⁹ The monad is the logical subject elevated to the status of substance; its attributes become the accidents "inherent" in the essence of the substance. It contains in itself the entire sequence of its states (and hence the principle or law of their succession), because its essence includes all its past, present, and future accidents. It is a mirror or a perspective of the universe, because its notion implies all the things to which it stands in relation. Now, since there are no purely extrinsic characteristics, every external relation of a substance is expressed by an internal modification, that is, by an accident; and that is why "the monads are windowless." Therefore, every reciprocal action between two monads reduces to the correspondence of their respective perceptions, more distinct in the one which is said to act, more confused in the one which is considered to be passive. And this explains the pre-established harmony. In a word, all the metaphysical properties of the "individual substance" derive, by virtue of the principle of reason, from the logical properties which the "complete and singular" idea possesses.¹⁰

In the second place, one can no longer fail to recognize the absolutely universal applicability Leibniz attributes to the principle of reason. It holds equally for all kinds of truths, universal as well as singular, necessary as well as contingent. This is rigorously logical, since the principle constitutes the very definition of truth in general and expresses its "nature."¹¹ With respect to contingent truths in particular, Leibniz affirms their subordination to the principle of reason with a clarity and an insistence which leave no room for doubt.¹² It follows that contingent truths are not synthetic to any degree whatsoever, as is generally believed; they are just as analytic as necessary truths are. But then, it will be asked, how do they differ from necessary truths? They differ from them, replies Leibniz, as the infinite differs from the finite, or as irrational and rational numbers differ.¹³ Contingent truths are analytic, as are all truths; only the analysis of their terms is infinite, so that we cannot demonstrate them by reducing them to propositions of identity. They are no less identities in the eyes of God, who alone can complete this infinite analysis "in a single act of mind." This is how Leibniz believes he can escape the doctrine of universal necessity (to which he was averse for moral and theological reasons) and how he finds the solution to the difficulty in the consideration of mathematical infinity.¹⁴

Thus the comparison of contingent truths with irrational numbers is not a simple metaphor, but an analogy which Leibniz develops confidently and with a rigorous parallelism; he states many times that contingency is rooted in infinity,¹⁵ and that it is thanks to mathematics (to the infinitesimal calculus) that he has been able to understand and explain the nature of contingent truths. Now, as one readily notices, this difficulty (which, by his own account, had long troubled him) exists only as long as contingent truths are analytic: it is a question of understanding how an analytic proposition can fail to be necessary.¹⁶ As soon as contingent truths are considered to be synthetic, the question disappears and the solution no longer has any sense.

Is the difficulty thus really resolved? We are far from so affirming. But here (as in our book) we are writing as an historian, not as a critic; we are seeking what Leibniz actually thought and not trying to determine whether he was right or wrong to think it. From this point of view, it is interesting to know how he was led to this theory. He states it expressly: what rescued him from (Spinozistic) fatalism was the consideration of the possibles which are not realized and which, indeed, will never be realized.¹⁷ In fact, "nothing is necessary of which the opposite is possible".¹⁸ If there are unrealized possibles, then the realized possibles can only be contingent. (These realized possibles comprise the entire real universe: not only individuals but also the general laws of nature.) By 2 December 1676 (the day after his meeting with Spinoza), Leibniz was denying the Spinozistic thesis—"Everything possible exists"—and he was already opposing to it his own theory that only those compossibles containing the greatest reality exist.¹⁹ The point is that not all possibles are compossibles (otherwise there would be no reason why all possibles should not exist).²⁰ The only raison d'être of the possibles is their quantity of reality or of essence. Each possible tends toward existence in proportion to its degree of "perfection"—that is, of reality. All the possibles struggle among themselves for existence in the Mind of God, which is "the land of the possible realities,"²¹ and the outcome of this struggle is the infallible and automatic (not to say necessary) triumph of the system of compossibles which contains the most essence or "perfection." The world is thus the product of a "metaphysical mechanism" and of a "divine mathematics."²² The creation is the solution to a problem of maximization, and this maximization has a significance much more metaphysical than moral. Such is the logical origin of Leibnizian optimism; and this is why it is a speculative and intellectual optimism rather than a teleological and practical one.

It is apparent what we must think of the synthetic character generally attributed to existential judgments.²³ First of all, existential propositions are not the only contingent propositions. All the laws of nature are equally so, according to Leibniz, and for the same reason—namely, because they include an infinity of elements or of conditions [réquisits]. Second, they are analytic in the same sense as the other contingent truths. To make of existence an exceptional predicate, whose affirmation would be synthetic, is quite simply to confuse Leibniz with Kant. For Leibniz, existence is nothing more than l'exigence de l'essence; it is contained in the essence and can be deduced from it by a simple analysis. It is wrong, said Leibniz, to think of existence as having nothing in common with essence; there is something more in the concept of what exists than in the concept of what does not exist. And in fact existence consists, by definition, in taking part in the most perfect order of things; that is to say, in the system of compossibles which contains the most essence. It is in this sense that existence is a "perfection"—that is, an integrating element of the essence.²⁴ Such is the reply Leibniz made in advance to the Kantian critique of the ontological argument. Now it is worth noticing that this reply is a logical consequence of the principle of reason: if existence were something other than a requirement of the essence, it would be necessary to seek the reason for existence elsewhere—that is, in another essence.²⁵ In other words, existence is an attribute which, like every other attribute, must be contained in the subject to which it belongs; otherwise existential judgments would have no "reason." Here as everywhere else, praedicatum inest subjecto.

Here an objection arises which we find in a variety of critiques of Leibniz: "Logic has doubtless only to analyze the subjects once they are formulated, but it is metaphysics which formulates them; thus logic is subordinate to metaphysics, all things considered, as is analysis to synthesis." This objection is in a thoroughly modern spirit; Leibniz would not have admitted it, nor perhaps even have understood it. In fact, for him synthesis (like analysis) is a function of logic, of that Real Logic which he identified with metaphysics.²⁶ It is logic, and more specifically the art of discovery, which must generate all the possible concepts and which will thus construct the subjects which the art of judgment will have to analyze. This inventive and synthetic branch of logic, the most important in his eyes, Leibniz often calls Combination (la Combinatoire), because it is the art of combinations which directs the ordered formation of complex concepts by means of the simple and primitive concepts which are the "primary possibles." Human Combination can only imitate and imperfectly reproduce the divine Combination, which gives rise to all the possibles which, as we have seen, struggle for existence. Now by the mere fact that each of these possibles is the combination of a certain number of "primary possibles," it possesses a certain degree of reality. It is this quantity of essence it contains which constitutes its right to existence, and which, if it is realized, will be the "cause" or the "sufficient reason" of its realization. In a word, one can say that its existence is prescribed [inscrite d'advance] in its essence, that it is a part of its meaning. Only, in order to extract the existence from the essence, an infinite analysis, indeed an infinitely infinite analysis, would be necessary. It would be necessary to relate this possible to the possible world it implies, and to compare this world with all the other possible worlds. That is why this existence is contingent, inasmuch as it implies an infinity of logical conditions [réquisits]. One must not say, accordingly, that logic receives its subjects ready-made from metaphysics; quite the contrary, it is metaphysics which receives its objects (the real beings) from logic and above all from that divine logic which presides at the creation: Cum Deus calculat…, fit mundus.

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It will undoubtedly be objected that the choice among possibles is mechanical only apparently and metaphorically. According to Leibniz's own statements, this choice results from the free decrees of God. It depends not on his intelligence, but on his will; not on his wisdom, but on his goodness. Let us therefore examine what Leibniz means by freedom, in man and in God.

We know that he defines freedom as an intelligent or rational spontaneity. Now the spontaneous is that which contains within itself its principle of action.²⁷ Freedom thus consists in the ability to act or not to act (or to act otherwise), given the same external conditions: for action depends on the internal dispositions of the agent, and notably on its intelligence. Peter and Paul are free because, placed in exactly the same conditions, they will act or react differently. This is not to say that they will act irrationally, nor that their action is undetermined. It has its (logical) reasons in their individual natures; it is contained from all eternity in the notions of "Peterhood" and "Paulhood."²⁸ Also, God can foresee their action with certainty and infallibility. This freedom has nothing in common with the freedom of indifference, which would be the power to act or not to act, given all the external and internal conditions of the action. That, according to Leibniz, is an "impossible chimera," since it is obviously contrary to the principle of reason.²⁹ He remarks that this conception of freedom was unknown to the ancients and to the great scholastics, and that it originates with the Jesuits (Fonseca and Molina). And to the moderns who reproach him with ignorance of the true idea of free will, Leibniz would undoubtedly reply by asking them if they themselves understand their empty concept of an irrational and undetermined activity, and if they can really think something which violates, by definition, the laws of thought.³⁰

Thus freedom, no more than the contingence of which it is but a special case, by no means excludes determinism. On the contrary it implies it, because freedom consists in the determination of action by reason.³¹ Spontaneous and intelligent action is free only in the sense that it is unpredictable, because it escapes every general law. In this respect, freedom constitutes a higher degree of contingence. For, as we have seen, the laws of nature are already contingent to the same degree as nature itself; but free actions are independent of the laws of nature, not at all because they violate or suspend these laws but because these laws, being general, do not suffice to determine the individual action of "intelligent substances." It is in fact intelligence which delivers man from physical determinism, because it complicates to an infinite degree the processes which determine his action (namely, attention and reflection) in such a way that one can never predict with certainty which motive will prevail in him. Human actions are, strictly speaking, "incalculable," at least for a finite understanding; but this does not prevent them from being absolutely determined in themselves, nor does it prevent God from knowing them in advance—not through a simple "visual knowledge," which would be nothing but a purely empirical foresight, but through an "intelligent knowledge" which permits him to see its reason and, if necessary, to "give reason to it."³²

From the psychological point of view, the will is always determined by the apparent good; it tends toward it irresistibly.³³ All differences among individuals, and among their actions, thus derive from the intelligence—that is, from the more or less perfect knowledge of the good. Here again one sees how the intelligence is the condition of freedom. It furnishes the determining motives for action and, through more or less attentive and prolonged reflection, it causes a real good to be preferred over an apparent good; that is, it causes the motive that is rightfully strongest to triumph instead of the one that prevailed at first. It is this operation of reflection which, infinitely complicating the givens of the problem, makes its solution incalculable and unpredictable. The entire difference between the will of man and that of God comes from the difference in their intelligences. The former chooses the apparent good, the latter the real good. Or rather both equally choose the apparent good; only it is clear that what appears good to God is the absolute and real good. It could, in one sense, be said that man is freer than God, for the weakness of man's intelligence gives rise to all sorts of depravities and perversions which make him prefer, under the aspect of apparent goods, evils which are all too real. God, on the other hand, can will only the good; he is in some sense condemned by his infinite wisdom to realize the good unfailingly. This is what the freedom of choice attributed to him comes down to.

But then, it will be said, in what does this "good" or this "better" which God wills and infallibly realizes finally consist? What is the significance of distinguishing his wisdom from his goodness, if his will is entirely determined by his intelligence? From the metaphysical point of view this distinction vanishes, since not only the divine will but all will, however perverse, tends essentially toward the good. Moreover, this "good" which is the object of the creating will does not have, nor could it have, any moral character. It consists uniquely in metaphysical "perfection"—that is, in the degree of essence or of reality—so that the "principle of perfection" reduces to "God realizes the maximum of essence or of reality," which is a simple consequence of the principle of reason.

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There remain one or two apparently insurmountable objections. What becomes, in our interpretation, of the famous distinction between efficient and final causes and of the no less classic distinction between mechanical and metaphysical principles? In order to appreciate the first, one must remember the circumstances in which Leibniz enunciated and adopted it. In 1682 he published his Unicum opticae, catoptricae et dioptricae principium,³⁴ in which he deduced all the laws of the reflection and refraction of light from this single principle: Lumen a puncto radiante ad punctum illustrandum pervenit via omnium facillima. [Light travels from the radiating point to the point to be illuminated via the easiest path.] And it is to this memorandum that he repeatedly refers when he maintains (against the Cartesians) the usefulness of studying final causes. Now (without emphasizing what is artificial and paradoxical in considering the "point to be illuminated" as the end toward which the illuminating ray tends, when the rays spread out into space without seeking to illuminate what happens to be there), it suffices to remark that this (apparent) finality translates simply into a problem of maximum and minimum, to which it is difficult to attribute a moral significance. Moreover, the scientific interest in the consideration of finality is not only that the "best" consists in a maximum or a minimum. It is above all that it corresponds to a particular determined instance, mathematically speaking, to a singularity. Leibniz recognizes this implicitly in the same passages in which he exalts the "principle of perfection." The forms he calls the "best" are those "which provide a maximum or a minimum"; "nature acts along the shortest paths, or at least along the most determined paths," or again, "God acts in the easiest and the most determined ways." It is apparent that what is essential in this finality that Leibniz investigates is not a quantitative maximum or minimum; it is rather the logical or mathematical determination of the problem to be resolved. This is what Leibniz finds the "most beautiful" in the idea.³⁵ It suffices to say that the beauty and goodness in question here are entirely rational and metaphysical, having no ideological or moral significance.³⁶

Let us go on to the distinction between mechanical and metaphysical principles. What exactly does Leibniz mean when he endlessly repeats that if everything in nature is explained by mechanical laws, then these mechanical laws themselves rest on metaphysical principles? Perhaps one already suspects: these metaphysical principles are the principle of reason and all its corollaries. And if these principles have a logical and not a moral character, it follows that Leibniz's mechanics is subordinated to his logic and not to his theory of morals or to his theodicy. Moreover, the finality Leibniz thinks he has discovered in the laws of mechanics is not of a different nature from that which he recognized in the laws of optics. In all the instances in which he appears to subordinate mathematical principles to metaphysical principles, he is really subordinating them to the principles of his logic, as is shown by the allusions he makes in those instances to the Universal Characteristic.³⁷ Indeed, according to him, popular mathematics—the sciences of number and of size (objects of imagination)—depend on a more general science. Sometimes he called this more general science the Combinatory [la Combinatoire] or Art of Discovery; sometimes he called it the Universal Mathematics, because it would subordinate to a rigorous calculus even abstract notions which do not depend on the imagination, such as those of metaphysics and mechanics.³⁸

This is also evident from certain unpublished texts which date from Leibniz's youth. In the Consilium de Encyclopaedia nova conscribenda methodo inventoria (June 1679) he said of mechanics (which he called scientia de actione et passione, de potentia et motu): Haec scientia Physicam Mathematicae connectit. Neque hic agitur quomodo delineanda sint motuum … vestigia: id enim pure geometricum est;³⁹sed quomodo ex corporum conflictu motuum directiones et celeritates immutentur: quod per solam imaginationem consequi non licet, et sublimioris est scientiae.⁴⁰ [This science connects physics with mathematics. And it is not here a question about tracing the paths of motion, for that is a purely geometrical task; rather it is a question of how the direction and speed of motion are changed through the collision of bodies. This cannot be ascertained through the imagination alone and is a question for a more sublime science.] Mechanics does not reduce to geometry nor even to cinematics, because of the mass which intervenes in collisions to modify the movements; it is this element—the mass, revealed by the active force—which escapes the spatial "imagination" and prevents the geometric prediction of the result of the collision, which Descartes thought possible.⁴¹ Mass and active force are what Leibniz invoked when he maintained (against the Cartesians) that the essence of body does not consist in extension. This is indeed the major point on which he breaks with the Cartesian mechanism or rather with its "geometrism." What, then, is this "more sublime science" which will permit the treatment of the problems of mechanics and the penetration of nature? Is it metaphysics? By no means. It is Logic, or Characteristic. Here in fact is what Leibniz wrote in May 1676: Vera ratiocinandi ars in rebus difficilibus et nonnihil abstrusis, quales sunt physicae, frustra speratur, quamdiu non habetur ars characteristica sive lingua rationalis, quae miriflce in compendium contrahit operationes mentis, et sola praestare potest in Physicis, quod Algebra in Mathematicis.⁴² [The true art of reasoning in difficult and profound matters, such as those of physics, will be sought in vain as long as we do not have an art of characteristic or a rational language, which will wondrously unify mental operations and which alone will be able to serve Physics as Algebra does Mathematics.] And this idea—that the Characteristic is the logic of physics,⁴³ and the true experimental method⁴⁴—reappears constantly in the writings of this period. Later he enumerated among the many applications of his universal characteristic the science of cause and effect, of action and passion, i.e., mechanics: "I reduce all mechanics to a single proposition of metaphysics, and I have several important geometrical propositions concerning cause and effect."⁴⁵ Now the "metaphysical" principle from which Leibniz deduces all of mechanics is this: "There is always a perfect equation between the full cause and the entire effect."⁴⁶ This really means that something remains constant in mechanical phenomena (notably in collisions); and it is this "something" which Leibniz calls "force," as we shall see later. For the moment it is enough to remark that, by virtue of its entirely formal character, this proposition is more a logical than a metaphysical principle, and that in any case it has no teleological significance.⁴⁷

This leads us to explain briefly our position regarding the similarities between Leibniz's metaphysics and his mechanics, similarities which have been peculiarly exaggerated and misrepresented. We do not mean that the studies of mechanics Leibniz pursued from 1678 to 1686 (evident from his unpublished manuscripts⁴⁸) had no influence whatsoever on the formation of his system, but rather that they were no more influential than his other scientific studies. Everything considered, his metaphysics inspired his mechanics much more than vice versa; and his metaphysics follows essentially from the logical principles Leibniz adopted at a very early date. We by no means deny that his metaphysics, like all metaphysics worthy of the name, was nourished by critical scientific study, of all the sciences (and not merely of one, as is too frequently believed). But this critical study was itself constantly directed by certain a priori principles, metaphysical or logical (the name matters little), of the sort we have just mentioned and which Leibniz, far from borrowing from experience, employed to judge and to explain experience.⁴⁹

And now, we must put an end once and for all to that conception of the monad which is still advanced in textbooks and courses and even in certain scientific works,⁵⁰ namely, that monads are forces (the more scholarly say "centers of force"). To refute this totally, it ought to suffice to recall that Leibniz never admitted what we call a force in mechanics. We know how he protested against the hypothesis of attraction, accusing Newton of reinstating the occult qualities of the scholastics, which violate the principle of reason.⁵¹ In the Tentamen de motuum caelestium causis (1689), which he proposed in opposition to the Newtonian theory, he excluded all action at a distance and tried to explain the movement of the stars by the pressure of a fluid in which they are immersed.⁵² It is a commonplace to oppose Leibniz's dynamism to the mechanism of Descartes. This distinction does not have the slightest justification. Leibniz is as much a mechanist as Descartes; even more so, for he is a rigorous determinist. If he modifies the formulas of Cartesian mechanics he nonetheless entirely accepts its principle, which is to explain all natural phenomena by collisions or contacts without the intervention of any force. What Leibniz calls force, and sometimes even motor force, is always active force.⁵³

It seems however that his theory of active force suggested to him his idea of substance, and he himself often presents the latter as a consequence of the former. For example, in the De causa gravitatis (1690), after having opposed the motor force, which alone is constant, to the quantity of motion, which varies, he concludes: Unde etiam discimus aliquid aliud in rebus esse quam extensionem et motum.⁵⁴ [Wherefore we say there is something in things other than extension and motion.] This idea goes back to 1686, when Leibniz published his Brevis demonstratio erroris memorabilis Cartesii.⁵⁵ Summarizing this memorandum in the Discours de métaphysique, § 17, Leibniz draws from it the following conclusion: "The distinction between the force and the quantity of motion is important, among other things, in showing that one must return to metaphysical considerations separate from extension in order to explain bodily phenomena."⁵⁶ But this consideration has for him only a negative and polemical value. He used it only to prove, against the Cartesians, that "the essence of body does not consist in extension" (and especially to humiliate them by showing that their master committed gross scientific errors); but it was of no use to him for the discovery and positive determination of this "essence." Moreover, even this negative thesis itself does not originally derive from mechanical considerations, but rather from logico-metaphysical speculations on the nature of substance, which Leibniz summarized in the following way: "If body is a substance and not merely a simple phenomenon like the rainbow nor a being united by accident or through aggregation like a heap of stones, then it cannot consist of extension, and one must necessarily conceive something which one calls substantial form and which corresponds in some sense to the soul."⁵⁷ Now this thesis proceeds from the remark that, since extension is infinitely divisible, one could not discover any unity in it nor, accordingly, any substantiality.⁵⁸ Should one therefore say that Leibniz's metaphysics depends on his geometry? This would indeed be more exact than to make it depend on his mechanics: for he already professed this thesis in his first Lettre à Arnauld (1672),⁵⁹ at a period when he had ideas totally different from his mechanical theories of the future, and when, on the contrary, he believed he could explain all mechanical phenomena geometrically.⁶⁰ Finally, in the Discours de métaphysique itself, the thesis "that the notions which rely on extension include something imaginary and could not constitute the substance of body" (§ 12) comes well before the considerations regarding active force (§ 18) and is established independently of these latter. Let us therefore conclude that the concept of substance owes nothing to Leibniz's mechanics and proceeds uniquely from his logical and metaphysical principles.

It is the same with the pre-established harmony, which is the keystone of the system. Without doubt, in what he wrote toward the end of his life, Leibniz seems to recognize that this "hypothesis" derives from his mechanical conceptions. In the Theodicy (§ 61), after having recalled his law of active force, he says: "If this rule had been known to M. Descartes…, I believe that it would have led him straight to the hypothesis of the pre-established harmony, to which these same rules have led me."⁶¹ About the same time, he persuaded Christian Wolff to study mathematics rather than philosophy, praesertim cum ipsa Mathematica potissimum juvent philosophantem, neque ego in Systema Harmonicum incidissem, nisi leges motuum prius constituissem, quae systema causarum occasionalium evertunt,⁶² [chiefly because Mathematics is a very pow erful aid in philosophy, and I would not have arrived at my System of Harmony unless I had previously known the laws of motion which overthrow the systems of occasional causation]. This is undeniably quite unequivocal. But alas, Leibniz's memory deceived him on this point. This is explained by the fact that discussions regarding mechanics had assumed an important role in his battle against the Cartesians and against Malebranche, and thus were inextricably intermingled in his later exposition of his system. For he wrote in 1686: "The hypothesis of concomitance follows from my notion of substance,"⁶³ and this notion, as we have seen, has a purely logical origin. Moreover, this hypothesis is established in § 14 of the Discours de métaphysique by reasons of a metaphysical nature and independently of any mechanical consideration: "God produces diverse substances according to the different viewpoints he has of the universe, and through the intervention of God the individual nature of each substance ensures that what happens to one corresponds to what happens to the others, without their acting directly upon one another." But there is a yet more decisive proof. It is an unpublished text, dated 1676, in which one finds such statements as these: Every soul perceives the entire universe, but confusedly; these confused perceptions constitute sensations; God created a multitude of souls in order to have as many different perspectives of the world. In this text Leibniz again declares himself an advocate of atoms (and of spherical atoms!), which he tries to reconcile with the plenum by means of the idea of infinitely small particles.⁶⁴ Here is, it seems to us, a decisive proof that his essential metaphysical theses are well prior to his mechanical theories, to which they owe absolutely nothing.⁶⁵

Furthermore, if one analyzes these theories themselves one finds nothing in them which could justify either the concept of the monad or, especially, the hypothesis of the pre-established harmony. As Mr. Cassirer has shown perfectly, the law of the conservation of (active) force never had for Leibniz anything but a purely phenomenal value—like motion, mass, and space itself.⁶⁶ If Leibniz could for a moment have dreamed of making a substance of the active force (as certain modern thinkers make a substance of energy), that would have brought him to a monistic and not to a monadistic metaphysics; for the active force of each body varies, and it is only the sum of the active forces which is constant. Shall we then say that the analysis of elastic collision led him to think that every body really is moved only by its own elastic forces which operate, it is true, upon contact with other elastic bodies? But we do not see how this concept would refute the hypothesis of occasionalism, with which it seems perfectly compatible. Actually, it is for purely logical reasons that Leibniz denies all "physical impulse" and all real action of one substance on another, and the phenomenon of elastic collision is nothing for him but a confirmation after the fact, or rather a simple "experimental illustration" of his metaphysical theses. The pre-established harmony is no more a consequence of the laws of mechanics than the monad is an atom or a billiard ball.

Notes

¹ [Translator's note: We indicate by asterisks the omission of the Latin text of the manuscript Primae Veritates, which Couturat includes in this paper. This manuscript was discovered by Eduard Bodemann among the non-philosophical manuscripts of Leibniz. See Bodemann, Die Leibniz-Handschriften (Hanover, 1895), p. 102. The text is catalogued Phil. VIII, 6-7 in L. Couturat, Opuscules et fragments inédits de Leibniz (Paris, 1903); there is an English translation in L. Loemker, Leibniz: Philosophical Papers and Letters (Chicago, 1956), p. 411. In the footnotes which follow, Ger. Phil, designates C. I. Gerhardt, ed., Philosophische Schriften von G. W. Leibniz, 7 vols. (Berlin, 1960-61); Ger. Math, designates C. I. Gerhardt, ed., Mathematische Schriften, 7 vols. (Berlin and Halle, 1849-55). We have revised Couturat's occasional footnote references to the Primae Veritates text.]

² Let us say, on this point, that the numerous dated texts which we have found show that Leibniz's system was much more precocious than has been thought; it was already preformed in the theories of his early youth. See the texts dated 1676 which we will cite later (Couturat, Phil. I, 14, c, 8; VIII, 71).

³Lettre à Arnauld, 14 July 1686 (Ger. Phil. II, 56). Specimen inventorum (Ger. Phil. VII, 309).

⁴Letter d' Arnauld, 28 Sept. 1686: "J'ay sur tout esté frappé de cette raison, que dans toute proposition affirmative véritable, necessaire ou contingente, universelle ou singulière, la notion de l'attribut est comprise en quelque façon dans celle du sujet: praedicatum inest subjecto." [I was especially struck by this reason, that in every true affirmative proposition, necessary or contingent, universal or singular, the notion of the attribute is contained in some fashion in that of the subject: praedicatum inest subjecto.] (Ger. Phil. II, 64).

⁵ "Principium omnis ratiocinationis primarium est, nihil esse aut fieri, quin ration reddi possit, saltern ab omniscio, cur sit potius quam non sit, aut cur sic potius qual aliter; paucis, omnium rationem reddi posse." [The primary principle of every method of reasoning is that nothing is or happens for which it is not possible for the reason to be given, at least from an omniscient point of view, why it is rather than is not or why it is so rather than otherwise; in short, it is possible for the reason of everything to be given.] (Couturat, Phil. IV, 3, c, 13). "Principium ratiocinandi fundamentale est, nihil esse sine ratione, vel … nullam esse veritatem, cui ratio non subsit. Ratio autem veritatis consistit in nexu praedicati cum subjecto, seu ut praedicatum subjecto insit…" [The fundamental principle of reasoning is that nothing is without reason, or that there is no truth for which there is no underlying reason. However, the reason of the truth consists in the connection between the predicate and the subject, whether the predicate is contained in the subject…] (Couturat, Phil. I, 15). Cf. (De Synthesi et Analyst universali (Ger. Phil. VII, 296); Specimen inventorum (Ger. Phil. 309); Ger. Phil. VII, 199; Bodemann, p. 115.

⁶ Already in November 1677 he wrote, "Principium illud summum: nihil esse sine ratione, plerasque metaphysicae controversias finit." [This principle is of the highest importance: nihil esse sine ratione, and it will put an end to many of the controversies of metaphysics.] Scientia media (Couturat, Phil. IV, 3, c, 15). And, in fact, he used it on November 27, 1677, to demonstrate the existence of God in his Conversatio cum D. Episcopo Stenonio de libertate (Bodemann, p. 73).

⁷ An unpublished fragment begins with this sentence: "Maxime in tota philosophia ipsaque theologia momenti haec consideratio est, nullas esse denominationes pure extrinsecas…" [The following consideration is of the utmost importance in all of contemporary philosophy and theology: there are no purely extrinsic characteristics…]; and ends with the following remark: "Omnia quae hac et praecedenti pagina diximus oriuntur ex grandi illo principio, quod praedicatum inest subjecto." [Everything which we have said on this and the preceding pages derives from that important principle, the predicate is contained in the subject.] (Couturat, Phil. I, 14, c, 7). Now the content of this frag ment is entirely metaphysical; it includes in particular a refutation of atomism and a study of the principle of the activity of monads. Elsewhere Leibniz invokes the principle of reason to exclude from physics occult qualities, such as attraction, and to demonstrate mechanism: "Omnia in corporibus fieri mechanice." [In bodies, everything occurs mechanically.] (Couturat, Phil. I, 15).

⁸ Compare this deduction with that contained in another unpublished fragment, already cited: Couturat, Phil. I, 15.

⁹ This reversal of the order of the metaphysical theses in the Monadology is explained by the late date of this short work (1714).

¹⁰ Cf. Russell, A Critical Exposition of the Philosophy of Leibniz, ch. iv.

¹¹ "Verum est affirmatum, cujus praedicatum inest subjecto, itaque in omni Propositione vera affirmativa, necessaria vel contingente, universali vel singulari, Notio praedicati aliquo modo continetur in notione subjecti; ita ut qui perfecte intelligeret notionem utramque, quemadmodum earn intelligit Deus, is eo ipso perspiceret praedicatum subjecto inesse." [A statement the predicate of which is in the subject is true, and so in every true affirmative proposition, necessary or contingent, universal or singular, the notion of the predicate is in some way contained in the notion of the subject; and so whoever perfectly understands these notions, in the way that God understands them, thereby perceives that the predicate is in the subject.] (Couturat, Phil. IV, 3, a, 1). Cf. the similar passages De libertate (L. A. Foucher de Careil, 1857, p. 179); Letter à Arnauld, 14 July 1686 (Couturat, Phil. II, 56), cited in La Logique de Leibniz, pp. 208, 209.

¹² "Utrumque (namely: necessarium et contingens) aeque certum seu a Deo a priori seu per causas cognitum est. Utrumque vi terminorum verum est, seu praedicatum utrobique inest subjecto, tarn in necessariis quam contingentibus." [And both (namely: necessary and contingent truths) are known certainly whether a priori by God or through analysis of their reasons. And both are true by virtue of their terms, or the predicate is contained somewhere in the subject, as much in necessary as in contingent truths.] (Couturat, Phil. VII, B, 11, 71). Cf. De libertate: "Sed in veritatibus contingentibus, etsi praedicatum insit subjecto…" [But in contingent truths, although the predicate be in the subject…] (Foucher de Careil, 1857, p. 182) cited in La Logique de Leibniz, p. 211, note 2.

¹³ "Origo veritatum contingentium ex processu in infinitum, ad exemplum Proportionum inter quantitates incommensurabiles" (Couturat, Theol. VI, 2, f, 11-13.) Cf. Generales Lnquisitiones de Analyst notionum et veritatum, 1686, § 135 (Couturat, Phil. VII, c, 29); Couturat, Phil. IV, 3, a, 1, and Ger. Phil. VII, 200, 309.

¹⁴ "Tandem nova quaedam atque inexpectata lux oborta est unde minime sperabam: ex considerationibus scilicet mathematicis de natura infiniti." [A new and unanticipated light finally arose from the least expected source: namely, from mathematical considerations concerning the nature of the infinite.] De libertate (Foucher de Careil, 1857, pp. 179-80).

¹⁵ "Contingentiae radix infinitum." [Contingency is rooted in infinity.] (Bodemann, p. 121). "Ex his apparet radicem contingentiae esse infinitum in rationibus." [From this it appears that the root of contingency is an infinity of reasons.] (Couturat, Theol. VI, 2, f, 12).

¹⁶ "Atque ita arcanum aliquod a me evolutum puto, quod me diu perplexum habuit, non intelligentem, quomodo praedicatum subjecto inesse posset, nee tamen propositio fierit necessaria. Sed cognitio rerum geometricarum atque analysis infinitorum hanc mihi lucem accendere, ut intelligerem, etiam notiones in infinitum resolubiles esse." [And so I thought I had formulated some sort of mystery, which puzzled me daily; I could not understand how the predicate could be in the subject without the proposition being necessary. But my knowledge of geometry and analysis of infinites showed me the light so that I understood that these notions are also infinitely analyzable.] (Couturat, Phil. IV, 3, a, 1).

¹⁷ Beginning of De libertate (Foucher de Careil, 1857, p. 178). Leibniz there argues against Descartes's assertion (Principles of Philosophy III, 46) that matter must assume successively all possible forms. He maintains, on the contrary, that matter can really be infinitely divisible without thereby realizing all possible divisions (v. Primae Veritates). Cf. the Origo veritatum contingentium: "Si omne quod fit necessarium esset, sequeretur sola quae aliquando existunt esse possibilia (ut volunt Hobbes et Spinosa) et materiam omnes formas possibiles suscipere (quod volebat Cartesius)." [If everything which exists were necessary, it would follow that only those things are possible which do in fact in some way exist (as Hobbes and Spinoza hold) and matter would assume all possible forms (as the Cartesians claimed)]. (Couturat, Theol. VI, 2, f, 11).

¹⁸Discours de métaphysique, § XIII (Ger. Phil. IV, 438).

¹⁹ "Principium autem meum est, quicquid existere potest, et aliis compatible est, id existere…. Itaque nulla alia ratio determinandi, quam ut existant potiora, quae plurimum involvant realitatis." [However, my principle is that whatever is able to exist, and is compatible with the other things, will exist…. And so there is no reason determining existence other than the maximization of reality.] (Couturat, Phil. VIII, 71). It is unnecessary to add that this text suffices, in our opinion, to destory the hypothesis of a lasting and dominating influence exercised by Spinoza on Leibniz.

²⁰ "Ratio existendi prae omnibus possibilibus non alia ratione limitari debet quam quod non omnia compatibilia." [For there is no reason limiting the existence of everything possible other than the fact that not all possibles are compatible.] (Ibid.) This fact, that all possibles are not compatible, is apparently explained by the negation which is necessarily introduced into the complex concepts resulting from the combination of simple concepts. On the contrary, the latter, which Leibniz calls the "primary possibles" and the "absolute attributes of God," are essentially positive and hence compatible. It is thus that the proposition "God is possible" is justified—a proposition which is for Leibniz the indispensable premise of the ontological argument. It is for this reason that he said that his Characteristic had the same basis as the demonstration of the existence of God (Lettre à la duchesse Sophie [Ger. Phil. IV, 296], cited in La Logique de Leibniz, p. 195, note 2). Cf. Couturat, Phil. V, 8, f, 25 (April 1679).

²¹Letter à Arnauld, 1686 (Ger. Phil. II, 55).

²²De rerum originatione radicali, 1697 (Ger. Phil. VII, 304).

²³ Mr. Russell maintains that all existential judgments are synthetic for Leibniz, with the exception of the affirmation of the existence of God, which would be analytic. This exception is nowhere indicated, and it is unjustifiable in Leibniz's system.

²⁴ " … Existentia a nobis concipitur tanquam res nihil habens cum Essentia commune, quod tamen fieri nequit, quia oportet plus inesse in conceptu Existentis quam non existentis, seu existentiam esse perfectionem; cum revera nihil aliud sit explicabile in existentia, quam perfectissimam seriem rerum ingredi." [We conceive of Existence as having nothing in common with Essence, which is nevertheless not the case, because it is necessary that there be more in the concept of that which exists than of that which does not exist, if existence is a perfection; for indeed nothing would be explicably in existence except as participating in the most perfect order of things.] (Couturat, Phil. I, 14, c, 7 v⁰).

²⁵ "Si Existentia esset aliud quiddam quam Essentiae exigentia, sequeretur ipsam habere quandam essentiam seu aliquid novum superaddere rebus, de quo rursus quaeri posset an haec essentia existat, et cur ista potius quam alia." [If Existence were something other than the exigency of Essence, it would follow that this itself would have some essence and something new would be added to things about which one again could ask whether this essence existed, or why this one rather than that.] (Ger. Phil. VII, 195, note). [Editor's note: It should be noted that this interpretation requires a rather different reading of the maxim nihili nullae proprietates sunt than Benson Mates gives it in his article "Leibniz on Possible Worlds," which is included in the present volume.]

²⁶ "J'ay reconnu que la vraye Metaphysique n'est guères differente de la vraye Logique, c'est-a-dire de l'art d'inventer en general." [I recognized that the true metaphysics hardly differs from the true logic, that is, from the art of discovery in general.] Lettre à la duchesse Sophie (Ger. Phil. IV, 292).

²⁷ Couturat, Phil. IV, 3, c, 13.

²⁸Scientia media, Nov. 1677 (Couturat, Phil. IV, 3, c, 15).

²⁹ Couturat, Phil. IV, 3, c, 13.

³⁰ It is unnecessary to note that the "contingence" he attributes to the laws of nature has nothing in common with what our modern "irrationalists" mean thereby. Leibniz summarized his theory of contingence in this concise formula: "Nulla est in rebus singularibus necessitas, sed omnia sunt contingentia. Vicissim tamen nulla est in rebus indifferentia, sed omina sunt determinata." [There is no necessity in things; everything is contingent … on the other hand, however, there is no indifference in things; everything is determined.] (Ger. Phil. VII, 108).

³¹ This notion of freedom is much closer to Kant's than is generally believed. In fact, the concept of freedom as independence of natural laws is for Kant only a negative concept; freedom consists not in the absence of all determination, but in the determination of the will by reason. Kant explicitly states: "a free will (that is, without law) would be an absurdity." (Groundwork of the Metaphysics of Morals, 3rd section). Freedom too has its laws; this is why Kant constantly talks of "causality by freedom." A free will is a will submitted to the moral law; the positive concept of freedom is autonomy.

³²Scientia media, Nov. 1677 (Couturat, Phil. IV, 3, c, 15).

³³ "Voluntatis objectum esse bonum apparens, et nihil a nobis appeti nisi sub ratione boni apparentis, dogma est vetustissimum communissimumque." [The object of the will is the apparent good, and we desire nothing except under the form of apparent good. This belief is very old and widespread.] (Couturat, Phil. IV, 3, c, 13).

³⁴ L. Dutens, ed., God. Guil. Leibnitii … Opera omnia. (Geneva, 1768), III, 145.

³⁵ V. the Tentamen Anagogicum, "où l'on monstre…que dans la recherche des Finales il y a des cas où il faut avoir égard au plus simple ou plus determiné, sans distinguer si c'est le plus grand ou le plus petit." [in which one shows…that in the study of Finalities there are cases where one must be concerned with the simplest or the most determined, without distinguishing whether it is the largest or the smallest.] (Ger. Phil. VII, 270).

³⁶ Cf. La Logique de Leibniz, pp. 230-32.

³⁷ See especially the end of the Réponse aux réflexions de M. Bayle (1702), cited and commented on in La Logique de Leibniz, p. 238.

³⁸ "Constat principia naturae non minus metaphysica quam mathematica esse, vel potius causas rerum latere in metaphysica quadam mathesi quae aestimat perfectiones seu gradus realitatum." [The principles of nature are not less metaphysical than mathematical, or rather the causes of things lie in a certain mathematical metaphysics which calculates the perfections and the degrees of reality.] (Ger. Phil. II, 213). This "metaphysical mathematics" is the Characteristic or Combinatory: one sees that its object is to calculate the degree of reality of the possibles, and thus to explain the real by a simple analysis.

³⁹ This is the definition of cinematics, which Leibniz (as well as Kant) calls "Phoronomy."

⁴⁰ Couturat, Phil. V, 7, 4 v⁰.

⁴¹ "Quanti autem momenti sit, recte constitui principia hujus Matheseos vel Physico-Matheseos tarn late patentis, quae considerationem virium (rem imaginationi non subditam) addit Geometriae deu scientiae imaginum universali, facile intelligis." [However, as to the quantity of motion, you will easily see that I correctly established the principles of this Mathematics or Physico-Mathematics which is so broadly applicable and which supplements Geometry or the science of universal imagination by consideration of forces (which cannot be subsumed under things of the imagination).] (Ger. Math. III, 243).

⁴² Couturat, Phil. V, 8, g, 30-31.

⁴³ See, for example, the beginning of the Pacidius Philalethi (October 1676), which is published in its entirely in Couturat, Math. X, 11, and the end of the De modo perveniendi ad veram corporum analysin et rerum naturalium causas (May 1677), in which he says: "Haec autem [the analysis of physical qualities] per defmitiones et linguam philosophicam egregie fient." [This however can be achieved splendidly through definitions and a philosophical language.] (Ger. Phil. VII, 269).

⁴⁴ "Ars characteristica ostendet non tantum quomodo experimentis sit utendum, sed et quaenam experimenta sint sumenda et ad determinandam rei subjectae naturam sufficientia…" [The art of Characteristic will show not only how experiments are to be interpreted, but also which experiments are to be undertaken and which are sufficient for determining the nature of the subject in question…] (Couturat, Phil. V, 8, g, 31).

⁴⁵Lettre à Arnauld, 14 July 1686 (Ger. Phil. II, 62). Cf. Lettre à Foucher, 1687 (Ger. Phil. I, 391); Lettre à Arnauld, 14 Jan. 1688 (Ger. Phil. VII, 199); these texts are cited in La Logique de Leibniz, p. 304.

⁴⁶Ger. Phil. III, 45. Cf. Essai de Dynamique (Foucher de Careil, I, 653).

⁴⁷ Just when we finished this article, we received Mr. Cassirer's study, Leibniz' System in seinen wissenschaftlichen Grundlagen (Marburg, Elwert, 1902), in which (despite certain divergences in interpretation) we found a valuable confirmation of the thesis we are here holding. Mr. Cassirer states as we do that what Leibniz calls "metaphysical principles" are really logical principles and remarks that he criticized the theological considerations from which Descartes claimed to deduce the law of conservation in mechanics (pp. 315-16).

⁴⁸ See Bodemann, pp. 301-2, 328-29.

⁴⁹ Cf. Cassirer, op. cit., pp. 308 ff, and the texts cited there.

⁵⁰ Dühring, Geschichte der mechanischen Prinzipien, p. 229 (cited by Cassirer, op. cit., p. 314).

⁵¹Antibarbarus physicus pro philosophia reali, contra renovationes qualitatum scholasticarum et intelligentiarum chimaericarum (Ger. Phil. VII, 337); cf. Couturat, Phil. I, 15, Ch. 2.

⁵² "Omnia corpora quae in fluido lineam curvam describunt, ab ipsius fluidi motu agi" since bodies can interact only through contact. [All bodies which describe a curve in a fluid are set in motion by that fluid.] (Ger. Math. VI, 149, 166).

⁵³ One must radically distinguish between primitive force (vis primitivd), a metaphysical quality which Leibniz attributes to the monads, and derived force (vis derivativd), which is a mechanical and phenomenal property of bodies (cf. Cassirer, op. cit., p. 315). Here we are speaking only of the latter.

⁵⁴Ger. Math. VI, 202. One reads, on the same page: "VIRES MOTRICES, id est, eas quae conservandae sunt." [MOTOR FORCES, they are what are to be conserved.]

⁵⁵Ger. Math. VI, 117.

⁵⁶ Summary of § 18 of the Discours de métaphysique in the Lettre au landgrave of 11 Feb. 1686.

⁵⁷ Cf. Lettre à l'étectrice Sophie, 4 Nov. 1696: "Mes méditations fondamentales roulent sur deux choses, sçavoir sur l'unité et sur l'infini." [My basic meditations concern two topics, namely, unity and infinity.] (Ger. Phil. III, 542); cf. Primae Veritates.

⁵⁸Lettre à Arnauld, 14 July 1686. Cf. Primae Veritates.

⁵⁹Ger. Phil. I, 72.

⁶⁰ See Hannequin, Quae fuerit prior Leibnitii philosophia … ante annum 1672, p. 110 (Masson, 1893). From 1669 Leibniz made the essence of matter consist in antitype or impenetrability (Lettre à Thomasius, Ger. Phil. I, 17). In 1670 he made it consist in motion, in velocity (Hypothesis physica nova), from which he concluded that mechanics is reducible to geometry.

⁶¹ Cf. Monadology, § 80.

⁶²Briefwechsel mit Chr. Wolf, ed. Gerhardt (1860), p. 51.

⁶³Projet de lettre à Arnauld (Ger. Phil. II, 68); see the development which follows (p. 70).

⁶⁴ Couturat, Phil. I, 14, c, 8.

⁶⁵ Certain texts which seem contrary to our thesis really only confirm it. For example, Leibniz said with respect to his Dynamics: "Vous avez raison, Monsieur, de juger que c'est en bonne partie le fondement de mon système, parce qu'on y apprend la différence entre les verités dont la necessité est brute et géométrique, et entre les verités qui ont leur source dans la convenance et dans les finales." [You are right, Monsieur, to think that it is in large part the basis of my system, because one sees in it the difference between those truths whose necessity is brutish (brute) and geometrical and those truths which have their source in purpose (convenance) and in finalities.] There follows the classical allusion to the Phaedo (Lettre à Remond, 22 June 1715; Ger. Phil. III, 645). We see in what sense mechanics could be said to serve as the basis of the system: it is not at all that it gives rise to the concept of substance but rather that it confirms the principles of Leibnizian logic. And yet it is able to provide only a confirmation: for we know, from texts contemporaneous with the formulation of the system, that the theory of contingent truths was suggested to Leibniz by his infinitesimal calculus. See above, notes 14 and 16.

⁶⁶ "Vires quae ex massa et velocitate oriuntur derivativae sunt et ad aggregata seu phaenomena pertinent." [The forces which arise out of mass and velocity are derivative and belong to the aggregate or the phenomena.] Lettre à de Voider (Ger. Phil. II, 251). "Vires derivativas ad phaenomena relego." [I relegate the derived forces to phenomena.] (Ger. Phil. II, 275)…. [However I of course put corporeal qualities such as corporeal forces among the phenomena.] (Ger. Phil. II, 276).