Leibnitz

Philosophy.—The central point in the philosophy of Leibnitz was only arrived at after many advances and corrections in his opinions. This point is his new doctrine of substance (p. 702),12 and it is through it that unity is given to the succession of occasional writings, scattered over fifty years, in which he explained his views. More inclined to agree than to differ with what he read (p. 425), and borrowing from almost every philosophical system, his own standpoint is yet most closely related to that of Descartes, partly as consequence, partly by way of opposition. Cartesianism, Leibnitz often asserted, is the ante-room of truth, but the ante-room only. Descartes’s separation of things into two heterogeneous substances only connected by the omnipotence of God, and the more logical absorption of both by Spinoza into the one divine substance, followed from an erroneous conception of what the true nature of substance is. Substance, the ultimate reality, can only be conceived as force. Hence Leibnitz’s metaphysical view of the monads as simple, percipient, self-active beings, the constituent elements of all things, his physical doctrines of the reality and constancy of force at the same time that space, matter and motion are merely phenomenal, and his psychological conception of the continuity and development of consciousness. In the closest connexion with the same stand his logical principles of consistency and sufficient reason, and the method he developed from them, his ethical end of perfection, and his crowning theological conception of the universe as the best possible world, and of God both as its efficient cause and its final harmony.

The ultimate elements of the universe are, according to Leibnitz, individual centres of force or monads. Why they should be individual, and not manifestations of one world-force, he never clearly proves.13 His doctrine of individuality seems to have been arrived at, not by strict deduction from the nature of force, but rather from the empirical observation that it is by the manifestation of its activity that the separate existence of the individual becomes evident; for his system individuality is as fundamental as activity. “The monads,” he says, “are the very atoms of nature—in a word, the elements of things,” but, as centres of force, they have neither parts, extension nor figure (p. 705). Hence their distinction from the atoms of Democritus and the materialists. They are metaphysical points or rather spiritual beings whose very nature it is to act. As the bent bow springs back of itself, so the monads naturally pass and are always passing into action without any aid but the absence of opposition (p. 122). Nor do they, like the atoms, act upon one another (p. 680); the action of each excludes that of every other. The activity of each is the result of its own past state, the determinator of its own future (pp. 706, 722). “The monads have no windows by which anything may go in or out” (p. 705).

Further, since all substances are of the nature of force, it follows that—“in imitation of the notion which we have of souls”—they must contain something analogous to feeling and appetite. It is the nature of the monad to represent the many in one, and this is perception, by which external events are mirrored internally (p. 438). Through their own activity the monads mirror the universe (p. 725), but each in its own way and from its own point of view, that is, with a more or less perfect perception (p. 127); for the Cartesians were wrong in ignoring the infinite grades of perception, and identifying it with the reflex cognizance of it which may be called apperception. Every monad is thus a microcosm, the universe in little,14 and according to the degree of its activity is the distinctness of its representation of the universe (p. 709). Thus Leibnitz, borrowing the Aristotelian term, calls the monads entelechies, because they have a certain perfection (τὸ ἐντελές) and sufficiency (αὐτάρκεια) which make them sources of their internal actions and, so to speak, incorporeal automata (p. 706). That the monads are not pure entelechies is shown by the differences amongst them. Excluding all external limitation, they are yet limited by their own nature. All created monads contain a passive element or materia prima (pp. 440, 687, 725), in virtue of which their perceptions are more or less confused. As the activity of the monad consists in perception, this is inhibited by the passive principle, so that there arises in the monad an appetite or tendency to overcome the inhibition and become more perceptive, whence follows the change from one perception to another (pp. 706, 714). By the proportion of activity to passivity in it one monad is differentiated from another. The greater the amount of activity or of distinct perceptions the more perfect is the monad; the stronger the element of passivity, the more confused its perceptions, the less perfect is it (p. 709). The soul would be a divinity had it nothing but distinct perceptions (p. 520).

The monad is never without a perception; but, when it has a number of little perceptions with no means of distinction, a state similar to that of being stunned ensues, the monade nue being perpetually in this state (p. 707). Between this and the most distinct perception there is room for an infinite diversity of nature among the monads themselves. Thus no one monad is exactly the same as another; for, were it possible that there should be two identical, there would be no sufficient reason why God, who brings them into actual existence, should put one of them at one definite time and place, the other at a different time and place. This is Leibnitz’s principle of the identity of indiscernibles (pp. 277, 755); by it his early problem as to the principle of individuation is solved by the distinction between genus and individual being abolished, and every individual made sui generis. The principle thus established is formulated in Leibnitz’s law of continuity, founded, he says, on the doctrine of the mathematical infinite, essential to geometry, and of importance in physics (pp. 104, 105), in accordance with which there is neither vacuum nor break in nature, but “everything takes place by degrees” (p. 392), the different species of creatures rising by insensible steps from the lowest to the most perfect form (p. 312).

As in every monad each succeeding state is the consequence of the preceding, and as it is of the nature of every monad to mirror or represent the universe, it follows (p. 774) that the perceptive content of each monad is in “accord” or correspondence with that of every other (cf. p. 127), though this content is represented with infinitely varying degrees of perfection. This is Leibnitz’s famous doctrine of pre-established harmony, in virtue of which the infinitely numerous independent substances of which the world is composed are related to each other and form one universe. It is essential to notice that it proceeds from the very nature of the monads as percipient, self-acting beings, and not from an arbitrary determination of the Deity.

From this harmony of self-determining percipient units Leibnitz has to explain the world of nature and mind. As everything that really exists is of the nature of spiritual or metaphysical points (p. 126), it follows that space and matter in the ordinary sense can only have a phenomenal existence (p. 745), being dependent not on the nature of the monads themselves but on the way in which they are perceived. Considering that several things exist at the same time and in a certain order of co-existence, and mistaking this constant relation for something that exists outside of them, the mind forms the confused perception of space (p. 768). But space and time are merely relative, the former an order of coexistences, the latter of successions (pp. 682, 752). Hence not only the secondary qualities of Descartes and Locke, but their so-called primary qualities as well, are merely phenomenal (p. 445). The monads are really without position or distance from each other; but, as we perceive several simple substances, there is for us an aggregate or extended mass. Body is thus active extension (pp. 110, 111). The unity of the aggregate depends entirely on our perceiving the monads composing it together. There is no such thing as an absolute vacuum or empty space, any more than there are indivisible material units or atoms from which all things are built up (pp. 126, 186, 277). Body, corporeal mass, or, as Leibnitz calls it, to distinguish it from the materia prima of which every monad partakes (p. 440), materia secunda, is thus only a “phenomenon bene fundatum” (p. 436). It is not a substantia but substantiae or substantiatum (p. 745). While this, however, is the only view consistent with Leibnitz’s fundamental principles, and is often clearly stated by himself, he also speaks at other times of the materia secunda as itself a composite substance, and of a real metaphysical bond between soul and body. But these expressions occur chiefly in the letters to des Bosses, in which Leibnitz is trying to reconcile his views with the doctrines of the Roman Catholic Church, especially with that of the real presence in the Eucharist, and are usually referred to by him as doctrines of faith or as hypothetical (see especially p. 680). The true vinculum substantiale is not the materia secunda, which a consistent development of Leibnitz’s principles can only regard as phenomenal, but the materia prima, through which the monads are individualized and distinguished and their connexion rendered possible. And Leibnitz seems to recognize that the opposite assumption is inconsistent with his cardinal metaphysical view of the monads as the only realities.

From Leibnitz’s doctrine of force as the ultimate reality it follows that his view of nature must be throughout dynamical. And though his project of a dynamic, or theory of natural philosophy, was never carried out, the outlines of his own theory and his criticism of the mechanical physics of Descartes are known to us. The whole distinction between the two lies in the difference between the mechanical and the dynamical views of nature. Descartes started from the reality of extension as constituting the nature of material substance, and found in magnitude, figure and motion the explanation of the material universe. Leibnitz, too, admitted the mechanical view of nature as giving the laws of corporeal phenomena (p. 438), applying also to everything that takes place in animal organisms,15 even the human body (p. 777). But, as phenomenal, these laws must find their explanation in metaphysics, and thus in final causes (p. 155). All things, he says (in his Specimen Dynamicum), can be explained either by efficient or by final causes. But the latter method is not appropriate to individual occurrences,16 though it must be applied when the laws of mechanism themselves need explanation (p. 678). For Descartes’s doctrine of the constancy of the quantity of motion (i.e. momentum) in the world Leibnitz substitutes the principle of the conservation of vis viva, and contends that the Cartesian position that motion is measured by velocity should be superseded by the law that moving force (vis motrix) is measured by the square of the velocity (pp. 192, 193). The long controversy raised by this criticism was really caused by the ambiguity of the terms employed. The principles held by Descartes and Leibnitz were both correct, though different, and their conflict only apparent. Descartes’s principle is now enunciated as the conservation of momentum, that of Leibnitz as the conservation of energy. Leibnitz further criticizes the Cartesian view that the mind can alter the direction of motion though it cannot initiate it, and contends that the quantity of “vis directiva,” estimated between the same parts, is constant (p. 108)—a position developed in his statical theorem for determining geometrically the resultant of any number of forces acting at a point.

Like the monad, body, which is its analogue, has a passive and an active element. The former is the capacity of resistance, and includes impenetrability and inertia; the latter is active force (pp. 250, 687). Bodies, too, like the monads, are self-contained activities, receiving no impulse from without—it is only by an accommodation to ordinary language that we speak of them as doing so—but moving themselves in harmony with each other (p. 250).

The psychology of Leibnitz is chiefly developed in the Nouveaux essais sur l’entendement humain, written in answer to Locke’s famous Essay, and criticizing it chapter by chapter. In these essays he worked out a theory of the origin and development of knowledge in harmony with his metaphysical views, and thus without Locke’s implied assumption of the mutual influence of soul and body. When one monad in an aggregate perceives the others so clearly that they are in comparison with it bare monads (monades nues), it is said to be the ruling monad of the aggregate, not because it actually does exert an influence over the rest, but because, being in close correspondence with them, and yet having so much clearer perception, it seems to do so (p. 683). This monad is called the entelechy or soul of the aggregate or body, and as such mirrors the aggregate in the first place and the universe through it (p. 710). Each soul or entelechy is surrounded by an infinite number of monads forming its body (p. 714); soul and body together make a living being, and, as their laws are in perfect harmony—a harmony established between the whole realm of final causes and that of efficient causes (p. 714)—we have the same result as if one influenced the other. This is further explained by Leibnitz in his well-known illustration of the different ways in which two clocks may keep exactly the same time. The machinery of the one may actually move that of the other, or whenever one moves the mechanician may make a similar alteration in the other, or they may have been so perfectly constructed at first as to continue to correspond at every instant without any further influence (pp. 133, 134). The first way represents the common (Locke’s) theory of mutual influence, the second the method of the occasionalists, the third that of pre-established harmony. Thus the body does not act on the soul in the production of cognition, nor the soul on the body in the production of motion. The body acts just as if it had no soul, the soul as if it had no body (p. 711). Instead, therefore, of all knowledge coming to us directly or indirectly through the bodily senses, it is all developed by the soul’s own activity, and sensuous perception is itself but a confused kind of cognition. Not a certain select class of our ideas only (as Descartes held), but all our ideas, are innate, though only worked up into actual cognition in the development of knowledge (p. 212). To the aphorism made use of by Locke, “Nihil est in intellectu quod non prius fuerit in sensu,” must be added the clause, “nisi intellectus ipse” (p. 223). The soul at birth is not comparable to a tabula rasa, but rather to an unworked block of marble, the hidden veins of which already determine the form it is to assume in the hands of the sculptor (p. 196). Nor, again, can the soul ever be without perception; for it has no other nature than that of a percipient active being (p. 246). Apparently dreamless sleep is to be accounted for by unconscious perception (p. 223); and it is by such insensible perceptions that Leibnitz explains his doctrine of pre-established harmony (p. 197).

In the human soul perception is developed into thought, and there is thus an infinite though gradual difference between it and the mere monad (p. 464). As all knowledge is implicit in the soul, it follows that its perfection depends on the efficiency of the instrument by which it is developed. Hence the importance, in Leibnitz’s system, of the logical principles and method, the consideration of which occupied him at intervals throughout his whole career.

There are two kinds of truths—(1) truths of reasoning, and (2) truths of fact (pp. 83, 99, 707). The former rest on the principle of identity (or contradiction) or of possibility, in virtue of which that is false which contains a contradiction, and that true which is contradictory to the false. The latter rest on the principle of sufficient reason or of reality (compossibilité), according to which no fact is true unless there be a sufficient reason why it should be so and not otherwise (agreeing thus with the principium melioris or final cause). God alone, the purely active monad, has an a priori knowledge of the latter class of truths; they have their source in the human mind only in so far as it mirrors the outer world, i.e. in its passivity, whereas the truths of reason have their source in our mind in itself or in its activity.

Both kinds of truths fall into two classes, primitive and derivative. The primitive truths of fact are, as Descartes held, those of internal experience, and the derivative truths are inferred from them in accordance with the principle of sufficient reason, by their agreement with our perception of the world as a whole. They are thus reached by probable arguments—a department of logic which Leibnitz was the first to bring into prominence (pp. 84, 164, 168, 169, 343). The primitive truths of reasoning are identical (in later terminology, analytical) propositions, the derivative truths being deduced from them by the principle of contradiction. The part of his logic on which Leibnitz laid the greatest stress was the separation of these rational cognitions into their simplest elements—for he held that the root-notions (cogitationes primae) would be found to be few in number (pp. 92, 93)—and the designation of them by universal characters or symbols,17 composite notions being denoted by the formulae formed by the union of several definite characters, and judgments by the relation of aequipollence among these formulae, so as to reduce the syllogism to a calculus. This is the main idea of Leibnitz’s “universal characteristic,” never fully worked out by him, which he regarded as one of the greatest discoveries of the age. An incidental result of its adoption would be the introduction of a universal symbolism of thought comparable to the symbolism of mathematics and intelligible in all languages (cf. p. 356). But the great revolution it would effect would chiefly consist in this, that truth and falsehood would be no longer matters of opinion but of correctness or error in calculation,18 (pp. 83, 84, 89, 93). The old Aristotelian analytic is not to be superseded; but it is to be supplemented by this new method, for of itself it is but the ABC of logic.

But the logic of Leibnitz is an art of discovery (p. 85) as well as of proof, and, as such, applies both to the sphere of reasoning and to that of fact. In the former it has by attention to render explicit what is otherwise only implicit, and by the intellect to introduce order into the a priori truths of reason, so that one may follow from another and they may constitute together a monde intellectuel. To this art of orderly combination Leibnitz attached the greatest importance, and to it one of his earliest writings was devoted. Similarly, in the sphere of experience, it is the business of the art of discovery to find out and classify the primitive facts or data, referring every other fact to them as its sufficient reason, so that new truths of experience may be brought to light.

As the perception of the monad when clarified becomes thought, so the appetite of which all monads partake is raised to will, their spontaneity to freedom, in man (p. 669). The will is an effort or tendency to that which one finds good (p. 251), and is free only in the sense of being exempt from external control19 (pp. 262, 513, 521), for it must always have a sufficient reason for its action determined by what seems good to it. The end determining the will is pleasure (p. 269), and pleasure is the sense of an increase of perfection (p. 670). A will guided by reason will sacrifice transitory and pursue constant pleasures or happiness, and in this weighing of pleasures consists true wisdom. Leibnitz, like Spinoza, says that freedom consists in following reason, servitude in following the passions (p. 669), and that the passions proceed from confused perceptions (pp. 188, 269). In love one finds joy in the happiness of another; and from love follow justice and law. “Our reason,” says Leibnitz,20 “illumined by the spirit of God, reveals the law of nature,” and with it positive law must not conflict. Natural law rises from the strict command to avoid offence, through the maxim of equity which gives to each his due, to that of probity or piety (honeste vivere),—the highest ethical perfection,—which presupposes a belief in God, providence and a future life.21 Moral immortality—not merely the simple continuity which belongs to every monad—comes from God having provided that the changes of matter will not make man lose his individuality (pp. 126, 466).

Leibnitz thus makes the existence of God a postulate of morality as well as necessary for the realization of the monads. It is in the Théodicée that his theology is worked out and his view of the universe as the best possible world defended. In it he contends that faith and reason are essentially harmonious (pp. 402, 479), and that nothing can be received as an article of faith which contradicts an eternal truth, though the ordinary physical order may be superseded by a higher.22

The ordinary arguments for the being of God are retained by Leibnitz in a modified form (p. 375). Descartes’s ontological proof is supplemented by the clause that God as the ens a se must either exist or be impossible (pp. 80, 177, 708); in the cosmological proof he passes from the infinite series of finite causes to their sufficient reason which contains all changes in the series necessarily in itself (pp. 147, 708); and he argues teleologically from the existence of harmony among the monads without any mutual influence to God as the author of this harmony (p. 430).

In these proofs Leibnitz seems to have in view an extramundane power to whom the monads owe their reality, though such a conception evidently breaks the continuity and harmony of his system, and can only be externally connected with it. But he also speaks in one place at any rate23 of God as the “universal harmony”; and the historians Erdmann and Zeller are of opinion that this is the only sense in which his system can be consistently theistic. Yet it would seem that to assume a purely active and therefore perfect monad as the source of all things is in accordance with the principle of continuity and with Leibnitz’s conception of the gradation of existences. In this sense he sometimes speaks of God as the first or highest of the monads (p. 678), and of created substances proceeding from Him continually by “fulgurations” (p. 708) or by “a sort of emanation as we produce our thoughts.”24

The positive properties or perfections of the monads, Leibnitz holds, exist eminenter, i.e. without the limitation that attaches to created monads (p. 716), in God—their perception as His wisdom or intellect, and their appetite as His absolute will or goodness (p. 654); while the absence of all limitation is the divine independence or power, which again consists in this, that the possibility of things depends on His intellect, their reality on His will (p. 506). The universe in its harmonious order is thus the realization of the divine end, and as such must be the best possible (p. 506). The teleology of Leibnitz becomes necessarily a Théodicée. God created a world to manifest and communicate His perfection (p. 524), and, in choosing this world out of the infinite number that exist in the region of ideas (p. 515), was guided by the principium melioris (p. 506). With this thorough-going optimism Leibnitz has to reconcile the existence of evil in the best of all possible worlds.25 With this end in view he distinguishes (p. 655) between (1) metaphysical evil or imperfection, which is unconditionally willed by God as essential to created beings; (2) physical evil, such as pain, which is conditionally willed by God as punishment or as a means to greater good (cf. p. 510); and (3) moral evil, in which the great difficulty lies, and which Leibnitz makes various attempts to explain. He says that it was merely permitted not willed by God (p. 655), and, that being obviously no explanation, adds that it was permitted because it was foreseen that the world with evil would nevertheless be better than any other possible world (p. 350). He also speaks of the evil as a mere set-off to the good in the world, which it increases by contrast (p. 149), and at other times reduces moral to metaphysical evil by giving it a merely negative existence, or says that their evil actions are to be referred to men alone, while it is only the power of action that comes from God, and the power of action is good (p. 658).

The great problem of Leibnitz’s Théodicée thus remains unsolved. The suggestion that evil consists in a mere imperfection, like his idea of the monads proceeding from God by a continual emanation, was too bold and too inconsistent with his immediate apologetic aim to be carried out by him. Had he done so his theory would have transcended the independence of the monads with which it started, and found a deeper unity in the world than that resulting from the somewhat arbitrary assertion that the monads reflect the universe.

The philosophy of Leibnitz, in the more systematic and abstract form it received at the hands of Wolf, ruled the schools of Germany for nearly a century, and largely determined the character of the critical philosophy by which it was superseded. On it Baumgarten laid the foundations of a science of aesthetic. Its treatment of theological questions heralded the German Aufklärung. And on many special points—in its physical doctrine of the conservation of force, its psychological hypothesis of unconscious perception, its attempt at a logical symbolism—it has suggested ideas fruitful for the progress of science.

Bibliography.—(1) Editions: Up to 1900 no attempt had been made to publish the complete works. Several editions existed, but a vast mass of MSS. (letters, &c.) remained only roughly classified in the Hanover library. The chief editions were: (1) L. Dutens (Geneva, 1768), called Opera Omnia, but far from complete; (2) G. H. Pertz, Leibnizens gesammelte Werke (Berlin, 1843-1863) (1st ser. History, 4 vols.; 2nd ser. Philosophy, vol. i. correspondence with Arnauld, &c., ed. C. L. Grotefend; 3rd ser. Mathematics, 7 vols., ed. C. J. Gerhardt); (3) Foucher de Careil (planned in 20 vols., 7 published, Paris, 1859-1875), the same editor having previously published Lettres et opuscules inédits de Leibniz (Paris, 1854-1857); (4) Onno Klopp, Die Werke von Leibniz gemäss seinem Handschriftlichen Nachlasse in der Königlichen Bibliothek zu Hannover (1st series, Historico-Political and Political, 10 vols., 1864-1877). The Œuvres de Leibnitz, by A. Jacques (2 vols., Paris, 1846) also deserves mention. The philosophical writings had been published by Raspe (Amsterdam and Leipzig, 1765), by J. E. Erdmann, Leibnitii opera philos. quae extant Latina, Gallica, Germanica, omnia (Berlin, 1840), by P. Janet (2 vols., Paris, 1866, 2nd ed. 1900), and the fullest by C. J. Gerhardt, Die Philosophischen Schriften von G. W. Leibniz (7 vols., 1875-1890); cf. also Die kleineren philos. wichtigeren Schriften (trans. with commentary, J. H. von Kirchmann, 1879). The German works had also been partly published separately; G. E. Guhrauer (Berlin, 1838-1840). Of the letters various collections had been published up to 1900, e.g.: C. J. Gerhardt (Halle, 1860) and Der Briefwechsel von G. W. Leibnitz mit Mathematikern (1899); Corrispondenza tra L. A. Muratori e G. Leibnitz (1899); and cf. Neue Beiträge zum Briefwechsel zwischen D. E. Jablonsky und G. W. Leibnitz (1899).

In 1900 it was decided by scholars in Berlin and Paris that a really complete edition should be published, and with this object four German and four French critics were entrusted with the preliminary task of correlating the MSS. in the royal library at Hanover. This process resulted in the preparation of the Kritischer Katalog der Leibnitz-Handschriften zur Vorbereitung der interakademischen Leibnitz-Ausgabe unternommen (1908), and also in certain other preliminary publications, e.g. L. Couturat, Opuscules et fragments inédits (1903); E. Gerland, Leibnizens nachgelassene Schriften physikalischen, mechanischen und technischen Inhalts (1906); Jean Baruzi, Leibniz (1909), containing unedited MSS. and a sketch-biography; cf. the same author’s Leibniz et l’organisation religieuse de la terre (1907).

Translations.—Of the Systema Theologicum (1850, C. W. Russell), of the correspondence with Clarke (1717); Works, by G. M. Duncan (New Haven, 1890); of the Nouveaux Essais, by A. G. Langley (London, 1894); the Monadology and other Writings, by R. Latta (Oxford, 1898).

Biographical.—The materials for the life of Leibnitz, in addition to his own works, are the notes of Eckhart (not published till 1779), the Éloge by Fontenelle (read to the French Academy in 1717), the “Eulogium,” by Wolf, in the Acta Eruditorium for July 1717, and the “Supplementum” to the same by Feller, published in his Otium Hannoveranum (Leipzig, 1718). The best biography is that of G. E. Guhrauer, G. W. Freiherr von Leibnitz (2 vols., Breslau, 1842; Nachträge, Breslau, 1846). A shorter Life of G. W. von Leibnitz, on the Basis of the German Work of Guhrauer, has been published by J. M. Mackie (Boston, 1845). More recent works are those of L. Grote, Leibniz und seine Zeit (Hanover, 1869); E. Pfleiderer, Leibniz als Patriot, Staatsmann, und Bildungsträger (Leipzig, 1870); the slighter volume of F. Kirchner, G. W. Leibniz: sein Leben und Denken (Köthen, 1876); Kuno Fischer, vol. iii. in Gesch. der neuern Philosophie (4th ed., 1902).

Critical.—The monographs and essays on Leibnitz are too numerous to mention, but reference may be made to Feuerbach, Darstellung, Entwicklung, und Kritik der Leibnitz’schen Phil. (2nd ed., Leipzig, 1844); Nourrisson, La Philosophie de Leibniz (Paris, 1860); R. Zimmermann, Leibnitz und Herbart: eine Vergleichung ihrer Monadologien (Vienna, 1849); O. Caspari, Leibniz’ Philosophie beleuchtet vom Gesichtspunkt der physikalischen Grundbegriffe von Kraft und Stoff (Leipzig, 1870); G. Hartenstein, “Locke’s Lehre von der menschl. Erk. in Vergl. mit Leibniz’s Kritik derselben dargestellt,” in the Abhandl. d. philol.-hist. Cl. d. K. Sächs. Gesells. d. Wiss., vol. iv. (Leipzig, 1865); G. Class, Die metaph. Voraussetzungen des Leibnitzischen Determinismus (Tübingen, 1874); F. B. Květ, Leibnitzens Logik (Prague, 1857); the essays on Leibnitz in Trendelenburg’s Beiträge, vols. ii. and iii. (Berlin, 1855, 1867); L. Neff, Leibniz als Sprachforscher (Heidelberg, 1870-1871); J. Schmidt, Leibniz und Baumgarten (Halle, 1875); D. Nolen, La Critique de Kant et la Métaphysique de Leibniz (Paris, 1875); and the exhaustive work of A. Pichler, Die Theologie des Leibniz (Munich, 1869-1870). Among the more recent works are: C. Braig, Leibniz: sein Leben und die Bedeutung seiner Lehre (1907); E. Cassirer, Leibniz’ System in seinem wissenschaftlichen Grundlagen (1902); L. Couturat, La Logique de Leibniz d’après des documents inédits (1901); L. Davillé, Leibniz historien (1909); Kuno Fischer, G. W. Leibniz (1889); R. B. Frenzel, Der Associationsbegriff bei Leibniz (1898); R. Herbertz, Die Lehre vom Unbewussten im System des Leibniz (1905); H. Hoffmann, Die Leibniz’sche Religions-philosophie in ihrer geschichtlichen Stellung (1903); W. Kabitz, Die Philosophie des jungen Leibniz (1909), a study of the development of the Leibnitzian system; H. L. Koch, Materie und Organismus bei Leibniz (1908); G. Niel, L’Optimisme de Leibniz (1888); Bertrand A. W. Russell, A Critical Exposition of the Philosophy of Leibniz (1900); F. Schmöger, Leibniz in seiner Stellung zur tellurischen Physik (1901); A. Silberstein, Leibnizens Apriorismus in Verhältnis zu seiner Metaphysik (1904); Stein, Leibniz und Spinoza (1890); F. Thilly, Leibnizens Streit gegen Locke in Ansehung der angeborenen Ideen (1891); R. Urbach, Leibnizens Rechtfertigung des Uebels in der besten Welt (1901); W. Werckmeister, Der Leibnizsche Substanzbegriff (1899); F. G. F. Wernicke, Leibniz’ Lehre von der Freiheit des menschlichen Willens (1890).