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System of Leibniz

The System of Leibniz


Gottfried Wilhelm von Leibniz was born at Leipzig on 21 June (1 July), 1646. In 1661 he entered the University of Leipzig as a student of philosophy and law, and in 1666 obtained the degree of Doctor of Law at Altdorf. The following year he met the diplomat Baron von Boineburg, at whose suggestion he entered the diplomatic service of the Elector of Mainz. The years 1672 to 1676 he spent as diplomatic representative of Mainz at the Court of Louis XIV. During this time he paid a visit to London and made the acquaintance of the most learned English mathematicians, scientists, and theologians of the day. While at Paris he became acquainted with prominent representatives of Catholicism, and began to interest himself in the questions which were in dispute between Catholics and Protestants. In 1676 he accepted the position of librarian, archivist, and court councillor to the Duke of Brunswick. The remaining years of his life were spent at Hanover, with the exception of a brief interval in which he journeyed to Rome and to Vienna for the purpose of examining documents relating to the history of the House of Brunswick. He died at Hanover on 14 Nov., 1716.

As a mathematician Leibniz claims with Newton the distinction of having invented (in 1675) differential calculus. As a scientist he appreciated and encharged the use of observation and experiment: "I prefer," he said, "a Leeuwenhoek who tells me what he sees to a Cartesian who tells me what he thinks." As a historian he emphasized the importance of the study of documents and archives. As a philologist he laid stress on the value of the comparative study of languages, and made some contributions to the history of German. As a philosopher he is undoubtedly the foremost German thinker of the eighteenth century, Kant being generally reckoned among nineteenth-century philosophers. Finally, as a student of statecraft he realized the importance of freedom of conscience and made persistent, well-meant, though unsuccessful efforts to reconcile Catholics and Protestants.


When Leibniz became librarian and archivist of the House of Brunswick in 1676, the Duke of Brunswick was Johann Friedrich, a recent convert to Catholicism. Almost immediately Leibniz began to exert himself in the cause of reconciliation between Catholics and Protestants. At Paris he had come to know many prominent Jesuits and Oratorians, and now he began his celebrated correspondence with Bossuet. With the sanction of the duke and the approval, not only of the vicar Apostolic, but of Innocent XI, the project to find a basis of agreement between Protestants and Catholics in Hanover was inaugurated. Leibniz soon took the place of Molanus, president of the Hanoverian Consistory, as the representative of the Protestant claims. He tried to reconcile the Catholic principle of authority with the Protestant principle of free enquiry. He favoured a species of syncretic Christianity first proposed at the University of Helmstadt, which adopted for its creed an eclectic formula made up of the dogmas supposed to have been held by the primitive Church. Finally he drew up a statement of Catholic doctrine, entitled "Systema Theologicum", which he tells us met the approval not only of Bishop Spinola of Wiener-Neustadt, who conducted, so to speak, the case for the Catholics, but also of "the Pope, the Cardinals, the General of the Jesuits, the Master of the Sacred Palace and others." The negotiations were continued even after the death of Duke Johann Friedrich in 1679. Leibniz, it should be understood, was actuated as much by patriotic motives as he was by religious considerations. He saw clearly that one of the greatest sources of weakness in the German States was the lack of religious unity and the absence of the spirit of toleration. Indeed, the role he played was that of a diplomat rather than that of a theologian. However, his correspondence with Bossuet and Pelisson and his acquaintance with many prominent Catholics produced a real change in his attitude towards the Church, and, although he adopted for his own creed a kind of eclectic rationalistic Christianity, he ceased in 1696 to frequent Protestant services. The causes of the failure of his negotiations have been variously summed up by different historians. One thing seems clear: Louis XIV, who, through Bossuet, professed his approval of Leibniz's project, had very potent political reasons for placing obstacles in the way of Leibniz's irenic efforts. Leibniz, it should be added, met with little success in his other plan of conciliation, namely, his scheme for the union of Protestants among themselves.


In 1700 Leibniz, through the munificence of his royal pupil Princess Sophie Charlotte, wife of Frederick the First of Prussia, founded the Society (afterwards called the Academy) of Sciences of Berlin, and was appointed its first president. In 1711, and again in 1712 and 1716 he was accorded an interview with Peter the Great, and suggested the formation of a similar society at St. Petersburg. In 1689, during his visit to Rome, he was elected a member of the pontifical Accademia Fisico-Mattematica .


Since the discovery in 1903 of fifteen thousand letters and unedited fragments of Leibniz's works at Hanover, the learned world has come to realize the full force of a saying of Leibniz himself: "He who knows me by my published works alone does not know me at all" (Qui me non nisi editis novit, non novit). The works published during his lifetime or immediately after his death are, for the most part, treatises on particular portions of his philosophy. None of them gives an adequate account of his system in its entirety. The most important are

  • "Disputatio metaphysica de principio individui,"
  • "La monadologie ","Essais de théodicée", and
  • "Nouveaux essais sur l'entendement humain," a reply, chapter by chapter, to Locke's "Essay".

Of Leibniz's treatises on religious topics the most important are:

  • "Dialogus de religione rustici", a fragment, dated Paris, 1673, and treating of predestination;
  • "Dialogue effectif sur la liberté de l'homme, et sur l'origine du mal," dated 1695, and treating of the same topic;
  • "Letters" to Arnauld and others on transubstantiation,
  • Letters, tracts, opuscula, etc., of an irenic character, e. g. "Variae definitiones ecclesiae" "De persona Christi", "Appendix, de resurrectione corporum", "De cultu sanctorum", letters to Pelisson, Bossuet, Mme de Brinon, etc.
  • contributions to mystical theology, e.g. "Von der wahren Theologia Mystica", "Dialogues" on the psychology of mysticism.


As a philosopher Leibniz exhibited that many-sidedness which characterized his mental activity in general. His sympathies were broad, his convictions were eclectic, and his aim was not so much that of the synthetic thinker who would found a new system of philosophy, as that of a philosophic diplomatist who would reconcile all existing systems by demonstrating their essential harmony. Consequently, his starting-point is very different from that of Descartes. Descartes believed that his first duty was to doubt all the conclusions of all his predecessors; Leibniz was of the opinion that his duty was to show how near all his predecessors had come to the truth. Descartes was convinced, or at least assumed the conviction, that all the philosophers who went before him were in error, because they appeared to be involved in inextricable contradictions- Leibniz was equally well convinced that all the great systems agree fundamentally, and that their unanimity on essentials is a fair indication that they are in the right. Leibniz therefore resolved, not to isolate himself from the philosophical, scientific, and literary efforts of his predecessors and contemporaries, but, on the contrary, to utilize everything that the human mind had up to his time achieved, to discover agreement where discord and contradiction semed to reign, and thus to establish a permanent peace among contending schools. Even thinkers so widely separated as Plato and Democritus, Aristotle and Descartes, the Scholastics and modern physicists, hold certain doctrines in common, and Leibniz makes it the business of his philosophy to single out those doctrines, explain the manifold bearings of each, remove apparent contradictions, and so accomplish a diplomatic triumph where others had like Descartes, but made confusion worse confounded. The philosophy, to which Leibniz thus ascribed irenics as one of its chief aims, is a partial idealism. Its principal tenets are:

  • The doctrine of monads,
  • pre-established harmony,
  • the law of continuity, and
  • optimism.

(1) The Doctrine of Monads

Like Descartes and Spinoza, Leibniz attaches great importance to the notion of substance. But, while they define substance as independent existence, he defines substance in terms of independent action. The notion of substance as essentially inert (see OCCASIONALISM) is fundamentally erroneous. Substance is essentially active: to be is to act. Now, since the independence of substance is an independence in regard to action, not in regard to existence, there is no reason for maintaining, as Descartes and Spinoza maintained, that substance is one. Substance is, indeed, essentially individual, because it is a centre of independent action but it is no less essentially manifold, since actions are many and varied. The independent, manifold centres of activity are called monads. The monad has been compared to the atom, and is, indeed, like it in many respects. Like the atom, it is simple (devoid of parts), indivisible, and indestructible. However, the indivisibility of the atom is not absolute but only relative to our power of analysing it chemically, while the indivisibility of the monad is absolute, the monad being a metaphysical point, a centre of force, incapable of being analysed or separated in any way. Again, according to the Atomists, all atoms are alike: according to Leibniz no two monads can be exactly alike. Finally, the most important difference between the atom and the monad is this: the atom is material, and performs only material functions; the monad is immaterial and, in so far as it represents other monads, functions in an immaterial manner. The monads therefore, of which all substances are composed, and which are, in reality, the only substances existing, are more like souls than bodies. Indeed, Leibniz does not hesitate to call them souls and to draw the obvious inference that all nature is animated (panpsychism).

The immateriality of the monad consists in its power of representation. Each monad is a microcosm, or universe in miniature. It is, rather, a mirror of the entire universe, because it is in relation with all other monads, and to that extent reflects them all, so that an all-seeing eye looking at one monad could see reflected in it all the rest of creation. Of course, this representation is different in different kinds of monads. The uncreated monad, God, mirrors all things clearly and adequately. The created monad which is the human soul-the "queen-monad"-represents consciously but not with perfect clearness. And, according as we descend the scale from man to the lowest mineral substance, the region of clear representation diminishes and the region of obscure representation increases. The extent of clear representation in the monad is an index of its immateriality. Every monad, except the uncreated monad, is, therefore partly material and partly immaterial. The material element in the monad corresponds to the passivity of materia prima, and the immaterial element to the activity of the forma substantialis. Thus, Leibniz imagined, the Scholastic doctrine of matter and form is reconciled with modern science. At the same time, he imagined, the doctrine of monads embodies what is true in the atomism of Democritus and does not exclude what is true in Plato's immaterialism.

The universe, therefore, as Leibniz represented it, is made up of an infinite number of indivisible monads which rise in a scale of ascending immaterialism from the lowest particle of mineral dust up to the highest created intellect. The lowest monad has only a most imperfect glimmering of immateriality, and the highest has still some remnant of materiality attached to it. In this way the doctrine of monads strives to reconcile materiaiism and idealism by teaching that everything created is partly material and partly immaterial. For matter is not separated from spirit by an abrupt difference, such as Descartes imagined to exist between body and mind. Neither are the functions of the immaterial generically different from the functions of material substance. The mineral, which attracts and is attracted, has an incipient or inchoate power of perception; the plant, which in so many different ways adapts itself to its environment, is in a sense aware of its surroundings, though not conscious of them. The animal by its power of sensation rises by imperceptible steps above the mentality of the Plant and between the highest or most "intelligent" anii mals and the lowest savages there is no very violent break in the continuity of the development of mental power. All this Leibniz maintains without any thought, apparently, of genetic dependence of man on animal, animal on plant, or plant on mineral. He has no theory of descent or ascent. He merely records the absence of "breaks" in the plan of continuity, as it presents itself to his mind. He is not concerned with the problem of origins, but rather with the Cartesian problem of the alleged antithesis between mind and matter. How to bridge the imaginary chasm between mind which thinks, and matter which is extended, was the problem to which all the philosophers of the eighteenth century addressed themselves. Spinoza merged mind and matter in the one infinite substance; the materialists merged mind in matter; the immaterialists merged matter in mind; Hume denied the terms of the problem, when he reasoned away both matter and mind and left only appearances. Leibniz, diplomat and peacemaker, toned matter up and toned mind down until they gave forth what he considered unison. Or, if we are to go back to the original figure of speech, he spanned the chasm by his definition of substance as action. Representation is action; representation is a function of so-called material things as well as of those which are generally called immaterial. Representation, rising from the most rudimentary "little perception" (petite perception) in the mineral up to "apperception" in the human soul, is the bond of substantial continuity, the bridge that joins together the two kinds of substances, matter and mind which Descartes so inconsiderately separated. There is no doubt that Leibniz was conscious of this aim of his philosophy. His opposition to "immoderate Cartesianism" was openly acknowledged in his philosophical treatises as well as in his lectures. He looked upon Spinoza's conclusions as being the logical outcome of Descartes's erroneous definition of substance. "Spinoza", he wrote, "simply said out loud what Descartes was thinking, but did not dare to express". But while he had in view the refutation of extreme Cartesianism, he must have intended also by means of his doctrine of monads to stem the current of materialism which had set in in England and was soon to sweep before it in France many of the ideas which he cherished.

(2) The Doctrine of Pre-established Harmony

"Every present state of a simple substance is a natural consequence of its preceding state, in such a way that its present is always the cause of its future" ("Monadologie," thesis xxii). "The soul follows its own laws, and the body has its laws. They are fitted to each other in virtue of the pre-established harmony among all substances, since they are all representations of one and the same universe" (op. cit., thesis lxxviii) . From Descartes's doctrine that matter is essentially inert, Malebranche (q. v.) had drawn the conclusion that material substances cannot be true causes, but only occasions of the effects produced by God (Occasionalism). Leibniz wished to avoid this conclusion. At the same time, he had reduced all the activity of the monad to immanent activity. That is he had defined substance as action, and explained that the essential action of substance is representation He saw clearly, then, that there can be no interaction among monads. The monad, he said, has "no windows" through which the activity of other monads can enter it. The only recourse left him is to maintain that each monad unfolds its own activity, pursues, as it were, its career of representation independently of other monads. This would make each monad a monarch. If, however, there were no control of the activities of the monad, the world would be a chaos, not the cosmos that it is. We must, therefore, conceive that God at the beginning of creation so arranged things that the changes in one monad correspond perfectly to those in the other monads which belong to its system. In the case of the soul and body, for instance, neither has a real influence on the other: but, just as two clocks may be so perfectly constructed and so accurately adjusted that, though independent of each other, they keep exactly the same time, so it is arranged that the monads of the body put forth their activity in such a way that to each physical activity of the monads of the body there corresponds a psychical activity of the monad of the soul. This is the famous doctrine of pre-established harmony. "According to this system", says Leibniz, "bodies act as if (to suppose the impossible) there were no souls at all, and souls act as if there were no bodies, and yet both body and soul act as if the one were influencing the other" (op. cit., thesis lxxxii). Thus the monad is not really a monarch, but a subject of God's Kingdom, which is the universe, "the true city of God".

If we take this doctrine literally, and deny all influence of one monad on another, we are forced at once to ask: How, then, is it possible for the monad to represent, if it is not acted upon? Leibniz's answer would be that he denied to the monad all communication from without, he affirmed that the monad has no windows on the outside, but he did not deny that in the heart of the monad is a door that opens on the Infinite and from that side it is in communication with all other monads. Here Leibniz passes over the problem from metaphysics to mysticism. If harmony is unity in diversity, the unity in the pre-established harmony is not so much a unity of source, as a unity of final destiny. All things "co-operate" in the universe not only because God is the Source from whom they all spring, but still more so because God is the End towards which they are all tending, and the Perfection which they are all striving to attain.

(3) Law of Continuity

From the description of the monads given above, it is clear that all kinds and conditions of created things shade off by gradual differences, the lower appearing to be merely an inferior degree of the higher. There are no "breaks" in the continuity of nature, no "gaps" between mineral plant, animal, and man. The counter-view is the law of indiscernibles. There can be no meaningless duplication in nature. No two monads can be exactly alike. No two objects, no two events can be entirely similar, for, if they were, they would not, Leibniz thinks, be two but one. The application of these principles led Leibniz to adopt the view that, while every thing differs from every other thing, there are no true opposites. Rest, for instance, may be considered as infinitely minute motion; the fluid is a solid with a lower degree of solidity, animals are men with infinitely small reason, and so forth The application to the theory of the differential calculus is obvious.

(4) Optimism

In the center of the vast harmonious system of monads which we call the universe is God, the original, infinite monad. His power, His wisdom, His goodness are infinite. When, therefore, He created the system of monads, He created them as good as they could possibly be, and established among them the best possible kind of harmony. The world, therefore, is the best possible world, and the supreme law of finite being is the lex melioris. The Will of God must realize what His understanding recognizes as more perfect. Leibniz represents the possible monads as present for all eternity in the mind of God -- in them was the impulse towards actualization -- and the more perfect the possible monad the more strongly did it possess this impulse. There went on, therefore, so to speak, a competition before the throne of God, in which the best monads conquered, and, as God could not but see that they were the best, He could not but will their realization. Behind the lex melioris is therefore, a more fundamental law, the law of sufficient reason, which is that "things or events are real when there is a sufficient reason for their existence." This is a fundamental law of thought, as well as a primary law of being.

The four doctrines here outlined may be said to sum up Leibniz's metaphysical teaching. They find their principal application in his psychology and his theodicy.

(5) Psychology

In the "Nouveaux Essais," which were written in refutation of Locke's "Essay", Leibniz develops his doctrines regarding the human soul and the origin and nature of knowledge. The power of representation, which is common to all monads, makes its first appearance in souls as perception. Perception, when it reaches the level of consciousness, becomes apperception. The Cartesians "have fallen into a serious error in that they treat as non-existent those perceptions of which we are not conscious." Perception is found in all monads; in those monads which we call souls there is apperception, but there is a large subconscious region of souls in which there are perceptions. Perceptions are the source of apperceptions. They are the source also of volitions, because impulse, or appetite, is nothing but the tendency of one perception towards another. From perception, therefore, which is found in everything, up to intelligence and volition, which are peculiar to man there are imperceptibly small grades of differentiation.

Whence, then, come our ideas? The question is already answered in Leibniz's general principles. Since intelligence is only a differentiation of that immanent action which all monads possess, our ideas must be the result of the self-activity of the monad called the human soul. The soul has "no doors or windows" towards the side facing the external world. No ideas can come from that direction. All our ideas are innate. The Aristotelian maxim, "there is nothing in the intellect that was not previously in the senses," must be amended by the addition of the phrase, "except the intellect itself". The intellect is the source as well as the subject of all our ideas. These ideas, however subjective their origin, have objective value, because, by virtue of the harmony pre-established from the beginning of the universe, the evolution of the psychic monad from virtual to actual knowledge is paralleled by the evolution in the outside world of the physical monad from virtual to actual activity.

Leibniz has no difficulty in establishing the immateriality of the soul. All monads are immaterial or rather, partly immaterial and partly material. The human soul is no exception- its "immateriality" is not absolute, but only relative, in the sense that in it the region of clear representation is so much greater than the region of obscure representation that the latter is practically a negligible quantity. Similarly, the immortality of the human soul is not absolutely speaking, a unique privilege. All monads are immortal. Each monad being an independent self-active, source of action, neither dependent on other monads nor influenced by them, it can continue acting without interference forever. The human soul is peculiar in this, that its consciousness (apperception) enables it to realize this independence, and therefore the soul's consciousness of its immortality is what makes human immortality to be different from every other immortality.

(6) Theodicy

The work entitled "Théodicée", a treatise on natural theology, was intended as a refutation of the Encyclopeedist, Bayle, who had tried to show that reason and faith are incompatible. In it Leibniz takes up:

  • the existence of God
  • the problem of evil, and
  • the question of optimism.

Existence of God

Leibniz, true to his eclectic temperament, admits the validity of all the various arguments for the existence of God. He adduces the argument from the contingency of finite being, recasts the ontological argument used by Descartes (see GOD), and adds the argument from the nature of the necessity of our ideas. The third of these arguments is really Platonic in its origin. Its validity depends on the fact that our ideas are necessary, not merely in a hypothetical, but in an absolute and categorical sense, and on the further contention that a necessity of that kind cannot be explained unless we grant that an absolutely necessary Being exists.

(b) Problem of Evil

This problem is discussed at length in the "Théodicée" and in many of Leibniz's letters. The law of continuity requires that there be no abrupt differences among monads. God, therefore, although He wished to create the best possible world, and did, in fact, create the best world that was in se possible, could not create monads which were all perfect, each in its own kind. He was under no necessity of His own Nature, but He was obliged, as it were, by the terms of the problem, to lead up to perfection by passing through various degrees of imperfection. Leibniz distinguishes metaphysical evil, which is mere finiteness, or imperfection in general, physical evil, which is suffering, and moral evil, which is sin. God permits these to exist, since the nature of the universe demands variety and gradation, but He reduces them to the minimum, and makes them to serve a higher purpose, the beauty and harmony of creation as a whole. Leibniz faces resolutely the problem of reconciling the existence of evil with the goodness and omnipotence of God. He reminds us that we see only a part of God's creation, that part, namely, which is nearest to ourselves, and, for that reason, makes the largest demand on our sympathy. We should learn he says, to look beyond our own immediate environment, to observe the larger and more perfect world above us. Where our sympathies are involved, we should not allow the prevalence of evil to overpower our feelings, but should exercise our faith and our love of God, where we can view God's works more impersonally, we should realize that evil and imperfection are always and everywhere made to serve the purpose of harmony, symmetry, and beauty.

(c) Optimism

Leibniz is, therefore, an optimist, both because he maintains as a general metaphysical principle that the world which exists is the best possible world, and because in his discussion of the problem of evil he tries to trace out principles that will "justify the ways of God to man" in a manner compatible with God's goodness. It had become the fashion among materialists and freethinkers to draw an over-gloomy picture of the universe as a place of pain, suffering, and sin, and to ask triumphantly: "How can a good God, if He is omnipotent, permit such a state of things?" Leibniz's answer, though not entirely original, is correct. Evil should be considered in relation not to the parts of reality, but to reality as a whole. Many evils are "in other respects" good. And, when, in the final resort, we cannot see a definite rational solution of a perplexing problem, we should fall back on faith, which, especially in regard to the problem of evil, aids reason.

(7) Leibniz's Ethics

We have seen that, although the monad is by definition independent, and, therefore, a monarch in its own realm, vet, by virtue of preestablished harmony the multitude of monads which make up the universe are organized into a kingdom of spirits, of which God is the Supreme Ruler, a city of God, governed by Divine Providence, or, more correctly still, a family, of which God is the Father. Now, there is "a harmony between the physical realm of nature and the moral realm of grace" (" Monadologie ", thesis lxxxviii); monads making progress along natural lines towards perfection are progressing at the same time along moral lines towards happiness. The essential perfection of a monad is, of course, perfect distinctness of representation. The more the human soul progresses in distinctness of ideas, the more insight it obtains into the connection of all things and the harmony of the whole universe. From this realization springs the impulse to love others, that is to seek the happiness of others as well as one's own. The road to happiness is, therefore through an increase of theoretical insight into tie universe and through an increase in love which naturally follows an increase of knowledge. The moral man, while he thus promotes his own happiness by seeking the happiness of others, fulfils at the same time the Will of God. Goodness and piety are, therefore, identical.


Through his controversy with Clarke concerning the nature of space and the existence of atoms, and also on account of the rivalry between himself and Newton in respect to the discovery of the calculus, Leibniz came to be well known to the learned world in England at the end of the seventeenth century and the beginning of the eighteenth. His residence in Paris brought him into contact with the great men of the court of Louis XIV, as well as with almost all the writers of that age who were distinguished either in the world of science or in that of theology. It was, however, in his own country that he became best known as a philosopher. The multiplicity of his interests and the variety of the tasks he set himself to accomplish were unfavourable to the systematic development of his philosophical doctrines. It was due to the efforts of his follower Christian Wolff (1679-1754), who reduced his teachings to more compact form, that he exerted the influence which he did on the movement known as the German Illumination. In point of fact, until Kant began the public exposition of his critical philosophy, Leibniz was the dominant mind in the world of philosophy in Germany. And his influence was, on the whole, salutary. It is true that his philosophy is unreal. His fundamental conception, that of substance, is more worthy of a poet and a mystic than of a philosopher and a scientist -- nevertheless, like Plato, he is to be judged by the loftiness of his speculations, not by his lack of scientific precision. He did his share in stemming the tide of materialism, and helped to preserve spiritual and aesthetic ideals until such time as they could be treated constructively, as they were by the greatest thinkers in the nineteenth century.


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