Gottfried Wilhelm Leibniz was born in Leipzig in 1646. From a young age, he showed an interest in science. After finishing school, he continued his education at the University of Leipzig (1661-1666) and the University of Jena, where he spent one semester in 1663. In the same year, under the supervision of J. Thomasius, Leibniz defended his scientific work “On the Principle of Individuation” (written in the spirit of nominalism and anticipating some ideas of his mature philosophy), which earned him a bachelor’s degree. In 1666 in Leipzig, he wrote his habilitative work on philosophy “On the Combinatorial Art”, in which he outlined the idea of creating mathematical logic, and in early 1667 he became a doctor of law, presenting a dissertation “On Confused Cases” at the University of Altdorf.
Having given up his career as a university professor, Leibniz entered the service of the Elector of Mainz in 1668. In this service, he mainly carried out legal assignments, without, however, ceasing his scientific research. In 1672, Leibniz arrived in Paris on a diplomatic mission and remained there until 1676. Here he communicated a lot with scientists and philosophers, studied mathematical problems and designed a computer, improving Pascal’s calculating machine. In 1675, Leibniz created differential and integral calculus, publishing the main results of his discovery in 1684, ahead of I. Newton, who had arrived at similar results even earlier than Leibniz, but did not publish them (although some of them were apparently known to Leibniz privately). Subsequently, a long dispute arose on this topic about the priority of the discovery of differential calculus. In 1676, Leibniz, forced to look for permanent sources of income, entered the service of the Hanoverian dukes, which lasted about forty years. Leibniz’s range of responsibilities was wide – from the preparation of dynastic materials and the search for a basis for the unification of various Christian denominations to the design of pumps for pumping water out of mines. Most of his projects, however, were not completed.
In 1686, Leibniz wrote his “Discourse on Metaphysics”, which became an important stage in his work, since it was here that he first fully and systematically set out the principles of his philosophical teaching, although this work was not yet terminologically complete, and it was published only after the death of the author. The last fifteen years of Leibniz’s life turned out to be unusually fruitful in philosophical terms. In 1695, he published his programmatic article “A New System of Nature and Communication between Substances, as well as on the Connection Existing between Soul and Body”, which was not ignored by the philosophical community. In 1705, Leibniz completed his New Essays Concerning Human Understanding (first published in 1765), a unique commentary on J. Locke’s Essay Concerning Human Understanding. In 1710, he published Essays on Theodicy, a summation of his optimistic worldview, and wrote Monadology (1714), a short treatise containing a brief exposition of his metaphysics. Of great importance for understanding Leibniz’s later ideas is his correspondence with N. Remond and the Newtonian S. Clarke.
Not many of Leibniz’s works were published during his lifetime (he wrote mostly in French and Latin). Nevertheless, he was a well-known figure in scientific and political circles. He corresponded with hundreds of different people and did a great deal of organizational work, participating in the creation of several European academies of science. Nevertheless, his death in 1716 caused almost no response from scientific societies, which is partly explained by the consequences of his lawsuit with Newton.
Leibniz was an exceptionally erudite man in philosophy and in many scientific fields. He was most influenced by the philosophical ideas of Descartes, Hobbes, Spinoza, Malebranche, Weil and others. While adopting some of their ideas, Leibniz sharply distanced himself from others. Leibniz also showed great interest in Antiquity and the Middle Ages, which was not typical for a philosopher of the New Age. He especially valued the scholastic concept of substantial form, dating back to Aristotle’s teaching on entelechy, which Leibniz became acquainted with as a child. But when he was about 15 years old, under the influence of modern philosophy, he reoriented himself towards fashionable mechanistic views and mathematics. However, having begun “to search for the ultimate foundations of mechanism and the laws of motion itself,” he “saw with surprise that it was impossible to find them in the sphere of mathematics and that it was necessary to turn to metaphysics” (1: 1, 531). This returned him to Aristotle’s entelechies and dynamic interpretation of being, which became the core of his mature metaphysics.
Philosophical calculus. Another specific feature of Leibniz’s philosophizing, which manifested itself in his early period, was the aspiration of this thinker to the mathematization of human knowledge by constructing a universal “philosophical calculus” that would allow solving even the most complex problems by means of simple arithmetic operations. When disputes arose, philosophers “would only have to take up their pens, sit down at their counting boards and say to each other (as if in a friendly invitation): let’s count!” (1: 3, 497). Philosophical calculus should help both in the formalization of existing knowledge (Leibniz paid special attention to the mathematization of syllogistic), and in the discovery of new truths (drawing a parallel with Bacon’s inductive logic, he believed that this calculus could become the “New Organon”), as well as in determining the degrees of probability of empirical hypotheses. The basis of philosophical calculus is the “art of characterization,” i.e. the search for symbols (Leibniz thought of them as numbers or hieroglyphs) that correspond to the essence of things and replace them in knowledge.
Methodology. Leibniz combined his innovative search for the foundations of philosophical calculus, which, however, never brought any real results, with the construction of a more traditional methodology. In methodological issues, he sought to take a balanced position, trying to reconcile opposing approaches. He considered it necessary to combine empirical knowledge with rational arguments, analysis with synthesis, and the study of mechanical causes with the search for target bases. Leibniz’s attitude to J. Locke’s empiricist position that all human ideas come from experience and the famous principle “there is nothing in the mind that was not first in the senses” is indicative. Leibniz supplements it with a rationalistic reservation: “except the mind itself.” The mind contains innate truths, but not in a finished form, but as certain predispositions or dispositions that can be compared to veins in a block of marble, along which an artist could carve a sculpture.
Descartes interpreted the nature of innate ideas in a similar vein. But his rationalistic line is also modified by Leibniz. He considers the Cartesian concept of self-evidence as a criterion of truth to be heuristically unsuitable and suggests relying on the logical principles of identity (or contradiction) and sufficient reason in cognition.
The principle of “contradiction, or identity, i.e. the proposition that a judgment cannot be true and false at the same time, that therefore A is A and cannot be not = A” (1:1, 433), is, according to Leibniz, the general formula of “truths of reason”, an example of which is the law of identity itself, geometric axioms, etc. Truths of reason are such that their opposite is impossible, i.e. contains a contradiction and cannot be clearly conceived. They express “absolute” or “metaphysical” necessity. Truths of fact, such as “the sun will rise tomorrow,” are connected with “physical” or “moral” necessity and can be explained from the principle of “sufficient reason,” “by virtue of which we see that no phenomenon can be true or actual, no assertion just, without a sufficient reason why the matter is so and not otherwise” (1: 1, 418). Indeed, since truths of fact are not self-evident and the opposite can always be thought of in relation to them, their truth must rest on some external reason. Such a reason can be, for example, the contemplation of the present state of affairs or, if we judge not about the present but about an unobservable actual event, the conformity of this event to some laws of nature or to the principle of the best, which, in turn, can be explained by a higher reason, namely, God, the all-perfect being. One of its perfections is goodness, and if God created a world that did not meet the criteria of the best, he would do so contrary to his good will. However, he cannot have reasons not to follow this will. Therefore, the world as the creation of a good God can only be the best of all possible worlds.
Leibniz’s doctrine of our world as the best of all possible worlds has always caused much controversy and objection. To clarify it, it is necessary to clarify several fundamental points. First of all, Leibniz understands a possible world as a certain set of things, the idea of which does not contain contradictions. Everything that is not contradictory is possible. The number of possible worlds cannot be counted. These worlds can differ from each other in two main parameters – order and diversity. These parameters are not mutually exclusive. The best world turns out to be the one in which the greatest diversity is combined with the highest order. Such a world contains expediency and universal harmony. This is the world that the all-good being, God, chooses for creation. But is our world really God’s creation? The answer to this question presupposes proof of God’s existence. To do this, Leibniz again resorts to the principle of sufficient reason and asserts that God is a sufficient reason for our world. The world exists, but its existence is not necessary, which means that it must have an external foundation, which turns out to be God. Leibniz also expresses his willingness to support the corrected ontological argument. He accepts the logic of this proof, which deduces from the concept of God as an all-perfect being the thesis that such a being cannot fail to exist, since otherwise it is deprived of all-perfection, but notes that a necessary condition for the correctness of this conclusion is the consistency of the concept of God. After all, if it is contradictory, then it can be completely devalued. Leibniz, however, does not see any great difficulties in this question. The consistency of the concept of God, in his opinion, is evidenced by the fact that this concept consists of only positive predicates. It is curious, however, that while fully aware of the contradictoriness of such extreme concepts as “the greatest number” or “the fastest movement”, Leibniz does not emphasize the fact that the concept of an all-perfect being can be fraught with contradictions to no lesser extent. In fact, Nicholas of Kuzan clearly showed that opposites coincide in the Absolute, and A turns out to be identically not = A. Nicholas himself, however, was not afraid of these conclusions, which were actually more or less acceptable within the framework of his doctrine of “learned ignorance.” But they pose a real threat to Leibniz’s cataphatic and anthropomorphic theology.
However, some of Leibniz’s contemporaries believed that there was no need to go into such metaphysical subtleties in order to undermine his teaching on the existence of God and the best world. Life itself, they said, full of misfortunes and suffering, testifies against Leibniz. Can a world with so much evil be called the best? In response to such objections, Leibniz put forward a whole battery of arguments. Firstly, our world is indeed imperfect, but this does not contradict its optimality. After all, even a perfectly perfect being cannot create a world devoid of imperfections. Such a world would simply reproduce God, and would not be his creation. Secondly, the imperfections of the world are ultimately for the good of all that exists, and “the best choice is not always associated with the elimination of evil, for it is possible that evil is accompanied by the greatest good” (1:4, 402-403). Thirdly, when speaking about disasters and sufferings, people tend to put themselves at the center of the universe, which is not entirely justified. When looking at the world from a more general position, it does not seem so nightmarish. Fourthly, we must not forget that the world does not stand still, but develops, moves towards perfection. Fifthly, God is not responsible for evil in any case. Evil can be metaphysical, physical and moral. Metaphysical evil is an ontological imperfection, it cannot be avoided, although it can be minimized, which is what God does. Physical evil is pain and suffering. Moral evil is sin. People often bring them on themselves.
Thus, people themselves are partly responsible for evil and suffering; this is the price they pay for the freedom that God has given them. Leibniz is a consistent opponent of fatalism and the doctrine of metaphysical necessity in the determination of human will. He explains in detail that although a person’s volitional decisions cannot be groundless and are subject to “moral necessity,” this does not mean that his will is not free. After all, freedom requires that a person have the opportunity to act differently, and this opportunity is present in voluntary actions.
By choosing in favor of good, i.e. by maximally promoting the improvement of oneself and others, thereby demonstrating love for God and elevating the human to the divine, a person, according to Leibniz, is not left without a reward. After all, in our world there is a “pre-established harmony” between virtue and bliss. This concept of “pre-established harmony” has become a kind of calling card of Leibniz’s philosophy. Leibniz considered it an exceptionally successful invention. The main area of application of the concept of such harmony was initially the psychophysical problem. At that time, as, incidentally, in our days, there were heated debates about how the mental can correspond to the physical. Particularly popular was the occasionalist theory of N. Malebranche, according to which the soul and body cannot directly interact, and psychophysical correspondence is ensured by God, who monitors bodily and mental changes. Leibniz criticized this concept, arguing that God’s continuous intervention in nature led to the absurd situation of a constant miracle. He proposed replacing occasionalism with a theory that God had coordinated souls and bodies at the creation of the world so that they would naturally correspond to each other without any additional intervention on his part. This theory was called the doctrine of pre-established harmony. Leibniz opposed it not only to occasionalism, but also to the concept of “physical influence”, according to which the soul can directly affect the body, and vice versa. Descartes was inclined to this view, but Leibniz claimed that this was solely because he mistakenly believed that the soul could change the direction of movement of the smallest particles in the brain without violating the law of conservation of forces. In reality, this is impossible, and understanding this circumstance, he believed, directly leads to the theory of pre-established harmony between soul and body. This harmony can even be interpreted as an argument in favor of the existence of God, although it can equally be seen as a consequence of the thesis about the existence of an all-good Creator.
But in any case, the pre-established harmony concerns not only bodies and souls. It is universal. In specifying the details of this universal correspondence, Leibniz developed an original ontological theory, which was called monadology.
Monadology. Although Leibniz arrived at monadology by difficult paths, generalizing data from a wide variety of sciences, from physics to biology, in his systematic exposition of the doctrine of monads he takes as his starting point the indisputable fact of the existence of complex things. The complex must consist of the simple, and monads are nothing other than simple substances, units of being. They are devoid of parts, i.e. immaterial, and can be called spiritual atoms. This means that they cannot disintegrate and cease to exist in a natural way. From this, however, it does not follow that monads are immutable. Experience shows that something is constantly changing in the world. These changes must be associated with monads, since nothing else exists in the world. Changes in monads cannot consist of external movements, since monads are not located in space. This means that changes must occur within the monads themselves and be caused by internal causes, since they have “no windows” and cannot really interact with other monads. Monads, therefore, are not lifeless elements of existence at all, but inexhaustible sources of energy, terminologically updated heirs of substantial forms and Aristotelian entelechies. Although they have no parts, they have an internal structure. They can be in different states and change them under the influence of aspirations, “appetitions”. States, or “perceptions”, i.e. perceptions of monads, unlike parts of a complex thing, do not exist in themselves and therefore do not cancel the simplicity of substance. These states cannot arise in monads from nowhere, rather they must be thought of as inherent in them from time immemorial, but folded up for the time being. The unfolding of the states of monads occurs in accordance with the law of continuity, without any leaps, according to a kind of schedule drawn up for each monad by God at the creation of the world.
In principle, the states of each of the countless monads could be completely uncoordinated with each other. But such a world would not be the best; the inexhaustible diversity would not reveal any signs of unity and order in it. To meet the criteria of optimality, God had to, first, make each monad unique (there cannot be two identical things in the world – the famous Leibniz principle of the “identity of indistinguishables”), and second, program the monads so that their states would be in harmony with each other for all eternity. Thus, in our world there is a pre-established harmony between the perceptions of the monads.
The existence of this harmony can be illustrated (though not proved) by a simple example. Suppose two people are standing side by side and watching the sunrise. Their perceptions are in agreement, but how can this agreement be explained? Perceptions are mental states, states of souls. Each soul is a monad. They are independent of each other, and the change of their states is determined by a chain of sufficient reasons stretching from the time of the creation of the world, for souls, like all monads, live forever, although they may not remember the past. But how is it that monads independent of each other perceive the world as if it really affected them? It cannot be said that they perceive the sunrise because it illuminates them with its rays – neither the sun nor anything else can really affect monads, and the sun itself is a perception of such monads. And although there may be something quite real behind the perception of the sun, some set of monads, they still cannot directly affect other monads. In a word, the agreement of people’s perceptions – assuming the truth of all the assumptions made – can be explained only by the original coordination of their monadic lives, the synchronization of these “spiritual automata”, where God acts as the world clockmaker, winding up different clocks so that they show the same time. Leibniz’s theory seemed fantastic to many, since it assumed that God had initially taken into account an innumerable number of factors influencing the future course of events. This shortcoming of the concept of pre-established harmony was stated, for example, by the famous French skeptic P. Bayle. Leibniz, however, wittily replied that there is no real task that would be too difficult for God, and the best in this regard is precisely that theological concept that exalts the divine intellect to the greatest possible degree.
The harmony of the perceptions of the monads creates the phenomenon of a single world and makes all monads “living mirrors of the universe.” But these mirrors are certainly not the same. Ascent up the steps of perfection of the pyramid of monads corresponds to an increase in the clarity and distinctness of their perceptions. The more distinct the perceptions of the monads, the less passive the latter are, the more activity can be attributed to them (although in a certain sense all monads are equally active). The foundation of this pyramid is made up of countless “unities,” sleeping monads, deprived of developed psychic abilities and clear perceptions. Above them are animal souls, possessing feeling, memory, imagination, and an analogue of reason, the nature of which consists in the expectation of similar cases. The next step in the world of monads are human souls. In addition to the abilities listed, man is also endowed with consciousness, or “apperception.”
The conscious aspect of human existence, however, should not be exaggerated. Leibniz criticizes Descartes, who denied the existence of unconscious mental states. In reality, conscious perceptions are lost in the ocean of the unconscious. Unconscious states are such because of their “smallness.” Man simply does not notice them. Sometimes this leads to them taking over his will – Leibniz specifically discusses the influence of unconscious factors on human behavior. And yet, human souls are distinguished precisely by the presence of consciousness, apperception, and other higher faculties, reason (entendement) and reason (raison). They allow man to clearly comprehend things, to judge them coherently, and open to him the realm of eternal truths, moral laws, and God himself, who is at the top of the pyramid of monads.
God’s openness to the minds of men distinguishes their souls from other monads. Leibniz calls human souls and similar substances spirits. Spirits, unlike other monads, which reflect the world rather than God, “express God rather than the world” (1:1, 162). They are citizens of the City of God and can hope not only for eternal existence but also for the preservation of their Self, the self-identical personality, by God.
God, this “absolute Monarch” of the spiritual community, like every monad created by him, is threefold. The subjective basis in him corresponds to omnipotence, on which even the possibility of things depends, perceptions to omniscience, aspiration to good will, without which things cannot acquire real existence. These three qualities are related to the three hypostases of the Christian Deity, the Father, the Son and the Holy Spirit. God, according to Leibniz, is an absolutely unique monad. First, he cooperates with other monads, and their existence depends on God, and secondly, “God alone is completely free from body” (1:1, 426). This thesis gave rise to numerous questions in the subsequent history of philosophy. Indeed, why should other monads be associated with bodies? After all, in principle they are isolated from everything except God, and they can represent the world, even if this world does not exist at all. Leibniz nevertheless insists on his own, although, in order to reconcile his position with the thesis of the natural immortality of monads, he has to invent bold hypotheses, such as the assumption of a certain “coagulation” of the body after the death of a living being.
The doctrine of matter. The concept of corporeality and materiality is, of course, not self-evident, and Leibniz tried to clarify it. He denied the real existence of a special corporeal substance, i.e. matter in the form in which it appears to human senses in experience. Matter is only a phenomenon, albeit “well-founded”, since real monads correspond to it. This is also true for the main phenomenon for each monad – the phenomenon of its own body. The body, Leibniz argues, is a state of monads, and the soul is the central monad in the role of their “ideal” ruler. Subordinate monads themselves are centers for other monads, and those for others, and so on ad infinitum. What seems to be lifeless matter is in fact teeming with life. The specificity of the phenomenon of matter is explained by the imperfection of created monads. Corporeality, materiality is characterized by inertia and impenetrability, and what is this if not a reflection of the limitations of perceiving entities? If they were perfect, the world would appear in their perceptions in a fundamentally different form: matter would disappear, and only active unities, monads, would remain.
This is how God contemplates the world. The disappearance of the phenomenon of continuous, inert and impenetrable matter should be accompanied by the transformation of the sensuality of monads into reason. After all, the same monads are given in the senses as in the reason, but indistinctly. Therefore, in sensory perception we do not see the discrete monadic structures of real being, but contemplate a continuous environment in which these structures merge into vague, impenetrable images. But even sensory perception allows us to distinguish things. In other words, there is some clarity in it. Its increase leads to the emergence of distinct ideas, when not only the contours of things can be distinguished, but also their discrete structure, which allows us to identify the signs that distinguish these things from others. Phenomena turn into noumena, sensuality into reason. In addition to distinct ideas, Leibniz also allows the existence of adequate ideas. An adequate idea is one in which there is nothing indistinct, as in the idea of a number. But only in God’s thinking is there nothing but intuitive adequate ideas. Other monads are imperfect and cannot be completely devoid of sensibility, unless we are talking about the most primitive monads, existing in the darkness of unclear perceptions.
It cannot be claimed that Leibniz worked out this doctrine of sensuality and reason in detail. But thanks to his supporters, it became firmly associated with his name. This happened with other theories of Leibniz. In general, one can only speak of Leibniz’s system with great reservations. Rather, it is a scattering of ideas, and the contrast between the extravagance of a number of his theoretical constructions and the strict scientific methodology that Leibniz tried to follow in his works is striking. True, the “scientific nature” of Leibniz’s methodology does not mean that it is completely flawless. Even in Leibniz’s time, his opponents drew attention to certain internal inconsistencies.
At first glance, Leibniz’s methodological toolkit seems simple and logical. There are two “great principles,” the law of identity and the law of sufficient reason, which allow us to explain everything that exists and to substantiate all truths of reason and truths of fact. But behind the appearance of simplicity lie problems. The Achilles’ heel of Leibniz’s methodology is perhaps the question of what kind of truth is expressed by the law of the necessity of sufficient reason. If it is a truth of fact, then it contains an element of chance and, as follows from the definition of truths of fact applied to a given situation, the existence of something without a sufficient reason is conceivable. In order to be convinced of the falsity of such an assumption, without which it is impossible to assert the truth of the law of sufficient reason, one must either 1) acknowledge the possibility of discerning sufficient reasons for everything that exists in experience, or 2) say that the assumption of the existence of things or events without sufficient reasons does not have a sufficient basis. However, the first is unrealistic, and the second presupposes the truth of the law of sufficient reason, which has yet to be proven, i.e., a logical circle arises. If we consider the law of sufficient reason to be a truth of reason, then it turns out that this is not an independent, but a derivative principle – all truths of reason depend on the law of identity.
The problem of finding an epistemological place for the law of sufficient reason prompted Kant at the end of the 18th century to reject the dichotomy of truths of reason and truths of fact and to admit the existence of special truths expressed by “a priori synthetic judgments.” The orthodox followers of Leibniz, choosing between interpreting this law as a truth of reason and as a truth of fact, nevertheless leaned toward the former, believing that it was better to lose the independence of the law of sufficient reason than to undermine its claims to truth. True, already in the middle of the 18th century Hume directly refuted the thesis that the law of the necessity of sufficient reason could be interpreted as a truth of reason. But the early Leibnizians did not yet know about Hume. And in reducing this law to the law of identity, they in some sense followed the instructions of Leibniz himself, who made it clear that for the human mind the truths of fact for which the law of sufficient reason is responsible can be transformed into truths of reason in potential infinity. The truth is that it follows from this that in the divine intellect there is no difference between them at all, which threatens Leibniz’s theory of the best world, since it assumes that our world is chosen by God from an infinite number of possible worlds, and if the truths about our world are identical with the truths of reason for God, then any other world in which they would not be truths turns out to be contradictory, and nothing remains of the multitude of possible worlds, and therefore of the freedom of divine choice.
These and other problems of Leibniz’s metaphysics, it would seem, did not promise it good prospects. Meanwhile, Leibniz had a colossal influence on European philosophy. This is partly explained by the fact that he was one of the few thinkers of the New Age who proposed a complete ontological system built on the basis of clear methodological principles. Echoes of Leibniz’s monadic ontology can be found even in the 20th century. But the real triumph of Leibniz’s ontological ideas came in the first half of the 18th century and coincided with the heyday of the school of Chr. Wolff in Germany. Wolff was an associate of Leibniz, and soon after the philosopher’s death he reoriented himself from mathematics to metaphysics. He naturalized monadology, narrowed the scope of the concept of pre-established harmony to the relationship between soul and body, and placed Leibniz’s ideas on a powerful evidentiary foundation. However, Leibniz’s influence in the 18th century experienced not only by German, but also by French, British and Russian thinkers. It can be felt, for example, in the teachings of D. Diderot on organic molecules, in the theory of matter of P. M. Maupertuis, in the anthropology of A. P. Kolyvanov (whose important treatise, a kind of manifesto of the late Enlightenment, Observations on the Human Spirit and Its Relation to the World, published in Altona in 1790, was actually lost and found only in 2002) and even in the philosophical constructions of D. Hume. At the end of the 18th century, in connection with the flourishing of Kantianism, the influence of Leibniz’s monadology diminished, although in subsequent times it was sometimes addressed by famous thinkers, from J. F. Herbart to E. Husserl. Much more noticeable was the impact on modern philosophy of Leibniz’s concept of possible worlds, which, as was shown in the 20th century, S. Kripke, is a successful tool for various kinds of thought experiments. They are especially successful in the English-language analytical tradition, where no major treatise can do without them.
The influence of Leibniz’s methodological ideas was also impressive. His treatment of the distinction between truths of reason and truths of fact is one of the most indisputable achievements of world philosophy, an important component of modern philosophical culture. It should also not be forgotten that Leibniz is one of the prophets of mathematical logic and a pioneer of computing technology. Leibniz also contributed to the development of historical and philosophical science. He did not consider previous philosophy a parade of errors, but believed that most schools “are right in a significant part of their assertions, but are mistaken in what they deny” (1: 1, 531). Leibniz also introduced the famous terminological opposition of materialism and idealism. He himself believed that his system of pre-established harmony united all the best that was in the teachings of materialists and idealists, the followers of Epicurus and Plato.
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