LEIBNIZ AND THE LABYRINTH OF DETERMINISM

G ottfried Wilhelm Leibniz, the savant, the polymath, may have been the last great philosopher of the 17th century. Harnessing an extremely conflicted time that has been rich in discoveries, such as troubled times often are – by the time he was born, the Thirty Years’ War had not been over yet, the Germanic Roman Empire was only a set of discontinuous territories and principalities, and Catholicism counteracted the strong criticism suffered by the Protestant Reformation2 – Leibniz has been greatly influenced by the development of science in the 17th century and strongly participated in all metaphysical discussions of his time. Hence, there are three consequences for his philosophy: а deep faith in human knowledge, a great concern with methodology and a greater freedom to question ecclesiastical dogmas.3 The relation of acceptance and disagreement with his predecessors is easily noticed in his work: while Leibniz may be said to be a Cartesian, since many of his concepts come from Descartes, it is also true that he criticizes him greatly, as he does to all modern thinkers.

of harmony and moderation: it reconciles science and religion, ancient and modern, scholasticism and seventeenth-century philosophy.
An example of this risk of undermining fundamental truths of "natural theology" is in the work of Pierre Bayle, especially in his Historical and Critical Dictionary. Leibniz even writes in the preface to Theodicy Essays, published in 1710, that the production of a text discussing one of the labyrinths of human reason, "namely: the labyrinth of the free and the necessary, particularly regarding the production and origin of evil" 7 was owed to the comments and conversations with people of the court about this book. This reaction was caused by the feeling that "Mr. Bayle 'fait entrer partout' the matter of use of philosophy in theology." 8 As a result, the theme of the relation between faith and reason will appear throughout Leibniz' work: the author will try to demonstrate that, contrary to what Bayle says -making faith triumph over reason, 9 -reason can, without addressing the details of natural phenomena, explain the positive truths by considering the convenience that justifies the choice of these laws and their suspension at the time of the miracle. 10 Thus, our reason becomes capable of explaining the natural laws a priori, therefore philosophically, by weakening the miracle and strengthening the role of the revelation experience which confirms the truth of religion as a mystery to be rationally sustained. As reason now feels liberated to speak about the mysteries of religion, the philosopher frees himself from the bonds and now possess the right-duty to speak of the labyrinth of the free and the necessary.
The present article seeks to discuss this labyrinth exposed by Leibniz and how the solution he exposes allows us to think of a naturalistic and anti-voluntarist conception of law in opposition to the doctrines of modern Natural Law. The path, therefore, takes place in three stages: in the first, we discuss the labyrinth of Free and Necessary, in the second, the exit from the labyrinth, and finally Leibniz's critique of modern Natural Law.

I. Leibniz in Context
Briefly, I intend to focus on how the complex Leibnizian discussion on freedom and determinism largely stems from the legal debates of its time and how the Leibnizian metaphysical discussion itself is riddled with legal terminology. For this, we need to situate Leibniz in the intellectual debates of the science of law of his time. The author does not consider the philosophy of law as a philosophical and autonomous subsystem. It seems, in reality, to provide the philosophy of law with the dignity of "first philosophy" when 7 Tessa Moura Lacerda, A Política da Metafísica: Teoria e Prática em Leibniz (São Paulo: Humanitas, 2005), 21. 8 Ibid. 9 According to Pierre Bayle, three qualities would ensure this triumph: the incomprehensible character of faith's truths, the fact that these truths conflict with appearances and the impossibility of sustaining what we believe (Ibid, 23). 10 Ibid, 28. working its metaphysics with legal concepts and reasoning. Above all, what he wants to do is answer: "What is the law?", A typical formulation of a "metaphysica Juris".
Leibniz writes in the context of what is called "Modern Natural Law", whose main representatives can be said Grotius, Hobbes, and Pufendorf. A caveat must be made: the rationalizing impulse of the philosophy of law in the 17th and 18th centuries does not mean 11 a unity of thought among the authors mentioned. However, some fundamental traits can be found: human beings no longer have a supernatural purpose and can be found outside of history, therefore natural law and its rules must seek the satisfaction of individual ends within the world. Naturally, these rules are commanded by God and the object of a transcendent obligatory relationship. 12 The philosophy of modern natural law has two main characteristics. The authors of the period draw from Euclid's geometry a model of deductive rationality, of a more geometrico, even though it appears mixed with arguments of authority and other elements of experience to define the legal rules. The second of the characteristics is the appearance and expansion of the notion of subjective right. If until then the law was seen as a relationship, a means of attributing to each one what is theirs (jus suum cuique tribuendi), the moderns come to understand the law as multivocal: jus can mean the law, it can mean a set of laws or the science of law or a moral faculty attributed to an individual or collective being. 13 In most authors of the period, this subjective right is dependent on the natural law emanating from God.
What matters to us is that this distinction between a subjective right distinct and dependent on the natural law emanating from God produces a rupture with Aristotelian-Thomistic morality concerned with virtues and supra-mundane purposes. To act well and morally becomes to act according to a rule created by a superhuman legislator. In his works Elementa jurisprudentiae universalis, De Jure naturae et gentium, and in De Officio humanis, Pufendorf exemplifies this point of view. He says that the science of law must be built more geometrically from undoubted principles. However, these undoubted principles can only be formulated by analyzing human reality: there is a distinction between moral and natural beings. In Pufendorf, divine natural law imposes obligations on men who, using their faculties of understanding and will, can deduct a right from it and thus submit to it. There is, therefore, an explicit dualism between nature and freedom that is unacceptable to Leibniz and has worked on to resolve it.
Frontally, in Monita (1709), Leibniz responds to Pufendorf. Leibniz's philosophical project is of a rationalist monism where there is an interdependence of all entities in the universe described by the philosopher and natural law, submitted to the orders of higher Reason, has a primordial place. Instead of considering, as in Pufendorf 's "modern natural law," that legal obligations occur vertically between the subjects and the Law (or the divine legislator), Leibniz refuses this notion, returning to the classic legal definition of the obligation as a binding necessary interhuman. The Leibnizian moral world is not a world of relations between hierarchically situated wills, but a horizontal gathering of spirits situated in the "universal divine monarchy" who tend towards God. Solving the problem of the labyrinth of freedom and necessity is essential to understand how one can be free in this Leibnizian moral world and, ultimately, how legal obligations can be established.

II. The Labyrinth of Free and Necessary
Cependant, comme un géomètre n'a pas besoin de s'embarrasser l'esprit du fameux labyrinthe de la composition du continu, et qu'aucun philosophe moral et encore moins un jurisconsulte ou politique n'a point besoin de se mettre en peine des grandes difficultés qui se trouvent dans la conciliation du libre arbitre et de la Providence de Dieu... 14 The famous problem of the Labyrinth of the free and the necessary is announced from Leibniz' first systematic text, Discours de Métaphysique (1786). A comment to be made before we address the themes of the Leibnizian systems regards the change of rhythm and composition of the author's texts in the course of his bibliographic production: the first texts of the philosopher were constructed under a binary rhythm of descent (from God to the world) and ascent (from the world to God), which made way, afterwards, for a progressive construction from the simple (substance) to the complex (God) in his texts from 1714. 15 One possible explanation for this is the gradual independence from the tradition acquired by the author, being able to freely express his thought in a more liberated way.
In the context of paragraph X of this work -situated in between two important aspects of the problem of substance: paragraph VIII, where the logical unity, or subject, is determined; and paragraph XVIII, where it is considered as force, -Leibniz unites the problem of need and contingency to the one of the continuum. These two are the famous labyrinths continuously united by Leibniz, although the second one is a concern for the whole human race, whereas the first one is a concern for philosophers only. The approximation of the two problems, which are different and extremely complex, happens 14 "However, as a geometer does not need to bother with the mind of the famous labyrinth of the composition of the continuous, and no moral philosopher, and still less a jurisconsult or politician, does not need to worry about great difficulties in reconciling free will and the Providence of God" (Leibniz, Discours de Métaphysique, § 10). 15 Lacerda, A Política da Metafísica, 14.
LEIBNIZ AND THE LABYRINTH OF DETERMINISM for a reason: both give rise to the idea of infinity. Since the first one is a concern for the whole human race, it shall be tackled here. 16 The second labyrinth regards the antinomy of divine predestination and human freedom. 17 Classically, as regards the freedom of the will, philosophers had until then been divided into two main alternatives: some defended determinism, tending to identify freedom with willingness. Any action would be free, provided it was not the result of coercion. All voluntary actions are univocally determined, although free. Freedom and need would coincide. Others (the followers of indeterminism), however, believed that not every voluntary action is free, but only those arising from free choice. One is not free when one is unequivocally determined to want something, but only when the choice could have been different. Freedom, in this case, would only be present in a subset of voluntary acts. Reasoning within the indeterminist logic, Descartes distinguished actions whose choice could have been different from univocally determined actions. Nevertheless, he states the will is free in both cases, or rather that, in the case of voluntary but necessary assent, the will is freer. Descartes states that man enjoys the freedom of indifference, i.e., the freedom of error, but identifies the essence of freedom in the necessity of assenting to the truth, in order to defend the moral value of this assent, and to assure not only willingness, but also freedom itself.
Leibniz enters this debate in a very explicit and specific manner, particularly in Discours: in this work, Leibniz was concerned with the ontological statute of substances 18 that consti-16 However, let us say some words about the first one: it concerns the antinomy of the discontinuous and the continuous, a classic one since Zeno of Elea. Throughout his life, Zeno has sought to demonstrate that the motion existent in the sensitive world is unintelligible and, since it is unintelligible, it does not exist. For, if the examination of motion leads us to the conclusion that it is unthinkable, and that we come to insoluble contradictions when we think about motion, the conclusion is obvious: motion does not exist, it is only an illusion. Isn't motion, after all, the displacement of a point in space that goes from a place to another? Space is infinitely divisible. A piece of space, no matter how small, either is or is not. If it is space, it is extensive. If it is extensive, it is divisible. Therefore, space is divisible into an infinite number of points. Thus, since motion consists of the transit from one point in space to another, and since there are infinite points between two points in space, the consequence is that this transit can only take place in an infinite amount of time, and therefore is unintelligible. This is Zeno's argument aimed at thinking that motion, conceived around the principle of identity, is unintelligible. 17 Lacerda, A Política da Metafísica. 18 Let us see, for instance, how it becomes clear in paragraphs 8 and 13 of this work. While the first seven chapters defined who God is and how he acts, going from the general to the particular, in the eighth chapter, a distinction between the actions of creatures and creator starts to be made. Therefore, it is necessary to know what the creature is in order to know in what sense it acts or stops acting. The theme of paragraph is action: metaphysics concerns the beings who act and examines them in relation to this action. From this, it "builds" the logical notion of substance as the unity of multiplicity. It is based initially on the tradition, and the logical subject is the one who receives attributes without being able to be an attribute; it would be the true being (according to Burgelin, it is maybe an attempt to make reference to Arnauld). The religious setting of Discours leads us to emphasize the substance not as a center of force, but as soul and even spirit. He himself invokes Alexander's example. At the same time, tute the universe. Leibniz believed that the aforementioned Spinozan and Malebranchist routes could be avoided if the individual notion of each creature contained, once and for all, everything to happen to them, and developed over time through an own spontaneity. According to the philosopher, "his theory of individual substance assured a role for creatures in the causality of the world without limiting God's action to the conservation of the same amount of motion in the universe"; however, "by assuring the existence of individual substances distinct from God and capable of their own action, Leibniz had threatened not only man's freedom, having also limited God's freedom in the creation of the world." 19 That is why there is nothing odd about the reaction of Arnauld, who reacted by stating, in a letter dated April 12, 1686: "hence the consequence that everything that happens to a person, and even to all mankind, must happen by virtue of a more than fatal need." 20 For this reason, it will be up to Leibniz to show that the definition of a creature by a complete notion does not endanger neither man's morality, nor divine freedom. In order to respond to Arnauld and to give a satisfactory solution to the question of the labyrinth of the free and the necessary, it will be necessary to demonstrate that the complete notions do not transform the contingent into necessary, and that it is only through this theory of individual substance, as he conceives it, that it is possible to explain and ensure human freedom. the author is concerned with the idea that God may have of each being he will create. God wants the individuals. Secondarily, he wants the genus and the species. The distinction between necessary and contingent truths follows from that. He wants to show, against Malebranche, that beings are intelligible in themselves: In the first place, let us call "substance" a subject of many attributes. It is the unity of this multiplicity. Here, the substance is foremost manifold in its attributes, which have no other access to the being except in its connection with a unifying principle. The substance requires a real unity. The author adds, in this paragraph, that the predication is only true if founded on reason. The nature of things can only designate the logical nature of things. It is in the very analysis of the terms that we must find the foundation: the subject must manifest itself as the sufficient reason of every attribution, and it is this passage to sufficient reason that introduces us to metaphysics Every simple substance must be the true immediate cause of all his inner actions and passions. Then, in the same § 8, the problem of the free and the necessary is introduced by means of Alexander's example. For the author, there are two notions of necessity: a metaphysical one, which solely depends on the principle of contradiction; and a physical one, if we proceed to the individual and the real, which supposes the free decrees of God, which are the main sources of existence or facts. Paragraph 13 reproduces and explains the consequences and difficulties of the question as to which substance contains everything that can happen to it. The notions of existent things are treated as those essential ones, whose attributes do not allow for a deduction from the definition. Arnauld would react to this notion by stating, in a letter dated April 12, 1686: "Hence the consequence that everything that happens to a person, and even to all mankind, must happen by virtue of a more than fatal need." This paragraph, according to Burgelin, will try to answer this objection by Arnauld. For all comments on the paragraphs contained in this note, see Pierre Burgelin, Commentaire du Discours de Métaphysique de Leibniz (Paris: PUF, 1959), 138. 19 Lacerda, A Política da Metafísica, 31. 20 Arnauld apud Burgelin (Burgelin, Commentaire du Discours de Métaphysique, 177), our translation.

III. The Exit from the Labyrinth: Brief Notes
The solution brought by Leibniz is extremely complex. It is impossible to demonstrate how all concepts are articulated in a brief work like this one. For that reason, we will briefly address the solution brought by him.
First of all, it is important to bear in mind that Leibniz's philosophy has two essential principles, which would be essential to all human knowledge, since they would be implicated in the very definitions of truth and falsehood: the principle of contradiction, i.e., the one that established that a proposition may not be true and false at the same time; and the principle of sufficient reason, the one by virtue of which we consider that we cannot find any true or existent fact, or any true statement, without there being a reason why it is this way instead of another way, i.e., every effect must have a sufficient cause to explain it. 21 From these two truths, some consequences follow. The supposed sufficient reason for the existence of anything specific in the world would involve the whole world. In Leibniz, this reflects the fact that all things are interconnected. Thus, the fact that the whole universe is implied in the existence of every individual substance means that God's choice to create it instead of any other substance is a choice to create this world as a whole. Thus, as we have already said, because the complete notion of an individual substance contains the whole infinitely in a relation of expression, only God could know this notion perfectly.
Before we go on with this explanation, it is important to say that Leibniz develops a distinction between kinds of truth: The necessary truths and contingent truths. The necessary ones would be those whose opposites are impossible. The contingent ones, in turn, are the ones about which it is equivalent to say that their existence or nonexistence are both possible, depending, in this case, on an act of divine will. 22 In Monadology, in § 32 et seq., Leibniz will address this question. Because it is a systematic exposition of his thinking, we will now attempt to interpret these paragraphs. After differentiating the three types of monads, whose general characteristic is to have appetite and perception, and reintroducing the finality thanks to the notion of laws of series, since a finite formula comprises or programs an infinite series, he will defend the thesis that the principles of contradiction and sufficient reason apply to both types of truth, but in reverse order. Whereas one can always decompose truths of reason into mathematical truths and find their sufficient reason, this is more difficult to do with truths of fact, "but the sufficient reason must also exist in the contingent truths or truths of fact", i.e., "in the sequence of things dispersed by the universe of Creatures," for otherwise we would fall into the labyrinth of 21 For a brief discussion on the relation between the two principles, see: Lacerda,A Política da Metafísica,[53][54][55][56][57][58][59][60][61][62][63][64] Which is not what we usually call perception, but rather a simple presence of different states within the unit of a monad (Perkins,Compreender Leibniz,27).
the continuum, where each event is the sum of other events, and so on infinitely. Given the difficulties of applying the principle of sufficient reason to truths of fact, paragraph 37 brings the idea that the real sufficient reason should be sought outside the series, with respect to contingent truths: which leads directly to the issue of God. Therefore, Leibniz will prove God as the sufficient reason for the contingen. 23 The divine attributes correspond to the three aspects of the monad: Will corresponds to appetite, knowledge corresponds to perception and the power of God corresponds to the substance, to the base of the monad, to the substrate that constitutes the aforementioned unity of the perceptions. God would not arbitrarily create the eternal truths, but the logical truths would necessarily result from his understanding and, as the source of contingent truths, God acts by his will to put them into existence. God, however, chooses according to the principle of the best: the possible chosen ones are necessary, but only by virtue of a principle of convenience, i.e., not absolutely necessary. It is a moral necessity. Hence, the famous -discussed and criticized -Leibnizian thesis of the best of all possible worlds.
There is still a last element to cover in order to determine the terms of solution of the labyrinth of the free and the necessary in Leibniz: the thesis of preestablished Harmony, presented in Monadology's § 56-61. The harmony or accommodation of all things to one another is presented in terms of reciprocal symbolization: each part symbolizes with the whole; each part only exists in function of the whole and in order that the totality is as good as possible Since each monad expresses its relation to the whole, the universe is the totality of these perspectives, and therefore God is considered the monad of the monads, i.e., the sum of all possible perspectives.
Once such matters are established, we can finally say that "for an action to be deemed free, there must be no metaphysical necessity of action, i.e., that a different action is logically possible or non-contradictory and that, therefore, the agent chooses one among many possible parties." 24 The contingent is not opposed to the determinate, but to the absolutely necessary. Thus, it may be said that voluntary actions are doubly determined: by God's foreknowledge or providence and by the soul's inclinations. Thus, the labyrinth is solved by the realization of the falsehood of the idea of freedom as complete indifference, as if no determination were to act upon it. "Freedom of action exists within the domain of the morally necessary. God always acts freely; we may or may not act freely. What makes the difference is the extent and the clarity of our awareness of the good that drives us to act." 25 A will not moved in consideration of the good would be a will chosen at random, or in an arbitrary and inexplicable way.

Conclusion
The labyrinth is solved with the realization that freedom, after all, is a matter of degree. The more clear and distinct are the perceptions moving the individual substances towards good, the more they are spontaneous, active and free. 26 Therefore, let us follow Monadology's §79, which reads: "Souls act according to the laws of final causes, by means of appetites, means and ends. Bodies act according to the laws of efficient causes or of motion. And both realms, that of efficient causes and that of final causes, are harmonious with each other." This is equivalent to saying that the soul seems to act in function of final causes, by will, whereas the body seems to act in function of efficient causes, by determinism. Here, it seems, is the problem of Kant's third antinomy: faced with the same phenomenon, how to think it, in turn, in terms of freedom and mechanical philosophy?
In the perspective of a theory of preestablished harmony, the mystery is dissipated, although Leibniz does not really provide the solution for the problem. The solution must be found in the preestablished harmony: between the two realms, there is no opposition, but continuity, i.e., the soul has the impression that the body acts by mechanical causes, by determined causality, but, in fact, on the plan of the in-itself, the body, which is formed by monads (therefore, by souls), acts in the same way as God, each one of its elements being a force tending to develop itself, i.e., acting by purpose. Hence, as stated by Lacerda,27 because man finds within himself the principle of his action and because man is rational, he does not need any external principle to impose upon him a need to act or to dictate a different purpose from the good he seeks spontaneously. Here is the solution for the labyrinth point to the Leibnizian purpose of a finished science of natural law.