Justice and Truth: A Leibnizian Perspective on Modern Jurisprudence

: The purpose of this essay is to outline the signiﬁcance of Leibniz’s philosophy of law for the present. The essay traces the main features of Leibniz’s theory and points out what further developments of his approach are pending today. Finally, it shows how similar Leibniz’s basic convictions are to those of Ronald Dworkin.


Introduction
Leibniz's philosophy of law is still largely unknown among lawyers today. This is not least due to the fact that he did not write a summarizing work on this subject. His jurisprudence must be painstakingly reconstructed from some published works, countless unpublished drafts, and fragments written in Latin or sometimes in French. This paper may serve to illustrate some impulses of his jurisprudence for the present.
As is well known among Leibniz researchers, justice and truth are very important pillars of his philosophy. He defended both concepts against Hobbes's skepticism, according to which justice and truth are arbitrary and depend on the will of man. Against Hobbes's voluntaristic and super-nominalistic standpoint, Leibniz advocated a strict rationalism according to which neither justice nor truth depend on the will of man nor even on the will of God (Armgardt 2019). On this basis Leibniz developed his theory of law, which he, unfortunately, never summarized in a book or essay. After all, as a very young man he wrote several drafts under the title Elementa Juris Naturalis (A VI 1, 481-485), but they cannot be considered a summary of his entire legal thought. Nevertheless, the main features of his legal thinking can be gleaned from his published and unpublished writings (for a short summary, Armgardt and Sartor 2019). Since Leibniz's philosophy of law has received little attention, especially from lawyers, this paper may serve to illustrate the impulses of his jurisprudence for the present. Moreover, we give some hints on how these impulses can be used for the further development of modern legal theory.

The Strict Distinction between Positive Laws and Natural Law
As Leibniz pointed out, especially in his Méditations sur la notion commune de la justice (Mollat 1893, pp. 41-70) written in 1703, a strict distinction must be made between natural law (droit) and positive laws (loi). Natural law cannot be unjust; this would be a contradiction in itself because only positive laws can be unjust. Natural law is not based on will, either human or divine, positive laws, however, are based on the will of the legislator. The former is completely independent of any power, whereas the latter depends on the legislative and executive power of the sovereign. According to Leibniz, the mixing of these two levels was a main reason for the confusion in the jurisprudence of his time (Armgardt 2015a). The strict distinction between natural law and positive laws is still of utmost importance today. Even in a democratic context, majority cannot substitute for rightness because the majority can support unjust decisions. Without the assumption of natural law, or at least an intuition of justice, there is no solid basis for critiquing existing Laws 2023, 12, 38 2 of 9 law. The difficulty of recognizing natural law or elucidating the intuitions of natural law does not change this. It follows, of course, that the accurate exploration and elucidation of our intuitions about justice are an exceedingly important task of jurisprudence. For Leibniz, this was perfectly clear, and to this day, nothing has changed. In the following, approaches to solving this difficult task will be shown on the basis of Leibniz's philosophy of law and with the inclusion of modern legal theory.

Leibniz's Three-Stage Model as Defeasible Reasoning
As Busche, in particular, has elaborated, Leibniz used a three-stage model (Busche 2003). The three levels of strict law (jus strictum), equity (aequitas), and piety (pietas) form a hierarchy, which is characterized by the fact that the next level can correct the previous level(s). From today's point of view, one would speak of defeasible reasoning. The threestage model was not invented by Leibniz, but it was profoundly developed by him in terms of content. First, Leibniz paralleled the three stages with the three Roman legal principles: neminem laedere, suum cuique tribuere, and honeste vivere. In a second step, he related the three stages with the Aristotelian doctrine of justice: jus strictum corresponds to the Aristotelian justitia commutativa, equity to justitia distributiva, and piety to justitia universalis (A IV 5, 61 f.). However, he went far beyond these historical harmonizations. Recent research has revealed the progress Leibniz made in concretizing these stages. In the following, these results will be related to modern legal theory.

Jus Strictum and Legal Logic
On the level of jus strictum, Leibniz developed approaches to an analytical philosophy of law. He saw clearly that the classical Roman jurists had applied Stoic propositional logic to law. In particular, Leibniz elaborated on this in his theory of conditions (Armgardt 2014). In the Elementa Juris Naturalis, he developed approaches to a deontic logic (Kalinowski and Gardies 1974). He also produced considerable analytic work in the field of legal presumptions (Armgardt 2015b). In addition, he wrote considerable studies on the development of a conceptual logic (Lenzen 2004). Leibniz can thus be regarded as the father of modern legal logic and computational legal theory.
On this basis, it is today necessary to develop powerful logical theories for legal norms, legal concepts, legal argumentation, and questions of evidence. As Leibniz foresaw, modern logic has taken off and made huge leaps. Especially in the field of modal logic, his idea of possible worlds has gained great influence, although one has to be careful with a direct transfer of his thought into a modern possible-worlds-semantics (Adams 1994, pp. 46-50). Neither did Leibniz hold Lewis's view that all possible worlds (outside the mind of God) exist, nor did he hold the view of a transworld identity as Kripke did (a more differentiated analysis can be found in Adams 1994, pp. 71-74).
Counterfactual reasoning is essential to jurisprudence. One needs counterfactual structures, especially in causality, damages, and legal conditions. Therefore, the development of logics for legal counterfactuals is necessary. Counterfactual logics are inconceivable without a semantics of possible worlds. Therefore, there is a close connection between Leibnizian logic and the latest developments in the field of computational legal theory.
On the basis of a possible-worlds-semantics, logical investigations of legal conditions using STIT-logic (Armgardt et al. 2018) and of causality using iterative counterfactual conditionals (Andreas et al. 2023) have recently been developed. Furthermore, the work of Rahman on the application of constructive type theory to the elaboration of Leibniz's theory of conditions deserves mention (Rahman 2015). These studies may well be regarded as the further development of Leibniz's ideas on strict law. There is still much to be done in this realm. We are only at the beginning of an enormous development. As Leibniz clearly foresaw, the logical tools for analyzing law are yet to be developed. Even today, it is by no means sufficient to use existing logics.
Leibniz saw that a purely conceptual derivation of law cannot lead to perfect legal solutions. The need for the correction of jus strictum was clearly before his eyes. For him, legal rules were always only presumptions that could be refuted. Leibniz said this explicitly in de legum interpretatione (A VI 4 C, 2791). Therefore, he developed aequitas and pietas as modes of correction. In modern terms, the Leibnizian system is characterized by defeasible reasoning. In this way, he, already at the outset, countered the criticism of any form of conceptual jurisprudence (Begriffsjurisprudenz).

Correction of Jus Strictum by Equity
According to Leibniz, every result found on the level of jus strictum must be checked for its correctness on the basis of aequitas. If the result corresponds to aequitas, it is confirmed; otherwise, the result is corrected as equity requires. According to Leibniz, aequitas thus has the character of meta-law. The view that equity is meta-law is distinctly modern and is advocated today, for example, by Henry E. Smith for the common law (Smith 2021).
If we keep in mind that Leibniz was fighting Hobbes' voluntarism, it is obvious that Leibniz had the problem of clearly defining equity. It is, therefore, not surprising that Leibniz made great efforts in this regard.
In the introduction to the Codex juris gentium diplomaticus, Leibniz defined justice as charity of the wise: justitia est caritas sapientis (Riley 1996;Johns 2013, p. 112). According to Leibniz, charity is part of equity (A IV 5, 61 f.). Charity or benevolence is, for him, the only structurally conceivable way to resolve the contradiction between egoism and altruism (Goldenbaum 2009). With Hobbes and against Grotius, Leibniz takes natural self-interest from the instinct of self-preservation as the basis of his theory of motivation (Busche 2003, 91 fn. 5). Because of this realistic basic assumption, balancing egoism and altruism posed a serious problem for him. His solution was charity or love. Leibniz defines charity as follows: to love is to seek one's own happiness in the happiness of others. Leibniz wrote to Claude Nicaise (19 August 1697): [I]t is evident from the notion of love. . . how we seek at the same time our good for ourselves and the good of the beloved object for itself, when the good of this object is immediately, finally and in itself our end, our pleasure, and our good. (A II 3, 369; translation by Brown 2018, p. 633) Brown rightly calls this "disinterested love" (Brown 2018, pp. 631-37). It is clear that Leibniz did not want to fundamentally separate law and morality. For him, law is merely the enforceable part of morality. Against Locke, Leibniz assumed that there are innate ideas whereby legal intuitions are additionally assigned the character of innate moral reflexes (Nouveaux Essais, I 2 § § 1-2).
In the Elementa Juris Naturalis we find a precisely elaborated system of equity. Based on the concepts of innoxia utilitas, cautio damni infecti, and the gradation of need according to necessity (necessitas), usefulness (utilitas), and superfluity (superfluitas), Leibniz developed clear rules that can easily be formalized (Armgardt 2022a). At this point, Leibniz succeeded in making a tremendous advance, for before him, one searches, largely in vain, for a definition or substantive elaboration of equity.
This development also opens the way to the protection of the needy in the Leibnizian sense. To what extent moral and philosophical considerations should find their way into legal systems is an important and pressing question today. In the Elementa Juris Naturalis, Leibniz, at any rate, granted the needy enforceable claims for emergencies, even if the other side thereby loses something useful (Armgardt 2022a;Busche 2021).
Corrections of rules by way of weighing and balancing interests, and taking into account values, are also a subject of today's legal logic. It is perfectly clear that legislative rules can never be perfect. However, in order to avoid arbitrariness, the precise formal notation of the requirements for the correction of legislative rules requires the development of new logics. Initial proposals have recently been developed in this regard (Sartor 2018;Armgardt 2022b). The objection that this higher level of legal reasoning is not amenable to logical modeling thus proves to be untenable. Leibniz's strictly rationalist approach can also be followed at this level.

Piety-The Highest Level of Justice
Leibniz does not stop at the principle of charity. On the level of pietas, he adds the legal relationship of man to God. At the end of the Monadology, he describes this relationship as something that actually exists independently of belief or unbelief (Monadology, § § 84-90). Consequently, natural law is something that exists and is self-executing because God has contingently inscribed it in the order of the world (Monadology, § 89). Even if the consequences of evil do not show themselves immediately, they inevitably follow later in the beyond.
This means that natural law exists. It is by no means only an ideal ought, but it is in force. Natural law is what counts, not positive laws, which can be unjust. Positive laws are mere fictions. Insofar as they are just, they receive existence through the natural law they represent. If we do not want to dismiss justice as a mere dream, as Kelsen did, this is the only way left to us. Leibniz saw this with all clarity. As a jurist active in practice, he was realist enough to see that not every evil can be apprehended and punished during the lifetime of the offender. Nothing has changed since.
Whoever denies its eschatological dimension reduces justice to a mere pale fiction without any real content. That reduction would not be appropriate. Just like truth, justice must be defended as something that exists and is in force.

Inalienable Rights of the Individual as the Model's Practical Consequences
In 1703, Leibniz gave a lecture on the concept of justice to George August, Elector of Hanover and later King of England, which he wrote down but did not publish. In these Méditations, Leibniz uses his three-stage model of justice to show that slavery is unjust. He argues there as follows: even if slavery were permissible according to jus strictum (he leaves this question open), strong restrictions would follow due to aequitas, i.e., the master must provide for the happiness of his slave. Due to the correction on the level of pietas, however, slavery presents itself as standing against the right of God and, thus, as impermissible. The property of the rational soul is entitled to the human being according to divine right, because they are naturally and inalienably free. Since the body is the property of the soul, it is inalienable, as is the soul (Mollat 1893, p. 68; for a philosophical analysis: Jorati 2019). Cassirer was one of the first who appreciated Leibniz in view of the development of inalienable human rights (Cassirer 1929, pp. 13-15). Leibniz develops, on the level of piety, the concept of universal, inalienable human rights to delegitimize slavery. There are, of course, antecedents for this thinking in late scholastic moral philosophy. Today, slavery has been abolished. However, there are dependencies similar to slavery. In this regard, pietas also points in the right direction.
The example of slavery shows how disruptions can occur at the level of jus strictum. Human legislation or customary law can create legal institutions that exist as positive laws but which can (and must) be delegitimized by aequitas and pietas. At this point, it becomes clear that Leibniz was not only concerned with an ideal legal system where something like slavery would not occur but also with influencing the positive laws in force.
Another example that demonstrates the interplay of jus strictum and aequitas is the question of the right of resistance against the state. Unlike Hobbes, Leibniz advocates a right of resistance in exceptional cases, which he derives from aequitas and corrects jus strictum. The prerequisite for the right of resistance is that it is the goal of a government to deliberately destroy the welfare of the community (Armgardt 2020, pp. 159-62).

Conclusions: Protection of the Individual's Freedom and Responsibility
For Leibniz, the development of individual human rights is based on the idea that divine creation places immeasurable value on the individual. This finds its origin, above all, in the idea that every human being was created in God's image (imago dei), as Gen. 1,26 states. Julia Borcherding's forthcoming dissertation will show the influence of this doctrine on Leibniz's concept of justice. In contrast to Spinoza's strict necessity, Leibniz developed his monadology to capture the value, freedom, and uniqueness of each individual (for a short introduction to monads, Schepers 2016). Each monad, especially the rational monads, expresses the entire world from a unique perspective (even more, it constitutes the world from within by way of perception) and is therefore irreplaceable (Schepers 2016, p. 24). Against this background, all legal and political concepts that disregard the individual are out of the question. The principle of charity, to which all human beings are committed, ensures that the legal order does not disintegrate into egoistic particular interests and thereby destroys itself.
According to Leibniz, harmony is unity in diversity. This balance alone leads to perfect order. It is clear that the world is currently far from such harmony. By the way, things did not look much better during Leibniz's lifetime. However, this very fact shows the necessity of dealing with Leibniz's philosophy today.

Truth, Evidence, Presumptions, Conjectures, Probability
From a logical perspective, Leibniz advocated a conceptual containment theory of truth (Adams 1994, pp. 57-71). From the practical point of view of the lawyer, however, the question of the proof of facts, the burden of proof, and presumptions are much more relevant. Leibniz has developed approaches to an analytical legal theory of evidence that can also provide inspiration for this important field from today's perspective (Armgardt 2015b). Leibniz repeatedly spoke of how important it would be to develop a logic of probability in order to, in uncertain situations, make as few mistakes as possible. Unfortunately, he did not realize this project. However, we have some valuable advice from him on presumptions and conjectures. Especially in the writing de legum interpretatione there are very stimulating explanations on this topic (A VI 4 C, 2789-90). The core idea for conjectures, which Leibniz takes from Roman law, is that, in cases of doubt, one should assume what is easier (facilius) to happen, i.e., that which in its genus involves fewer requisites or smaller ones (A VI 4 C, 2789-90; an analysis is found in Armgardt 2015b, p. 66). While, in the case of conjectures, positive facts have to be proved, the case of presumptions is easier: if a presumption disputes in favor of a party, its result has to be accepted, unless an impedimentum, i.e., a negative fact, stands in the way. This idea can be expressed using constructive type theory or defeasible inferences (Armgardt 2015b, pp. 64-65). Again, we find extremely interesting approaches to an analytic theory of proof that are worthy of further development. The development of a legal theory of proof with the help of Bayesian conditional probabilities is also likely to correspond to Leibniz's program.
With regard to proof, Leibniz strictly distinguished between necessary and contingent truths. While necessary truths can be proved in a finite number of steps, the proof of contingent truths requires an infinite analysis (McDonough 2018, p. 94). Since the latter is generally inaccessible to the human mind, presumptions and conjectures play an extremely important role in legal reasoning that generally deals with contingent truths.

Conclusions: Analytic Jurisprudence and Natural Law Need Each Other
Leibniz developed profound theoretical approaches to both the development of law and the problem of fact-finding from which modern jurisprudence can draw valuable inspiration. Since Leibniz's writings have remained largely hidden until modern times, they can only have an effect today. They deserve this effect.
The study of Leibniz's jurisprudence shows that analytical jurisprudence and natural law are by no means mutually exclusive. On the contrary, for Leibniz, logical analysis serves the deeper understanding of natural law. It was not without reason that he accused Pufendorf of having created only a more or less incoherent collection of natural law principles instead of a system of natural law (Armgardt 2015a, pp. 16-20).
Without a doubt, Leibniz had in mind something like an axiomatic foundation of natural law from which individual legal principles could be derived (Brewer 2013, p. 201). Instead of axioms, however, he chose definitions and theorems formed from them as a starting point for jus strictum (e.g., the 160 definitions in De Conditionibus, A VI 1, 102-110). His great plan of inventing a characteristica universalis to achieve certainty in all fields of inquiry (Antognazza 2009, p. 528 referring to his letter to Biber) is closely related to his countless drafts on legal definitions.
Whether the methodological tools available in his time would have allowed him to achieve this goal might be doubtful from today's perspective. Nevertheless, this does not mean that Leibniz was on the wrong path. Especially in the field of conceptual logic, he succeeded in making substantial progress (e.g., Lenzen 1990, pp. 28-83).
Since the great upswing of logic during the last 150 years, Leibniz's goal does not seem to be as far away as it was during his lifetime. Therefore, modern basic research in legal logic may be regarded as the pursuit of Leibniz's grand plan of an analytical science of natural law.
As for the limits of logic and legal conceptual analysis, it is important to see that Leibniz clearly did not believe in getting by with only one level of thought. His multi-level approach (jus strictum, aequitas, pietas) suggests that he was obviously aware of the inherent limitations of single-layered analyses. Viewing legal rules as defeasible and allowing corrections at meta-levels are very modern ideas (e.g., Smith 2021). The important question of exactly what concept of defeasibility Leibniz had in mind must be left open here.

Leibniz and Dworkin
Finally, Leibniz's philosophy of law shall be briefly compared with that of Ronald Dworkin. Perhaps the most important of Dworkin's principles is his firm rejection of positivism, as represented by Herbert Hart, for example. Dworkin's assumption of the existence of objective truth about values and the idea that "morality is not made by anyone" (Dworkin 2011, pp. 24 and 400-1) is very much in line with Leibniz's philosophy of law. Leibniz would also have agreed with Dworkin's view that law is "not a rival system of rules that might conflict with morality, but as such a branch of morality" (Dworkin 2011, p. 5). Dworkin's notion that laws can be unjust is obviously consistent with Leibniz's view (Dworkin 2011, p. 411 for Nazi laws).
Both Leibniz and Dworkin stand unreservedly for the suprapositive validity of universal and inalienable human rights. However, their justification differs significantly. Even if, for Leibniz, natural law, in contrast to positive laws, is completely independent of the will of men and even of the will of God, it still belongs to the realm of necessary truths, which have their basis in God's mind. Without the mind of God, there would literally be nothing at all, neither the necessary nor the contingent truths. Dworkin sees this differently: for him, law is independent not only of God's will but also of his existence (Dworkin 2013, pp. 1-44).
Both Leibniz and Dworkin approach the problem of hard cases in a very similar way. In contrast to Hart and Raz, Dworkin believes that, in law, there is always a uniquely correct decision (Ben Menahem 1993, p. 198). Ben Menahem has pointed out that Leibniz sees it the same way, which we can understand from Leibniz's doctoral thesis about perplex cases in law (Disputatio inauguralis de casibus perplexis in iure) published in 1666 (Ben Menahem 1993, p. 198). However, Ben Menahem is not to be followed insofar as he puts young Leibniz in the proximity of the modern positivists (Ben Menahem 1993, pp. 214-15). As Artosi, Pieri, and Sartor have shown, natural law plays a decisive role in the justification of law from the beginning (Artosi et al. 2013, pp. XX-XXIX and 120). Above all, this can be seen in the legal theory of the Nova methodus discendae docendaeque Jurisprudentiae from 1667. There Leibniz describes aequitas and pietas as necessary corrective mechanisms for jus strictum (Busche 2003, pp. LIX-CI). Meder speaks of a mutual interpenetration of the three levels (Meder 2018, p. 193). Hence, Leibniz is much closer to Dworkin and much further away from Hart than Ben Menahem thinks. From the very beginning, Leibniz developed an integral theory of law: moral philosophy and religion do not stand outside law but can and must, in case of conflict, correct jus strictum by way of equity and piety as part of the law. According to Leibniz, there are several levels of law that are hierarchical.
Another important aspect is their attitude toward utilitarianism. Dworkin clearly opposed utilitarianism (Dworkin 2013, p. 143). Since utilitarianism emerged only after Leibniz's death, Leibniz's view on the subject must be carefully reconstructed. Riley came to the conclusion that Leibniz would have rejected utilitarianism (Riley 1996, pp. 160-62). Notwithstanding the importance of self-interest that Leibniz, like Hobbes, assumed (Busche 2003, pp. 91 and 434 fn. 5), Riley emphasizes that self-interest is held in check by caritas sapientis as the definition of the concept of justice (Riley 1996, pp. 160-62). Indeed, the idea of a "pleasure of malevolence" found in Bentham is not compatible with Leibniz's definition of justice (Riley 1996, p. 161). Even if Leibniz always had the utility of a thing in mind, one will hardly be able to classify him as a utilitarian.
Differences between the two philosophers can be identified less in their basic assumptions than in the way law is to be derived from them. Here, the precision of Leibniz's thinking and the application of formal logic to law are of decisive importance. While Dworkin rejected a conceptual jurisprudence or Begriffsjurisprudenz (Dworkin 2011, p. 143), Leibniz's incredibly extensive and intensive definitional studies of law show that he wanted to develop a conceptual jurisprudence and one that really deserves the name (c.f., for instance, the countless definitions in his essay on legal conditions De Conditionibus, A VI 1, 99-150). However, it was quite clear to Leibniz that jus strictum derived from definitions alone is in need of correction: if the result does not correspond to equity or piety, it must be corrected by them.
The "calculus of concern" developed by Dworkin is very reminiscent of Leibniz's remarks on equity (Dworkin 2013, p. 271). According to Dworkin, three main factors must be taken into account: "the harm threatened to a victim, the cost a rescuer would incur, and the degree of confrontation between victim and potential rescuer" (Dworkin 2013, p. 275). Leibniz develops his doctrine of equity from the idea of innoxia utilitas (harmless utility). According to this doctrine, I am required to help someone if he is threatened with harm that I can avert if the assistance is harmless to me (Armgardt 2022a, pp. 90-96). This moral and philosophical concept was very well known in Leibniz's time. From this concept, Leibniz developed the following categories of neediness by generalization: necessity (necessitas), usefulness (utilitas), superfluity (superfluitas), and harmfulness (damnum). Whenever the plaintiff could claim a higher category than the defendant, he prevailed legally against the latter on the basis of equity. This can easily be formalized into a calculus of equity (Armgardt 2022a, pp. 92-96). The similarity to the harm and cost categories developed by Dworkin is obvious.
It should be noted that Leibniz stood in the tradition of Roman law, from which modern civil law has developed, while Dworkin worked in the common law tradition. Overcoming this division may be one of the most important tasks of contemporary legal theory. The similarity between Leibniz's and Dworkin's legal theories indicates that the legal rationality behind the two major legal traditions is very similar. In this regard, Leibniz's method can certainly provide valuable help.
Funding: This research received no external funding.