Part I: Von Wright on the possibility of a logic of norms
This two-part series discusses the philosophical roots of modern legal systems, focusing on the problematic relationship between logic and law, in particular in the uses of deontic logic for legal technologies. In this first part, Linus Hoffmann discusses the issues raised by the concept of deontic logic. A second article will offer solutions, inspired by the work of the Finish philosopher Georg Henrik Von Wright , arguing that deontic logic may one day support machine learning of the law.
“Logic has a wider reach than truth”
Classic logic is used to identify contradicting propositions: The phrases “The train 2133 has arrived in Brussels Central station” and “The train 2133 has not arrived in Brussels Central station” cannot both be true at the same time. Deontic logic is a system of logic that deals with norms: “You are allowed to take the train 2133 without a ticket” and “You are not allowed to take the train 2133 without a ticket” can be valid pieces of legislation that have both passed the legislative process of a given country, despite conflicting with each other.
Deontic logic is the group of rules that can be used to identify such inconsistent normative situations, especially when they are more complicated than in the given example. In that perspective, one can imagine that a fully functional deontic logic could be the core of future algorithms that treat data with normative content in order to identify those situations in which the regulation is inconsistent. Many other applications could be conceived for an algorithm that is based on deontic logic because this type of logic is especially designed in order to grasp the nature of norms. In any case, deontic logic can lead to different discoveries than those from algorithms that are based on statistics (like the one of the french firm Predictice).
Many can benefit from the discovery of inconsistent normative situations and other applications of deontic logic. Lawyers can be interested in interpreting inconsistent normative situations to the benefit for their clients. Political communities have an interest in eradicating conflicting norms because they are a source of legal insecurity. Besides, algorithms with a deontic logic at their core could also be used to rapidly compare the regulation of a certain situation in different countries, in order to help lawyers to do forum shopping or to help political communities to harmonise their respective systems of law.
Nevertheless, considerable metaphysical doubts persist about the very possibility of existence of a system of deontic logic. This article deals with this problem and with the different propositions that the philosopher Georg Henrik Von Wright (1916-2003) made in order to overcome it.
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Over the course of his entire philosophical career, Georg Henrik Von Wright investigated the interrelations between logic and norms. His view on the possibility to apply a system of logical relations on prescriptive statements (deontic logic) changed a lot during his live. In a late work he wrote that his “journey through the landscape of deontic logic has had many twists and turns” and that he had “gone full circle back to [his] original position. But (…) the journey was worth making.”.
The second part of this article intends to retrace Von Wright’s changing philosophical opinions about the issues of the very possibility of a deontic logic. The first part will be dedicated to the conceptual foundation of the problem. The assumption will be made that there is an ontological difference between descriptive and prescriptive propositions. Focusing on the concept of prescription, it will be shown that the concept of truth is not directly applicable to it. Though classic logic seems to rely on its function to enunciate logically true propositions, that can under certains conditions be converted into true propositions about reality. Unfortunately, prescriptive propositions cannot be true or false. This is the core of the issue. Can there be a deontic logic that produces logical truths about prescriptions?
The second part deals with von Wright’s contributions to the question of the possibility of a deontic logic, from his early works in the 1950’s to his late work in the 1990’s. The study will begin with the article “Deontic Logic” (1951) in which he enthusiastically exposes a first draft of a deontic logic and but seems to ignore the existential problem of such a system of logic. Later we will focus on the author’s pragmatic turn in “Norm and Action” (1963), where his doubts about the possibility of a deontic logic started. In the following two decades, these doubts became so strong that he started to believe that “there could be no such thing as a logic of norms”. In his late work, von Wright goes back and re-admits the possibility of a deontic logic. In “Is there a logic of norms?” (1991) he introduces the notion of rationality which opens new perspectives, although the fundamental construction of his late deontic logic is still based on his early work from 1951.
The ontological gap between description and prescription
The problem of the possibility of a logic of norms is based on the fundamental difference between the reasoning in terms of description and the reasoning in terms of prescription.
Kelsen illustrates the difference between both modes of reasoning with the description of human behaviour. He distinguishes between seiendes Verhalten, a human behaviour that really exists, which is indeed performed by someone, and sollendes Verhalten, a human behaviour that ought to be, that ought to be performed by someone. The spheres of Sein and of Sollen are not independently juxtaposed, but the conformity of the Sein to the Sollen can be evaluated.  When one makes a proposition about something that is seiend, then the proposition can be either true or false. Truth is here understood as the concordance between a proposition and material reality. True propositions help us to grasp the nature of reality. Reality is what is the case, what exists, what is seiend. The situation is much more difficult when it comes to the Sollen. When one makes a proposition that contains something that is sollend in order to influence the behaviour of someone, than this prescriptive proposition cannot be marked as true or false. This is so because the content of a prescriptive norm, the behaviour that ought to be, does not materially exist in any case (it is not part of material reality, but is has a sort of virtual existence in the will of the prescribing actor). On the other hand, when someone acts in accordance to how he ought to act, his behaviour is already seiend, that is to say a part of material reality. Therefore, it is impossible to establish a discordance or concordance between a prescriptive proposition and material reality. But as the concept of a truth about reality needs such a discordance or concordance, it cannot be applied to the relation between a prescriptive proposition and something that ought to be. There is an ontological gap. This is the central problem for the possibility of a deontic logic.
Classic logic is based on the truth-value (truth, falsehood and their derivatives) of a descriptive proposition. Propositions can be either true or false, but not both at the same time. Some argue that classic propositional logic is about the propositions itself (what is expressed through a sentence), others argue that logic is about the sentence expressing propositions. Langford thinks that the propositional sentence and the proposition are not identical. He proves this by juxtaposing three sentences in three different languages expressing exactly the same proposition (It is raining – Il pleut – Es regnet). There are three sentences, but they all express the same proposition. If sentences where identical to their expressed proposition than the three sentences would express three different propositions. This is not the case.
Langford articulates it in this way: “A sentence is peculiar to a given language, whereas a proposition is, so to speak, international.”  If logic were about sentences which are identical to their expressed propositions, than the three sentences could be expressed in three individual logical formulas, which has no sense. Thus, it seems that logic is about the propositions themselves. 
Classic logic permits to derive logically valid propositions from other propositions. A valid proposition is not a general truth about reality. If a statement is logically valid, it means only that an internal, formal truth can be attributed to it, which is only valid in terms of logical systemic consistency. Essentially, a logical truth does not indicates anything about reality. Nevertheless, as logic controls the systemic consistency of propositions, it can be used to derive one truth about reality from another truth about reality. This is the way how classic logic is continuously applied in the real world. Though, one must always remember that there is a fundamental difference between a logically valid proposition and a truth about reality; logic is an auxiliary system that can only be applied to reality, but which is not identical to reality.
The origin of its name is the greek word déon which means “what is binding”. Attempts to establish logic rules of norms were first made by the Indian Mimamsa school, and also by the ancient greek philosophers. In the fourteenth century, medieval philosophers discovered the similarities between the logic modalities of necessity – possibility – impossibility and the deontic notions of obligation – permission – prohibition. Later, Leibniz called the latter categories the “legal modalities”. According to him, the basic principles of propositional classic logic were also valid for his logic of norms. In the 1920s, the Austrian philosopher Ernst Mally conceived the first system of a logic of norms. He called his system “Deontik”. Nevertheless, it had significant issues. In 1951, Von Wright published his article “Deontic Logic” which has strongly influenced the debate since then.
Deontic logic is different from classical logic, although they have many similarities. Deontic logic is the logic of norms. It is not concerned with true or false propositions, but it is a formal system that tries to seize the essential logical characteristics of prescriptive propositions that contain notions like obligation, permission or prohibition. It is a study about the coherence of a system of prescriptions. In a nutshell, deontic logic is the logic of propositions about the prescriptions which cannot be true or false.
Therefore, when it comes to the question of the possibility of a logic of norms, the ontological gap between description and prescription keeps haunting us: Is the conversion of a logically valid proposition into a truth about reality inherently necessary for a system of logics, or could a system of logics also lead to other statements about reality than truth? Essentially, is there a system of logic capable of describing the reality of norms?
Editor/ Membre de l’équipe éditoriale
 Von Wright, during a lecture in 1957
 Von Wright: Is There a Logic of Norms? in Ratio Juris. Vol. 4 No. 3 December 1991. p. 265
 Von Wright: Is there a logic of norms? (1991), p. 265.
 H. Kelsen: Reine Rechtstheorie. p. 29-30.
 C.H.Langford and Marion Langford: Introduction to Logic. In: Philosophy and Phenomenological Research, Vol.14, No.4 (Jun.,1954), pp.560 – 564. An ontological difference between propositions about a material reality and the material reality itself must be assumed for this vision of truth.
 C.H.Langford and Marion Langford: Introduction to Logic. In: Philosophy and Phenomenological Research, Vol.14, No.4 (Jun.,1954), pp.560 – 562.
 op. cit.
 This idea has significant implications for a logic of norms, because norms also have the dual structure of the expressed prescription and the sentence expressing the prescription. This issue will be discussed later.
 Risto Hilpinen: Deontic Logic. pp. 159 – 162