Logic of Norms : Von Wright and deontic logic (Part 2)

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Part II: 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. While a first article discussed the issues raised by the concept of deontic logic, this second article offers solutions, inspired by the work of the Finish philosopher Georg Henrik Von Wright, exploring the various lights a logic of norms may shed on the law. 


“Logic has a wider reach than truth”[1]

“Deontic Logic” (1951)[2]: A first draft of a logic of norms

The first presentation of Von Wright’s logic of norms was published as an article in the journal “Mind” in 1951. From the onset, he draws an analogy between the three classic alethic modes, or modes of truth (the necessary, the possible and the contingent), the three epistemic modes, or modes of knowing (the verified, the undecided and the falsified) and finally the deontic modes, or modes of obligation (the obligatory, the permitted and the forbidden). Although he outlines that there are similarities between the groups of modalities, he does not clearly define them. While it is true that one can feel that the analogy is based on something, the essence of the similarities are hard to express.

Von Wright then defines the object of a prescriptive sentence, which is an act. The deontic modalities are all applied on acts, like in the examples « One must respect driving rules » (mode of obligation), « Minors are not allowed to enter the cinema without company » (mode of permission), « One shall not steal » (mode of prohibition). Von Wright defines that his logic only applies on statements about general and abstract acts, and not on statements about individual acts. The analogies between classic logic and his deontic logic are striking. He defines the notion of performance-function as “strictly analogous to the concept of truth-function in propositional logic”.

The performance-function can be positive or negative, and there is no possible third value, exactly like the truth-function in classic logic. The logical parameters of conjunction, disjunction, implication and equivalence have the same functionalities like in truth-logic. The notions of tautology and contradiction are also the same as in truth-logic. Furthermore, he outlines that there is a deontic mode of indifference, which is comparable to the alethic mode of contingency. His deontic logic can also be applied to express the systemic coherence of the realization of two different acts (notion of conjunction). Finally, he adds the two “deontic operators” P (stands for permission) and O (stands for obligation). The prescriptive propositions, or in Von Wright’s terms, the deontic propositions, are all expressed through a P- or an O-sentence. As one can see, Von Wright’s deontic logic of 1951 seems to be able to represent prescriptive situations.

The most interesting point is when he characterizes the product of his deontic logic: a “logical truth”! Though, what can be true about a logic that deals with prescriptive statements? Attempting to answer this question, he differentiates between two situations.

First, some complexes of P- and O-sentences would express truths of logic for reasons which are independent from “the specific character of deontic concepts” or in other words, they establish a logical truth that is independently from a truth about reality. In order to illustrate his point, he uses an example about the not-existing third option in two normative situations. If the act 1 is permitted only if the act 2 is permitted, then the act 1 is forbidden only if the act 2 is forbidden. He states that this is a logical truth which is valid for every sentence, wether the sentence has a deontic nature or not.

The second situation is the situation in which the complex of P- and O-sentences expresses a logical truth which is not independent from character of deontic concepts, but which relies on it. This is the part of deontic logic which is specific to this system of logic and which can not be found elsewhere. This is the part of deontic logic which gives the reason of existence to the ensemble of deontic logic. To illustrate, Von Wright gives the following example: If the act 1 is obligatory and if doing the act 1 obliges to do the act 2, then the act 2 is also obligatory. One can see from this example that deontic logic is not entirely independent from its object, the prescriptive propositions, but that the connection between both is very hard to characterise. Von Wright does not deliver any information about this connection. Maybe there is no rational connection? Do we deduce this connection only from the strange parallelism between deontic logic and classic logic because the conversion of logically valid propositions into truths about reality works quite well in classic logic? What does a logically valid statement from a deontic logic can expresses? Those questions are not clearly answered in 1951. Von Wright only states that it is not clear if the truth of some of the laws of deontic logic are connected to logical questions or to a “matter of moral code”, that is to say, that their truth would be based on extra-logical reasons. Unfortunately, he does not specify what he exactly means by “moral code”.


“Norm and action” (1963)[3]: The difference between a logic of norms and a logic of norm propositions

Twelve years later, Von Wright changed his mind on a logic of norms. Although he still admits to the possibility of a deontic logic, he differentiates between two systems of logic of norms. More precisely, he says that there are two identical systems of deontic logic that have to be interpreted differently.

Indeed, Von Wright outlines that one prescriptive proposition can be interpreted in two ways: such a sentence can have a normative meaning, but it can also have a descriptive meaning. By saying that “One must respect driving rules” one can express simultaneously a general truth about the existence of a rule (the rule to respect the driving rules) but the sentence can also be understood as a prescription that obliges someone to respect the driving rules. These two meanings can be described by two different forms of logic. The prescriptive meaning will be represented by a logic of norms which is similar to the deontic logic of 1951. The descriptive meaning, which expresses a truth-function about a given norm, can be represented by a logic of norm-propositions.

The logic of norm-propositions deals only with the existence of norms, that is to say, it deals with facts about reality. Facts can be true or false. In that way, the logic of norm-propositions is only a disguised type of classic logic. But what is the substantial content of the logic of norms (the real deontic logic)? In order to determine this, a short definition of norms should be added. In Reine Rechtslehre, Kelsen defines a norm as « der Sinn, den gewisse menschliche Akte haben, die intentional auf das Verhalten anderer gerichtet sind. Sie sind intentional auf das Verhalten anderer gerichtet, wenn sie, ihrem Sinne nach, dieses Verhalten gebieten (befehlen), aber auch wenn sie es erlauben und insbesondere wenn sie es ermächtigen ».[4]

The definition of a norm as the meaning of an prescriptive act is particularly interesting. Such a definition of norms implies that a logic of norms must neither deal with the sentence expressing a prescription, nor deal with the act of prescribing, because they are both seiend and because they both only express the real prescription. An authentic logic of norms must deal with the ideal construction that motivates that act of prescribing, which is the real prescription.

In Norm and Action, Von Wright states that the deontic logic he wants to create should be a hybrid logic that reunites the logic of norm-propositions and the logic of norms by taking into account the descriptive and the prescriptive aspect of a prescriptive proposition – he does not give any further details about the way the hybrid deontic logic could work. It seems that his argumentation struggles another time because of the ontological gap between prescription and truth, but that this time, he is conscious of the problem and tries to circumvent it. Nevertheless, by separating two logics (of which only one is a real deontic logic) that are ought to become one deontic logic through a magic merger process, Von Wright indirectly admits the difficulties to describe the connection between logic and norm.

He later admitted that he “radicalised” himself in the years that followed, up to the point where he totally denied any possibility of a link between a logic of norms and the norms themselves. In this time, he also denied the possibility to apply the notions of contradiction and entailment to a logic of norms (notions that he developed in Norm and Action).

“Is there a logic of norms?” (1991)[5]: Deontic logic and rationality

Almost 30 years later, Von Wright comes up with a new element, the concept of rationality. In « Is there a logic of norms? » he first describes the three main problems of deontic logic that has crystallized in the debate over the past decades.

The first and most important problem remains the inapplicability of a truth-function to a norm. The second problem is the incapacity of the already existing deontic logic to reflect all the fine distinctions in a set of norms. The formal representation was too primitive in order to grasp a useful amount of details of norms. Von Wright especially stresses out the difficulties to represent conditional norms. Finally, asks about the finality of a deontic logic. Can it really help to better understand a normative system? Will a deontic logic be able to describe problems like “gaps and contradictions” in a legal system?

In order to answer the most important question, Von Wright introduces the notion of rationality and points out the importance of the perspective when it comes to the analysis of a prescriptive proposition. When a prescriptive sentence exists, there is always someone who pronounces it (the norm-giver) and in order be useful, there must also be someone to whom the prescription is directed (the norm-receiver). Theoretically, the norm-giver can not oblige the norm-receiver to do something contradictory, something which is, in the words of Von Wright, “not doable”. Here, there is not only a logical contradiction, but also a contradiction in reality. Such a contradictory norm is called irrational. Von Wright adopts the perspective of a norm-receiver in order to determine wether a norm is rational or not. The concept of rationality is an intermediate concept that allows him to connect norms and logic. At the same time, he argues that rationality (in other words consistency) can be very well applied to norms! In this conception, deontic logic is the systemic study of consistency in a normative complex. In such a deontic logic, the concept of logically valid propositions still exists but it is not linked to truths about reality like in classic logic, but to „doable“ or to „undoable“ normative situations. This is linked to what Von Wright already said in the late 1950’s: “Logic has a wider reach than truth”.

The finality of a deontic logic

Von Wright describes the finality of his late deontic logic. Although he does not think that logic alone can prevent irrational norms and normative complexes to come to existence, he states that types of “meta-norms” can be built upon a fully functional deontic logic. These meta-norms can be the barrier that protects the norm-receiver from inconsistent normative situations, in which the prescribed attitude for the norm-receiver cannot be deduced from the prescriptive sentences because they are contradictory. One example for such a meta-norm is the rule lex posterior derogat legi anteriori, as it prevents older norms to enter into conflict with new norms. Another example could be the rule lex specialis derogat generali. These meta-norms can be compared to the norms of conflict of law in international private law, because they indicate the applicable norm if several contradictory norms are available in a given situation. The basis for meta-norms that prevent from inconsistent normative situations must be a fully-functional deontic logic, because it is the deontic logic that indicates the existence of an inconsistent normative situation.

Nevertheless, even the meta-norms can be insufficient in certain situations. For example, imagine that several norms are inconsistent and the principles of lex posterior derogat legi anteriori and of lex specialis derogat generali designating each a different norm for the same situation. In this case, a deontic logic with the notion of rationality will help us to understand that the normative situation is inconsistent, but new meta-meta-norms are necessary in order to find the prevalent and applicable norm in the situation.


Linus Hoffmann

Editor/Membre de la Rédaction



[1] Von Wright, during a lecture in 1957

[2] Von Wright: Deontic Logic. (1951) In: Mind, New Series, Vol. 60, no. 237, p. 1-15.

[3] Von Wright: Norm and Action. (1963) Chapter 6, section 9.

[4] Hans Kelsen: Reine Rechtstheorie. p. 27. The norm is defined as « the meaning of certain human acts directed toward the behaviour of others. They are so directed, if they, according to their content, command such behavior, but also if they permit it, and – particularly – if they authorize it » (translation by Max Knight, 1970)

[5] Von Wright: Is there a Logic of Norms? Ratio Juris, Vol. 4 No. 3 December 1991 (265-283)