Logic and Law
From IVR encyclopedie
What logic is, and what it is not.
Logic deals with the structure of ideas and their linguistic expressions. [Cf. Jaape Hage, Logic]. It is not a source of knowledge of actual facts or of right ought.
Logic is dominated by the principle „logique oblige“: the rules of logic must be strictly followed in all cases where they apply.
The main task of logical rules is to define consistency (or inconsistency) of ideas (sentences) and the definition of inferences.
Inconsistency of proposition is defined as impossibility of logical reason that the propositions p1 andp2 cannot be true at the same time. Inconsistency of norm sentences is given if in one and the same norm system at the same time „p ought to be“ and „non-p ought to be“ or „p ought to be“ and „p is permitted“ is produced. There is an important difference between inconsistency of propositions and inconsistency of norm sentences: inconsistent propositions do not describe a reality; such a state of affairs does not exist; yet inconsistent norms may be actually produced. E.g.: if somebody sells a picture to a person P1 and independently also to another person P2 he has two incompatible duties, namely to deliver the picture to P1and to P2.
There is an important philosophical insight: The realm of logic is not restricted to propositions and truth relations; norms and valuations (preferences, utiliy statements and the like) although not subjected to the characteristic of truth and falsehood, are objects of logical law.
The norm logical rules are differentiated in relation to the kind of norm sentence under consideration, which are:
(a) duty or permission stating sentences,
(b) power-conferring norms,
(c) legal principles.
Ad (a): From a general norm sentence a respective individual norm is deducible.
From a conditional norm sentence and the validity of the antecedent the consequent can be derived as a conclusion (modus ponens rule).
Ad (b): In the cases discussed in ad (a) the conclusion arises automatically (ipso facto). The production of norms on the basis of empowerment is bound to the execution of a norm-creating act of will. The scheme of empowerend inference reads: If an act of will be realized that p should be obligatory, then p is obligatory as a norm of the system under consideration. Essential here is the identity of the content of the act of will with the normative consequent.
Ad (c): Principles are a specific kind of practical information which stipulates criteria of optimization. Different principles may concern a case in a way which leads in the opposite direction. I may have at the same time reasons to continue writing and other reasons to stop my work and to take a walk. Principles as motives for acting must not be compatible inter se; it is a matter of choice which principle we will follow.
In a legal order there are valid principles established explicitly or only implicitly leading the processes of adjudication. They are helping to resolve so called gaps in the law. There have been proposed different systems of deontic logic which were intended to rule the essential logical relations in the legal order. They inserted deontic sentences (norm sentences) as arguments of truthfunctional connectives. In my opinion these systems are not appropriate as a logic of law. We must try to construct a genuine logic of norms.
The main logical rules of a genuine norm logic
Rules of incompatibility
„p ought to be“ and „non-p ought to be“ are incompatible. „p ought to be“ and „p is permitted“ are incompatible.
The rule of subsumtion
„For all subjects x p ought to be“ implies „for x1 p ought to be“. 
Norm logical modus ponens
If q, then p ought to be
p ought to be
From the power-conferring norm and the respective norm creating act of will follows the normative content of this act as a valid norm of the normative order under consideration. (The creation of norms by acts of will.)
Note on norm logical scepticism
The opinion that there are no logical relations between norm sentences and no logical inferences with normative elements has been argued by the Czech economist and logician Karel Engli. Kelsen’s exposition in his late teaching is a transposition of this view.
The judgement (das Urteil) is the essential unity of thought. Norms cannot take over this role:
(i) Judgements express a recognition, norms do not express a recognition.
(ii) A judgement is an answer to a question: norms are not answers to a question.
(iii) Every judgement is correct or incorrect, besides this empirical judgments are true or false; yet norms are neither correct nor incorrect, and neither true or false.
(iv) A judgement can be negated; a norm cannot be negated.
(v) Judgements can be elements of inference relations; norms cannot.
(i) Is true, but is is not convincing that logical law deals only with recognition.
(ii) There are of course questions where the appropriate answer has normative meaning.
(iii) Norms are not true or false, but there is another way of existence of norms: they may be valid or invalid.
(iv) Norms may be negated in two different ways: their validity may be negated or there may be formed a norm with opposite content. The situation is also analogous to the situation with propositions.
(v) Engli’s finding is valid only if we conceive inference as a truth relation. But if we adapt the notion of inference in an appropriate way, normological inferences become meaningful. In my opinion the essential argument against norm logical scepticism are its detrimental effects on analytical jurisprudence including the Pure Theory of Law.
(i) The idea of the unity of the legal order is conceived as a logical postulate and loses its sense if there were no logical relations between norms.
(ii) The theory of the generation of norms automatically or by acts of will is based on logical processes and in accordance with inference rules.
(iii) The essence of general norms is defined by the corresponding logical rule that individual norms are consequences of the general rule and the finding that a case of the field of the general quantifier is given. The same holds with the normative conditional on the basis of a conclusion of the modus ponens kind.
(iv) Material derogation is meaningful only if there exist logical conflicts between the former norm and a new norm.
(v) Legal force of a kind of norm in relation to another kind of norms depends on the possibility or impossibility of derogation in case of logical conflict in the flow of time.
Just to sum up this considerations we can say that analytical jurisprudence would be destroyed if there were not normlogical relations and no valid norm logical inference.
 There are of course also other relations in the concern of logic; e.g. in the erothetic logic the definition of questions and rules have to ascertain whether a sentence can be conceived as an answer to a given question.
 A rule of the modus tollens type is not valid.
 For details and expecially for the distinction of open and closed norm systems see O. Weinberger, Rechtslogik, 2nd ed. Berlin 1989.
 Between permission sentences there is no incompatibility.
 Here „all“ is understood in the distributive sense
 A rule of the kind modus tollens is not valid, because from two norm sentences a statement about a fact cannot be deduced.