Jusletter IT

Judgments of the numerous international courts and tribunals are characterised by meticulous application of legal methodology, in particular the various forms of norm interpretation and analogy. Additionally however, it is modes of logical inference which are at play and must be considered when law is applied in courts.¹

It is these modes of logical inference which are being applied and handled so naturally by judges that their correct employment is not being reviewed with recourse to the strict rules of formal logic. Since, at least implicitly, all reasoning in judicial decisions applies modes of logical inference,² considerations of formal logic merit a closer look.

Indeed, the implicit and seemingly natural application of logic in judicial decisions brings with it the fact that most legal arguments found in judicial decisions do not strictly follow a formal logical structure. Rather, most legal reasoning is enthymematic. This means that its logical form is not explicitly clear from its original mode of presentation (e.g. reasoning in a judgment).³ Such enthymematic reasoning obstructs the inherent logical structure of a given legal argument. Consequently, logical errors are easily made and retrospectively more difficult to reveal. This might be one reason why violations of formal logic (the strict laws of thought) are indeed often made in judicial as well as administrative practice,⁴ at least as many times as errors in law (if not even more).⁵

The great danger of errors in logic lies then in the fact that the violation of the laws of logic can have – especially if they relate to the evaluation of evidence – far more serious consequences than errors relating to legal interpretation or analogy.⁶ As a result, it is forwarded here that a breach of the rules of logical inference calls into question the very value, understanding, plausibility and acceptance of judicial reasoning, even more so than errors in analogy or law. In particular, unlike the latter errors, cases of violations of the laws of thought in judgments raise the question of their legal consequences. The subsequent analysis thus presents normative arguments for the use of logic in international law.⁷ It firstly lays out the doctrinal grounds for its application in international law with a view to international adjudication and then elaborates on the legal consequences of logical errors (fallacies) therein.

For the purpose of the present paper «logic» refers to the formal science as understood particularly in its sub-disciplines such as the deontic or «Imperativ»- and «Normenlogik».⁸ The words «laws of thought», «logic», «laws of logic» are used synonymously.

This means that this study is concerned only with the «inferential correctness» of legal reasoning. As with all reasoning, legal reasoning begins from premises and draws a conclusion. Here, logic is concerned with answering the question whether – given the premises – the argument supports the conclusion.⁹

This also demonstrates the limits of logic in legal reasoning. It does not answer the question whether the premises it assumes are true, but only establishes their inferential correctness. Indeed this is of fundamental importance, especially in law, where it is the courts that determine in their reasoning whether certain premises are true, and – based on these factual findings – render their decisions. Disagreements may be viewed as mere differences in opinions about the law or facts. On the other hand, logic as a discipline articulates universal «laws of thought», the rules of which are mathematically precise and are not a question of opinion. For exactly these reasons, logic’s utility for law was exemplified by the young Gottfried Wilhelm Leibniz, who proposed the transposition of the axiomatic approach of Euclidean geometry to law.¹⁰ In fact, «reducing judicial reasoning to logical deduction would ensure certainty and testability and it would constrain the arbitrariness of human decision-making».¹¹ This is a huge advantage for international law. When dealing with international courts, the factual findings of the court must be considered true. However, when the conclusion is based on an incorrect application of the rules of logical inference, formal logic gives us the tools to reveal these errors. Another aim of this normative approach is to make explicit all the assumptions used in our natural way of arguing¹² and, as shall be demonstrated later in this article, errors in logic constitute grounds for revision of a judgment.

International legal doctrine simply assumes the validity of logic in international law due to its self-evident character asserting that it is inherent to the functioning of any legal system, without having substantive contents of their own.¹³ In the opinion of the authors logic and its application and validity in international law can be deduced from the concept of logic itself. First, it must be reiterated that as human beings we are able to think only logically,¹⁴ and consequently the construction of a normative system such as international law, which is a metaphysical construction of thought, may only rest on the laws of thought which our mind cannot escape. Ubi ius, ibi logicus.

In fact, one method of logical inference and its application is the most fundamental when applying law: the logical syllogism.¹⁵ This illustrates the fact that the laws of logic, when they accompany legal syllogisms, follow the «axiomatic method». With this method, a result is deduced from given or non-given premises in application of modes of logical inference (in this case the syllogism).¹⁶

The doctrine of the axiomatic method itself pre-supposes that the axioms themselves are consistent/unambiguous and complete. ¹⁷ Albeit logic – or more specifically logical axioms – may only be conceivable a priori,¹⁸ this does not preclude the conclusion that logic is part of a general principle of international law pursuant to art. 38(1)(c) of the Statute of the International Court of Justice.¹⁹/²⁰

It follows then that logic – as demonstrated above – is inherent in legal reasoning and therefore must be considered the structural foundation of any legal reasoning. Art. 56 of the Statute of the International Court of Justice (Statute) stipulates that judgments shall state the reasons on which they are based.²¹ This requirement must be understood in relation to art. 38(1)(d) of the Statute which contemplates the use of judicial decisions as subsidiary means for the determination of rules of law. Here, the elaboration of reasons in a Court’s judgments helps to build a coherent body of jurisprudence.²² Furthermore, such duty to state reasons is recognized in other international courts and tribunals,²³ and it has been argued that sound reasoning constitutes a fundamental right (e.g. Art. 6 of the European Convention on Human Rights) which requires reasoned verdicts in criminal trials.²⁴ Indeed, as J. Dewey demonstrated (and what Alchourron calls the Principle of Justification),²⁵ the logical method in law serves an important purpose particularly in judicial decisions since «Courts not only reach decisions; they expound them, and the exposition must state justifying reasons. […] Its purpose is to set forth grounds for the decision reached so that it will not appear as an arbitrary dictum, and so that it will indicate a rule for dealing with similar cases in the future».²⁶ Adding to that, Lauterpacht wrote in The Development of International Law by the International Court (1958) that the «[a]bsence of reasons—or of adequate reasons—unavoidably creates the impression of arbitrariness»²⁷ When the reasons given for a judgment contain fundamental logical errors, they fail to fulfill this purpose.²⁸ As a consequence the very value, understanding, plausibility and acceptance of the decision is questionable.²⁹ Hence, art. 56 must be interpreted as requiring the ICJ to base its decisions on logically correct reasoning. Indeed this is also required by the principle of completeness (Vollständigkeitsgrundsatz) and the principle of non-contradiction (Gebot der Widerspruchslosigkeit) as well as the completeness of reasoning of the decision-making, which appear to be inherently part of international law.³⁰

It follows then from having established that logic is an inherent rule of international law and that art. 56 requires the correct application of logic, that the violation of the laws of thought in a judicial decision denies it to qualify as a subsidiary means for the determination of rules of international law pursuant to art. 38(1)(d) ICJ Statute.

This brings us to the question of the legal consequences of errors in logic in judgments of the ICJ contains errors in logic.³¹ It is controversial, whether judgments of international courts and tribunals are subject to revision. Most prominently, Georges Scelle considered revision, even in the absence of a provision to that effect, indispensable.³² This view must be supported in light of the fact that revision had already been applied in ancient times³³ and the importance of the right of revision on the international level has been widely recognized.³⁴ This is convincing. In fact, while according to art. 60 ICJ Statute, the judgments of the court are final and not subject to review, art. 61 allows for «revision of a judgment may be made only when it is based upon the discovery of some fact of such a nature as to be a decisive factor, which fact was, when the judgment was given, unknown to the Court and also to the party claiming revision, always provided that such ignorance was not due to negligence».³⁵ While there is no practice of the Permanent Court of International Justice regarding revision, the ICJ has confronted requests for revision, but in all three cases found the applications to be inadmissible.³⁶

Nevertheless, it is interesting to note that the Inter-American Court of Human Rights (IACtHR), where neither the statute nor the rules of the court provide for revision, admitted a request for revision.³⁷ It did so by reference to art. 61 of the ICJ Statute and Rule 80 of the Rules of the Court of the European Court of Human Rights, and considered it a general principle of domestic and international law that «the decisive or unappealable character of a judgment is not incompatible with the existence of the remedy of revision in some special cases».³⁸ Additionally the content and language of art. 61 is found in statutes and rules of other international courts and tribunals as well.³⁹

It is therefore established that there are convincing arguments for concluding that the remedy of revision of judgments of international courts or tribunals is indispensable under special circumstances. Whether errors of logic fall under such «special circumstances» is questionable.

To begin with, one must distinguish a mistake in a court’s assessment of the material, be it legal or factual (before it at the time of its decision) and errors of logic. For the former, it is widely agreed that no mechanism exists for effecting their correction at the international level.⁴⁰ As regards errors in logic, it is interesting to note that it appears that all major jurisdictions of the world recognize mistakes in logic as a ground for appeal of a judgment.⁴¹ In those jurisdictions errors in logic are either considered a crucial lack of or mistake in judicial reasoning and are therefore grounds for appeal. This further supports the above conclusion that the duty to give reasons in a judgement (e.g. art. 56 ICJ Statute) must be interpreted as requiring a logically correct reasoning. Not meeting this requirement, a judgment could be considered – in light of the absence of the possibility to appeal – to be subject to revision. Since all major jurisdictions of the world recognize this principle, it must be considered a general principle of international law (art. 38(1)(c) ICJ Statute).⁴² Consequently, art. 61 ICJ Statute could be interpreted as recognizing errors of logic as a ground for a revision of a judgment if this mistake of logic is of such a nature as to be a decisive factor.⁴³

Additionally, promoting legal arguments in judgments of international courts and tribunals which strictly follow a formal logical structure may also contribute to elucidating complex and very technical legal questions. Indeed, the resulting norm clarity would then in turn, as Chayes and Chayes have demonstrated, enhance norm compliance,⁴⁴ and with that, generally contribute to a persuasive and value-neutral method of determining a rule of international law (art. 38(1)(d) ICJ Statute).

Quite frequently, international courts and tribunals commit the fallacy of the so-called» quaternio terminorum». While the logically correct inference uses three elements:

1. middle term «Mittelbegriff» (in the initial example (X) Territory, population and State Sovereignty;
2. sub-term «Unterbegriff» (in the initial example (A) Germany);
3. generic term «Oberbegriff» (in the initial example (St) State under international law)

the «quaternio terminorum» uses four terms instead, by using two distinct meanings of the same term (Homonymie).

It appears that the «quaternio terminorum» fallacy is committed particularly in international decisions, due to the translation of certain terms into different languages without realizing that this adds a distinct meaning to the original meaning of the term.

A prominent example of «quaternio terminorum» is the LaGrand⁴⁵ decision on jurisdiction before the International Court of Justice:

Art. 36(1)(3) provided the basis of jurisdiction to the Court in connection with art. 1 of the Optional Protocol to the Vienna Convention on Consular Relations concerning the Compulsory Settlement of Disputes⁴⁶. Art. 1 leg cit provides that «Disputes arising out of the interpretation or application of the Convention shall lie within the compulsory jurisdiction of the International Court of Justice». The US challenged the jurisdiction of the ICJ in particular – under very narrow and specified interpretation of the term «Dispute» – by pointing out that Germany did not sought damages, but the assurance of omission of future violations of the Vienna Convention. This would not fall within the term of «disputes» of art. 1 of the Optional Protocol.

Having affirmed its jurisdiction because of other aspects, the ICJ also affirmed its jurisdiction based on this point. The court puts forward that a dispute could not be split up into its individual aspects. Therefore, the dispute as a whole must fall within the meaning of art. 1 of the Optional Protocol because the dispute may be settled only in this way.

The ICJ at this point committed «Quaternio terminorum». Since – in particular by pointing out that the dispute can only be resolved by the holistic acceptance of its jurisdiction – the court adopts in its argument the homonymous Middle term «Mittelbegriff» «disputes» with two distinct meanings: while the jurisdictional rule of art. 1 refers to the procedural meaning of «disputes» as the subject matter of the dispute (Disp¹ in the middle term of the first premise), the court uses the term «disputes» as a political, societal concept (Disp² in the middle term of the minor premise). Only the latter may be settled according to the ICJ. By this homonymous, double use of the term «disputes», the conclusion no longer uses (as logically required) three but four terms.⁴⁷

On the merits, this inference error has no impact on the quality of the decision, as the ICJ had (logically conclusive) already established its jurisdiction by virtue of two other aspects.⁴⁸

In various cases in international jurisprudence, logic or «logical proof» is used to support the pervasiveness of an argument presented.⁴⁹ While strictly speaking such rhetorical uses of logic are not the concern of formal logic, the argument loses its appeal when the statement invoking logic is in fact wrong. This is illustrated by the well-known Corfu-Channel Case, in which the ICJ famously recognized indirect evidence to be admissible.⁵⁰

While it was criticized for not elaborating on how the court arrived at this conclusion, the question of admission of indirect evidence as such is essentially a legal question.⁵¹ However, in supporting its argument, the court provides that «a State should be allowed a more liberal recourse to inferences of fact and circumstantial evidence. […] It must be regarded as of special weight when it is based on a series of facts linked together and leading logically to a single conclusion.»⁵² This is – logically speaking – not correct. Indeed, it is the distinct quality of indirect evidence that even if all facts are established to be true, this does not lead to only one possible conclusion. It might be leading to a conclusion which best explains the established facts, but logically this does not exclude the possibility that there might be another explanation for the facts. In logic, this mode of inference is called «inference to the best explanation» or «abduction». Abduction involves inference to an explanation of established facts. Viewed as an argument, «a statement of the phenomenon […] to be explained and the putative explanation both appear as premises of the argument and the explanation itself is the argument’s conclusion.»⁵³ However, this inference is not deductive but inductive. As an inductive argument, the truth of its premises does not guarantee the truth of the conclusion, but only makes it more or less probable. While not undisputed in philosophy,⁵⁴ this inferential process has a logical form, while not offering the same degree of rational force as deduction or induction.⁵⁵

The court then correctly points out in the following paragraph, that «[t]he proof may be drawn from inferences of fact, provided they leave no room for reasonable doubt.»⁵⁶ This statement is then correct, since the concept of reasonable doubt refers to the evaluation of the inference drawn and does not refer to logical proof.

Already this brief discussion demonstrates the importance of logic in and for international law. In this article, we have established that logic is an inherent principle of public international law. Consequently, requirements in public international law to state the reasons on which a decision or judgment is based, such as art. 56 of the ICJ Statute, must be interpreted as including the requirement that this must be logically correct reasoning. International judicial decisions not meeting this standard cannot be regarded as a subsidiary means for the determination of rules of international law within the meaning of art. 38(1)(d) ICJ Statute. We have further established that to give logically sound reasoning is a general principle of law as «recognized by civilized nations» within the meaning of art. 38(1)(c) ICJ Statute and that errors of logic pertaining to the reasons for the decision reached could be grounds for revision of that judgment.

It is conceded here however, that formal logic also has to recognise its limits.⁵⁷ Formal logic is concerned only with the inferential correctness of an argument and does not pronounce on the right or wrong of a decision. Nevertheless, logic is an important analytical tool to determine the coherence and correctness of legal reasoning adopted in decisions of international courts and tribunals. The utility of logic in international law then lies in promoting sensibility for precise and correct reasoning. Such sensitivity would makes judgments more comprehensible and arguably the resulting rule clarity could enhance norm compliance.⁵⁸ It follows then that the – at times extraordinarily – politicised matters at issue before international courts, call for a strict and correct application of the laws of logic in international judgments. Additionally, resorting to the universal and value-free language of formal logic – particularly in a fragmented, value-laden and politicised normative system such as international law – appears to be capable of having a stabilizing effect, contributing to the neutral settlement of arguments by virtue of neutral application of the laws of thought.

Additionally, the adopted approach towards logic in international law may also provide for the developing doctrinal foundation for the use of logic in analysing international law rules as groundwork for computerised tools⁵⁹ supporting the application of international law rules.⁶⁰ This development can already be witnessed in the field of artificial intelligence and law,⁶¹ with its influential contributions on logic programming and the law.⁶² A remarkable paper by P.M. Dung and G. Sartor, for example, provides a fascinating account of the logical analysis of private international law.⁶³

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Gabriel M Lentner, Research and Teaching Fellow, Danube University Krems, Department for Business Law, Dr.-Karl-Dorrek Strasse 30, 3500 Krems, AT, Gabriel.lentner@donau-uni.ac.at

 

Dieter Krimphove, Professor, University of Paderborn, Department for Business Law, Warburger Straße 100, 33098 Paderborn, DE, dieter_krimphove@notes.uni-paderborn.de