Law and Logic: Contemporary Issues [1 ed.] 9783428550869, 9783428150861

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Dieter Krimphove and Gabriel M. Lentner (Eds.)

Law and Logic Contemporary Issues

Duncker & Humblot · Berlin

D. KRIMPHOVE/G. M. LENTNER

Law and Logic

Law and Logic Contemporary Issues

By Dieter Krimphove and Gabriel M. Lentner

Duncker & Humblot  ·  Berlin

Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.

All rights reserved. No part of this book may be reproduced, translated, or utilized in any form or by any means, electronic or mechanical, without the expressed written consent of the publisher. © 2017 Duncker & Humblot GmbH, Berlin Printing: buchbücher.de gmbh, Birkach Printed in Germany ISBN 978-3-428-15086-1 (Print) ISBN 978-3-428-55086-9 (E-Book) ISBN 978-3-428-85086-0 (Print & E-Book) Printed on no aging resistant (non-acid) paper according to ISO 9706

Internet: http://www.duncker-humblot.de

Preface Preface

This edited volume seeks to revive the field of law and logic, by providing an up-to-date and accessible survey of several relevant areas that fall within that category. This is done through a consolidation of current and innovative scholarship in the aforementioned field. Each author is an expert in his or her field, and each chapter offers an analysis of current issues, challenges, problems, limitations and/ or developments. The general contribution of this book to existing scholarship is threefold. • First, it seeks to consolidate current and cutting-edge scholarship by bringing together the various approaches and different theories of law and logic in one volume. • Secondly, this consolidation is presented in a way that is both stimulating for current debates in the field, and at the same time, accessible to a wider audience (particularly to readers without prior knowledge of formal logic). • Finally, this book aims at highlighting the practical applicability, utility and relevance of logic for the study of law, and its application (including legal argumentation), whilst at the same time recognizing its limits. Part I: General Issues The first part of the book addresses general issues of law and logic. The first contribution sets the scene with an overview of the historical development of legal-logic along with an account of the new law and economics approach to legal logic by Dieter Krimphove. Matthias Armgardt provides a timely account of another historical topic entitled ‘Law and Logic in Leibniz’s Legal Philosophy’, which is just as relevant today as it has been hundreds of years ago. In the next contribution, Bartosz Brożek looks at the two faces of legal reasoning: rule-based and case-based reasoning. With the use of deontic logic, he demonstrates that legal reasoning is never purely rule-based nor case-based, but that it always requires some kind of interplay between abstract rules and concrete legal decisions. Then, Michael S Green discusses legal logic and (American) legal realism. He takes issue with the often misinterpreted quote of Judge Oliver Holmes that “[t]he life of the law has not been logic. It has been experience.” He demonstrates that, in fact, the set of loosely-related errors to which the realists thought traditionalists succumbed to, did not concern reliance on logic but had other sources.

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Preface

Part II: Specific Issues The second part of the book then addresses specific issues of law and logic. Scott Brewer introduces the Logocratic Approach, which uses propositional logic to evaluate legal arguments. His contribution will demonstrate its use for teaching and analyzing American contract law by presenting the relevant teaching materials he uses at Harvard Law School. Jaap Hage introduces the topic of logical techniques in avoiding conflicts of norms in international law. His contribution provides an extensive practical account of how logical techniques can (and are currently) used in order to deal with conflicts of norms in a field where such conflicts occur on a regular basis due to the continuous fragmentation of international law. Jan C. Joerden then presents the use of logic in (German) criminal law in solving selected legal issues. The author convincingly demonstrates the utility of logical instruments – particularly propositional logic, class logic and relational logic – for the analysis of the structures of criminal legal terms and dogmatic questions. What follows is a discussion and analysis of legal arguments in public international law, by Gabriel M. Lentner. He introduces the logocratic method as developed by Scott Brewer and applies this method to several arguments in international law, in order to develop criteria for the analysis of the strengths and weaknesses of international legal arguments. Antonino Rotolo follows, and he introduces the use of logic for legal interpretation. More specifically, he introduces the concept of ‘Meaning Negotiation’. He develops a framework to model meta-argumentation over the legal meaning of terms occurring within legal provisions, and to show how negotiations may take place in this context. Finally, Tanel Kerikmäe and Sandra Särav devote their contribution to the rather topical discourse of automation. Specifically, the authors address the questions on what information technology can do to make the legal administration and decision-making system more just, impartial, fair; and how the digital and technological developments (mainly in the sphere of Artificial Intelligence) impact or change legal reasoning. With this consolidation of contributions, the editors are confident to provide important impulses for the further development of this subject. Krems and Paderborn in spring 2017

Dieter Krimphove Gabriel M. Lentner

Contents Part I General Issues A Historical Overview of the Development of Legal Logic  .. . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Dieter Krimphove Law and Logic in Leibniz’s Legal Philosophy  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Matthias Armgardt Two Faces of Legal Reasoning: Rule-Based and Case-Based  .. . . . . . . . . . . . . . . . . . . . . . . . . 67 Bartosz Brożek Logic and Legal Realism  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Michael S. Green

Part II Specific Issues Using Propositional Deductive Logic as an Aid to Teaching American Contract Law: The Logocratic Approach  .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Scott Brewer Logical Techniques for International Law  .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Jaap Hage and Antonia Waltermann Logic and Criminal Law  .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Jan C. Joerden Logic and the Analysis of Legal Arguments in Public International Law  .. . . . . . . . . . . . . . 163 Gabriel M. Lentner Meaning Negotiation in Legal Interpretation  . ................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Antonino Rotolo Paradigms for Automatization of Logic and Legal Reasoning  . . . . . . . . . . . . . . . . . . . . . . . . . 205 Tanel Kerikmäe and Sandra Särav List of Contributors  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Part I

General Issues

A Historical Overview of the Development of Legal Logic By Dieter Krimphove Dieter Krimphove

I. Introduction This contribution presents an overview of the development of legal logic from a historical perspective. It will first outline the challenges and problems associated with the task of writing about the historical development of legal logic. Next, the main part of this contribution will present the development of legal logic along with its historic roots in antiquity to its modern application. Then, the theory of the new institutional economics is introduced and analysed. The final section will conclude looking at logic’s significance for law today.

II.  The problem For two main reasons, it is almost impossible to write a history of legal logic. First, it is difficult to chart roughly 2,500 years of intellectual development in the limited space available here. This allows only for the mention of the most important historical developments and cannot, therefore, do justice to all the intellectual heavyweights and innovations of the field. The other main reason for the difficulty to write about the history of legal logic are of methodological nature: how one may analyse the phenomenon of legal logic objectively? This last point may appear surprising. After all, logic (and legal logic in particular), is described as an objective, universally-accepted phenomenon and must therefore be untainted with human subjectivity, bias, narrow-mindedness or a person’s individual values formed by his or her experience. This uncompromising “objectivity of logic” is particularly well-illustrated by the universally accepted axiom, the “principle of non-contradiction”. This principle holds that contradictory statements cannot claim to be equally valid.1 In other words, S cannot be both P and not P at the same time [¬(S=P)ᴧ(S≠P)]. Black is simply not white [¬ (S = W)] and a coffee cup cannot exist and not exist simultaneously [¬(K = ¬ K)]. It follows, therefore, that one of the statements must always be wrong. 1  The first: Aristoteles, Metaphysik (τὰ μετὰ τὰ φυσικά ) Book (№ IV) Γ 6, 1011b, 13 f. 16 f. 20 f.

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Arguments for the universality of the principle of non-contradiction is also found elsewhere. For example, the encyclical letter “Fides et Ratio2” by Pope John Paul II, also emphasises logic’s absolute universality. It argues that the principle of the non-contradiction,3 as the centrifuge for all philosophical knowledge, represents mankind’s intellectual heritage which, although shared by all, takes different forms (much like its cultural heritage).4 It is not by chance that the encyclical letter also refers to fundamental moral views, which offer great insight into the nature of legal logic and to which it attributes the same fundamental significance as the principle of non-contradiction. Despite the postulate of objectivity, it cannot be denied that logic is also influenced by individual will.5 Throughout history and its various intellectual epochs (including rationalism), logicians have utilised the apparently objective science of logic for their own purposes, beyond the realm of formal logic. More or less subconsciously, they have allowed their unspoken aims to influence their use of logic or have dealt with logical questions in accordance with unspoken values. This is particularly true of the strictly formal “Mathematical Logic” of the late 19th and early 20th centuries, which believed that logic could be used to describe mathematical structures and problems. Eventually, the problem with objectivity was tackled by linguistics. Boole6 and Frege7 as well as Hilbert8, Pierce and Whitehead/Russell9 developed an auton2  Encyclical Letter Fides et Ratio of the Supreme Pontiff John Paul II to the Bishops of the Catholic Church on the Relationship between Faith and Reason of 14. 9. 1998. 3  Described here under “principle of non-contradiction”. 4  John Paul II: Fides et Ratio, nos. 4 and 34. 5  Concerning the following, see Chapter 2.1 and Chapter 2.2. below (both with further references). 6 See: Boole, The mathematical Analysis of Logic, being an essay towards a calculus of deductive reasoning, London 1847, pp. 15 ff.; the same, An Investigation on the Laws of thought, on which are founded the mathematical theories of logic and probabilities, London 1854, p. 27. 7  Frege, Begriffsschrift, eine der arithmetischen nachgebildete Formel Sprache des reinen Denkens, Halle 1879; Frege, Grundgesetze der Arithmetik – Begriff schriftlich abgeleitet jener 1893/1903 I, 1 ff.; concerning the development see also: Frege, Über formale Theorien der Arithmetik, in: Jenaische Zeitschrift für Naturwissenschaften 19 (1886), Supplement Heft), pp. 94 ff. 8  Hilbert, Neubegründung der Mathematik. Erste Abhandlung, in: Abhandlungen aus der Mathematik, 1922, Bd. 1, pp. 157 ff., see also: Hilbert, Gesammelte Werke, Bd. 3, Kapitel 10; the same, Die Grundlagen der Mathematik, Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität, VI. Band (1928); See also: the same, Über das Unendliche, Mathematische Annalen 95 (1926), p. 170; see also: Tapp, An den Grenzen des Endlichen. Das Hilbertprogramm im Kontext von Formalismus und Finitismus, Heidelberg 2013. 9  The latter in its revolutionary Principia Mathematica von 1910 – 1913; Whitehead/Russell, Principia Mathematica, 2. ed. Cambridge 1913.

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omous, formally abstract sign language for the use in logic, which should work independent of values. Through such abstract and strictly formal language, they tried to prevent any subjective influences affecting logical analysis. While such abstract sign language may function in vitro, it cannot – in the view of the author – be used for logical issues, which can only be expressed by natural language. Particularly problematic is therefore its use in law, a field that is geared towards practice.10 On this basis, a historical survey of logic – and legal logic in particular – may be better framed in terms of different philosophical, cultural and even economic developments. That insight guides the following inquiry.

III.  The fundamental problem presented by the history of legal logic Unlike, say, surveys of political and military history or the history of ideas, philosophy or culture, any attempt to describe the history of logic is hampered by two fundamental difficulties: on the one hand, its inability to develop and, on the other, its unequal historical development. 1.  The inability of logic to develop From the outset it must be stated that it is highly debatable whether logic, by its very nature, is capable of development. The assumption that logic is a universal and objective phenomenon (e.g. the principle of non-contradiction), gives rise to the basic question as to whether it is at all capable of development or progress – let alone be considered a product of cultural or philosophical evolution. Logic represents an intrinsic, basic human characteristic that an individual needs to cope with the environment he or she inhabits. It is bestowed on an individual only once and does not form the subject of his or her evolution. Moreover, it is not possible to improve logic qualitatively or dynamically. For example, in a bi-polar logical system there is only one logically right or wrong statement: one answer cannot be more logical or qualitatively better than another (i.e. there are no differing degrees of logic). Therefore, one cannot refer to an historical ‘development’ or ‘progress’ of logic. This historical survey accepts that logic is not capable of development. Whenever reference is made to ‘development’ in this context, it should be regarded not as relating to logic itself but rather to its perception within the evolving intellectual environment. That such an evolution must also affect the perception and significance of logic in terms of its causal connections and intellectual history is a different question. This can be dealt with in an historical overview of logic.

10 

See Chapter III. 11., III. 12. and III. 13. below (with further references).

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2.  Unequal historical development The second difficulty confronting an historical survey of the development of legal logic lies in the fact that the path taken by intellectual history – particularly in relation to legal logic – has been neither linear nor consistent. Developments have not occurred in sequence nor have they complemented each other. Legal logic has not benefited from individual intellectual phases consistently either. There have been fruitful phases, in which legal logic has blossomed, only to be followed by barren phases, whose ignorance of legal logic make it appear nothing more than a legal sub-discipline rather than as a philosophical, intellectual endeavour arising from general, formal logic. In contrast to other fields of science – and logic itself – the development of legal logic appears to be dependent on intellectual history and political developments. This is characteristic of the subject under investigation. 3.  Early beginnings The origins of legal logic are not found in the works of Aristotle, as is often and incorrectly assumed11. The work of the pre-Socratic philosophers shows that they were already studying legal logic. The early age of European philosophy was less concerned with mathematical minutae (which we find so interesting today), than with developing various types of arguments (or better, logical fallacies), with the aim of refuting the arguments of the opposing party. Even at this early stage, such arguments were referred to as “logoi”. This dismissal of earlier forms of legal logic as pure rhetoric in the negative sense of the word (i.e. in the sense of sophistry or pedantic hair-splitting and deceptively dazzling speech) is found today in the continental tradition, which still deems it necessary to separate rhetorical logic from classical and legal logic. This approach has largely dictated the development of logic: indeed, even today, continental philosophy regards it as self-evident that rhetorical forms of argumentation have no place in logic.12 At the same time, they must also be analysed, evaluated and classified along with all the other forms of argumentation using the instruments developed for propositional logic.13 In contrast to the fundamental rules of the modus ponens (familiar from Aristotelian logic and re-applied by the scholastic school), which jurists still use for subsumption on a daily basis, most arguments and procedures relating to “dialectics” were more complex. They are used in discourse to make statements about the subject of debate.14 11  One example of many who proceed sole from logic: Bocheński, Formale Logik. 3. Aufl. 1970, p. 13. 12  For details about this impractical division see Chapters III. 3., III. 4. a) and III.. 4.b) below (all with further references). 13  For details see Chapters III. 4. b) and III. 4. c) below (both with further references).

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This point is illustrated by Protagoras’ “legal paradox”:15 14

The famous Sophist Protagoras provided tuition in sophistry to his pupil Euathlos. It was agreed between the two that Euathlos would only pay the corresponding remuneration once he had won his first court case. Euathlos disappeared for a long time and did not plead any cases. Eventually, Protagoras sued him for the remuneration. He reasoned that either he would win the case and receive remuneration on the basis of the court’s judgement or he would lose. In the latter outcome, Euathlos would have won his first case and therefore be obliged to pay him on the basis of their agreement. Euathlos, trained in sophistry, countered this by arguing that if he won the case he would not have to pay anything. However, if he lost, he wouldn’t have to pay Protagoras anything either owing to their agreement.16

The early age of philosophy (which gave “logic” its name) was characterised by a comprehensive effort to “extrapolate” general rules from the world of phenomena. Already in 600 B.C. Anaximander posited that existence and order were mutually related.17 Later terms relating to the order of things – such as “harmony” (Pythagoras, 570 B.C.), the “general soul of the world” or “logos” (first coined by Heraclitus) suggest that, even at this early stage of philosophy there was an assumption that all things were pervaded by the logos. As a result, thinking (or better still, laws of thinking) reflected a divine universality that provided order or logic. In this sense, Heraclitus posited that “All human laws flow from the one divine law”18 (Γαϱ πάυτες όι άυϑςώπειοι υόμοι ἒύπò ςτοū ἕυòς τοῦ ϴείου). In deducing this one universal, divine law that governed the laws of thought, Heraclitus anticipated one of Leibniz’s fundamental concepts. Leibniz also established that nature and law are based in one uniform, harmonious and universal law.19 Zenon, in: Simplicius: On Aristotle, Physics 1.3–4, London 2004 ff., pp. 140 f., 29 – 23, 2 – 8; Simplicius, Kommentar zu Aristoteles: Sophistici Elenci, pp. 34, 183b 17 – 23 and 34.36. 15  There are many more examples, such as that of the Epimenides-paradox: Russell, Mathematical Logic as Based on the Theory of Types, in: American Journal of Mathematics, Vol. 30, No. 3. Johns Hopkins University Press, July 1908, pp. 222 ff. These and other sophisms often incorrectly deemed to be paradoxes still await a uniform and plausible solution. See Chapters 2.13, 2.3 and 2.5 below (all with further references). 16  The description of the trial works with the breach of the principle of identity. That is to say that in this example Euathlos performs two functions: as a pupil and as a (potential) winner of the case. For a comprehensive analysis see Peter Suber, Protagoras v. Euathlos, a section within: The Paradox of Self-Amendment, Frankfurt 1990 (with further references); see also: Roland Hagenbüchle/Paul Geyer (ed.), Das Paradox: eine Herausforderung des abendländischen Denkens, Würzburg 2002; a resolution of this apparent paradox is offered by Gerhard Vollmer, Paradoxien und Antinomien, Stolpersteine auf dem Weg zur Wahrheit, in: Roland Hagenbüchle/Paul Geyer (eds.) (n.14), pp. 159 ff., 186 f. 17 Erich Wolf, das Problem der Naturrechtslehre, Versuch einer Orientierung, 3. Aufl. 1964, p. 33, referring to Fragment 12; the same, griechisches Rechtsdenken, Bd. 1,19 150, pp. 226 ff., 233 f. 18  Heraklit, Fragment 114; H. Diels & W. Kranz, Berlin 1903 (DK 22 B) / German Hans Zimmermann Berlin 2007. 19  See Chapter III.8. below (with further references). 14 See:

Dieter Krimphove

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If the founding fathers of logic related their universal structures, principles or harmonies to natural phenomena, then one of Plato’s many contributions lies in relating the universal, fundamental law to thought itself. In his later work, Plato also provided a definition of a universal logic derived from the founding fathers of logic. In the fictitious discussion between Socrates, Critias, Timaeus of Locri and Hermocrates of Syracuse (Τίμαιος) it is stated (freely translated), … That God gave us the power of sight so that we may perceive the laws and reasoning that underpin the cosmos and apply them to our own thought processes, …, so that we may model our own, fallible way of thinking on the infallible, divine laws of reason by seeking to imitate them once we have investigated and understood their workings.20 Plato’s definition corresponds not only to the principle of non-contradiction stated in the introduction but to the concept of logic as a law or as possessing universal legitimacy. It is this legitimacy that justifies its generally-binding quality and ultimately results from Plato’s theory of forms (or ideas). It influenced the whole perception of European logic that followed. It is precisely logic’s universal and generally-binding character that separates the European concept of logic from that of the Far East. 4. Aristotle Nowadays, Aristotle is regarded as the true founder of logic. It is correct to say that the system of argumentation that he created has been used from the Middle Ages to the present day. Indeed, syllogism21 – a logical process, which he developed to a particularly refined degree – forms the basis of the subsumption technique22 20  Plato, Timaios; Tim 47a at paras. b-c; in: Plato, Sämtliche Werke in 3 Bänden, 1930 Heidelberg; see also: Gutz (Hg.): Plato, Timaios, Berlin 2013, p. 33, para. 128; see also: Nicolai Hartmann, Platos Logik des Seins, 2. Aufl., Berlin 1965 (first published in 1909), pp. 424 ff. 21  Syllogism (συλ-λογισμός) means literally “to add”. 22 Syllogism: 1. A culpable homicide (P) exists, if one person has caused the death of another person (M). 2. A set his neighbour’s house on fire while the latter was in it (S). The neighbour suffocated on the fumes (M). 3. Therefore, A (S) has committed culpable homicide (P). All elements (M = middle term), (P = predicate), (S= subject) of syllogism can be freely exchanged with the result that there are four possible figures of deductive reasoning.

Figure 1

Figure 2

Figure 3

Figure 4

M f1 P S f2 M

P f1 M S f2 M

M f1 P M f2 S

P f1 M M f2 S

S f3 P

S f3 P

S f3 P

S f3 P

Our example uses figure 2.

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used by jurists today. This shows the influence that Aristotelian logic has exercised over legal theory. However, it is the author’s view that the persisting influence of Aristotelean logic is due to repression of megarian logic23 and its somewhat haphazard historical reception towards the end of the middle ages as well the renaissance in Aristotle’s works in the 19th century. Syllogism is a deductive form of reasoning based on propositions previously believed to be true (endoxa). Aristotle explained this as follows: “Logic is all about finding a method we can use to form a line of reasoning about the problem at hand from a probable (state of affairs) … However, reasoning is an argument which – by making certain propositions – inevitably gives rise to assumptions which are different from those previously held.”24

It is also correct to say that he uses this logic not only to answer the question of what follows from a given premise but also asks the reverse, namely what is the premise for an existing conclusion (ie. invention medii)? This approach assumed great importance for legal logic – especially when examining chains of evidence. a)  The reception of Aristotelian logic or the exclusion of rhetorical legal logic Strange as it may seem, considering Aristotle’s contributions to formal logic, it cannot be denied that his whole work (especially in his later years) resembles a step backwards in the history of legal logic. That is to say that Aristotelean logic (or better, formal logic), shifts both the interest and subject of statements in logic to pure questions of fact.25 In the annex to his ninth book (The Topics), Aristotle deals with sophistry in the relatively short treatise “Rejection of Sophism” (Περὶ σοφιστικῶν ἐλέγχων). He denounces the sophist form of reasoning as rhetorical attempts at deception and fallacies26 and banishes them from his system of logic. Since Aristotle, logic has been separated from rhetoric despite the fact that both tackle similar questions using the same tools and methods of formal logic to attain their different aims.27 The Socratic ideal of logic, namely to persuade the opposing party through force of argument (i.e. the whole questions posed by rhetorical logic), was abandoned once it had been refuted by Aristotle.

23 

Concerning this point, see: Chapter 2.5. below (with further references). Aristotle, The Topics, in: Zekl: Philosophischen Bibliothek, Berlin 1997, Topik I 1, 100a, pp. 25 – 27. 25 This also applies to his approaches in developing a later logic of probability (i.e. “modal logic”). 26  Concerning this see: Übersetzung der Sophistischen Widerlegungen – P.S. Hasper: http://www.philosophie.uni-muenchen.de/lehreinheiten/philosophie_3/personen/hasper/ verg_sem/lv_sose_2011/betrug/sophist_widerleg_d.pdf, pp. 9 ff. 27  For details on this, see Chapter III. 4. below. 24 

Dieter Krimphove

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b)  The consequences of Aristotelian polemic that still resonate today Even today, continental legal logic separates logical fallacy (i.e. a violation of the laws of formal logic) from substantive fallacy (i.e. a logically correct conclusion lacking persuasive argument).28 Unlike Anglo-American logic, continental legal logic excludes the latter from the scope of formal logic. Thereby, many errors in reasoning and argumentation considered to be substantive fallacies also turn out to be violations of formal logic,29 so that there is no justification for distinguishing rhetorical and formal logic. This is particularly apparent in the treatment of the substantive fallacy of modem ponens (sometimes incorrectly referred to as the fallacy of affirming the consequent). This common fallacy results from an erroneous application of deductive reasoning that implies a certain result30. Example of fallacy relating to modem ponens • If the electricity is switched off, the lights will not be on. • The lights are not on. • Therefore, the electricity is not on. Modem ponens mixes up the order of the correctly reasoned conclusion. It does this by confusing phenomenon A (the antecedent) with phenomenon B (the following consequence). As a result, one jumps from the second to the first phenom28  Such as the appeal to fear (argumentum ad metum), appeal to ignorance (argumentum ad ignorantiam), appeal to the middle ground (argumentum ad temperantiam), appeal to prior admission (argumentum ex concesso), appeal to poverty (argumentum ad lazarum), appeal to authority (argumentum ad verecundiam), appeal to experience (argumentum ad lapidem) or tradition (argumentum ad antiquitatem), appeal to the generally-applicable solution (argumentum a tuto), appeal to contradiction (argumentum a post argumentum e contrario), appeal to obvious contradiction (argumentum ad oculos), appeal to constant repetition (argumentum ad nauseam), appeal to exaggerated consequence (argumentum ad consequentiam), argument by logical reasoning (argumentum a priori), argument based on threat (argumentum ad baculum), appeal to vanity (argumentum ad superbiam), appeal to success (argumentum ad crumenam), appeal to hate (argumentum ad odium), hypothetical argument (argumentum ad novitatem), causal argument (Cum hoc ergo propter hoc), utility argument, manipulative exaggeration or belittling, appeal to pity (argumentum ad misericordiam), appeal to morals or ideology, Nazi-comparison argument, appeal to envy (argumentum ad invidiam), argument using personal attack (argumentum ad personam), appeal to common sense, (argumentum ad iudicium), appeal to the silence of the law (argumentum ex silentio), strawman argument, homicide argument, appeal to a thing of greater force (argumentum a fortiori), appeal to common human consent (argumentum e consensu / argumentum consensu gentium), appeal to the majority view (entum ad populum), argument using circular reasoning (argumentum in circulo or petitio principii). 29  For example, the rhetorical fallacy of the “Quarterino terminorum”. 30  According to a recent study, more than 2/3 of all people not schooled in logic accept this kind of material fallacy without criticism.

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enon which serves to invert the order of the correctly deduced conclusion. It is not enough to confirm the existence of the consequence (phenomenon B = no light), in order to arrive at the truth of the preceding cause (here: phenomenon A = electricity switched off). This is because there may be another reason why phenomenon B (the light) may be off (damaged bulb, missing or defect lamp socket, mains, bulb covering etc.). The correct reasoning would have to be: Modus ponens • If the electricity is switched off, the light will not be on. • The electricity is switched off. • Therefore, the light is not on.31 The “modem ponens” can be proved as incorrectly argued in analytical terms and can also be proved as “logically incorrect” using the “truth tables”, which are tools of formal logic.32 Truth table for modus ponens = (A → B ᴧ A) → B (A

→①

B

ᴧ②

A)

w

w

w

w

w

f

f

f

f

w

w

f

w

f

w

→③

B

w

w

w

w

f

w

f

w

w

w

f

w

f

Concerning the substantive fallacy of modem ponens, there is an anomaly in the truth value w of the 6th column. This reveals modem ponens as incorrect not only in terms of argumentation but also formal-logic. Truth table for modem ponens = (A → B ᴧ B) → A (A

→①

B

ᴧ②

B)

w

w

w

w

w

f

f

f

f

w

w

f

w

f

w

→③

A

w

w

f

w

w

w

w

f

f

f

f

w

f

31  De facto the person concerned in modem ponens mixes up steps 2 and 3 of the reasoning. Thereby, he does not deduce a result but rather works with subtle suppositions: whenever the light is not on, the electricity is off. However, there may be other reaons why the light may not be on. 32  A statement is plausible in terms of formal-logic if the final result (column 6 = →3) of all logical operations (→, ᴧ, ¬ ) is true (= w): this is the case with modus ponens.

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c)  Fateful separation of logic and legal logic The historical development of logic shows that legal logic did not follow its own path but rather occurred in other ways, via the “diversion” of formal factual logic. This shift in perspective highlights a fundamental methodological defect in the research of legal logic. 5.  Continuance of “legal logic” in megarian/stoic school of logic The species of a more rhetorical, confrontational logic lived on in the megarian/ stoic school of logic of Apollonius, Diogenes Laertius, Stilpo; Zeno, Theophrastus, Diodoros, Cleanthes, Chrysippus of Soli. This movement in intellectual history ended with Philo shortly before the end of the epoch. It had prominent predecessors such as Epimenides and Plato and developed many other arguments and argumentative techniques. Megarian/stoic logic is characterised by the emergence of numerous sophisms or paradoxes such as the liar-paradox that already existed at the beginning of the sixth century33 and which pre-occupied philosophers such as Plato, Aristotle, Eubulides, Diogenes Laertius, Theophrastus, Philitas of Cos up to Chrysippus. This paradox essentially exists in a self-referential statement that reveals its own untruthfulness. There are several such examples in existence. The most wellknown is that of the Epimenides paradox,34 which Paul the Apostle himself reports in his epistle to Titus (Titus 1.1235). There have been many attempts at a solution and not only in the ancient period of legal logic. Even today, interest in this and similar problems continues unabated.36 However, if one examines the attempted solutions of the Epimenides paradox, one comes away feeling that this philosophical conundrum still awaits a satisfactory solution. Here too, the fateful division between Aristotelean logic and “rhetorical logic” takes its toll. This is because the systems of formal logic that build on the Aristotelian tradition (such as such those of Leibniz, Freges and Russels), fail in their inadequate treatment of paradoxes.37

33  Paradoxon des Epimenides (6th or 7th century B.C.) Epimenides der Kreter stated: “All Cretans are liars.”; see: (Diels-Kranz, Die Fragmente der Vorsokratiker, 2005, I 3B1); see: Russell, Mathematical logic as based on the theory of types, in: American Journal of Mathematics 30 (1908), p. 222.; Rüstow, Der Lügner, p. 40. 34  φευδὀμευος. 35  Paul the Apostle, Epistle to Titus 1,12: εἶπέν τις ἐξ αὐτῶν ἴδιος αὐτῶν προφήτης· Κρῆτες ἀεὶ ψεῦσται, κακὰ θηρία, γαστέρες ἀργαί. One of your own, your own prophet has declared: Cretans are always liars, fierce beasts and slothful gluttons. 36  Concerning the Epimenides Paradox, see: Russell, Mathematical Logic as Based on the Theory of Types, in: American Journal of Mathematics, Vol. 30, No. 3. Johns Hopkins University Press, Juli 1908, pp. 222 ff.

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This essential difference to the conceptual logic of Aristoteles is found not only in the “continuance of sophist rhetoric and argument”. Another characteristic of megarian-stoic school of logic is that its viewpoints and subjects of enquiry differ from those of Aristotelian logic. If the latter was largely pre-occupied with defining terminology and its elements to describe logical processes (i.e., Aristoteles asks: is B attributable to A?), the megarian-stoic school of logic uses methodical questioning in order to determine how claim x can be refuted, thereby revealing its sophist origins (i.e. arguing with an opponent convincingly on the basis of science or ability). 37

Thereby, the line of enquiry pursued by megarian-stoic logic is not limited to individual concepts and their qualities but embraces the statement as a whole. It is this school of logic (and not Aristotelian laws of logic) that formulated and developed the propositional logic that we know today. In comparison with Aristotelian logic, modern formal logic does not attach great significance to the propositions of megarian-stoic logic. This belies the latter’s strong emphasis on logical argumentation.38 For example, the megarian-stoic school precisely describes the conditions under which arguments are to be deemed plausible (περαυτιχοί) or implausible (ảπεραυτιχοί). Like Aristotelian or formal logic, the megarian/stoic school seeks to prove the plausibility of statements by adhering to a certain logical procedure. Here too, the megarian-stoic school makes a very strong and formal distinction between an argument, the different ways it is used and the sequence of argumentation. Thereby, it distinguishes between the logicality of arguments (i.e. their formal accuracy and the truth) and divides truthful statements into evidential and non-evidential statements. Early on in the history of philosophy, the megarian/stoic school discovered just how problematic semantics (language) could be in constructing and assessing logical conclusions. This difficulty was thoroughly dealt with 2,100 years later in the works of Hilbert, Russel, Davidson, Turing, Tarsky and Wittgenstein (albeit in the context of formal logic). Megarian/stoic logic also divides the substantively plausible types of argumentation into those which are: • generally plausible (homonymous)39 and • syllogistic (hypothetical) arguments, that are based on partial, unprovable pro­ positions or rules.40 Epimenides paradox has been tackled in different epochs. This also shows the dependence of logic and legal logic in particular on the influences in intellectual history (see above). 38  Dihairesis, διαίρεσις; Plato, The Sophist; Friedrich Schleiermacher, Der Sophist, in: Erich Loewenthal (ed.), Platon: Sämtliche Werke in drei Bänden, Bd. II, 8. Aufl., Darmstadt 2004, 218c–219a, 221c. 39  For instance: it is wrong that when it is day, it is night. It is day. Therefore, it is not night. 40  For instance: X states that it is day. X is telling the truth. Consequently, it is day. 37 The

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In the latter case, megarian/stoic logic distinguishes certain types of propositions on the basis of their linguistic formulation41 and rejects many arguments as lacking method (ảμεϑὀδως περαίυουτες) and logic.42 This gives rise to an unclear causal distinction regarding the language versions of logical conclusions43 and suggests that the megarian-stoic school was unable to manage the burden of considering individual cases in a systematic and methodical way. It is astounding that the megarian/stoic school already anticipated exceptions from the evidential rules for hypothetical arguments and (besides its linguistic distinctions) the special treatment of modal logic. Admittedly, the basis for this was provided by Aristoteles or Scotus in the late middle ages or Leibniz in the modern era. However, their full significance was only appreciated and realised in the 20th century (1921 by Lewis, or 1936 by Langford/Lewis or 1963 by Kripke). Early on in its development, the megarian/stoic school also developed “truth tables”,44 which it used to test the plausibility of argumentation in cases where one or both premises of the proposition were true or untrue. The truth table system was adopted in the 19th and 20th century by Frege45, Pierce46 and, in particular, Wittgenstein. 6.  Logic and legal logic in late antiquity The ancient world did not offer any alternatives of its own to either Aristotelian or megarian/stoic logic. As exemplified by Aristo of Alexandria and others,47 this age of intellectual history was more interested in refining details and developing the categorisation of the four figures or moods48 to which it added some inferences 41  Alexander von Aphrodisias, in: Wallies (ed.): Alexander von Aphrodisiensis: Aristoteles Analyticorum Priorum Liberu I Commentarium Berlin 1883, pp. 373, 29 – 35, 22, 17 ff. 345, 27 ff. 21, 30 – 22,1. 42  For instance, concerning arguments that only show one premise. 43  Diogenes Laertius, in: Cobet, De clarorum philoophorum vitis, Dogmatibus et apophtegmatibus, Paris 1888, (DL VII 79 – 81); Sextus Empiricus, Adversus Mathematicos, in: Mutschmann: Πυρρωυείον ύποτυπώσεων libros 3 continens, Leipzig 1912. Adversus Dogmmaticos libros quinque (Adversus Mathematicos libros VII – XI) Leipzig 1914, Bd. VIII, pp. 223 – 228, see also: Cicero, Topica 57 M. Tullius Cicero: Topica. Edited, translated and explained by Karl Bayer, 1993. Cicero, Top 57. 44  See: Sextus Empiricus, Adversus Mathematicos; in: H. Mutschmann, Πυρρωνείον ύποτυπώσεων, Leipzig 1913, Vol. VIII, p. 113 f.; see also, Benson Mates, Stoic Logic. University of California Press, Berkeley 1953 (University of California Publications in Philosophy, 26), pp. 42 ff. 45 Begriffsschrift, eine der arithmetischen nachgebildete Formel Sprache des reinen Denkens, Halle 1879, pp. 5 ff. 46  Peirce, The simplest mathematics 1902, in: Collected Papers Vol. IV, pp. 189 ff, 212 f. 47  Apuleius Peri hermēneías (lat.: De interpretatione) 213.5–10, Mariano Baldassarri (ed.): Apuleio, L’interpretazione, Como 1986. 48  See Chapter III. 4. above.

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of its own. Accordingly, the various schools published a number of commentaries. Arguably, the most significant of these was the compendium of Aristotelian logic by his pupil Theophrastus. 49 Later, independent categorisations can be found in the logic of Boethius.50 This age is remarkable for its tendency to subsume terminology into an almost geometric system. Apuleius was the first to attempt to refine Aristotle’s logical square,51 in which antonyms of predicate logic are shown to oppose each other in the corners. In the case of legal logic, this depiction is specifically elaborated by additional criteria. Some authors believed it was necessary to expand the square to include 12 or 24 corners in order to accommodate the peculiarities of the normative law of legal logic.52 7.  The legal logic of the Middle Ages The fact that the scholastic school was preoccupied with Aristotelian logic was largely due to the limited sources available to scholars in the Middle Ages. Although the megarian-stoic logic was just as important as Aristotelian logic in solving legal logical problems53, it was largely lost during the Middle Ages and almost completely overshadowed by Aristotelian – scholastic logic. The re-discovery of megarian/stoic logic in the 20th century was due to the efforts of Łukasiewicz in 1934.54 As a result, the megarian/stoic school has lacked almost 2000 years of influence from which legal logic could have benefitted. Unfortunately, Łukasiewicz’s work was not continued by later scholars and the 20th century also failed to reinvigorate the school of megarian/stoic logic. In particular, scholars preferred to concentrate on other schools of logic (e.g. mathematical logic55), thereby preventing its revival. Bocheńsky, La logique de Theopraste, 1947, pp. 27 ff. 128 ff. Boetius, De hypotheticis syllogismis, in: librum Aristotelis de Interpretatione Commentaria, in: Opera Omnia (Migne, Patrologie cursus completus, Patres Ecclesiae Latinae) Paris 1860, I 837, D – 838, 835 A – C ; see also: 846 A ; 848 A ; 852 A, B; see van den Dries­ sche, Le “De syllogismo”, pp. 294 – 299. - 13. 51 See: Apuleius, Peri hermēneías, p. 269, in: P. Thomas (ed.) Apuleius Madaurensis: Opera quae supersunt III opera, Leipzig 1938, Vol. III 180,18; Chr. Thiel: Logisches Quadrat, in: Jürgen Mittelstraß (ed.): Enzyklopädie Philosophie und Wissenschaftstheorie, 2004, Bd. 3, p. 423. 52 See: Joerden, Logik im Recht, 2. Aufl. 2009; pp. 197 ff., 218 ff. (with further references). 53  See Chapter III. 5. above. 54 See: Benson Mates, (Stoic logic and the text of Sextus Empiricus, in: American Journal of Philosophy, Vol. 70, 1949, pp. 290 f.) and Michael Frede (Die stoische Logik, Abhand­ lungen der Akademie der Wissenschaften in Göttingen, Phil.-hist. Kl. 3. Folge Bd. 88, Göttingen 1974) wrote monographs on megarian-stoic logic. The sources are still limited today and one is dependent on e.g. Sextus Empiricus, Diogenes Laertios and Galen. 55  For more on this see Chapter III. 11. below (with further references). 49 See: 50 

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Returning to the medieval history of intellect and logic, the question arises whether it is even possible to distinguish the Middle Ages from antiquity and modern times. After all, the term “Middle Ages” was only coined by the Renaissance to emphasise its own values and superiority. Even if one accepts this term as “common sense”, the medieval contribution to historical development was not simply limited to the reception of ancient and Aristotelian texts (the latter were particularly important for legal logic).56 Medieval scholars studied the sources of ancient logic that were available and thereby extracted their own concepts and forms of logic.57 Scholars of the Middle Ages typically deduced logical rules from their physical manifestations. As a result, logic was no longer confined to describing the interrelationship between natural phenomena and now operated with concepts reasonably deduced from circumstances.58 Medieval logic separated the subject of enquiry from the method of enquiry, thereby freeing logic to focus on purely formal elements.59 This gave rise to a form of formal logic, which as “secundam intentionem”,60 was solely concerned with analysing the laws of thought rather than investigating scientific questions of truth. Accordingly, if the logical process were valid (i.e. 56 

There are different epochs of intellectual history. The following categorisation may be crude but it is sufficient for the purposes of illustrating the historical intellectual development of legal logic. It reflects the philosophical steps of development rather than historical epochs: • Early Middle Ages: Alcuin († 804); Theodulf of Orléans († 821); Alcuin’s pupils (8/9th centuries.); John Scotus Eriugena (9th century); Silvester II († 1003), Abbo of Fleury († 1004); Notker III († 1022); Anselm of Canterbury († 1109); • High Middle Ages: Gerlandus von Besançon (12th century); Peter Abelard († 1142); • Late Middle Ages: Robert Kilwardby († 1279); Albertus Magnus († 1280); Lambert of Auxerre (13th century); John Duns Scotus († 1308); • End of the Middle Ages: Ramon Llull († 1316); William of Sherwood (†  1266 – 1272); Petrus Hispanus (13th century); William of Ockam († 1347); Jean Buridan († after 1358); Walter Burley († after 1344); Ralph Strode (14th century); Albert of Saxony (14th century); Paulus Venetus († 1429); Peter Tarteretus († approx. 1522); Stephan de Monte (15th century); • Beginning of the early modern period: Vinzenz Ferrer († 1419); Petrus Ramus († 1572). 57  At this point it should once again be pointed out that this contribution does not seek to provide a complete outline of the history of logic. There are a number of extensive surveys which serve this purpose, including: Feys: De entwikkeling van het logisch denken, Antwerpen 1949; De Cesate, Evollución de la lógica, in: Rev. De. Ciec, econ. 1941, pp. 1 ff. Enriques, Évolluion de la logique, Paris 1926; Ueberweg, Grundriss der Geschichte der Philosophie, 5. Bd. 1951 – 1953. 58  Concerning the theory of “second intention”, see Thomas Aquinas, De potentia 9,4, c; the same: Summa theologika I, XXVIII 1  f.; William of Ockham, Summa Logica I 4, pp. 3 – 22; see also: Albert of Saxony, Albertueii Perutilis Logica 9,4. 59 See, in particular: Buridan, Shyreswood, Syncategremata, 28; see also: Ockham, Summa Logica I, 4, pp. 3 – 22. 60  Hervaeus Natalis, De intentionibus secundis Venedig, um 1500, Bd. I 1 fol. a. iii. Rb.

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plausible) then it would be irrelevant whether the resulting statement was materially correct or not. This abstraction is very important for legal logic. It eliminated the casuistry of various conclusions61 that still existed in the stoic school and created generally binding rules of logic to link the statement in order to arrive at a formally valid result.62 Accordingly, the scholastic school of medieval logic focussed on the various deductive techniques and types of statement: medieval logic combined the elements (M,P,S) of the four syllogisms63 identified by megarian-stoic and Aristotelian logic to create many other syllogisms or syllogistic figures64 whose propositional character they then tested and presented in detail.65 Term logic (or categorical syllogism) was another school of logic characteristic of the Middle Ages. It gave rise to a wide-ranging theory in which categorical propositions were used to form different categories of syllogism.66 Generally-speaking, the technique of combining different elements of syllogisms67 and using mnemonics to communicate the result68 played an important role in medieval logic. Leaving aside the question whether Albertus Magnus was actually the first to introduce the combination technique from Arabian scholarship,69 this technique of scholastic logic also contributed to the expansion of human knowledge.70 61 

See Chapter III. 5. above. Approaches were already developed in: Abbo of Fleury, Über hypothetische Syllogismen (lat.: De syllogismis hypotheticis; Über kategorische Syllogismen (lat.: De syllogismis cathegoricis); see also: Boethius, De hypotheticis syllogismis 875 B. 63  See Chapter III. 4. above. 64 Syllogisms: • Figure 1: Barbara, Celarent, Darii, Ferio, Barbari, Celaront • Figure 2: Baroco, Cesare, Camestres, Festino, Camestrop, Cesaro • Figure 3: Bocardo, Darapti, Datisi, Disamis, Felapton, Ferison • Figure 4: Bamalip, Calemes, Dimatis, Fesapo, Fresison, Calemop. 65  Combing the individual components of a logical form not only with and (∧,) or (∨), leading to (→) is identical (=), either or not (⊕) inter alia (¬,∣⟹, ⊃ →, ↔, >− ¬q) → Pr(q) In De legum interpretatione, rationibus, applicatione, systemate written in 1678/167933 (DLI) Leibniz defines presumptions as follows: It is a presumption if the proposed statement [necessarily34] follows from what is […35] true, without any requirement other than [negative ones36], namely that no impediment [for its truth 37] obtains. Therefore, we will always have to declare ourselves in favor of he who has the presumption unless the other party38 demonstrates the contrary. Such is most of the moral reasoning39.40, 41 Armgardt (2015), pp. 51 – 69. Armgardt (2015), pp. 52 ff. (54). 32  A VI 1, p. 472: Omne ergo praesumendum est facilius, non contra. Quia etiam omnis pars est minor toto, non omne minus est pars majoris. 33  A VI 4 C, pp. 2782 ff. 34  Dascal (2008), p.86 omits necessario. 35  Dascal adds surely. 36  Dascal (2008), p. 87: “the negative one”. 37  Addition of Dascal. 38  Dascal: someone else. 39  Dascal: “are … reasonings”. 40  Translation according to Dascal (2008), pp. 86 f. 41  A VI 4 C, p. 2789. PRAESUMTIO est, si ex his quae vera esse constat necessario sequitur enuntiatio proposita, nullis alliis praeterea requisitis, nisi negativis, ut scilicet nullum extiterit impedimentum. Itaque semper pro eo pronuntiandum est, qui praesumtionem habet, nisi ab altero contrarium probetur. Et tales sunt pleraque rationcinationes in moralibus. 30  31 

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Leibniz makes use of a special form of a strict implication (necessario sequitur). He who has the advantage of the presumption only has to prove the truth of circumstances that strictly imply the controversial fact at issue (enuntiatio proposita) if there is no impediment (impedimentum).42 But the other party at court has the possibility to prove the contrary43 and carries the burden of proof. Let C represent the circumstances being true, F the controversial fact, I the impediment and □ the symbol of necessity. Then we can write the following, making use of some kind of logical language (such as Constructive Type Theory) where true can be expressed at the object language level : □([C ∧ ¬I] ↔ F) true (provided C true)

(where C true amounts to establish that there is some kind of evidence a in Court for C) We need the bi-conditional, because the party fighting against the presumption wins if it can prove I. We also have to consider that C is certainly true (vera esse constat) and it is only uncertain if I or ¬I. The latter means that the party fighting against the presumption has to prove I to win the case – otherwise this party loses the battle. For this reason, concerning the winning strategy, the truth value of F only depends on I or its negation. In other words, since we already know that C is true the debate will only concern the truth or the falsity of I. Thus, from the viewpoint of the strategy the truth value of F depends only on the value of ¬I (provided, as mentioned above that we know C to be true) ¬I ↔ F Another possibility to reconstruct the Leibnizean idea of presumptions could be to make use of the non-monotonic logic of presumptions developed by Prakken and Sartor.44 Making use of their inference system IS the impediment “I” would be interpreted with the aid of a meta-rule r2 as follows:45 r1: C => F This means that you have to prove C for F. The symbol => shows that the rule is defeasible (not strict). r2: I => ¬appl (r1) This means: if there is an impediment I, r1 is not applicable or r1 is overruled by r2. Of course, it is not at all easy to define impedimentum. We find this idea already 7 years earlier in a letter to Chapelain (1670): “…uti quorum praesumptio contrariâ probatione evacuatur, eorum praesumptio, si non nulla, saltem nulli aequivalens, id est elisa est.” Cf. Busche (2003), pp. 363 ff. A II 1, 50 – 56. 44  Prakken/Sartor (2006), p.  176 – 185. 45  Prakken/Sartor (2009), p.  176 – 178. 42  43 

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V.  A Formal Model of Equity In his EJN Leibniz developed his ideas about equity in a very strict argumentation making use of the concepts of innoxia utilitas (explicitly) and of something similar to the caution damni infecti of Roman Law (implicitely): Ut lucrum meum minus postponam tuo majori […] amicitia exegit. Sed non statim aeqvitas. […] Ut tibi utilitatem mihi non innoxiam vel etiam mihi utilem praestem, à te cogi non possum. Ut necessitatem, possum. Hoc est principium aeqvitatis. Damnum ferre cum recipiendi certitudine seu credere aeqvum est, qvia est utilitas innoxia. Qvin et miseriam aliqvam ferre cum certitudine alterius contra vitandae est utilitatis. Imò fortasse videor me cogi posse ad praestandam innoxiam imò utilem utilitatem, si mihi cavetur de innoxietate.46

U (x,y) = x is useful for y N (x,y) = x is necessary for y I (x, y) = x is innoxious for y A (x) = x is an action (e.g. to give an object to somebody else) P (x) = x is an indulgence (e.g. to suffer a damage) S (x,y,z) = x presents y security for z O (x, y, z) = x has a claim against y for z Plain (x)= x is plaintiff Def (x) = x is defendant A logical reconstruction of this text could be: Principle 1: ∀x∀y∀z {A(x) ∧ Plain(y) ∧ Def(z) ∧ U(x; y) ∧ [¬I(x; z) ∨ U(¬x; z)] → ¬O (y; z; x)}

The formula reads as follows:

For all x, y and z the following applies: If x is an active doing and y is plaintiff and z is defendant and x is useful for y but at the same time x is not innoxious for z or non-x is useful for z, then y won’t have an entitlement to x against z. In contrast, when the other person necessarily needs the item: … Ut necessitatem, possum. Hoc est principium aequitatis.

Principle 2: ∀x∀y∀z {A(x) ∧ Plain(y) ∧ Def(z) ∧ N(x; y) ∧ [¬I(x; z) ∨ U(¬x; z)] → O (y; z; x)}

The formula reads as follows:

For all x, y and z the following applies: 46 

A VI 1, p. 444.

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If x is an active doing and y is plaintiff and z is defendant and x is necessary for y and x is not innoxious for z or non-x is useful for z, then y will have an entitlement to x against z. The necessity for the other person is thus predominant over my loss of benefit. Therefore, there is an obligation. Now a thought comes up, which reminds me of the cautio damni infecti being combined with the idea of the innoxia utilitas. It deals with the case where I will have to incur a loss if the other one provides a security for its refund. It is therefore about a passive damnum ferre resp. miseriam ferre instead of an active praestare: Damnum ferre cum recipiendi certitudine seu credere aequum est, quia est utilitas innoxia. Quin et miseriam aliquam ferre cum certitudine alterius contra vitandae est utilitatis.

Principle 3: ∀x∀y∀z {P(x) ∧ Plain(y) ∧ Def(z) ∧ U(x; y) ∧ S[y; z; I(x; z)] → O (y; z; x)}

For all x, y and z the following applies:

If x is a sufferance and y is plaintiff and z is defendant and x is useful for y and if y provides a security for x being innoxious for z, y will have an entitlement to x against z. In other words: There is a passive duty to suffer a loss when there is a security deposit47. According to Leibniz this would correspond to the innoxia utilitas. Conclusively Leibniz considers whether this principle can also be transferred to an active praestare. However, he has doubts: … Imo fortasse videor me cogi posse ad praestandam innoxiam imo utilem utilitatem, si mihi cavetur de innoxietate.

Principle 4?: ∀x∀y∀z {A(x) ∧ Plain(y) ∧ Def(z) ∧ U(x; y) ∧ [I(x; z) ∨ U(¬x; z)] ∧ S[y; z; I(x;z)] → O (y; z; x)} ?

For all x, y and z the following applies:

If x is an active doing and y is plaintiff and z is defendant and x is useful for y and if y provides a security for x being innoxious for z, then y will have an entitlement to x against z? Leibniz doubts whether there is a duty to actively grant the innoxia utilitatis when a security is provided. In my opinion, this fragment of the EJN shows that Leibniz wanted to specify the blurry term of the aequitas with the help of the concepts of innoxia utilitas and cautio damni infecti. In the core he works formally, which helps to transfer his thoughts into formulas.

47 

Cum recipiendi certitudine means: with certainty to get it back.

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VI. Conclusion Leibniz was one of the most fruitful legal theorists of all time. He developed new ideas in both fields logic and law. Far beyond the standards of jurisprudence of his time still in the 21th century his works about logic and law have to be detected by logicians and jurists.48 These few remarks may be helpful for that.

References Armgardt, M. (2001): Das rechtslogische System der Doctrina Conditionum von G. W. Leibniz, Computer im Recht, Bd. 12, Marburg: Elwert 2001. – (2015): Presumptions and Conjectures in Leibniz’s Legal Theory, in: M. Armgardt/P. Canivez/S. Chassagnard-Pinet (ed.), Past and Present Interactions in Legal Reasoning and Logic, Springer 2015, pp. 51 – 69. – (2016): The Role of aequitas in Leibniz’s Legal Philosophy – a formal reconstruction, in: W. Li (ed.), “Für unser Glück oder das Glück anderer”, Vorträge des X. Internationalen Leibniz-Kongresses Hannover, 18.-23. Juli 2016, Band VI, Hildesheim 2017, pp.  305 – 314. Artosi, A./Pieri, B./Sartor, G. (2013): Leibniz: Logico-Philosophical Puzzles in the Law, Dordrecht: Springer, 2013. Artosi, A./Sartor, G. (2016): Leibniz as Jurist, in: M. R. Autoguazza, The Oxford Handbook of Leibniz. Boucher, P. (2008): Leibniz: What kinds of legal rationalism?, in: Leibniz: What kind of rationalist? ed. M. Dascal, 231 – 249, Dordrecht: Springer. Dascal, M. (2008): G.W. Leibniz – The Art of Controversies, Dordrecht: Springer 2008. Kalinowski, G./Gardies, J. L. (1974): Un logicien déontique avant la letter: Gottfried Wilhelm Leibniz, ARSP 60 (1974), pp. 79 – 112. Lenzen, W. (1990): Das System der Leibniz’schen Logik, Berlin: de Gruyter 1990. – (2001): “Zur Logik alethischer und deontischer Modalitäten bei Leibniz”, in: W. Stelzner/M. Stöckler (eds.), Zwischen traditioneller und moderner Logik – Nichtklassische Ansätze, Paderborn (mentis) 2001, pp. 335 – 351. – (2004): Calculus Universalis. Studien zur Logik von G. W. Leibniz, Paderborn: mentis 2004. – (2005): “Leibniz on Alethic and Deontic Modal Logic.” In Leibniz Et Les Puissances Du Langage, ed. by Berlioz, Dominique/Nef, Frédéric. 341 – 362. Paris: Vrin, 2005. Magnier, S. (2015): Suspensive Condition and Dynamic Epistemic Logic: A Leibnizian survey, in: M. Armgardt/P. Canivez/S. Chassagnard-Pinet (ed.), Past and Present Interactions in Legal Reasoning and Logic, Springer 2015, pp. 72 – 94. Martin-Löf, P. (1984): Intuitionistic Type Theory – Notes by Giovanni Sambin of a series of lectures given in Padua, June 1980, Naples: Bibliopolis, 1984.

48  Very helpful is the translation of De casibus perplexis into English. Artosi/Pieri/Sartor (2013).

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Prakken, H./Sartor, G. (1996): A dialectical modul of assessing conflicting arguments in legal reasoning. Artificial Intelligence an Law 4. 331 – 368, 1996. – (2006): Presumptions and burdens of proof, in: van Engers, T. (ed.), Proceedings of the Nineteenth Annual Conference on Legal Knowledge and Information Systems (JURIX), pp. 176–185. IOS, Amsterdam. Poser, H. (1969): Zur Theorie der Modalbegriffe bei G. W. Leibniz. Wiesbaden: Franz Steiner 1969. Rahman, S. (2015): On Hypothetical Judgements and Leibniz’s Notion of Conditional Rights, in: M. Armgardt/P. Canivez/S. Chassagnard-Pinet (ed.), Past and Present Interactions in Legal Reasoning and Logic, Springer 2015, pp. 51 – 69. Schepers, H. (1965): Zum Problem der Kontingenz bei Leibniz. Die beste der möglichen Welten, in: Collegium philosophicum, Studien, Joachim Ritter zum 60. Geburtstag, Basel 1965, pp. 326 – 350. – (1975): Leibniz’ Disputationen ‚De Conditionibus‘: Ansätze zu einer juristischen Aussagenlogik, in: Akten des II. Internationalen Leibnizkongresses in Hannover, Wiesbaden 1975, Bd. IV, S. 1 – 17. Thiercelin, A. (2011): Epistemic and practical aspects of conditionals in Leibniz’s legal theory of conditions: In Approaches to legal rationality, ed. D. M. Gabbay/P. Canivez/S. Rahman/A. Thiercelin, 203 – 215. Dordrecht: Springer.

Two Faces of Legal Reasoning: Rule-Based and Case-Based By Bartosz Brożek Bartosz Brożek

I. Introduction In this chapter I would like to substantiate the thesis that legal reasoning is never purely rule-based nor case-based, as it always requires a kind of interplay between abstract rules and concrete legal decisions. In order to do so, I begin by formulating two thought experiments: one, in which a highly abstract normative order is imagined and its limitations analysed; and the other, which considers a normative order consisting of particular cases only and pinpoints its failure to deliver a solid foundation for legal decisions. I further argue that the problematic features of purely abstract and purely concrete normative systems detected in both experiments are also present in, respectively, the civil law and the common law traditions. I conclude by indicating that there is no functioning legal system without a constant “dialogue” between the abstract and the concrete.

II. Two Thought Experiments Let us begin by carrying out two thought experiments. The goal of the first is to understand the limitations of legal systems which consist solely of abstract rules. In order to determine those limitations, it is reasonable to analyse an extreme form of such a system. Therefore, we will investigate some logical aspects of an imaginary legal system which has only one universal rule of conduct. This will enable us to clearly identify the problems that accompany the utilisation of any normative system which consists of abstract rules only. The second thought experiment, in turn, will concern a different approach to constructing legal orders. We will imagine a normative world in which there are no abstract rules, only particular obligations. In this way, the limitations of the “concrete” legal thinking will be exposed. Let us consider first the following situation. A legal system – LS1 – consists of only one, highly universal norm, say: (N1) Good should be done.1 1  This example is taken from Thomas Aquinas’ view of the natural law. He believes that the highest norm of this normative order is bonum est faciendum, malum vitandum. Some of the commentators of Aquinas’ thought claim that from this general norm all our rights

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This norm can be formalised in the first-order extension of the standard deontic logic as: (1) ∀xO(GOOD(x))

where O is the deontic operator “it ought to be the case that”, and GOOD is a predicate which stands for ‘does good’. Let us further assume that LS1 is complete, i.e. it can serve as the basis for answering any legal question. Moreover, let us agree – for the sake of simplicity – that legal questions concern whether there exists an obligation of a concrete person to perform some particular action. Thus, a legal question may be presented as a set {O(ACTION(name)), ~O(ACTION(name))}, where ACTION is a predicate describing some particular action and name is a proper name of a concrete individual. The problem we face, therefore, is to determine, on the basis of whether

(1) ∀xO(GOOD(x))

(2’) O(ACTION(name))

or (2’’) ~O(ACTION(name))

The only way to do this is to assume that the legal system LS1 establishes an obligation of an individual in the form O(ACTION(name)) if this obligation is derivable from (1), and otherwise establishes no such obligation (i.e., ~O(ACTION (name)) is true). The problem is that O(ACTION(name)) does not follow logically from ∀xO(GOOD(x)) alone. What we additionally need is what may be called ‘concretisation rules’. In the standard deontic logic the following rule of inference is valid:2 If ⊢ A→B then ⊢ OA → OB

where A and B stand for certain courses of action. Therefore, in order to get (2’) from (1) it is necessary to establish that (3) ∀x(GOOD(x) → ACTION(x))

If doing good involves performing ACTION, then if one ought to do good, one ought to perform ACTION: (4) ∀x(O(GOOD(x)) → O(ACTION(x)))

from which by universal instantiation it follows that:

(5) O(GOOD(name)) → O(ACTION(name)) and duties follow deductively. Cf. G. Kalinowski, Le Problème de la vérité en morale et en droit, E. Vitte 1967. 2 Cf. McNamara, Paul, “Deontic Logic”, The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta  (ed.), URL = .

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Since from (1), again by universal instantiation, it follows that (6) O(GOOD(name))

we may conclude from (5) and (6) by modus ponens that (7) O(ACTION(name))

Moreover, if there was no such deductive passage from (1) to (7), i.e. if there was no concretisation rule in the form of (3), we would be forced to conclude that ~ O(ACTION(name)). This shows that in the case of highly abstract normative system the key role is played by concretisation rules. The problem is: where do they come from? What are the bases for formulating them? Let us observe that concretisation rules such as (3) are non-normative, in the sense that they involve no deontic operators (although they are formulated with the use of normatively-loaded concepts such as ‘good’). For example, a particular concretisation rule may look as follows: (8) ∀x(GOOD(x) → PAY_TAX(x))

which says that if someone does good, then she pays taxes. As soon as we consider this example, it becomes clear that the formulation of the concretisation rules is not an easy task. It amounts to imagining a deontically perfect world, i.e. a world in which everyone behaves in the desired way. It is a world in which everyone pays taxes, does not steal or kill anyone, etc. The problem is that one should rather speak of a set of deontically perfect worlds, not a unique such world. For example, in a dentically perfect world the natural environment is protected - but there are many particular ways in which such a protection may be implemented. Plastic bottles may be recycled or their production may be banned. Therefore, if doing good requires protecting the natural environment, both a world in which plastic bottles are recycled, and a world in which they are not manufactured at all, are deontically perfect. In this way we get two incompatible concretisation rules: (9’) ∀x(GOOD(x) → RECYCLE_PLASTIC_BOTTLES(x))

(9’’) ∀x(GOOD(x) → ~PRODUCE_PLASTIC_BOTTLES(x))

This point may be made also in a different way. In the theory of obligations a distinction is introduced between individual and group obligations3. An individual obligation is a duty of one concrete person, while group obligations are to be realised by groups of people. Importantly, the category of a group ought may be further divided into two subsets: obligations that may be fulfilled by the actions of all the members of the group only (e.g., during the lecture students should be silent) and those which may be fulfilled by the action of some subgroup of the group under obligation (e.g., students should prepare the blackboard before the lecture). It is convenient to refer to the former type as proper group obligations, and to the latter as improper group obligations. Now, I posit the abstract obligation to do good is 3 Cf.

J.F. Horty, Agency and Deontic Logic, Oxford University Press, Oxford 2001.

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an improper group ought. Various particular good actions may be undertaken by different individuals yielding the same deontically acceptable outcomes. The protection of the natural environment may be realised by the manufactures who do not produce plastic bottles, or by the consumers who recycle them. In other words, the abstract duty to do good is multiply realisable: there is always more than one way to find oneself in (one of) the deontically perfect worlds. The general moral from the above considerations is that a normative system of purely abstract rules is never self-sufficient: it cannot constitute the sole basis for arriving at a particular duty of a particular person. This is the case for purely logical reasons: any system of abstract rules necessarily expresses improper group obligations and hence may be realised in a number of ways. In order to better grasp this point let us contrast normative considerations with physics. A physicist’s goal is to uncover a unique set of laws which govern the actual world; meanwhile, a lawyer or a moralist imagine sets of worlds which are deontically perfect. Those worlds differ from one another, and hence represent different sets of particular obligations of concrete persons. It follows that – to a certain extent at least – any abstract normative system must be augmented by particular decisions in particular cases. The dream of developing a complete system of abstract rules of conduct, similar to an axiomatic system, can never be fulfilled. The second thought experiment is the following. Let us assume now that in a different legal system, LS2, there are no abstract norms. What we have is only a finite number of particular cases, in which an obligation of a particular agent is established. In order to capture this, we need to use first order deontic logic: (Case 1) SELLS_GOODS(a) FOREIGNER(a) RESIDENT(a) SELLS_ALCOHOL(a) O(PAY_TAX(a))

(Case 2) SELLS_GOODS(b) ~FOREIGNER(b) RESIDENT(b) SELLS_ALCOHOL(b) O(PAY_TAX(b))

(Case 3) ~SELLS_GOODS(c) ~FOREIGNER(c) RESIDENT(c) ~SELLS_ALCOHOL(c) ~O(PAY_TAX(c))

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(Case 4) SELLS_GOODS(d) FOREIGNER(d) ~RESIDENT(d) ~SELLS_ALCOHOL(d) ~O(PAY_TAX(d))

Thus, LS2 addresses the obligations of four different persons, a, b, c, and d. The persons a and b ought to pay tax, while c and d have no such obligation. Moreover, we know that a sells goods, including alcohol, is a foreigner and a resident in the jurisdiction governed by LS2; b also sells goods, including alcohol, is not a foreigner and resides in the LS2 jurisdiction; c does not sell any goods, is not a foreigner and is a resident, while d sells goods, but not alcohol, is a foreigner and not a resident. Let us assume now that we have another person, e, and we need to decide whether e has the obligation to pay tax. We know that e sells goods, but not alcohol, is a foreigner and a resident: (Case 5) SELLS_GOODS(e) FOREIGNER(e) RESIDENT(e) ~SELLS_ALCOHOL(e)

In order to make a rational, not a random decision in the matter at hand, we need to treat e in the similar way as a, b, c, and d. The reasonable way to proceed would be to discern some pattern in the already decided cases 1 – 4, or – in other words – to spell out a universal and abstract rule or rules that govern those cases. The problem is that there is no way to do it in a uniform way. The decisions in the cases 1 – 4 are compatible with different (sets of) rules, such as: (R1) ∀x((SELLS_GOODS(x) ∧ RESIDENT(x)) → O(PAY_TAX(x))) (whoever sells goods and is a resident, ought to pay tax). (R2) ∀x(SELLS_ALCOHOL(x) → O(PAY_TAX(x)) (whoever sells alcohol, ought to pay tax). (R3) ∀x((SELLS_GOODS(x) ∧ x≠d) → O(PAY_TAX(x))) (whoever sells goods and is not the person d – who apparently enjoys a personal exemption from paying taxes – ought to pay tax).

This shows that the ‘hidden rules’ which govern the decisions in LS2 may be reconstructed in various, incompatible ways; the crucial point is that all the rules (R1) - (R3) yield the same normative outcomes in cases 1 – 4: a and b ought to pay taxes, while c and d do not. The problem is with the new Case 5. If we reconstruct the norm governing LS2 as (R1) or (R3), we will conclude that e ought to pay tax; if instead we accept (R2) as the correct reconstruction, e will have no such obligation. This analysis may be generalised along the lines of Quine’s underdetermination thesis. Quine’s claim pertains to theoretical discourse and states that no amount of

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evidence (i.e., the sentences that express the facts we observe) gives rise to a unique theory. Any theory „is underdetermined by past evidence; a future observation can conflict with it. Naturally it is underdetermined by past and future evidence combined, since some observable event that conflicts with it can happen to go unobserved. Moreover many people will agree, far beyond all this, that physical theory is underdetermined even by all possible observations.“4 In the same way, no number of past and future individual legal decisions, as well as all possible decisions, determines a unique set of rules of behaviour. There is no legal system without abstract and universal rules. The two above described thought experiments give rise to the following conclusion: legal thinking cannot dispense with neither abstract rules nor individual cases. It is a constant interplay between the abstract and the concrete. Importantly, the reasons behind this fact are purely logical. Abstract legal rules do not fully determine all particular obligations, while any finite set of particular cases is compatible with many different systems of abstract rules.

III. Rule-Based Legal Reasoning Rule-based reasoning is characteristic of the approach to the law embraced by civil law systems. A good example of this way of thinking is encapsulated in Robert Alexy’s philosophy of law. Alexy claims that among legal norms, which constitute any legal system, one should distinguish between rules and principles. Rules “are norms which are always either fulfilled or not. If a rule validly applies, then the requirement is to do exactly what it says, neither more nor less”5. For example, Article 347§1 of the Polish Civil Code states that “the possessor of an immovable property shall be entitled to claim the suspension of the construction of a building if such construction might infringe his possession or threaten it with a damage.” Principles, on the other hand, “are norms which require that something be realised to the greatest extent possible given the legal and factual possibilities. [They] are optimisation requirements, characterised by the fact that they can be satisfied to varying degrees, and that the appropriate degree of satisfaction depends not only on what is factually possible but also on what is legally possible”6. An example can be found in the Constitution of the Republic of Poland, which in Article 5 states that “the Republic of Poland shall (…) ensure the protection of the natural environment pursuant to the principles of sustainable development”. Let us observe that – at least when taken at their face value – legal rules differ from principles in character. The former are norms which ascribe rights and obligations to individuals – it is an individual who, as a possessor, is 4  W.V.O. Quine, “On the Reasons for Indeterminacy of Translation”, The Journal of Philosophy 67(6), 1970, p. 178 – 179. 5  R. Alexy, A Theory of Constitutional Rights, translated by J. Rivers, Oxford University Press, Oxford 2002, p. 48. 6  Ibidem, p. 47.

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entitled to claim the suspension of the construction of a building if such construction might infringe his possession or threaten it with a damage; it is an individual, who – according to Article 415 of the Polish Civil Code - is obliged to remedy a damage caused by her fault to another person. Principles, on the other hand, express improper group obligations. When the Polish Constitution speaks of the protection of the natural environment pursuant to the principles of sustainable development, no concrete obligation is placed on an individual; rather, it is an expression of a conviction that a certain state of affairs (protection of the environment) is deontically desirable. The necessity of introducing legal principles into a legal system springs from the nature of rule-based reasoning described in the previous section. Since there is no unique deontically perfect world, but a set thereof, at least some of the legal norms must express improper group oughts, i.e. be legal principles. Because of their character, in concrete cases principles may be in conflict with one another or with a legal rule. Let us recall a famous example, often analysed in legal theory: (Vehicle in the park) A local ordinance includes a norm that bans all vehicles from entering a public park. An ambulance carrying a seriously injured person has to go to the hospital. The shortest way to the hospital is through the park. The question arises of whether the ambulance can enter the park.

The rule expressed in the ordinance leads to the conclusion that the ambulance cannot drive through the park. This seems unjustified, since human life is at stake. According to Alexy, our case is a good example of a conflict between a rule (“No vehicles can enter the public park”) and a principle (“Human life and health should be protected by law”). In order to resolve this conflict one must identify the principle backing the rule. Given that the rule bans vehicles from entering a green area, it is reasonable to assume that the rule is a concretisation of the principle requiring the protection of the natural environment. Thus, the conflict we are considering is ultimately a conflict between two principles: (P1) “Human life and health should be protected by law.” (P2) “Natural environment should be protected by the law.”

(P1) leads to the conclusion that the ambulance can drive through the park, while the outcome of applying (P2) is opposite. In Alexy’s theory, such conflicts are decided through the Weight Formula:



Ii · Wi · Ri Ij · Wj · Rj

Wi,j=

where Wi, j stands for the concrete weight of the principle Pi relative to the principle Pj, i.e. relative to the case at hand; Ii stands for the intensity of interference of Pj with Pi; Wi stands for the abstract weight of the principle Pi, i.e. irrespective of any circumstances. Finally, R i stands for “the reliability of the empirical assumptions

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concerning what the measure in question means for the non-realisation of Pi and the realisation of Pj under the circumstances of the concrete case.”7 The principle that has a greater weight prevails in the concrete case over the other principle. The last sentence needs to be stressed: the way Alexy accounts for the balancing process illustrates that an exclusively rule-based reasoning is impossible. In the case of a conflict between a rule and a principle, or between two principles, the decision determined with the use of the Weight Formula is case-relative; moreover, it cannot be reconstructed as a deductive argument in any non-trivial way. The essence of balancing boils down to the determination of the intensity of interference between the two conflicting principles, as well as the reliability of the empirical assumptions one makes. This Alexian insight reaffirms our findings from the first thought experiment described in Section 2: legal reasoning based solely on abstract rules is insufficient to yield a unique answer to every legal question. The above considerations lead to one more crucial observation. The rule-based approach to legal reasoning requires utilising the so-called defeasible logic. The concept of defeasibility was introduced into legal theory by H.L.A. Hart in 1949, and has been analysed and often redefined since. For our purposes, it is reasonable to define defeasibility as a feature of rules: A rule of the form A => B is defeasible if it is possible that although A obtains, B does not follow8.

From this definition, it is clear that defeasible rules cannot be modelled with the use of the material implication of the classical logic. A different formal system is called for, and, in fact, a number of such formalisms have been developed9. An example is a system proposed by Henry Prakken and Giovanni Sartor10. On their account, the given set of premisses, where legal norms are expressed as defeasible implications, serves to construct arguments, which often lead to conflicting conclusions. In the case described above, one can develop an argument based on the principle that human life and health should be protected by the law, to the effect that the ambulance can enter the park, as well as an argument based on the principle that the natural environment should be protected by the law, with the outcome that the ambulance is banned from entering the park. Those two arguments attack one another, and the goal is to determine which one prevails. The conclusion of the winning argument becomes the logical conclusion of our case (of the set of premises we

R. Alexy, “On Balancing and Subsumption. A Structural Comparison”, Ratio Juris, vol. 16, no. 4, p. 446. 8 Cf. B. Brożek, “Law and Defeasibility”, Revus, 23 (2014), pp. 165–170. 9 Cf. H. Prakken/G. Vreeswijk, “Logics for Defeasible Argumentation”, Handbook of Philosophical Logic, vol. 4, eds. Dov M. Gabbay et al., Kluwer Academic Publishers, Dordrecht 2002. 10 Cf. H. Prakken: Logical Tools for Modelling Legal Argument. Study of Defeasible Reasoning in Law, Kluwer Academic Publishers, Dordrecht 1997. 7 

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have). However, the determination of which of the arguments prevails is, in general case, based on an extra-logical considerations (such as the Weight Formula). The use of defeasible logic has a number of interesting features. First, it is a natural way to model conflicts between legal rules and principles. This cannot be easily done in the classical logic, since it embraces the ex contradictione quodlibet inference rule – once a contradiction is established (e.g., the sentences “The ambulance can enter the park” and “It is not the case that the ambulance can enter the park” are simultaneously derived), anything follows from the given set of premises (e.g., that taxis can enter the park, that the constitution is not binding, or that God does not exist, etc.). Meanwhile, the defeasible logic under consideration has a built-in mechanism for handling such contradictions. Second, the use of the defeasible logic makes it possible to preserve a structural resemblance between a legal norm and its formalisation11. Let us assume that – in the Vehicle in the Park case – the legal rule “Vehicles are not allowed into the park” is valid, but on the basis of the principle which requires human life and health to be protected by the law we make an exception for the ambulance carrying a seriously injured person. If we attempted a formalisation with the use of the classical logic, we would be forced to include this exception – and any other such exception! – in the formulation of our rule (“Vehicles – with the exception of ambulances carrying seriously injured persons – are not allowed into the park”). The defeasible formalisation does not require such a manoeuvre. We may stick to the “original” formulation of the rule, while the exceptions are introduced in particular cases through balancing of competing arguments. The rule-based approach to legal reasoning, which posits that a legal system is a set of abstract norms, is compatible with the utilisation of defeasible logic. On the one hand, this formal tool – in contrast with the classical logic – makes room for decisions which are case-relative. Since – as I have argued in Section 2 – no set of abstract rules can fully determine answers to all possible legal questions, this must be reflected in the formalisation of rule-based legal reasoning. On the other hand, defeasible logic also enables the preservation of the structural resemblance between legal norms and their formal counterparts. When formalising a legal norm, there is no need to incorporate all the possible exceptions into its logical formulations. In this way, the idea that a legal system consists of explicitly introduced norms is preserved at the logical level12.

11 Cf. B. Brożek, Defeasibility of Legal Reasoning, Zakamycze, Kraków 2004, pp.  143 – 145. 12  Cf. ibidem, p. 145.

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IV. Case-Based Legal Reasoning The basic tenet of the case-based approach to legal reasoning – highly characteristic of the common-law systems – is that legal decisions are made on the basis of previously decided cases (precedents). In the common-law it is called the doctrine or the rule of stare decisis. The classic Blackstone’s Commentary defines it in the following way: The doctrine of the law then is this: that precedents and rules be followed, unless flatly absurd or unjust; for though their reason be not obvious at first view, yet we owe such a deference to former times as not to suppose that they acted wholly without consideration13.

What does it mean, however, to follow a precedent in the case at hand? It is assumed that each precedent consists of two parts: ratio decidendi and obiter dicta. Ratio decidendi is the foundation for the decision in the given case, i.e. whatever aspects thereof justified the ruling; obiter dicta is everything else, i.e. those features of the case that did not influence the ruling. Let us have a look at a classic case from the English law: Mrs Donoghue went to a cafe with a friend. The friend brought her a bottle of ginger beer and an ice cream. The ginger beer came in an opaque bottle so that the contents could not be seen. Mrs Donoghue poured half the contents of the bottle over her ice cream and also drank some from the bottle. After eating part of the ice cream, she then poured the remaining contents of the bottle over the ice cream and a decomposed snail emerged from the bottle. Mrs Donoghue suffered personal injury as a result. She commenced a claim against the manufacturer of the ginger beer14.

Mrs. Donoghue’s claim was successful. The House of Lords decided that Stevenson is liable for the injury she suffered. What was the ratio decidendi here? The simple inspection of the facts of the case show that the decision of the House of Lords is compatible with many rules: that Stevenson (i.e., a particular entrepreneur) is liable for the injury suffered by Mrs. Donoghue (i.e., a particular consumer); that Stevenson is liable for the injury suffered by anyone in connection with a defective product he manufactured; that producers of beer are liable for the defects of their products; that manufacturers of any goods are liable for the defects of their products; etc. Of course, the House of Lords did provide a justification for their decision. As Lord Atkin put it: The rule that you are to love your neighbour becomes in law you must not injure your neighbour; and the lawyer‘s question „Who is my neighbour?“ receives a restricted reply. You must take reasonable care to avoid acts or omissions which you can reasonably foresee would be likely to injure your neighbour. Who then in law is my neighbour? The answer seems to be persons who are so closely and directly affected by my act that I ought reasonably to have them in contemplation as being so affected when I am directing my mind to the acts or omissions which are called in question15. 13  W. Blackstone, Commentaries on the Laws of England, vol. 1, New York 1827, p.  47 – 48. 14  http://e-lawresources.co.uk/Donoghue-v-Stevenson.php. 15 Ibidem.

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Therefore, the reason behind the decision of the House of Lords seems to be the rule that a manufacturer of goods is under a duty to take reasonable care for the consumers of his products. This means that some of the particular features of the Donoghue vs. Stevenson had no bearing on the court’s decision: the fact that the defective product was beer, that the plaintiff was a woman, or that Mrs. Donoghue’s injury was psychological rather than physical in nature. This shows that the doctrine of precedent requires a constant interplay between particular cases and abstract rules, since the sole facts of the case are not sufficient to justify the decision. To further illustrate this point it is reasonable to consider another aspect of the common-law approach to decision-making. i.e. the process of distinguishing. It boils down to declaring that the case at hand is dissimilar to some previous precedent, and hence its ratio decidendi does not have to be followed. Let us consider the following case: Mr. McTear, who smoked cigarettes produced by Imperial Tobacco, was diagnosed with lung cancer in 1992 and died the following year. His wife filed a suit against the tobacco manufacturer, seeking damages for Mr. McTear’s death. One of the questions before the court was that of Imperial Tobacco’s duty of reasonable care for their customers. Should the court follow the precedent set forth in Donoghue vs. Stevenson and hold Imperial Tobacco liable for the death of Mr. McTear?16

Prima facie, it seems that the situation in the case under consideration is analogous to the Donoghue vs. Stevenson: a manufacturer did not exhibit the adequate duty of care and delivered a product that caused the death of Mr. McTear. However, in their ruling the court noted that “there is no breach of a duty of care on the part of a manufacturer, if a consumer of the manufacturer’s product is harmed by the product, but the consumer knew of the product’s potential for causing harm prior to consumption of it. The individual is well enough served if he is given such information as a normally intelligent person would include in his assessment of how he wishes to conduct his life, thus putting him in the position of making an informed choice.17” In other words, the court distinguished between two kinds of situations: when the product causes harm and one cannot reasonably expect of the consumer to know it, and when the product is harmful, but the consumer has all the information required to be aware of this fact and make an informed decision whether to use the product or not. Once again, we can see the interplay between cases and abstract rules. McTear vs. Imperial Tobacco is a particular case which influences our understanding of the rule governing an earlier precedent. The facts of Donoghue vs. Stevenson together with the explicit statements of Lord Atkin are compatible with two different rationes decidendi: that a manufacturer is always liable for the damage caused by their products and that a manufacturer is liable for such damages only if the consumer is (reasonably) unaware of the potentially dangerous features of the product. The process of distinguishing – such as applied in McTear vs. Imperial Tobacco – serves to 16 http://swarb.co.uk/mctear-v-imperial-tobacco-ltd-ohcs-31-may-2005/. 17 Ibidem.

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state more clearly rationes decidendi of precedents. As we have seen in the second thought experiment of Section 2, any number of previously decided cases is compatible with many mutually exclusive rules of conduct. The decision in Donoghue vs. Stevenson was compatible with many rules, such as: R1: “A manufacturer is always liable”; R2: “A manufacturer is liable only when a reasonable customer is not informed or cannot easily foresee the danger associated with using the product”; R3: A manufacturer is liable only when the particular customer, e.g. Mr. McTear, is not informed about the danger associated with using the product”; R4: “A manufacturer is liable unless everyone knows about the danger associated with using the product”; etc.

From this perspective, distinguishing may be described as dispensing with some of those rules and retaining others. The decision in McTear vs. Imperial Tobacco excluded R1, R3, and R4, but retained R2. However, if the court decided to follow Donoghue vs. Stevenson, no rule from the above set would be excluded. If, in turn, the decision was to overrule the previous precedent, all the rules would be dispensed with and a new (set of) rules introduced.

V. Conclusion I hope to have illustrated above the impossibility of arriving at a legal decision by purely abstract or purely concrete reasoning. Even if the civil law systems are constructed with the idea in mind that the law is a set of abstract rules introduced by the legislator, they cannot – for logical reasons – ignore solutions to concrete cases. This is reflected in the growing literature on the important role of precedents in the civil law systems.18 The theorists of the common law, on the other hand, have long struggled to explain what aspects of the precedents have the constraining power over future decisions19. There is little doubt, however, that the power lies with an abstract pattern of conduct “hidden” in the previously decided cases. The problem is that no set of precedents generates only one such pattern – again, for purely logical reasons, there are always alternative ways of “extracting” rationes decidendi from precedents. Rule-based and case-based approaches may be two different sides of legal reasoning, but they are sides of the same coin.

18 Cf. D.N. MacCormick/R.S. Summers: Interpreting Precedents. A Comparative Study, Ashgate, Dartmouth 1997, passim. 19 Cf. J. F. Horty, “Rules and Reasons in the Theory of Precedent”, Legal Theory 17 (2011), pp.  1 – 33.

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References Alexy, R.: “On Balancing and Subsumption. A Structural Comparison”, Ratio Juris, vol. 16, no. 4. – A Theory of Constitutional Rights, translated by J. Rivers, Oxford University Press, Oxford 2002. Blackstone, W.: Commentaries on the Laws of England, vol. 1, New York 1827. Brożek, B.: “Law and Defeasibility”, Revus, 23 (2014). – Defeasibility of Legal Reasoning, Zakamycze, Kraków 2004. Horty, J. F.: “Rules and Reasons in the Theory of Precedent”, Legal Theory 17 (2011). – Agency and Deontic Logic, Oxford University Press, Oxford 2001. Kalinowski, G.: Le Problème de la vérité en morale et en droit, E. Vitte 1967. MacCormick, D.N./Summers, R.S.: Interpreting Precedents. A Comparative Study, Ashgate, Dartmouth 1997. McNamara, Paul: “Deontic Logic”, The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/win2014/ entries/logic-deontic/. Prakken, H.: Logical Tools for Modelling Legal Argument. Study of Defeasible Reasoning in Law, Kluwer Academic Publishers, Dordrecht 1997. Prakken, H./Vreeswijk, G.: “Logics for Defeasible Argumentation”, Handbook of Philosophical Logic, vol. 4, eds. Dov M. Gabbay et al., Kluwer Academic Publishers, Dordrecht 2002. Quine, W.V.O.: “On the Reasons for Indeterminacy of Translation”, The Journal of Philo­ sophy 67(6), 1970.

Logic and Legal Realism By Michael S. Green Michael S. Green

“The life of the law has not been logic: it has been experience.”1

It appears that the American legal realists — and progenitors like Holmes, quoted above — believed that relying on logic in legal reasoning is, in some way, mistaken and that certain contemporaries (whom we can call “traditionalists,” avoiding the realists’ pejorative term “mechanical jurisprudents”2) succumbed to this mistake. But appearances can be deceiving. In fact, the set of loosely-related errors to which the realists thought traditionalists succumbed did not concern reliance on logic. It had other sources.

I. Logic Consider the following syllogism:3 (1) (2) (3)

Major Premise: Minor Premise: Conclusion:

All men are mortal. Socrates is a man. Socrates is mortal.

This inference is logically valid, for two reasons. First, it is necessarily truth-preserving. There is no possible world in which (1) and (2) are true and (3) is not true. Second, one can be confident that it is necessarily truth-preserving without knowing the meaning of all of the words in the sentences involved. In particular, one does not have to know the meaning of “men” or “mortal,” or to whom “Socrates” refers. One way of putting this is that all inferences of the same form are necessarily truth-preserving:

Major Premise: Minor Premise: Conclusion:

All Xs are Y. a is an X. a is Y.

Holmes, p. 1. The term mechanical jurisprudence was coined by a progenitor, Roscoe Pound. Pound (1908). Pound, it should be noted, was a critic of the movement too. Pound (1931). 3  Sometimes the term “syllogism” is reserved for the categorical syllogisms described by Aristotle. Aristotle, 40b24 – 26. In a categorical syllogism the two premises and the conclusion are categorical propositions (that is, propositions that assert or deny that all or some of the members of one category are included in another category). My example is what might be called a singular syllogism, in which the major premise is a categorical proposition, and the minor premise and conclusion are singular propositions, that is, propositions in which a named item is said to exist and to be included under a category. 1  2 

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The requirement of formality helps distinguish logically valid inferences from other necessarily truth-preserving inferences, such as:

Premise: Conclusion:

The glass Fred is holding is filled with water. The glass Fred is holding is filled with H 2O.

It is true that there is no possible world in which the glass Fred is holding is filled with water and it is not filled with H2O. But the inference is not logically valid, because inferences of the same form are not necessarily truth-preserving. The inference’s form can be characterized as follows:

Premise: Conclusion:

a is X. a is Y.

An inference of the same form that is not necessarily truth-preserving is:

Premise: Conclusion:

Joe is a Texan. Joe is a Republican.

The formality of logically valid inferences helps explain another important feature of such inferences, namely that they can be arrived at a priori, that is, without reliance on empirical evidence. We can know that “a is Y” is true, given that “All Xs are Y” and “a is an X” are true, without empirical inquiry into what a is or what being X or being Y are.

II. Legal Irrationalism? To repeat, the distinguishing characteristics of a logically valid inference are that it is necessarily truth-preserving, formal, and knowable a priori. A legal inference that appears to have the same form as our syllogism is: (4) (5)

Major Premise: Minor Premise:

(6)

Conclusion:

All oral agreements to sell land are unenforceable. The agreement between Smith and Jones is an oral agreement to sell land. The agreement between Smith and Jones is unenforceable.

This inference too, it would seem, is necessarily truth-preserving. In every possible world in which all oral agreements to sell land are unenforceable and the agreement between Smith and Jones is an oral agreement to sell land, the agreement between Smith and Jones is unenforceable.4 Furthermore, we can know this without knowing what “oral agreement to sell land” or “unenforceable” mean, or what “the agreement between Smith and Jones” refers to. Thus, the appropriateness of the inference can be known in advance of any experience. Nevertheless, one often sees the realists criticizing reliance on such syllogistic reasoning in the law.5 Frank describes the criticized form of reasoning this way: 4  It is likely, of course, that in a possible world it would be true only under the law of a particular jurisdiction that all oral agreements to sell land are unenforceable. We can ignore this wrinkle. 5 E.g., Yntema, p. 477; Frank (1930), pp. 69, 71, 101.

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This theory may be crudely symbolized thus: if we call the rule R, the facts F, and the decision D, then R×F=D. It seems to assure us that, if we know the judge’s R and the F, we can critically examine his D. We may disagree with his D because we think (1) that his F is wrong (i.e., his statement of the facts is mistaken), (2) that the R he used is an improper R, or (3) that he has incorrectly applied a proper R to facts which he correctly found (i.e., he has erred in his logic).6

Traditionalists, the realists argued, wrongly treated adjudication as consisting of such “purely logical deductions.”7 Of course, simply because legal reasoning does not, as a matter of psychological fact, conform to logic does not mean that it is right for it not to conform to logic. But the realists clearly had a normative as well as a descriptive point to make.8 It appears that they thought that the traditionalists were wrong to insist on conformity to logical norms when engaging in legal reasoning. One way of reading these claims is that the realists thought that the essential qualities of logically valid inference — its necessity, formality, and aprioricity — do not apply to legal reasoning like the derivation of (6) from (4) and (5). It is not the case that (6) is true in every possible world in which (4) and (5) are true. There is at least one possible world in which the agreement between Smith and Jones is enforceable even though, in that world, all oral agreements to sell land are unenforceable and the agreement between Smith and Jones is an oral agreement to sell land. To determine whether (6) should be derived from (4) and (5), a court must look to the sentences’ content, which means that the inference cannot be arrived at in advance of experience. If this were in fact the realists’ position, they could fairly be described as legal irrationalists. And it is true that the realists were accused of irrationalism by their contemporaries.9 But other, more charitable, readings are possible.

III. Legal Indeterminacy Sometimes it is clear that what the realists criticize is not the derivation of (6) from (4) and (5), but rather the acceptance of the major premise (4). Walter Wheeler Cook makes this point particularly clearly: [H]owever great the appearance of purely deductive reasoning may be, the real decision where a case presents novel elements consists in a redefining of the middle term of the major and minor premises of the syllogism; that is, of the construction or creation of premises for the case in hand, which premises did not preexist. The statement of the Frank (1948), p. 922. Yntema, p. 477. 8  The descriptive claim that judges ignore how a decision follows deductively from legal rules and the facts of the case — due to irrationality, dishonesty, or incompetence — is itself a theme among the realists, particularly Jerome Frank. Leiter, p. 10. 9  Harris, pp.  177 – 182; Fuller, pp.  443 – 447. 6  7 

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premises of the deductive syllogism is therefore a statement of the conclusion which has been reached on other grounds, and not of the real reason for the decision. When once the premises have been thus constructed, the conclusion inevitably follows.10

Cook does not deny that if all oral agreements to sell land are unenforceable and the agreement between Smith and Jones is an oral agreement to sell land, it follows necessarily that the agreement between Smith and Jones is unenforceable. As he puts it, “When once the premises have been thus constructed, the conclusion inevitably follows.” The question is the acceptance of the premise that all oral agreements to sell land are unenforceable. This premise, he argues, is created after the acceptance of the Conclusion on different grounds. Such a reading helps explain why the realists’ skepticism about reliance on logic in legal reasoning was primarily directed at syllogisms, in which there is a categorical major premise like (4). It is hard to find antipathy to other logical restrictions on belief formation, like the law of non-contradiction, even though it is an easy matter to show that anyone who, having accepted (4) and (5), refused to accept (6) has violated that law. The problem was not logic per se, but premises like (4). As Cook describes it, the problem is the assumption that a legal rule like (4) exists in circumstances in which the law is in fact rationally indeterminate, in the sense that no particular decision is justified (given the facts of the case) by existing legal materials — statutes, constitutional provisions, past judicial decisions, and the like.11 A premise like (4) is “created” for a case that “presents novel elements” and so is not governed by preexisting law. So understood, the realists’ criticism of reliance on syllogistic reasoning is really about a refusal to recognize the scope of legal indeterminacy. Although no particular decision follows from existing law — forcing the judge to decide the case on the basis of non-legal considerations — the traditionalist judge, having arrived at a decision on the basis of those non-legal considerations, justifies his decision after the fact by reference to a legal rule like (4). For many realists, the non-legal considerations driving judicial decision-making were morality and morally-relevant social facts.12 But others — particularly Jerome Frank and Joseph Hutcheson — appeared to point to more idiosyncratic factors: the judge’s “hunches.”13 The realists’ views about legal indeterminacy certainly explain much of their criticism of syllogistic reasoning in the law. They thought that the law was more indeterminate than traditionalists assumed. Indeterminacy was not merely the result of vagueness and ambiguity in language.14 It was also the result of the fact that a number of competing, but equally legitimate, canons of interpretation could be applied even to material with precise and unambiguous language, yielding differCook, p. 44. For a more detailed description of legal indeterminacy, see Leiter, pp.  9 – 12. 12 E.g., Cook, p. 45. 13  Frank (1930), p. 112; Hutcheson. 14  Hart, pp.  124 – 135. 10  11 

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ent interpretations.15 Further complicating matters, judicial behavior might show that the actual standards being applied by judges — the “law in action” — are something different from the “paper rules,” or the law in the books.16 To the extent that law exists by virtue of its actual employment by judges and other officials, the law in action, and not the paper rules, are arguably the law.17 No matter how precise and unambiguous the paper rules might be, the law in action could still be indeterminate. But the realists did not appear to believe in global legal indeterminacy, that is, indeterminacy in every case faced by a judge.18 It would appear to follow, therefore, that when the law is determinate, a reliance on syllogistic reasoning is appropriate. And yet the realists often suggested that in every case a court cannot arrive at its decision syllogistically. As Frank put it, “[T]ry as men will to avoid it, judging involves discretion and individualization. The judge, in determining what is the law of the case, must choose and select, and it is virtually impossible to delimit the range of his choice and selection.”19 Such discretion and individualization, Frank argues, is unavoidable.20 If the reason is not global legal indeterminism, what is it?

IV. Legal Particularism Another explanation is legal particularism. Moral particularism, roughly, rejects the view that proper moral reasoning consists of the application of absolute moral principles, under which all actions of a type have a certain moral valence (obligatory, permitted, or forbidden). An example is the moral principle that all promises ought to be kept. We can call such absolute moral principles moral rules.21 Notice that moral particularism does not follow from the fact that moral rules have exceptions, for example, when Smith, having promised to take Jones to the zoo, is morally permitted to break his promise because his ill mother must go to the hospital. If the exceptions are finite in number and are themselves rule-like — in Llewellyn; Leiter, pp.  74 – 76. Schauer. 17  This approach to identifying the content of the law diverges from Hart’s theory, which privileges what officials say over what they do. For a discussion, see Green (2005), p. 1935. 18  Leiter, p. 19. Leiter argues the realists primarily limited their claims of legal indeterminacy to those cases that reached “the stage of appellate review.” Leiter, p. 77. For the argument that this is too narrow, see Green (2011), pp. 383 – 89. 19  Frank (1930), p. 149. 20  Frank (1930), p. 399. 21  Ross. I concentrate here on weak moral particularism. Strong moral particularism rejects not merely moral rules but moral principles of any sort. For the strong moral particularist, there is no sameness in the way that an aspect shared by a set of actions contributes to the actions’ moral valences. Dancy. 15  16 

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the sense that all actions that satisfy the criteria in terms of which the exception is formulated are indeed excepted from the rule — the inapplicability of these exceptions can simply be folded into the rule. The moral particularist must argue that the way moral considerations come together to contribute to an action’s moral valence is necessarily contextual and individualized, allowing for no moral rules. If so, the moral particularist would deny that determining the moral valence of an action is a matter of syllogistic reasoning of the following sort:

Major Premise:



Minor Premise:



Conclusion:

All promised actions (to which exceptions e1-en do not apply) are morally obligatory. Smith’s taking Jones to the zoo is a promised action (to which exceptions e1-en do not apply). Smith’s taking Jones to the zoo is morally obligatory.

Notice that the moral particularist can deny that moral reasoning is syllogistic, while nevertheless insisting that morality is rationally determinate, in the sense that moral considerations fully determine the moral valence of any action. By analogy, a legal particularist argues that even when the law is rationally determinate, arriving at the unique decision recommended by the law is never a matter of applying legal rules to the facts. Although legal materials are often formulated as rules, the way legal considerations come together to determine a court’s decision is necessarily contextual and individualized. Even in an easy case a balancing of legal considerations occurs, although the balance is strongly in favor of one decision. Thus, legal reasoning cannot be syllogistic in character. A particularist theme is evident in some realists’ writings. Sensitivity to context, they argue, is needed to determine how the law recommends a result in a case. So understood, their criticisms of syllogistic reasoning would be compatible with the law’s being rationally determinate. Particularism can explain, for example, why Frank argues that adjudication always involves “individualization” in addition to “discretion.” Individualization arguably refers to contextualized judgment about how the law determines a case’s result. In describing this judgment as a hunch, Frank may not have meant that it was the product of personality or caprice.22 He may instead have meant that it was a conclusion that, despite being legally justified, could not be accounted for by the application of legal rules to the facts. As Frank put it: Since the trial judge is not, then, engaged in a wholly logical enterprise, the effort to squeeze his “hunch,” his wordless rationality, into a logical verbal form must distort it, deform it. His ineffable intuition cannot be wholly set down in an R and an F. There are overtones inexpressible in words.23

Here Frank describes the hunch as wordless rationality — it is a process of legal reasoning, not whim.

22  23 

Although that is also a theme in his works. Frank (1948), pp. 932 – 933.

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Judge Joseph Hutcheson also suggests that a hunch is an ineffable contextual understanding of the way that legal materials rationally recommend a decision given the facts of the case: I, after canvassing all the available material at my command, and duly cogitating upon it, give my imagination play, and brooding over the cause, wait for the feeling, the hunch — that intuitive flash of understanding which makes the jump-spark connection between question and decision, and at the point where the path is darkest for the judicial feet, sheds its light along the way.24

Like legal indeterminacy, legal particularism can explain the realists’ criticism of syllogistic reasoning in the law without attributing to them legal irrationalism. The problem with traditionalists was not that they relied on logic when adjudicating, but rather that they mistakenly assumed that legal conclusions follow from legal rules, like (4), when they actually follow from the contextual application of legal materials to the facts of the case. It is not clear, however, that all legal realists thought that legal rules are inappropriate or impossible, provided that they were sufficiently nuanced in their formulation. Some — particularly Herman Oliphant, Leon Green, and Karl Llewellyn — appeared to think that legal rules within certain well-defined contexts (or situation types) are possible.25

V. Judicial Supremacy A third explanation of the realists’ rejection of syllogistic reasoning in the law is judicial supremacy — the fact that a court’s judgment is binding, unless overturned on appeal, even if the court misapplied or misinterpreted the law.26 A rejection of syllogistic reasoning in the law might appear to follow from judicial supremacy. Assume that Smith entered into an oral agreement to sell Blackacre to Jones for $100,000. Jones refuses to abide by the agreement and Smith sues him for breach of contract. If we understand the conclusion of our legal syllogism (“The agreement between Smith and Jones is unenforceable”) as a statement that the only legally permissible judgment in the case is one in favor of Jones, then the conclusion arguably does not follow. The following inference is also permissible:

Hutcheson, p. 21. Leiter, pp. 21 – 24, 29 – 30, 109 – 111. Schauer argues that most realists were not particularists for this reason. Schauer, p. 755 n. 22. 26  Green (2011), p. 408 and Green (2005), pp. 1987 – 1993. In particular, the realists’ concern was weak judicial supremacy — the fact that a court’s judgment (for example, that Jones is liable to Smith for $100,000) is binding despite any errors. In legal systems with strong judicial supremacy, by contrast, not only is the court’s judgment binding, its interpretation of the law is binding on officials beyond the judgment in which the interpretation was issued. For a discussion of the distinction between weak and strong judicial supremacy in the context of the realists, see Green (2011), pp. 390 – 391. 24  25 

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Major Premise: Minor Premise:



Conclusion:

All oral agreements to sell land are unenforceable. The agreement between Smith and Jones is an oral agreement to sell land. Judgment for Smith (the agreement between Smith and Jones is enforceable).

Under this reading, the traditionalists’ commitment to syllogistic reasoning was the result of their failure to recognize the discretion that judicial supremacy gives judges when issuing judgments. The realists’ argument that legal discretion follows from judicial supremacy was famously criticized by H.L.A. Hart for failing to distinguish between whether a court’s judgment is legally binding and whether the court abided by the law in issuing its judgment.27 Without drawing the distinction, Hart argued, we cannot make sense of how a court issuing a binding judgment can nevertheless be criticized for being legally in error. For our purposes, however, it is enough to note that even if the realists’ argument succeeded, it would not amount to a rejection of logic in legal reasoning. As the realists themselves recognized, their position, in effect, denied that statutes, prior judicial decisions, and the like are law. The law concerning a set of facts is actually whatever a court with legal power to issue a judgment says about the facts.28 Here is Frank: All … decisions are law. The fact that courts render these decisions makes them law. There is no mysterious entity apart from these decisions. If the judges in any case come to a “wrong” result and give forth a decision which is discordant with their own or any­ one else’s rules, their decision is none the less law.29

But that amounts to rejecting the major premise in legal syllogisms (such as the premise that all oral agreements to sell land are unenforceable) and replacing it with the premise that the law concerning a set of facts is whatever the court that gets jurisdiction of the case says it is. Concerning that premise Frank himself reasons syllogistically:

Major Premise:



Minor Premise:



Conclusion:

An agreement is enforceable if a judge with jurisdiction says it is. A judge with jurisdiction says that the agreement between Smith and Jones is enforceable. The agreement between Smith and Jones is enforceable.

Hart, pp.  141 – 146. Green (2011), pp. 402 – 408. 29  Frank (1930), p. 134, see also p. 298. 27 

28 

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VI. Fact-Skepticism A fourth explanation of the realists’ rejection of syllogistic reasoning in the law focuses on the minor premise, concerning the facts of the case. As some realists emphasized, no matter how determinate and absolute legal rules happen to be, no conclusion is necessitated if there is rational indeterminacy, or discretion, concerning the facts.30 The facts would be rationally indeterminate if the evidence presented does not justify a particular decision.31 Furthermore, even when a particular decision is justified, the court could be understood as having discretion concerning the facts, because a decision contrary to the evidence will nevertheless be binding, unless it is overturned on appeal.32 To be sure, Hart’s criticism would again apply: If the binding nature of a court’s decision concerning the facts really meant that it has discretion, one would be unable to criticize a court for making a legal error concerning the facts.33 For our purposes, however, it is enough to observe that, here too, the realists’ criticisms are not directed at logic. The realists do not deny that (6) necessarily follows from the truth of (4) and (5). Their focus is on indeterminacy, or discretion, concerning the acceptance of (5).

VII. Positivism and Philosophical Anarchism The fifth reason the realists rejected syllogistic reasoning in the law is connected to their prediction theory of law. As we have seen, for some realists, judicial supremacy motivated them to offer what can be called a decision theory of law, under which the law concerning a set of facts is whatever decision will be issued by a court that gets jurisdiction of the case. But the most philosophically sophisticated of the realists — in particular Felix Cohen and Walter Wheeler Cook — offered a different theory, under which the law concerning any set of facts is reducible to patterns of behavior and attitudes of officials within the jurisdiction.34 When making a judgment about the law one is predicting that past patterns currently obtain.

30 Fact-skepticism is a particularly strong theme in Frank’s later writings. See, e.g., Frank (1949), p. 11. 31  See, e.g., Frank (1932), pp. 657 – 658, 660. 32  Of course, to the extent that it is a jury and not the judge that acts as the finder of fact, the realists point to it as a source of discretion. Frank (1932), pp. 651 – 652. 33  The relevant burden of persuasion might result in a decision concerning the facts being rationally determinate, even when the evidence presented by both sides leaves the question of what actually happened in doubt. For example, if the plaintiff has this burden and the evidence is insufficient to prove the plaintiff’s factual allegations, the court legally must decide for the defendant concerning the facts. 34  Green (2011), pp. 409 – 412.

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Notice that the prediction theory can accommodate Hart’s observation that a judgment can be both binding and contrary to the law. It is binding insofar as one predicts that other officials will enforce it.35 It is contrary to the law insofar as it diverges from one’s prediction of how most judges and other officials would have treated the facts of the case. The realists’ prediction theory of law is a positivist theory, because the existence and content of the law are ultimately solely a matter of social facts concerning officials within the relevant jurisdiction.36 Nevertheless, it differs from other prominent positivist theories of law, most notably Hart’s, in rejecting a role for what Hart calls “the internal point of view.”37 For Hart, the existence of a legal system requires more than official conformity to legal practices. Officials also must adopt the internal point of view, by responding to deviation from the standards used in those practices with criticisms (including self-criticisms) and demands for conformity.38 These criticisms and demands are expressed in internal legal statements framed in normative language like “You ought to do this” or “That is wrong.” Internal legal statements express acceptance of conformity with the standards; they do not describe this acceptance.39 In addition, an official making an internal statement presupposes, but does not describe, the existence of legal practices as social facts.40 It follows from Hart’s theory that a community in which officials always justified their decisions by describing legal practices as social facts (as well as describing other relevant social facts) and then justifying conformity morally would not have law.41 This is because the officials, although accepting conformity with legal practices, would not justify conformity through internal legal statements. They would not adopt the internal point of view, as Hart understands it. Cohen and Cook, by contrast, understood statements about the law — including such statements when made by officials engaged in legal practices — to be reducible to descriptions of social facts about legal practices.42 They dispense with the internal point of view. This is an important reason that Hart rejected the realists’ prediction theory of law.43 Indeed, Cohen and Cook did not merely believe the law could exist when officials take the external point of view, they argued that adopting the external point of view is ideal. A judge adjudicating a case should first describe the law in terms Cohen (1935), p. 844. Coleman and Leiter, p. 241. 37  Hart, p. 57. 38  Hart, p. 57. 39  Hart, p. 102. See generally Toh, pp. 81–105. 40  Hart, pp.  102 – 103. 41  Green (2017). 42  Cohen (1935), p. 839; Cook (1942), pp.  29 – 33; Green (2011), pp.  393 – 397, 409 – 416; Green (2005), pp. 1967 – 1998. 43  Hart, pp.  136 – 147. 35 

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of social facts about legal practices and then morally assess whether conformity to those practices is appropriate. If he does, he will describe the law more accurately, because he will not confuse the law with how the law morally ought to be.44 In addition, his moral criticism of the law will be more accurate, because he will not be tempted to assume that the existence of law necessarily entails justified reasons for conformity. Only in the light of moral norms can conformity to legal practices be recommended.45 Because they denied that the existence of law necessarily entails justified moral reasons for conformity, the realists were philosophical anarchists. Philosophical anarchists usually emphasize that citizens have no general prima facie moral duty to obey the law.46 The realists were unusual in extending philosophical anarchism to judges deciding cases. With the realists’ prediction theory of law and philosophical anarchism on the table, we can now offer another explanation of their rejection of syllogistic reasoning in the law. Let us return to our legal syllogism: (4) (5)

Major Premise: Minor Premise:

(6)

Conclusion:

All oral agreements to sell land are unenforceable. The agreement between Smith and Jones is an oral agreement to sell land. The agreement between Smith and Jones is unenforceable.

According to the prediction theory, the Major Premise is reducible to a description of official practices — roughly, that all oral agreements to sell land will generally not be enforced by officials. If we understand the Conclusion likewise as a description of official practices, it does indeed follow deductively.

Major Premise:

All oral agreements to sell land will generally not be enforced by officials.



Minor Premise:

The agreement between Smith and Jones is an oral agreement to sell land.



Conclusion:

The agreement between Smith and Jones will generally not be enforced by officials.

But the Conclusion can also be understood as a normative statement that a judge ought not enforce the agreement between Smith and Jones.

Major Premise:



Minor Premise:



Conclusion:

All oral agreements to sell land will generally not be enforced by officials. The agreement between Smith and Jones is an oral agreement to sell land. A judge ought not enforce the agreement between Smith and Jones.

So understood, the Conclusion does not follow from the premises. Moral reasons for action might recommend that a judge fail to conform to legal practices. Cohen (1935), p. 838; Cook (1935). Cohen (1935), pp. 828 – 829, 840. 46  Edmundson. 44  45 

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Under this reading, the realists criticized traditionalists for wrongly assuming that how a court morally ought to adjudicate a case could be derived from descriptive premises and logic alone:47 [T]he danger in continuing to deceive ourselves into believing that we are merely “applying” the old rule or principle to “a new case” by purely deductive reasoning lies in the fact that as the real thought-process is thus obscured, we fail to realize that our choice is really being guided by considerations of social and economic policy or ethics, and so fail to take into consideration all the relevant facts of life required for a wise decision.48

One might understand the above quotation as a statement about legal indeterminacy. The old rule fails to legally justify a decision. A judge must therefore rely on extra-legal — particularly moral — considerations to fill in the legal gap. But the realists thought moral considerations come into play in all adjudication, even when the law is rationally determinate: [A judge] must determine whether to fit a particular case into the terms of some old rules (either because they are working well, or because men have acted in reliance upon them and he considers the protections of such reliance socially valuable) or to “legislate” by revising and adjusting the preëxisting rules to the circumstances of the instant controversy.49

Frank is not describing situations where the old rules are indeterminate. Public reliance on the application of the old rules to the current controversy would not be possible if that were true. In addition, by speaking of revising and adjusting the preexisting rules, Frank suggests that the content of the rules is changed, not that gaps are filled. He is arguing that even when the law is rationally determinate, the judge must use moral reasoning to decide whether it should be followed at all. Of course, as the realists recognized, there are many very good moral reasons for adjudicating in accordance with legal practices, for example, because this will protect “human expectations based upon past decisions, the stability of economic transactions, and [ ] the maintenance of order and simplicity in our legal system.”50 But the fact remains that these are moral arguments that cannot be answered simply by looking to descriptive premises and logic. Philosophical anarchism stands at the heart of Frank’s use of psychoanalysis in Law and the Modern Mind.51 Frank relies on Freud to explain why judges wrongly take the mere existence of law to entail a duty of obedience — their “self-delusion” that they “are merely applying the commands given them by some external authorOliphant, pp.  159 – 161; Cohen (1933), pp. 307 – 308; Cohen (1934), p. 43. Cook (1942), pp. 44 – 45. 49  Frank (1930), p. 130; see also pp.  142 – 143. 50  Cohen (1935), p. 840. 51  Leiter argues that Frank uses Freud to explain the idiosyncrasies of the judicial personality that generate unpredictable judicial decisions. Leiter, p. 280. But this interpreta­ tion does not merely lack exegetical support, it is one that Frank himself repudiated. Green (2011), pp.  398 – 399. 47 

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ity.”52 They seek to escape the fact that adjudication is an autonomous moral decision. They “have not yet relinquished the childish need for an authoritative father and unconsciously have tried to find in the law a substitute for those attributes of firmness, sureness, certainty and infallibility ascribed in childhood to the father.”53

VIII. Conclusion The legal realists’ criticism of syllogistic reasoning in the law did not mean that they were legal irrationalists. Their target was not logic, but other errors, real or imagined. Sometimes it was the traditionalists’ misguided faith in the law’s rational determinacy. Sometimes it was the traditionalists’ commitment to categorical legal rules, when legal reasoning was in fact a matter of contextualized balancing. Sometimes it was the traditionalists’ belief (a correct belief, as it turns out) that statutes, past legal decisions, and the like put legal constraints on judges when deciding cases, judicial supremacy notwithstanding. Sometimes it was the traditionalists’ belief in legal constraints on judges when deciding the facts of the case. And sometimes — and most importantly — it was directed at the traditionalists’ misguided theory of political obligation: their belief that the existence of law necessarily entailed justified reasons for obedience.

References Aristotle. ca. 350 B.C.E. Prior Analytics. Trans. H. P. Cooke & Hugh Tredennick, 1938. Cambridge, Mass.: Harvard University Press. Cohen, Felix S. 1933. Ethical Systems and Legal Ideals: An Essay on the Foundations of Legal Criticism. Westport, Conn.: Greenwood Press. – 1934. “Modern Ethics and the Law.” Brooklyn Law Review 4: 33 – 50. – 1935. “Transcendental Nonsense and the Functional Approach.” Columbia Law Review 35: 809 – 49. Coleman, Jules L. and Leiter, Brian. 1996. “Legal Positivism.” In: A Companion to Philosophy of Law and Legal Theory, ed. Dennis Patterson, 241 – 60. Oxford: Oxford University Press. Cook, Walter Wheeler. 1935. Oliver Wendell Holmes: Scientist. American Bar Association Journal 21: 211 – 13. – 1942. The Logical and Legal Bases of the Conflicts of Laws. Cambridge, Mass.: Harvard University Press. Dancy, Jonathan. 2004. Ethics without Principles. Oxford: Clarendon Press. Edmundson, William A. 2004. “State of the Art: The Duty to Obey the Law.” Legal Theory 10: 215 – 259.

52  53 

Frank (1930), p. 130. Frank (1930), p. 21.

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Frank, Jerome. 1930. Law and the Modern Mind. Reprint Glousester, Mass.: Peter Smith 1970. – 1932. “What Courts Do in Fact.” Illinois Law Review 26: 645 – 66. – 1948. “Say It with Music,” Harvard Law Review 61: 921 – 57. – 1949. “Legal Thinking in Three Dimensions,” Syracuse Law Review 1: 9 – 25. Fuller, Lon L. 1934. “American Legal Realism.” University of Pennsylvania Law Review 82: 429–62. Green, Michael S. 2005. “Legal Realism as Theory of Law.” William and Mary Law Review 46: 1915 – 2000. – 2011. “Leiter on the Legal Realists.” Law and Philosophy 30: 381 – 418. – 2013. “On Hart’s Category Mistake.” Legal Theory 19: 347 – 69. – 2017. “A Puzzle about Hart’s Theory of Internal Legal Statements.” In Pragmatics and Law, eds. Francesca Poggi & Alessandro Capone, 195 – 221. Dordrecht: Springer Verlag. Harris, Rufus C. 1935. “Idealism Emergent in Jurisprudence.” Tulane Law Review 10: 169 – 87. Hart, H.L.A. 1994. The Concept of Law. 2nd ed. Oxford: Oxford University Press. Holmes, Oliver Wendell, Jr. 1881. The Common Law. Boston: Little, Brown, and Co. Hutcheson, Joseph C., Jr. 1938. Judgment Intuitive. Chicago: Foundation Press. Leiter, Brian. 2007. Naturalizing Jurisprudence: Essays on American Legal Realism and Naturalism in Legal Philosophy. Oxford: Oxford University Press. Llewellyn, Karl N. 1950. “Remarks on the Theory of Appellate Decision and the Rules or Canons About How Statutes Are to Be Construed.“ Vanderbilt Law Review 3: 395 – 406. Oliphant, Herman. 1928. “A Return to Stare Decisis.” American Bar Association Journal 14: 71 – 158. Pound, Roscoe. 1908. “Mechanical Jurisprudence.” Columbia Law Review 8: 605 – 23. – 1931. “The Call for a Realist Jurisprudence.” Harvard Law Review 44: 697 – 711. Ross, W.D. 1930. The Right and the Good. Oxford: Oxford University Press. Schauer, Frederick. 2013. “Legal Realism Untamed.” Texas Law Review 91: 749 – 80. Toh, Kevin. 2005. “Hart’s Expressivism and his Benthamite Project.” Legal Theory 11: 75–123. Yntema, Hessel E. 1928. “The Hornbook Method and the Conflict of Laws.” Yale Law Journal 37: 468 – 83.

Part II

Specific Issues

Using Propositional Deductive Logic as an Aid to Teaching American Contract Law: The Logocratic Approach The Logocratic Approach

By Scott Brewer Scott Brewer

I.  The goal of this chapter: To illustrate the use of logic in teaching the doctrinal course in Contracts at Harvard Law School I seek in this chapter to describe and explain a method of teaching and analysis I have developed over several years of teaching the doctrinal course in Contracts at Harvard Law School. Central to that method is the use of tools from logic to help students gain an analytically rigorous, lawyerly mastery of the dynamics of legal rules and the use of those rules to construct legal arguments. In some years I have used the full apparatus of propositional calculus, with the truth-functional operators and propositional constants – as I do in the handout material presented below. In other years I have stuck more closely to natural language (‘and’, ‘not’, ‘or’, etc.). But the basic method is the same either way, and either way it relies significantly on the resources of logical analysis. I have come to call this the Logocratic Method.1 I coined the term ‘logocratic’ to reflect the central concern of this method with assessing the strength [Greek κρατος – kratos] of premises that are claimed by their proponents to provide justification for a conclusion (such as the conclusion of a judge’s opinion or a lawyer’s brief) by means of argument [Greek λογος – logos]. A vital foundation of the Logocratic Method as I teach it to my Contracts class is a set of tools from basic propositional logic. (Although first-order predicate logic would in some ways be superior,

1  I have described the method briefly as it applies to the analysis of one case I teach in my Contracts class in Brewer, Satisfaction and Posner’s Morin Opinion. I have also outlined the use of the method as applied to the analysis of arguments offered by lawyers and judges under the aegis of American Evidence law rules in Brewer, Logocratic method, and Weinstein/Abrams/Brewer/Medwed, Evidence, Chapters 1 and 2. These two chapters reflect a broader concern of the Logocratic Method since this contribution was originally drafted. The broader concern is with three types of strength (reconcieved as virtues, that is, functional excellences, of arguments), which I label ‘internal’, ‘dialectical’, and ‘rhetorical’ virtues. The type of strength (virtue) at issue in the present chapter is, for the most part, only internal strength. See the cited chapters for further explanation.

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it is significantly harder to teach even the basics of predicate logic to students who have no background in logic.) Application of the Logocratic Method to assess the strength of the arguments in a judicial opinion requires the analyst (student, lawyer, judge, scholar) to answer seven questions regarding the arguments a judge proffers in a judicial opinion: (i)

How many distinct arguments are there?

(ii) What exactly are the premises and conclusions of each argument? (iii) How do those arguments relate to one another? For example, does the conclusion of one argument provide the premise for another argument? Is there a “lemma” for a principal “theorem” in the judicial opinion? (iv) What arguments are offered to resolve any unclarities in the applicable legal texts (unclarities such as semantic or syntactic ambiguity, or vagueness) that the judge encounters? (v) According to a fair interpretive judgment,2 what logical form does each argument have (i.e., deductive, inductive, analogical, or inference to the best explanation)? (vi) Given one’s interpretation of the logical form of a given argument, does it display the specific virtues that pertain to that logical form (such as either soundness or validity for a deductive argument)? (vii) Does the overall set of arguments succeed in justifying the result? As I have before described the overall jurisprudential motivation for the logocratic exercise, it is most clearly reflected in question (vii), namely: does the overall set of arguments succeed in justifying the result the judge reaches? Although judicial decisions serve several distinct and overlapping social and political functions, one central function – perhaps a sine qua non in the American legal system–is to provide a justification for the use of state power of the sort that judges wield (in cooperation, to be sure, with other branches of government). That is, broadly speaking, the power to redistribute wealth in the civil setting and the power to redistribute wealth or liberty (or life) in the criminal setting. The overarch­ing focus of this analytical method is to pursue the following inquiry: does this judge’s proffered justification for this particular use of state power actually succeed in doing its intended work? (See Brewer 2007, pp. 1124 – 25). A major part of my presentation in this chapter is one of the teaching materials I use in the Contracts class. It’s in the form of a handout that is available to the students both in a hard copy and on-line at the course web site. (I am increasingly moving to PowerPoint for some of this material supplemented by handouts distrib-

2  See footnote 18 and accompanying text for a brief discussion of the concept of a “fair interpretive judgment.” For discussion of the four modes of inference, see Brewer, Exemplary Reasoning, pp. 942 – 949.

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uted and posted.3) Throughout the semester I use handouts (and PowerPoint slides) that either teach or are guided by the Logocratic Method. I developed the particular handout presented below to help students get an overview of the complete logic of American Contract law. It presents a “master rule” for contractual liability. Armed, as it were, with this master rule and the basic logical techniques that underwrite it, a student should be able to consider any fact pattern – whether reported by a judge in an actual decided case, or presented by a client, or presented or alleged by an opposing counsel – and determine the plausibility of the claim that one party is, or is not, liable in contract to the other party. Before I present the handout, which itself develops the “master rule for contractual obligation,” it will be helpful if I explain some of the basic concepts I use when teaching or using the Logocratic Method for legal analysis. These are concepts I have presented to the students during the semester, that is, before they have gotten to the material on the master rule presented below.

3  This may seem contrary to the strongly-voiced advice of Edward Tufte, an important theorist and teacher of methods of visual presentation. In an essay on “The Cognitive Style of PowerPoint,” Tufte asserts, for example, that “[s]erious problems require a serious tool: written reports. For nearly all engineering and scientific communication, instead of Power Point, the presentation and reporting software should be a word-processing program capable of capturing, editing, and publishing text, tables, data graphics, images, and scientific notation. Replacing PowerPoint with Microsoft Word (or, better, a tool with non-proprietary universal formats) will make presentations and their audiences smarter.” Tufte, 2006 (emphasis in the original). Tufte’s argument should be taken seriously, and I do and have done so. Although in this passage Tufte discusses the specific, narrow presentation area of “engineering and scientific communication,” not university classroom presentation, his point has valuable application beyond that domain. A key, in my view, is his reference to tools in the phrase ‘[s]erious problems require a serious tool’. An analogy suggests itself to me. Against Plato’s broad and sustained attacks on the epistemic and moral worth of the discipline of rhetoric (the study and practice of persuasion), Aristotle argues, analogically: “And if it is argued that great harm can be done by unjustly using such power of words, this objection applies to all good things except for virtue, and most of all to the most useful things, like strength, health, wealth, and military strategy; for by using these justly one would do the greatest good and unjustly, the greatest harm..” Aristotle, 1355b. Like strength, health, wealth, military strategy, and rhetoric (and argument!), PowerPoint is a tool, and as Tufte acknowledges, a tool we can use well or ill, skillfully or unskillfully, virtuously or invirtuously. In their complexity, my word-processed handouts have had a tendency to be perhaps too complex and overwhelming for pedagogical efficacy. For me, the very narrowness of the basic Power Point format, and in particular the limited space on its slides, is a pedagogically useful discipline, requiring me to focus crisply on what I’m trying teach, whether about Contracts, Evidence, the logic of legal argument, or jurisprudence. And when teaching Contracts students the dynamics of Contracts arguments, the ability PowerPoint affords me to have controlled, point-by-point lines of text helps my Socratic-maieutic task of getting the students to think for themselves about the identity, structure¸ and strengths of arguments that occur in enthymematic form (on my concept of enthymeme, see pages 103 and following).

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II.  Some background concepts for the Logocratic Method of explaining the logic of legal rules and legal arguments4 1. Argument From an epistemic point of view, an argument is a set of propositions (one or more), called ‘premises’, that is offered to provide inferential warrant for another set of propositions (one or more), called ‘conclusions’. To say that one proposition, label it ‘ε’ (this is a premise in the sense just defined), provides inferential warrant for another proposition, label it ‘h’ (this is a conclusion in the sense just defined), is to say that, according to the argument presented, the truth of ε would to some extent support the claim that h is true. For example, the two premises ε1 and ε2 may be offered to provide inferential warrant for the conclusion h in this argument: ε1 All employees hired for an indefinite period of time can be fired for any reason or no (good) reason. ε2 Olga Monge was hired for an indefinite period of time. therefore h Olga Monge can be fired for any reason or no (good) reason. 2.  Logic and logical form Logic is the study of the different modes of logical inference that different kinds of arguments display. An argument’s mode of logical inference (or, synonymously, its logical form) is the evidential relation between the argument’s premises and its conclusion(s).5 In accord with this conception of logic, we may say that an argument’s logical form is the evidential relation between the argument’s premises, εi, and its conclusion(s), hi.6 3.  The four modes of logical inference In my view there are four “modes of logical inference” (or, synonymously, “logical forms”): deduction, induction, analogy, and inference to the best explanation. 4  I have presented these basic concepts in Brewer, Logocratic method. See also Weinstein/Abrams/Brewer/Medwed, Evidence, Chapters 1 and 2. I re-present them here because I also teach the concepts to the students and understanding my terms will help one understand the handout teaching tool I present later in this chapter. 5 Cf. Skyrms, p. 4 (“Logic is the study of the strength of the evidential link between the premises and conclusions of arguments.”). 6 This definition and concept of ‘logic’ call for a distinction between empirical and non-empirical evidentiary arguments. Under this definition of ‘logic’, every argument is “evidentiary” because in every argument premises are offered as providing some degree of evidentiary support for conclusions. For example, in a modus ponens argument ‘If ε then h and ε, therefore h’, premises ‘If ε then h’ and ‘ε’, taken together, provide evidential support for conclusion ‘h’ under this definition of ‘logic’, but it is not empirical evidential support – although a modus ponens can of course be used to establish empirical propositions.

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These modes are distinguished from one another by the nature and structure of the support that obtains between the premises of the argument and its conclusion. There is a disagreement among analysts about whether all arguments, including legal arguments, can fairly be represented by one or more of these four modes of logical inference, or indeed even whether all four of these modes exist irreducibly one to another. I believe that all arguments can indeed be fairly represented by one or more of these four modes of logical inference, and that all four of these modes exist irreducibly one to another (although, as I shall only briefly describe here, some modes are what I might call “intersective” – inference to the best explanation, and deduction or inductive specification – I define this term below – play a role within analogy, for example). Since these modes of logical inference – and the additional property of defeasibility, discussed below – are features of arguments in many different domains (law, empirical science, morality, etc.), it would be a mistake to refer to a special “logic of legal argument.” We may summarize the four modes of logical inference as follows. (Please note that the following descriptions are intended as brief summaries only. I offer more detailed analysis of each mode elsewhere.) a) Deduction: In a valid deductive argument, it is logically impossible that all the premises are true while the conclusion is false. That is, the truth of the premises of a valid deductive argument provides conclusive or incorrigible evidence for the truth of its conclusion. (‘Conclusive’ and ‘incorrigible’ and their counterpart terms ‘non-conclusive’ and ‘corrigible’ are, for our purposes, synonymous.) b) Induction: In an inductive argument, the premises provide corrigible, non-conclusive probabilistic evidential warrant for the conclusion (with probability less than 1). There are two main forms: inductive generalization from observation of several individuals (for example: because I’ve seen 1, 2, 3, … n objects that were swans and that were white, I generalize that all/most/x% of swans are white), and inductive specification, the application of a previously made generalization to an individual, often used to make a prediction (for example: because all/most/x% of swans are white, the next swan I see is likely to be white). There are notorious, still unresolved problems in establishing the rational basis of induction, even though it is used constantly in empirical science and serves as the foundation for a good deal of the reasoning that judges, legislators, administrative agencies make about the worlds they adjudicate, legislate, and regulate. c) Inference to the best explanation (“IBE”): Inference to the best explanation involves, as its name suggests, inference to an explanation of some fact or set of facts. In this argument, a statement of the phenomenon (or phenomena) to be explained and the putative explanation both appear as premises of the argument and the explanation itself is the argument’s conclusion. Although this mode of inference has been recognized by many philosophers, perhaps for centuries, it came into prominence in the modern period due to the work of the great American logician, philosopher, and mathematician Charles Sanders Peirce (1839–1914). (Peirce called it ‘abduction’, but both ‘abduction’ and ‘IBE’ refer

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to the same mode of logical inference.) Many scholars who study IBE, including Peirce, believe that all instances of IBE instantiate the deductively fallacious argument “affirming the consequent.” Unlike these scholars, I believe that some IBE explanations can fairly be explained as resting on valid deductive inferences. Consider, for example, an IBE that explains how a pawn in chess can appear on the same column as a pawn on the same “team.” The explanation must be that one pawn of the team took an opposing piece in a diagonal column, the same column in which his teammate was perched. Here the premises in that IBE seem to provide conclusive, incorrigible evidence for the truth of their conclusions, which they would not do if they instantiated a deductively invalid argument. IBE is also prominent in both mathematics and logic, where, again, it is IBE that rests on a deductive foundation. Some other IBE arguments, such as many of those offered in empirical science (or in evidence law or indeed in everyday life) provide only corrigible, non-conclusive evidence (probabilistic warrant with probability less than 1). Consider, for example, the IBE’s that would explain the cause of an accident, or a pain in one’s foot, or the cause of an illness. I regard inference to the best explanation to be the overarching logical form that guides lawyers, judges, students, in explaining the legal significance of a fact pattern (a dispute in contracts or torts, a criminal proceeding, etc.). I refer to this use of IBE as a special type of IBE (a logical species of the genus IBE), namely, “inference to the best legal explanation.” Other types include inference to the best logical explanation, inference to the best interpretive explanation, and inference to the best factual explanation. Inference to the best factual explanation usually plays a central role in informing an inference to the best legal explanation. For example, in order to explain whether a set of facts yields contractual obligation, a court will usually have to consider various forms of evidence, usually documentary or testimonial, to determine whether the best factual explanation of that documentary or testimonial evidence is that there was an agreement between the parties. I systematically use the concept of explanation from a legal point of view to characterize the arguments of competing litigants and competing judges. I also show the students that a fair formal representation of legal rules (which I call by the inelegant term ‘rulification’, see discussion below, pages 108 and following) offers a systematic method of inference to the best explanation, namely, determining whether the facts of an actual or hypothetical case seem to provide sufficient evidence for each element of either the antecedent of a legal rule, or the consequent, with the result that the assertion of the consequent (in modus ponens) or the negation of the antecedent (for modus tollens) seems warranted. d) Analogy: In an analogical argument, one reasons that because two or more items share some characteristics, one can infer that they share an additional characteristic that is of particular interest to the reasoner. Within analogical inference IBE operates to discern the pattern relating the sharing of some characteristics and the inferred sharing of an additional characteristic that is of interest to the reasoner. In analogical inference examples are used as heuristics to convert examples into rules. For some analogical arguments the premises provide incorrigible

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evidence for the truth of their conclusions, while in other analogical arguments, such as those used in empirical science, the premises provide only probabilistic evidential support. 4.  Two properties of arguments: defeasibility and indefeasibility Some arguments are defeasible and others are indefeasible. No argument is both defeasible and indefeasible. A defeasible argument from premises ε1-εn to conclusion h is one in which it is possible that the addition of some premise(s), εn+1, to ε1-εn, can undermine the degree of evidential warrant premises that ε1-εn provide for h. 5.  The enthymeme The procedures developed in the Logocratic Method for analyzing the logic of legal argument is are designed to handle a familiar problem in the evaluation of legal rules and legal arguments that occur in the natural language of judicial decisions, statutes, regulations, constitutions, and lawyers’ briefs: they are very often enthymematic. An enthymeme is any rule or argument (deductive, inductive, IBE, or analogical) whose logical form is not explicitly clear from its original mode of presentation (presentation, for example, in a judicial opinion or a lawyer’s brief). We might also use ‘non-formal’ as a synonym for ‘enthymematic’, and use ‘non-formal’ to mean precisely that the logical structure of the rule or argument is not explicit or clear from its original mode of presentation. This additional usage allows us to mark the fact that in another sense, legal rules and arguments are highly “formal,” and their language is not “natural,” in the sense of “plain” or “everyday.” We identify two types of enthymeme, the rule-enthymeme and the argument-enthymeme. a) Rule-enthymeme Here is an example of a rule-enthymeme: (R) Any person who knowingly transports stolen property over state lines is guilty of a felony. Is R equivalent to R1 or to R 2? R1

Any person who transports over state lines property that he knows is stolen is guilty of a felony.

R 2 Any person who knows that he is transporting over state lines property that is stolen is guilty of a felony. Note that under R 2 a person can be guilty of the felony even if he doesn’t know that the property is stolen, whereas under R1 he is not guilty unless he knows that it’s stolen (indeed, under R1 he need not even know that the stolen property has

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been taken over state lines). This is a particularly obvious example of a rule-enthymeme because R itself is ambiguous.7 But the phenomenon of rule-enthymemicity is far more pervasive than rule-ambiguity. Consider this statement by the court in Monge v. Beebe Rubber Co.,8 in which the Supreme Court of New Hampshire changed New Hampshire’s very long-established precedent rule for “employment at will” contracts. We may represent that precedent rule as follows: (R) Every employment contract that specifies no duration is terminable by either party for any reason or no (good) reason. In Monge, plaintiff Monge was a female employee in the defendant’s factory under a contract that specified no duration. When she was fired, she claimed, in an action for breach of contract against the company, that she was fired because she refused to date the factory foreman. If the Monge court had applied the precedent rule, it should have reasoned as follows, using the deductive inference modus ponens to conclude that the defendant company could terminate Olga Monge for any reason or no (good) reason, even if she was fired as an act of (what today would be characterized as) sexual harassment: ε1: Every employment contract that specifies no duration is terminable by either party for any reason or no (good) reason. [Note that the rule R here serves as the major premise for a deductive inference, a very common pattern of legal reasoning.] ε2: Olga Monge was hired under a contract that specifies no duration. Therefore, h:

The employment contract is terminable by the Beebe Rubber Company for any reason or no (good) reason.

The Monge court did not, however, reason in this way. Instead, it very substantially revised rule R for R’. R’ is Monge’s rule-enthymeme. (R’) “We hold that a termination by the employer of a contract of employment at will which is motivated by bad faith or malice or based on retaliation is not in the best interest of the economic system or the public good and constitutes a breach of the employment contract.” This is a rule-enthymeme because in the form in which it literally appears in the opinion, the exact logical elements and logical structure of the rule are not explicit. Let us introduce a term that identifies the process of attempting to offer a fair formal representation of a rule-enthymeme: “rulification.”

7  The ambiguity concerns what philosophers of language refer to as “opaque contexts” in which propositions occur, such as “knows that,” “believes that,” “is necessary that” and many others that occur in law. For good discussion see Rodes, Jr./Pospesel, chapter 6, “Intensional Contexts.” 8  316 A.2d 549 (N.H. 1974).

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Here is one effort to rulify the Monge rule-enthymeme, using the basic grammar of propositional deductive logic, and using what I have fashioned, and refer to, as the “indent-right” method of representation (presented in detail below): IF there is a termination by the employer of a contract of employment at will that is motivated by bad faith OR there is a termination by the employer of a contract of employment at will that is motivated by malice OR there is a termination by the employer of a contract of employment at will based on retaliation THEN the termination is not in the best interest of the economic system or the public good and constitutes a breach of the employment contract AND there is a breach of the employment contract. Even the shift from the court’s ‘We hold that’ to ‘if’ … ‘then’ is a move from the enthymematic form of the rule to a form whose logical form is clear. ‘We hold that’ seems grammatically to be an assertion, but it is not explicitly a conditional, which is the logical form of rules. We interpret the court to be declaring a rule, knowing what we know about the context of the statement and what courts do. This method of giving a fair formal representation of the Monge court’s rule-enthymeme facilitates inference to the best legal explanation. In this representational structure, I basically adhere to the grammar of propositional deductive logic, but do not use the full propositional grammar of assignments of propositional constants to propositions in the rule, nor do I use the logical constants. (I discuss the advantages of this type of representation in below, see pages 106 and following.) A few more terms are helpful here to understand rule-enthymemicity: the logical form of a rule consists of two components: (i) the logical elements of the rule (represented as ‘B’, ‘M’, ‘R’, and ‘E’, and possibly ‘I’ – more on this point in a moment), and (ii) the logical structure of the rule (represented by the logical operators ‘If … then’ and ‘or’ above). The logical structure of this rulified rule is three disjointly sufficient conditions, namely the propositions that are indented to the right of ‘If’ in the representation above (these are labelled ‘B’, ‘M’, and ‘R’ in a representation using the full propositional grammar, presented below, see page 108), for either two jointly necessary conditions (the two propositions indented under ‘then’ in the representation above, and as ‘I’ and ‘E’ in the representation on page 108 below).9 9 

See note 17 below.

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We have just noticed that the grammatical form of the court’s statement in Monge does not even make it explicitly clear that it is offering a rule. We need our knowledge of the context of the utterance to interpret the enthymematic natural language statement by the court into its logical form of a rule. There is another aspect of the rule as the Monge court stated it that makes the rule enthymematic. When we rulify, should we (as we have done above) treat I (“… is not in the best interest of the economic system or the public good …”) in the rule-enthymeme as part of the rule the court endorses? Or might that part of the enthymeme not be regarded as a rule-element and instead as a statement of the court’s rationale for the rule it adopts? I think the latter is the better reading that I is not a rule element. One reason for that interpretive judgment is that the court elsewhere uses a very similar rationale to the statement in I to justify this very significant change in law. (Another reason, though this is in a way cheating, is that the Supreme Court of New Hampshire made clear in a later opinion that it did not treat I as a rule element.10 One could debate this interpretation, but it’s clear that this is indeed a rule-enthymeme requiring the interpreter of Monge to make interpretive decisions about what a fair formal representation of the Monge rule is. This unclarity is potentially problematic, since it’s arguable that a subsequent decision by the same court, the Howard11 case (also the Supreme Court of New Hampshire but with membership different from the composition of the Monge court) exploited this unclarity substantially to narrow the Monge rule. Although it is unusual in the literature to find enthymemicity attributed to rules, there seems to be no good reason not to do so, for the reasons and with the illustrations just offered. Much more common in the literature is to find the property of enthymemicity attributed to arguments, and enthymemicity is indeed an important property of many arguments, and many legal arguments.12 b)  A note on the indent/right method of representing legal rules in the grammar of propositional logic We can make use of a concept that logician Bangs Tapscott refers to as “domination” among truth-functional operators.13 Here are the basics of Tapscott’s explanation: „When an operator attaches to a statement or a pair of statements to form a compound, the statement or statements to which the operator attaches are the components of the compound. However, for the sake of brevity, it is sometimes convenient to refer to them as components to the operator which generates the compound. Speaking in this loose fashion, we might say that in the statement Cloutier v. The Great Atlantic and Pacific Tea Co., 436 A. 2d 1140 (N.H. 1981). Howard v. Dorr Woolen, 414 A.2d 1273 (N.H. 1980). 12  For discussion of the evolution of logicians’ use of the term ‘enthymeme’ as a property of arguments, see Brewer, Exemplary Reasoning, p. 984 ff. 13 See Tapscott, pp. 35 – 36 (§ 3.4 Dominance and Subordination among Operators). 10 See 11 

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1. ~(A v B) • C the components to the dot[14] are the statements ‘~(A v B)’ and ‘C’, while the components to the wedge are the statements ‘A’ and ‘B’, and the component to the tilde is the statement ‘(A v B)’. One operator dominates another if the other occurs in a component to the one. Thus in (1), the tilde dominates the wedge and the dot dominates the tilde (and also the wedge). If one operator dominates another, the second is said to be subordinate to the first. In (1), the tilde is subordinate to the dot, and the wedge is subordinate to the tilde (and also to the dot). An operator is the dominant operator in a formula if it dominates all other operators in the formula. In (1), the dominant operator is the dot. But in the first conjunct of (1) the dominant operator is the tilde. Clearly, there are different levels of domination.–a “pecking order” among the operators in compound statements. One operator directly dominates another if the second is the dominant operator in a component to the first. If one operator directly dominates another, the second is directly subordinate to the first. Thus in (1), the dot directly dominates the tilde. The dot does not directly dominate the wedge, since the wedge is not the dominant operator in either of the components of (1)… . If one operator dominates another, but does not directly dominate it, it is then a case of indirect domination. In (1), the dot indirectly dominates the wedge.”15

We use Tapscott’s discussion of dominance among logical operators, within the framework of propositional deductive logic, to create what we will call the “indent-right” method of representing rule enthymemes. The key thing to understand about this method of representing rule enthymemes is that we fully represent the logical structure of a rule enthymeme, but without using the symbols for truth-functional operators (“ ~ ”, “ ˄ ”, “ v ”, “ ⊃ ”, “ ≡ ”) and while using natural language, rather than substituting abbreviations for propositions. The rules for using the indent-right method of rulification are straightforward: (i)

The dominant operator stands furthest to the left.

(ii) Any operator that the dominant operator dominates is indented once to the right (hence, “indent-right” method) (iii) More generally, any operator that dominates another operator stands to the left-indent of that operator. I’ve already presented an example of the indent-right method from the Monge case. Recall the rule-enthymeme that the court offers as its principal holding is: 14  Tapscott uses ‘•’ to represent the conjunctive operator. Other logicians use either ‘&’ or ‘˄’. And Tapscott uses ‘~’ for the negational operator, while other logicians use ‘¬’. This is a difference in symbolism only. All of the truth-functional operators have the meaning precisely represented by their corresponding truth-tables, and the symbol one uses for the operator does not matter as long as one is consistent. 15  Tapscott, pp.  35 – 36.

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We hold that a termination by the employer of a contract of employment at will which is motivated by bad faith or malice or based on retaliation is not in the best interest of the economic system or the public good and constitutes a breach of the employment contract. We may assign propositional constants to elements of this rule to rulify the rule-enthymeme in the standard grammar of propositional logic, as follows. Give these assignments to the propositional variables that are propositional elements of this rule-enthymeme. It can be helpful to pick the abbreviatory letter in a way that helps you to recall what proposition in the rule enthymeme you’re using the letter to represent. B: there is a termination by the employer of a contract of employment at will that is motivated by bad faith M: there is a termination by the employer of a contract of employment at will that is motivated by malice R: there is a termination by the employer of a contract of employment at will based on retaliation I: the termination is not in the best interest of the economic system or the public good and constitutes a breach of the employment contract. E there is a breach of the employment contract With these assignments, and with standard logical constants for material implication, inclusive disjunction, and conjunction, the Monge rule-enthymeme rulified is: Representation 1: (B v M v R) ⊃ (I ∧ E)16 As I’ve done above, using the indent-right method, both sticking to the natural language of the rule-enthymeme instead of replacing it with propositional constants, and also using natural language to state the truth-functional connectives – ‘and’ ‘if … then’,” ‘or’, we represent the rule enthymeme as follows: 16

Representation 2: IF there is a termination by the employer of a contract of employment at will that is motivated by bad faith OR there is a termination by the employer of a contract of employment at will that is motivated by malice OR there is a termination by the employer of a contract of employment at will based on retaliation 16  For reasons beyond the scope of my discussion in this chapter, I believe that element I should not be included in the best representation of the Monge rule. However, if we represent the rule-enthymeme literally, we should include it, as I have done in the text above.

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THEN the termination is not in the best interest of the economic system or the public good and constitutes a breach of the employment contract AND there is a breach of the employment contract. Note that, in Tapscott’s terminology, the truth-functional operator “if … then” dominates the truth-functional operator “or” (which we are assuming is inclusive or – in the context, this is clearly a good interpretation), and so it stands farthest to the left while the “or” operators are indented right. My experience of using rulification within the grammar or propositional logic, to teach legal rules and arguments in courses like Contracts and Evidence is shaped by the fact that most of my students in these classes have not been trained in symbolic logic (and many of them are what I might call logophobic, made anxious by overt references to logico-symbolic methods of representing legal rules). An American law professor faces a particular challenge in teaching logic as a basic tool of legal analysis in an American law school. That challenge is the continuing and, in my view, baneful and substantial, influence of Oliver Wendell Holmes, Jr.’s assertion (and its many offspring) that “the life of the law has not been logic: it has been experience.”17 In my view, this declaration makes its way into American law-professor and law-student legal culture in such a way that logic is not taken seriously as a discipline for teaching and learning substantive and procedural doctrines of law. Some of the material in the handout below attempts to overcome the intellectual harm that this culture has caused.18 The indent-right method allows me to use (and teach) the basic grammar of propositional logic without exciting the logophobia of students that I would arouse were I systematically to use the “full monty” of symbolic propositional grammar, as in representation 1, above. It also allows me to give the students the basic Logocratic-Methodical tool for executing an inference to the best legal explanation. That tool is to rulify the rule-enthymeme, using, if possible (and sufficiently concise) the indent-right method of rulification, and then 17  The fuller quotation is this: The object of this book is to present a general view of the Common Law. To accomplish that task, other tools are needed besides logic. It is something to show that the consistency of a system requires a particular result, but it is not all. The life of the law has not been logic: it has been experience. The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, even the prejudices which judges share with their fellow men, have had a good deal more to do than the syllogism in determining the rules by which men should be governed. The law embodies the story of a nation’s development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics. Holmes, Jr., p. 1. 18  See for example the discussion in the section at the end of this chapter, “Special note on the use of formal logical tools,” p. 120. I’ve argued for my own chiasmic correction of Holmes, Jr.’s assertion, see Brewer, Traversing Holmes’ Path (“The life of the law is, and should be, logic suffused by experience and experience tempered by logic.”).

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seeing whether, on the facts of the case or hypothetical, there was in the actual case, or likely would be in the hypothetical case, sufficient evidence for each element of the antecedent (for use of modus ponens) or consequent (for use of modus tollens). However, I should also note that some legal rule-enthymemes are sufficiently long and complex that using the indent-right method would itself be very cumbersome and take up a good deal of space on the page (or computer screen). In some years I have in fact taught the full symbolic form of rules in propositional grammar, and indeed the handout material that I present below uses this more concise tool of representation as well. 6. Argument-enthymeme Here is an example of an argument-enthymeme. Suppose a judge writes in an opinion resolving a contracts dispute: “The plaintiff was an employee-at-will, so she could be fired for any reason or no reason at all.” (Compare the Monge case, discussed above.)

This might be represented as a premise ε1 that provides inferential warrant for conclusion h: ε1:

The plaintiff was an employee-at-will.

Therefore, h:

The plaintiff could be fired for any reason or no reason at all.

Is that a valid deductive argument? By definition, a valid deductive argument is an argument in which, whenever all the premises are true, the conclusion must be true. Taken as literally quoted, the argument seems not to be valid. By its literal terms the argument provides no reason to believe that every employee that is an at-will employee can be fired for any reason or no reason at all. Without more, it is conceivable that some types of employee-at-will can be fired only for cause. But perhaps we conclude that the argument, properly interpreted, is not deductively invalid. Perhaps we think of ourselves as interpreters of the judge’s argument who seek to give a fair formal representation of this argument that is presented in the non-formal setting of a judicial opinion. Perhaps we believe that the judge was using a shortcut and didn’t feel the need to state explicitly that he was assuming – and assuming that his interpreters would know that he was assuming – that all employees-at-will can be fired for any reason or no reason at all. If we believe that the judge offering this argument from ε1 to h was relying on the unstated but assumed premise, ‘All employees-at-will can be fired for any reason or no reason at all’, then we would conclude that the best way to interpret the judge’s argument is as follows: ε0:

All employees-at-will can be fired for any reason or no reason at all.

ε1:

The plaintiff was an employee-at-will.

Therefore, h:

The plaintiff could be fired for any reason or no reason at all.

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– which is a valid deductive argument (another instance of modus ponens). In this example of how we might interpret the judge’s argument, we conclude that the true logical form of the argument (that premises ε0 and ε1 provide inferential warrant for h) was not explicitly clear from the way in which it was originally presented; at first glance it seemed like the argument was that ε1 by itself provided the inferential warrant for h. But, on second glance, we might judge that the argument is an enthymeme, an argument, as defined above, whose logical form is not explicitly clear from its original mode of presentation but whose proper logical form is discernible by a fair formal representation. Note that we must give some attention to the circumstances under which we think we, as interpreters of arguments, are warranted in treating them as enthymemes.19 After all, if we add the right premise, every argument could be interpreted as a valid deductive argument. But surely we don’t believe that every argument is a valid deductive argument, or, indeed, is a deductive argument at all – some are inductive, some analogical, some abductive. Here is another example that calls attention to the need to be careful when interpreting enthymemes and attempting to give a fair representation of them in explicit logical form. Philosophers have long offered this argument as the paradigm of a valid deductive inference. ε1

All men are mortal.

ε 2

Socrates is a man.

Therefore, h

Socrates is mortal.

This does indeed seem to be a valid deductive inference, for it does seem that in any possible world in which ε1 and ε2 are true h must also be true. But consider what kind of justification there could be for the first premise, ‘All men are mortal.’ Surely it rests on an inductive generalization (highly confirmed, to be sure). Might one not fairly represent the “Socrates syllogism” not as a deductively valid inference but as an inductive specification, that is, an application of an inductive generalization to an individual, where the major premise is not assumed or known to be a true universal generalization, which inductive generalizations are incapable of producing? What criteria should we use? As analysts of the logic of legal argument we try to be sensitive to such questions.20

19 Etymologically,

the proper transliteration of the Greek plural for ‘enthymeme’ (ἐνθύμημα) is ‘enthymemata’ (ἐνθυμήματα). But since that is unwieldy to pronounce, a common convention is now to make ‘enthymemes’ the plural of ‘enthymeme’. The adjectival form is ‘enthymematic’, which is still a mouthful but we will stick with it. 20  It is beyond the scope of this chapter to explore that question. My view, developed elsewhere, is that in order to satisfy the criterion of offering a fair formal representation of an argument-enthymeme (or a rule-enthymeme), we must be guided by interpretive criteria, such as the author’s intent, literal meaning, and principle of charity. How these criteria

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The balance of this chapter is a handout I give to my Contracts students (both in a hard copy and online). It develops a master rule that a person (lawyer, judge, or law student) can use to assess contractual liability in any jurisdiction, state or federal, of American contract law. Although specific contract rules differ from one state jurisdiction to another and between state and federal jurisdictions, they share a deep logical structure, and that is the structure I reveal to the students gradually, over the course of the semester. I believe that, with a few adjustments, this method could be used to assess contractual liability under any legal system, including those in civil-law jurisdictions of Europe and elsewhere in the world.

III.  A brief word on how the Logocratic concepts just described are related to the “master rule” of Contracts handout presented below In terms of the Logocratic concepts just explained, this master rule helps the student (or other legal analyst) consider a particular fact pattern and, with the guidance of the rule, reason her way to the best legal explanation of that fact pattern: that there is contractual liability or there is not. (An iterated application of the method would help determine what the damages would be if there is contractual liability and breach.) Many Contract law rules that are only abstractly referred to in the handout, such as the rules for offer, acceptance, and consideration, are rule-enthymemes that need to be interpreted. And there will most often be cases applying those rules, offering argument enthymemes that must be “unpacked” by the student in order to know how a given jurisdiction understands a rule. And those arguments will have one or more of the four modes of logical inference, deduction, induction (usually inductive specification), analogy, and IBE (such as inference to the best factual explanation, while, as noted, the overall task of the Logocratic analyst is to give the best legal explanation of the fact pattern: contractual liability or not). The material presented in the handout typically comes toward the end of the semester, as a summing up of the method we have, by that time, been using to analyze cases and rules throughout the semester.

should be used when they conflict or point in different directions is a task for a project of “enthymeme-hermeneutics.”

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IV.  Handout given to students in the Contracts course at Harvard Law School, used to teach the overall logical structure of American contract law Inference to the best legal explanation for potential contracts disputes: discerning the “master rule” for contractual liability in American contract law Professor Scott Brewer Contracts Harvard Law School 1.  Introduction: purpose of this handout Taken together, two rules and one observation – all of which we discussed early in the semester – guide us in constructing a master rule for American contract law. This is an abstract rule that determines how the specific rules of contract law are coordinated in a case that you are analyzing to indicate whether, according to your inference to the best legal explanation of the facts of a dispute, there is contractual obligation. In this handout I do the following: (i)

Remind you of the rules and the observation that can help us construct the master rule.

(ii) Explain the master rule and its three elements. (iii) Explain how an understanding of this master rule can help us to construct a flow chart of analysis that can guide your inference to the best legal explanation whenever you encounter a fact pattern that might be best explained as the making of a contract between or among two or more parties. (iv) Repeat an observation I have made several times in class about the specific and limited role of logical analysis in analyzing fact patterns that might be explained as yielding contractual obligation. The remark about the specific and limited role of formal logical analysis of problems pertains not only to our work in this course (including on the exam), but also more generally to your lives as 2Ls, 3Ls, and lawyers. 2.  Discerning the “master rule” for contractual liability in American contract law: the concepts of “prima facie contractual obligation” and “defeater doctrines” a) Glossary O: There is an offer. A: There is an acceptance. C: There is consideration.

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F: There is prima facie contractual obligation [i.e., the basic requirements of formation have been satisfied]. T: The sufficient conditions for some “defeater doctrine” rule are true. K: There is contractual obligation, all things considered [i.e., there is an enforceable promise, see Restatement 2nd § 1]. P: There is a promise. R: There is a promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person. D: There is a promise which does induce such action or forbearance on the part of the promisee or a third person. I: Injustice can be avoided only by enforcement of the promise. The two rules that guide us in constructing the master rule for American contract law appear in § 1 and § 90(1) of the Restatement (Second) of Contracts. The observation that also guides us in this task appears in Justice Loevinger’s opinion in Baehr v. Penn-O-Tex. b)  Restatement 2nd of Contracts – Chapter 1. § 1 Meaning Of Terms A contract is a promise or a set of promises for the breach of which the law gives a remedy, or the performance of which the law in some way recognizes as a duty. c)  Chapter 4. Formation Of Contracts–Consideration; Topic 2. Contracts Without Consideration § 90. Promise Reasonably Inducing Action Or Forbearance (1) A promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person and which does induce such action or forbearance is binding if injustice can be avoided only by enforcement of the promise. The remedy granted for breach may be limited as justice requires. 3.  Baehr v. Penn-O-Tex “Unfortunately, contract, like most of the basic terms constituting the intellectual tools of law, is conventionally defined in a circular fashion. By the most common definition, a contract is a promise or set of promises for the breach of which the law gives a remedy or the performance of which the law recognizes as a duty. This amounts to saying that a contract is a legally enforceable promise. But a promise is legally enforceable only if it is a contract. Thus nothing less than the whole body of applicable precedents suffices to define the term ‘contract.’”

The master rule can be explained as the conjunction of three rule-elements that reflect both Restatement rules quoted above and Justice Loevinger’s observation. Using the glossary of propositional names provided above (on pages 113 – 114), we may express the first rule element (in the master rule) as follows.

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4.  First element: rule for “prima facie” contractual obligation Rule (1): There is offer and acceptance and consideration if and only if there is prima facie contractual obligation: (O ∧ A ∧ C) ≡ F Note that ‘O’, ‘A’, and ‘C’ are an abstract representation of all the sub-rules (in a given jurisdiction) that determine whether there is offer, acceptance, or consideration – including express contract provisions and provisions that are implied in fact or implied in law. See, e.g., the rules in Normile, Petterson, Baehr, Pennsy, Restatement (Second) of Contracts §§ 17, 24, 26, 33, 50, 58, 59, 60, 71, 73, 81

Using the same propositional variables, we may express the second rule-element in the master rule as follows. 5.  Second element: rule for (all) defeater doctrines Rule (2): If there is prima facie contractual obligation, and it’s not the case that the sufficient conditions for some defeater doctrine rule are true, then there is contractual obligation, all things considered: (F ∧ ~T) ⊃ K Note also that Rule (2) entails Rule (2’): ~K ⊃ (~F v T) Comments on Rule 1 and Rule 2 Rule (1) is a representation in logical language of a rule, a truth-functional logical proposition, that is true (that is, is endorsed and recognized by the proper legal authorities) in every American jurisdiction. When each of the logical criteria O, A, and C is true, the requirements of “formation” have been met, i.e., F is true. Note that the truth (authoritativeness) of Rule 1 and the truth of each of the logical criteria O, A, and C entail the truth of F. However, it is not the case that the truth (authoritativeness) of Rule 1 and the truth of each of the logical criteria O, A, and C entail the truth of K. Another way to express this point: when there is an offer, an acceptance, and consideration there is prima facie contractual obligation (i.e., F is true), but those facts are not sufficient to support the inference that there is contractual obligation all things considered (that is, those facts are not sufficient to support the inference that K is true). Why not? Because under Rule (2) there are some circumstances (truth conditions) in which the inference from the truth of each of the logical criteria O, A, and C to the truth of K is “defeated”: namely, when T (the proposition ‘the sufficient conditions for some “defeater doctrine” rule are true’) is true. Rule (2) is a truth-functional logical proposition, which that means both that the requirements of formation have been met, i.e., each of the logical criteria for the rule of prima facie contractual obligation (O, A, and C) is true, and that it is not the case that the sufficient conditions of any rule for any defeater doctrine are also

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true. In that case there is contractual obligation all things considered and not just “prima facie” contractual obligation (that is, the truth of F and ~T entails the truth of K). Note that the abstract logical form of all defeater doctrines represented by Rule (2) reflects the logic of all of the many specific rules for defeater doctrines (including mistake, fraud, duress, economic duress, undue influence, changed circumstances, statute of frauds, conditions, misrepresentation, and non-disclosure). 6.  Third element: rule for enforcement on grounds of reliance The final element in the master rule recognizes the special role that Restatement 2nd § 90 plays in the assessment of contractual obligation. Using the glossary of propositional names provided above, we may express the third rule element (in the master rule) as follows. Note: Although we use Restatement (Second) of Contracts § 90 as the central example of reliance-based enforcement of promises, other rules, such as those in Restatement (Second) of Contracts §§ 45, 87(2), and 139 are also rules that could yield enforcement of a promise that would not be enforceable on the basis of consideration. We could make simple adjustments to our master rule to reflect that fact for jurisdictions that enforce promises under those additional estoppel rules. Rule (3): “If there is a promise, and there is a promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person, and there is a promise which does induce such action or forbearance on the part of the promisee or a third person, and injustice can be avoided only by enforcement of the promise, then there is contractual obligation, all things considered”: (P ∧ R ∧ D ∧ I) ⊃ K Note that Rule (3) entails Rule (3’): ~K ⊃ (~P v ~R v ~D v ~I) Comments on Rule 3 Rule (3) is a truth-functional logical proposition, which means that when the logical criteria for the rule of reliance-based contractual obligation (P, R, D, and I) are all true, there is contractual obligation all things considered (i.e., the truth of each of P, R, D, and I, entails the truth of K). Note that this rule could be modified (slightly) to reflect the whole “family” of reliance-based enforcement rules (such as Restatement 2nd § 45, § 87(2), § 139). Please be careful to note that, as we have repeatedly observed in the cases, different jurisdictions may have different elements in the same “basic” rule, whether in their rules as stated (compare Restatement (Second) of Contracts § 90 with the promissory estoppel rule in Katz or in Kmoch) or in their rules as authoritatively applied (compare the promissory estoppel rule stated in Wright v. Newman with the promissory estoppel rule the court seems to have applied in that case).

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Note that neither this rule nor any other of the family of reliance-based rules is subject to any defeater doctrine. To see why, consider this question: given the rationales and rules of American contract law, is it possible to have merely “prima facie” contractual obligation on the basis of a reliance doctrine (Restatement (Second) §§ 45, 87(2), 90, 139) that is “defeated” by a defeater doctrine? Put another way, the question is this: could the sufficient conditions of Rule (3) all be true while K was false because T was also true? Why or why not? Here are the three rules, repeated from the discussion above, expressed in the form of propositional logic, that we will combine to form the master rule for contractual obligation. (Again, see the glossary above, pages 113 – 114.) Rule (1): (O ∧ A ∧ C) ≡ F Rule (2): (F ∧ ~T) ⊃ K Rule (3) (P ∧ R ∧ D ∧ I) ⊃ K Putting these three rules together, we arrive at the master rule for contractual obligation. 7.  Master rule for “all things considered” contractual obligation Rule (4): ((O ∧ A ∧ C) ≡ F) ∧ ((F ∧ ~T) v (P ∧ R ∧ D ∧ I)) ≡ K

Query: Why is the final logical operator a biconditional? Because Rules (2) and (3) specify the only ways we can reach K–that is, they are not only (disjointly) sufficient conditions, but they are the sole sufficient conditions for K.

Rule (4) entails a rule that may be easier to use: Rule (5): ((O ∧ A ∧ C ∧ ~T) v (P ∧ R ∧ D ∧ I)) ≡ K Finally, note that Rule (1), Rule (2’) and Rule (3’) entail a master rule for no contractual obligation (~K): Rule (6): ~K ⊃ ((~O v ~A v ~C v T) ∧ (~P v ~R v ~D v ~I)) 8.  Using the master rule: some examples To see how these rules might be put to use in analyzing a fact pattern, try to use the rule to help answer the following questions: (i)

Suppose a judge determines that O is true, and it seems that C is true, but not A. Do we know that K is false? No, under Rule 3.

(ii) Suppose the judge determines that O and C are true, but neither the writings nor oral communications explicitly show that A is true. Do we know that F is false? No, A could be implied in fact–inference to the best factual explanation could yield the conclusion that there is a contract even when neither the oral nor written

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(iii) Suppose the judge determines O, A, and C are all true. Do we know that there is K? No, we must consider potential defeater rules, Rule 2.

(iv) Suppose the judge determines that O, A, and C are all true, but that T is true by virtue of the specific defeater of unconscionability. In this circumstance, is there any way that K could be true? No, because for this defeater, I couldn’t be true while the sufficient conditions of unconscionability were also true, so there could be no liability under Restatement (Second) of Contracts § 90, nor would there be under traditional O, A, and C.

(v) Suppose the judge determines that O, A, and C are all true, and that T is also true. Do we know that K is false? The deep issue here is this: is it possible, for some defeater doctrines, that the abstract T could be true while I is also true? For some defeater doctrines – such as mutual mistake, changed circumstances, failed conditions (this is expressed in some rules on conditions) – it seems quite likely that their sufficient conditions could be true while I is also true. However, is this true under most versions of unilateral mistake? No, because that doctrine incorporates unconscionability.

(vi) In light of your answers to (i) through (v), using the glossary offered above, can you fashion a “master rule” that could help determine, for any fact pattern you encounter, whether the “best explanation” of that fact pattern from a legal point of view is that K is true? Note that if you understand the correct answers to (i) through (vi)–that is, if you understand why the answers that are correct are correct–you understand the logic of the master rule explained below! 9.  Comments on Master Rule: the analytical value of understanding this rule Recall that, as we have discussed earlier in the semester, the plaintiff typically bears the burdens of pleading, production, and persuasion for each of the logical elements in the antecedent of this rule except ~T (the defendant must carry the burdens of pleading and production for any defeater doctrine rule; but the plaintiff must then try to overcome such proof as the defendant pleads and attempts to prove, that is, the plaintiff must carry the burden of persuasion that ‘~T’ is true). Many, perhaps most, judges evaluating a contracts claim consider first the question of whether a contract has been formed on the standard “classical” basis of contractual liability, namely, whether there has been a bargained-for exchange (recall that, according to our class text, “While virtually every jurisdiction has accepted the doctrine…promissory estoppel claims are rarely successful”). Thus, when you are considering whether the best legal explanation of some facts is that there is contractual obligation all things considered you may wish to proceed in your analysis as follows.

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Determine whether each of the elements in the left side of Rule 1 (namely, each of O, A, and C) is true. If so, then there is prima facie contractual liability (F is true).

(ii) If F is true, determine whether the sufficient conditions of any defeater doctrine are true (which in turn would make ~T false, i.e., would make T true). (iii) If it is not the case that any set of sufficient conditions for any defeater doctrine are all true (that is, if T is false) and F is true (because each of the elements in the antecedent of Rule 1–O, A, and C–is true), you now know that there is at least one set of rule elements that makes K true (i.e., that there is contractual obligation, all things considered). However, for the sake of thoroughness, you should also consider whether, on the facts of your case, the sufficient conditions of any reliance-based rule are also true. (Recall Federal Rule of Civil Procedure 8(e)(2): “A party may also state as many separate claims or defenses as the party has regardless of consistency and whether based on legal, equitable, or maritime grounds.”) (iv) If some element in the antecedent of Rule 1 (namely, the elements O, A, C) is not true, then consider whether the sufficient conditions of any reliance-based rule are true (such as Restatement 2nd §§ 45, 87(2), 90, or 139). (v)

If the sufficient conditions of any reliance-based rule are true, then there is a set of rule elements that makes K true.

(vi) If in your analysis in steps (i) through (vi) you have concluded that there is no enforceable promise (i.e., that ~K is true), you may use Rule (6) to confirm your judgment by assuring yourself that at least one of the following elements in each of the following two sets is also true: set 1: ~O, ~A, ~C , T set 2: ~P, ~R, ~D, ~I (vii) If in either steps (iii) or (vi) you’ve determined that there is contractual obligation, all things considered, then you should assess whether there has been a failure to perform by one of the parties. If so, the other party may be entitled to damages (damages are due when there is a non-excused non-performance of a contractual obligation). 10.  Special note on the use of formal logical tools Taken together, a firm grasp of the logical facts of contract rules, together with an understanding of the rationales (policies and principles) that undergird those rules, will enable you to be a very skilled consumer, producer, and critic of arguments in contract law. But I close this handout by emphasizing a point I’ve made in class. You are not required–either in this class or other classes, or in your work as lawyers (or even judges!), to use the formal machinery of logic that we have developed. It was offered to you only because it is one method for sharpening your

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awareness of the logical facts of the application of contracts rules to a fact pattern. (An example of one “logical fact” about the rule in Restatement (Second) of Contracts § 90: if it’s not the case that injustice can be avoided only by enforcing a promise, then there will be no reliance-based enforcement of that promise.) As is obvious, judges and lawyers do not use logically formal terminology when they argue and assess arguments. But they clearly strive to be aware of the logical facts of the rules as they apply the rules to fact patterns. This is, however, not to say that they always are aware of those logical facts, or that they don’t make mistakes. They do, all too often, as we have seen (e.g., in Dale Horning’s reading of Comment 4 in UCC § 2 – 207). In fact, using the logical terminology we have developed to help analyze fact patterns (in inference to the best legal explanation) may help one avoid making mistakes about the logical facts, especially, but not only, when one encounters the kind of logically dense rules exemplified by UCC § 2 – 207. And recall that, as I’ve explained, logically dense rules like these are increasingly applicable to contracts fact patterns. In several of the cases we’ve read the judges have been very admirably aware of the logical facts of rules as applied to fact patterns. Among those that are exemplary are the opinions in Brown Machine, Watts v. Watts, and Commerce Partnership. What is needed, both in this course and beyond, is an acute awareness of the logical facts. You do not need to use logical terminology to display that awareness. Finally, note that an acute awareness of the logical facts of rules is not by any means the only or the most important part of your analysis. Understanding the policies and principles that serve as rationales for contract rules (classical vs. romantic) is a vitally important part of contract analysis. But without an awareness of the logical facts, one cannot well understand the policy or principle ramifications of a given rule – think, for example, about the way in which the Joyner court seems to have overlooked, because it apparently thought it was simply restating the Restatement version of the rule, which it in logical fact was not, the policy question of whether the “whose meaning prevails” rule should allow for degrees of fault. Or the way in which the Dale Horning court’s misreading of the logical facts of the rule in Comment 4 apparently led it to overlook the implausibility, as a matter of policy, principle, and statutory intent, of a rule that would allow any party who had in fact been surprised by a different or additional term to have that term excluded as a “material alteration” under 2 – 207(2)(b)–even if that surprise was unreasonable. [End of Handout Material]

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V.  Concluding comments on the Logocratic use of propositional deductive Logic to teach American Contract Law: On the criteria for using propositional vs. predicate logic for representing rule enthymemes As is evident from the foregoing handout, when I “rulify” a rule-enthymeme or argument-enthymeme in deductive logic, I use the form of propositional logic. I make this choice because teaching the basics of propositional logic is fairly straightforward – and there is a guaranteed proof procedure, the truth table, because propositional logic is truth functional. Nevertheless, it seems that first-order predicate logic is a better choice for representing legal rules and legal arguments. Legal process seems to be about individuals and their properties. But many believe that even predicate logic is inadequate to represent legal argument, that modal and deontic logic are needed, for example, to capture Hohfeldian modalities in logical form. My focus is not what is the ideal deductive form for legal argument, but what form is both accurate and pedagogically feasible. It would not be feasible to teach predicate, modal and deontic logic in any serious way during a Contracts class – I have a hard enough time getting the students to use the basic propositional calculus. And I rush to add, lest someone accuse me of being a “wooden formalist,” that I do not claim that all legal argument can be adequately represented by deduction. As I stated at the outset and have explored in other work, I believe that all four modes of logical inference operate in legal argument, induction, analogy, and IBE, along with deduction. My current concern is only with the criteria one uses to determine which form of deduction is either acceptable or required when the argument is fairly represented as a deductive argument. I think this is a very important issue, one that seems to have gotten very little attention from those of us who “take logic seriously” in using it to model and analyze legal argument. Again, robust discussion of this issue is beyond the scope of this paper, but some generalizations and a couple of examples occur to me. Consider again the rule enthymeme, examined above, in Restatement (Second) of Contracts § 90: A promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person and which does induce such action or forbearance is binding if injustice can be avoided only by enforcement of the promise. The remedy granted for breach may be limited as justice requires.

How should we rulify this rule? Is propositional logic sufficient? Do we need predicate (or modal, or deontic) logic adequately to represent it? In the discussion above, and for years in teaching Contract law, I use only propositional logic. Using these propositional constants –

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P:

There is a promise.

R:

There is a promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person.

D:

There is a promise which does induce such action or forbearance on the part of the promisee or a third person.

I:

Injustice can be avoided only by enforcement of the promise.

K:

There is contractual obligation, all things considered [i.e., there is an enforceable promise, see Restatement 2nd § 1]

I model the rule thus: (P ∧ R ∧ D ∧ I) ⊃ K This provides a pedagogically and conceptually simple way to determine where there is contractual liability under this rule: each of the jointly sufficient conditions P, R, D, and I must be true. (What I mean by ‘under this rule’ is that if we assume that the only way to get to K is by this rule’s antecedent, then the jointly sufficient conditions also become individually necessary. Some writers refer to this as the “sole sufficient condition rule,” namely, that if P is a sufficient condition for Q and it is the sole sufficient condition for Q, then it’s also a necessary condition for Q, and in effect, P ⊃ Q is operating as ‘P ≡ Q’21.) Is this adequate? One wonders especially about the uniqueness requirement in what I have labeled ‘I’ – Injustice can be avoided only by enforcement of the promise. I have glossed over that requirement, modeling it as if a judge just decides whether it is true or false, overall, that the enforcement of the promise (K) is the only way to avoid injustice. To ponder this question of adequacy of representation, consider how we might represent § 90 in predicate logic. Again, the rule-enthymeme is: A promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person and which does induce such action or forbearance is binding if injustice can be avoided only by enforcement of the promise. The remedy granted for breach may be limited as justice requires.

With these elements Px = x is a promise that the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person Dx = promise x does induce action or forbearance the part of the promisee or a third person Bx = x is binding Mx = the enforcement of x is a method of avoiding injustice we might rulify § 90 as follows: 21  The operation of this rule is vital for understanding why judicial decisions are not constantly committing the fallacy of denying the antecedent. See the discussion in Brewer, Exemplary Reasoning, p. 998 note 215.

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(x) (((Px ∧ Dx) ∧ ((Mx ∧ (y) (My ⊃ y = x)) ⊃ Bx) The predicate-logic rulification seems superior to the propositional-logical rulification in at least one way: it reveals more of the logical structure that a fair reading discloses is in the rule enthymeme. The rule does say that in order for a contract to be binding (what I labeled ‘K’ in the propositional logic version), enforcing the promise must be the only way to avoid injustice. My sense is that the less revealing, but pedagogically much easier-to-grasp propositional logical form is usually, perhaps always adequate. If there is a question about whether a given promise and that promise alone is required to avoid injustice, a legal analyst could reason separately about that, offering a kind of lemma to show that ‘I’ (injustice can be avoided only by enforcing the promise) is true. This is something of a workaround, but my current thought is that it’s workable. After all, one could unpack the old Socrates syllogism – surely a creature of predicate logic (‘All men are mortal, Socrates is a man, therefore Socrates is mortal), in propositional logic, thus: P:

Something is a man

Q:

Something is mortal P⊃Q P therefore Q

– although one would have to know “outside” the argument, as it were, that the something in question was the individual Socrates. If one keeps that in mind, the trade of transparency within the representation (which we get with predicate logic) against the comprehensibility and utility to the non-logician of a method like the Logocratic Method (which we get with propositional logic), seems worth it.

References Areeda, Phillip: The Socratic Method, in: Harvard Law Review, volume 109, issue 5, 1996, pp.  911 – 922. Aristotle: On Rhetoric: A Theory of Civic Discourse, (G. Kennedy trans.), 2nd ed., 2006. Brewer, Scott: Exemplary Reasoning: Semantics, Pragmatics, and the Rational Force of Legal Argument by Analogy, in: Harvard Law Review, volume 109, issue 5, 1996, pp. 923 – 1028. – Logocratic Method and the Analysis of Arguments in Evidence, in: Law, Probability and Risk, volume 10, 2011, pp. 175 – 202. – On the Possibility of Necessity in Legal Argument: A Dilemma for Holmes and Dewey, in: John Marshall Law Review, John Marshall Law Review, volume 34, issue 9, 2000, pp.  9 – 47. – Satisfaction and Posner’s Morin Opinion: Aliquando Bonus Dormitat Posnerus?, in: Harvard Law Review, volume 120, issue 5, 2007, pp. 1123 – 1136.

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– Traversing Holmes’ Path toward a Jurisprudence of Logical Form, in: Burton, Steven (ed) The Path of the Law and Its Influence: The Legacy of Oliver Wendell Holmes, Jr. Cambridge University Press, New York, 2007, pp. 94 – 132. Dorf, Michael: The Supreme Court 1997 Term: Foreword: The Limits of Socratic Deliberation, in: Harvard Law Review, volume 112, issue 4, 1998, pp. 4 – 83. Holmes, Jr., Oliver Wendell: The Common Law, 1881. Rodes, Jr., Robert/Pospesel, Howard: Premises and Conclusions: Symbolic Logic for Legal Analysis, 1997. Skyrms, Brian: Choice & Chance: An Introduction to Inductive Logic, 1966. Tapscott, Bangs: Elementary Applied Symbolic Logic, 1976. Tufte, Edward: The Cognitive Style of PowerPoint: Pitching Out Corrupts Within, 2nd ed., 2006. Weinstein, Jack/Abrams, Norman/Brewer, Scott/Medwed, Daniel: Evidence, 10th ed., 2017.

Logical Techniques for International Law By Jaap Hage and Antonia Waltermann* Jaap Hage and Antonia Waltermann Jaap Hage and Antonia Waltermann

I. Introduction Legal rules often conflict with one another. When a conflict occurs, it may be necessary not to apply a rule even though it is applicable to a certain case. Running ahead of a more precise characterization, we can call this making an exception to a legal rule. One of the reasons for making an exception to a rule is that this rule conflicts with some other rule and that it is not possible or desirable to apply both rules. Then at least one of the rules must give in, leading to an exception to that rule. This kind of rule conflict can occur within a single legal system, as when a municipality locally prohibits pubs to be open on Sundays, while that is allowed nationally. It can equally occur across different legal systems, for example when a Member State of the European Union taxes that which is not taxable according to EU law.1 We can also find rule conflicts between state law and religious laws, or between rules of law and rules of morality. International law is not exempt from this problematic of rule conflicts. In fact, it has many features that make conflicts of rules particularly frequent and recalcitrant. First, it is not clear whether international law constitutes a single legal system, or an archipelago of mutually interacting international legal regimes. This so-called fragmentation of international law conjoined with the growing interaction between the international, domestic and regional legal orders implies that any discussion of rule conflicts in international law will have to account for conflicts across different legal orders (Koskenniemi & Leino 2002, Koskenniemi 2006, 8). Second, the importance of the formal sources of international law has become smaller: the list of formal sources has little power to control what counts as law and what does not. In fact, many academics suggest that having a clear view of international law requires us to bypass the doctrine of sources and identify as law those rules that have real world effectiveness and/or political legitimacy (cf. Franck 1990 and Arend 1999). The resulting obscurity of what counts as international law is also a potential cause of rule conflicts. This second point is loosely related to a third: international law operates without a central legislator. Treaties and customs are generated through * The authors thank Gustavo Arosemena and Gabriel M. Lentner for many valuable suggestions that improved this article. Remaining errors are the sole responsibility of the authors, though. 1  Cf. ECJ 26/63 (Van Gend & Loos).

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the agency of more or less uncoordinated states, which means that no central authority can take efforts to minimize rule conflicts or prevent them from arising. In short, international lawyers as well as academics will inevitably be confronted with rule conflicts in international law. These rule conflicts may in turn necessitate exceptions to legal rules, whether these rules have their origin in international or in national or religious sources. In this contribution we attempt to give an overview of the ways in which law deals with conflicts between rules within and across normative systems and with exceptions to rules. The emphasis will be on rule conflicts in international law, but some other rule conflicts and causes of exceptions will also pass in review. Our approach is inspired by the tools that have been developed during the last three decades in logical research of legal reasoning (Schauer 1991; Gordon 1995; Prakken and Sartor 1996; Hage 1997 and 2005; Prakken 1997; Sartor 2005). We try to use these tools, but although our argument is inspired by research in formal logic, our approach will be completely informal. The argument of this contribution is structured as follows. In section II we will sketch the general background against which rule conflicts and exceptions to rules occur, and discuss several ways in which rule conflicts and their ensuing exceptions to rules can be avoided. If rule conflicts nevertheless occur, there is need to make an exception to one of the conflicting rules and this technique is discussed in section III Section IV concludes this contribution.

II.  Techniques to Avoid Conflicts 1.  Preliminary: the Nature of Rules A discussion of techniques to avoid rule conflicts presupposes a common understanding of what rules are. Such a common understanding is not obvious, if only because some assume that legislation and treaties contain legal rules, while others assume that although legislation and treaties are sources by means of which legal rules are created, they do not contain the rules themselves. Here we adopt the latter view: legislation in a broad sense, including the creation of treaties, is a means to create law, but means should not be confused with what they produce. This seemingly subtle distinction has immediate practical implications, because it is obvious that legislation needs to be interpreted, while it is far from obvious that rules are also in need of interpretation. Here we assume that a rule consists of conditions and a conclusion part, and that a rule is applicable to a case if the case satisfies the conditions of the rule. We will generally use ‘rule’ in a sense that encompasses principles throughout the rest of the paper. We will use the term ‘interpretation’ for the step from a rule-creating text to the formulation of the rules in terms of its conditions and its conclusion. The decision whether a set of concrete facts satisfies the conditions of a rule is not called ‘interpretation’ of the rule, as is often done, but rather ‘classification’ of the facts.

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Classification is always case-related; interpretation is, at least in theory,2 independ­ ent of cases. 2.  Kinds of Rule Conflicts Under international law, several distinctions can be made with regard to the existence of conflicts between rules. Firstly, there are two possible perspectives: that of subject-matter of the rules, and that of the legal subjects (Koskenniemi 2006, 21). We will here focus mainly on the perspective of the legal subject. Secondly, the term “conflict” can be interpreted broadly, meaning a conflict can arise, for example, between the aims of two treaties, or narrowly (Koskenniemi 2006, 24). We take a narrow interpretation here,3 and argue that there are at least two ways in which rules can conflict with each other. The one is that one rule makes that something is the case, while another rule makes that it is not. For instance, according to the principle of effective possession, a certain territory which has been in factual possession of a State for some considerable time, is deemed to be part of that state. According to the principle of stability of borders, however, that same territory is deemed to belong to a different State, because it reflects legally agreed upon borders. Given how territory works,4 the land cannot belong to both States at the same time, and the effects of the rules are incompatible.5 Another example is that the UN Charter prohibits the use of force, but that military action under the auspices of the Security Council is permitted. One rule prohibits an armed intervention into another sovereign state, while the other permits precisely this kind of behavior. The states of affairs that armed intervention is both prohibited and permitted are incompatible, and therefore these rules are in conflict. The conflicting rules impose incompatible facts upon the world, which cannot co-exist. Because rules impose 2  This does not mean to say that the interpretative step from a legislative text to a rule formulation is never inspired by a particular case. 3  Koskenniemi, in the International Law Commission’s study group’s report on the fragmentization of international law, argues that “Focusing on a mere logical incompatibility mischaracterizes legal reasoning as logical subsumption. In fact, any decision will involve interpretation and choice between alternative rule-formulations and meanings that cannot be pressed within the model of logical reasoning.”We will attempt to show, in this contribution, that this depends on the model of logical reasoning chosen. 4  This clause ‘given how territory works’ indicates that incompatibility of rule consequences, and therefore also rule conflicts, may depend on the existence of other rules, which exclude the co-existence of certain facts. If world history had been different, we might have ended up with a system where states could be co-owners of land and the conflict described above would not exist. This is not the case in the current political organization of the world. We will encounter a similar phenomenon, that conflicts result from the presence of certain facts, in section 2.6. A theoretical discussion of rule consistency which assigns a central role to rules in the determination of which other rules conflict, can be found in Hage 2000 and 2005 (p. 135 – 158). 5  For a discussion of this type of conflict, see Frontier Dispute, Judgment, I.C.J. Reports 1986, p. 554.

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facts upon the world – they make it the case that these facts obtain as legal consequences – we will call conflicts such as these ‘conflicts of imposition’.6 The second way in which rules can conflict with each other has to do with rules which prescribe incompatible forms of behavior. Such a conflict occurs if a State, because of the human rights to which it is committed, is obligated to invest more money in both education and health care, while the state has only money for one of them. Another example would be that a journalist is obligated to reveal the sources on which she based a controversial publication, while she promised her informant not to reveal his identity. Here, the conflict arises because the obliged agent cannot comply with both obligations, be it because the obligations themselves are in conflict (a prescription and a prohibition of the same behavior), or because factual circumstances make compliance impossible. Consequently, conflicts such as these may be called ‘conflicts of compliance’.7 Conflicts of imposition are to be avoided if one wants the set of institutional facts created by law to be consistent. Conflicts of compliance should be avoided to safeguard agents against the choice which obligation to violate. Conflicts of compliance can only exist between mandatory rules (prescriptions and prohibitions), while conflicts of imposition can exist between all rules, including rules that assign status (e.g. the status of a piece of land of belonging to a particular state).8 3. Subscripting Conflicts of imposition and conflicts of compliance can arise within one normative system, as was the case with the aforementioned example of the UN Charter which prohibits and permits the use of force. They can also arise between different normative systems, both as conflicts between law and other types of normative systems such as morality, or between different legal systems. The above example about the journalist who promised not to reveal her source illustrates a conflict between a legal requirement to reveal and a moral obligation not to do so. When law conflicts with some other normative system, Raz’s view on the authority of law raises relevant concerns. According to Raz, law claims authority (Raz 1979, 28 – 33) and this claim involves two things. First, law would provide us with reasons for action, and second, these reasons would exclude other reasons. With this last point, Raz means that according to law, reasons for deviating from what the law prescribes should in principle be ignored. It is true that law makes exceptions to this principle, for instance by sometimes allowing conscientious objections, but Raz’s starting point is that the law claims not only to provide reasons 6  Notice that this characterization of rule conflicts is ontological. It may be useful to employ different categorizations of conflicts if the intended use is not ontological. 7  This characterization of rule conflicts is pragmatic. Again, it may be useful to employ different categorizations of conflicts if the intended use is not pragmatic. 8  Distinctions between different kinds of rules are discussed more elaborately in Hage 2015, section 1.5.

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for action itself, but also to take away the reason-giving force of norms from other systems. From the legal point of view it would in principle be irrelevant if what the law prescribes conflicts with morality, or with some other legal system. In this way, a legal system distinguishes itself from those other systems. The distinction becomes visible in the necessity to add subscripts to legal judgments. For instance, it is not the case anymore that state A may not use military force to intervene in state B to prevent gross human rights violations. If normative systems are distinct, the judgement must be that legally, state A is prohibited from intervening (in the absence of Security Council authorization), but morally, it should intervene. In this example the subscripts distinguish between the legal and the moral point of view. However, it is also possible to distinguish between different legal points of view.9 For instance, according to European Union law, certain forms of positive discrimination are not permissible, whereas according to the Committee on the Elimination of Discrimination against Women, they are required (cf. Waddington and Visser 2012). If the legal and other judgments are subscripted, seemingly conflicting judgments are rendered logically consistent. This means that the rules that lead to these conflicts cannot create a conflict of imposition. However, an agent who is confronted with mandatory rules from different legal systems that both claim obedience but which rules cannot both be complied with, is still burdened with a conflict of compliance. Despite the fact that conflicts between rules of different legal systems cannot be conflicts of imposition, they may still be conflicts of compliance and therefore there is still pragmatic reason to avoid or to deal with them. Some of the logical techniques discussed in this paper also point toward solutions for compliance conflicts across legal systems. 4.  The Scope of Rules Most legal rules identify by means of their conditions the kind of cases or the persons to which they are applicable. This can be everybody, as in Art. 2 of the European Convention on Human Rights, or classes of agents, such as the judges in the European Court of Human Rights, as in Art. 21 of the same Convention. However, there are also limitations on the cases and persons to which a rule applies that are not mentioned in the conditions of the rule. These are scope conditions, which combine with the rule conditions in the narrow sense to determine to which cases or persons rules should be applied. There can be personal, spatial (territorial), and temporal scope conditions. Personal scope limitations occur when one rule applies to a certain class of persons 9  The following example presupposes that different legal regimes created by different legal instruments, such as the human rights regimes of the European Union and of the Convention on the Elimination of All Forms of Discrimination against Women, constitute differ­ent legal systems. Whether and to what extent this is the case is a difficult question, which cannot be dealt with in the present contribution.

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and the other rule applies to a different class of persons. So, for instance, Talmudic law applies to members of the Jewish people, but not to non-Jews. Spatial or territorial scope limitations, meanwhile, refer to a distinction depending on the place where certain events takes place. So for instance, the penal laws of States typically10 are applicable to events that took place in their own territory, but not in the territory of another state. Temporal scope limitations solve conflicts between rules by postulating that the rules are applicable in different time periods. For example the customary rules of treaty interpretation and the rules found in the Vienna Convention on the Law of Treaties 1969 are different and thus they seem bound to conflict, but the conflict can be avoided by postulating that the rules of the Vienna Convention are applicable only to treaties that entered into force after 1969, as in fact stated in the convention itself. In this way, the scope of a rule can prevent conflicts between rules from ever arising, at least where the potentially conflicting rules have different scopes. 5. Interpretation A conflict of rules is typically case-related: two rules impose incompatible consequences on a case, or demand incompatible lines of action in a particular situation. This means that only rules that are applicable to a case can lead to a conflict,11 and also that a potential conflict can be avoided by interpreting a legal source in such a way that the resulting rule is not applicable to the case in question. The following example, inspired by an ICJ case,12 illustrates this technique. Assume that the Constitution of a federal State prescribes that the State respect the constraints of federalism, while international law prescribes that the federal State stop one of its constituent States from engaging in internationally wrongful behavior. These actions cannot be performed both. The rule conflict is clear, and a breach of either an international or domestic duty seems unavoidable. Given this impasse, it may be possible to interpret a text that seemingly creates an obligation of a specific type – e.g. stop damage causing behavior - as a text creating an obligation of a more general type – e.g. avoid causing lasting damage. It is possible to comply with this latter obligation without violating the former obligation, for instance by compensating the damage that results from the behavior. If this is done, the demands of both legal systems are deemed to be satisfied, and the conflict is avoided. A related technique is that a new type of action is created that can solve the impasse between two colliding norms for an important range of cases. On a straightforward interpretation, the UN Charter rules out all acts of aggression that are 10  There are several exceptions to this principle of territorial scope, but they are exceptional. 11  More on the notion of applicability in section 3.1. 12 Avena and Other Mexican Nationals (Mexico v. United States of America ; ICJ 09/01/2003 General List No. 128).

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non-defensive and not authorized by the Security Council. Arguably there is a developing rule of customary international law that suggests that states have a duty to intervene in cases of genocide, war crimes and crimes against humanity to defend the civilian population, and this duty exists irrespective of whether Security Council authorization has been given or not. If a case of genocide breaks out, and the Security Council does not authorize action, the two rules seem to conflict. One way to avoid the conflict is to devise new action types such as ‘peacekeeping’ that do not fall within the concept of aggression that is prohibited by the UN Charter and that do not violate the principle of non-intervention in the same (cf. Thompson 2008). 6.  Changing the Background Conflicts of compliance exist when it is impossible for an agent to comply with two (or more) mandatory rules at the same time.13 This impossibility can be removed by changing the background facts that make it impossible to comply with both rules. Take again the obligations of a State to invest in both education and health care.14 The State cannot comply with both obligations because of a lack of financial means. By generating more money, for example by raising taxes, the State can take this cause of impossibility away. As soon as the State can invest in both education and health care, it can comply with both of its obligations, and there is no conflict of compliance anymore. 7. Derogation At times, rules conflict with factual necessity, or with rules made to cope with factual circumstances such as in states of emergency. Human rights on privacy might for instance conflict with measures taken to prevent terrorist attacks or investigate them. One technique to prevent such conflicts from arising is derogation. Derogation allows a state to take measures derogating from its obligations under a treaty, to the extent necessary to handle certain situations (see e.g. Article 15 of the European Convention on Human Rights). Logically speaking, there is no conflict in cases of derogation between the rule of the treaty and the rule on the basis of which the measures are taken, because derogation means that the treaty rule does not apply for the duration of the derogation. In short, derogation involves

13  The

discussion in this section will be confined to conflicts of compliance, and will only discuss facts as causes of rule conflicts. A more general discussion that also deals with conflicts of imposition and with rules as causes of conflicts can be found in Hage 2000 and Hage 2005, p. 135 – 157. 14  Cf. Article 24 and 28 Convention of the Rights of the Child and Article 12 and 13 of the International Covenant of Economic, Social and Cultural Rights. That both articles contain only obligations of progressive achievement does not take away from the argument of this section that changing the background can be a tool to deal with conflicts.

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the temporary suspension of applicability of a potentially conflicting rule, thereby avoiding the conflict.15 8.  Incorporation and Reference The easiest way to avoid the dilemma of inter-systemic rule conflicts is to ensure that such conflicts do not occur. We have seen that interpretation and derogation, but also scope limitations, can fulfil this function, in that e.g. the national law of one state is limited in its application to the territory of that State only. With regard to international law in particular, however, scope limitations do not manage to avoid all conflicts. Methods such as incorporation or reference can prevent inter-systemic conflicts from arising as well. Rules of a ‘foreign’ system can be used in a legal system through a technique which may be called ‘reference’. The foreign rules are not incorporated in the legal system, but their existence and content is considered by the system as facts that are legally relevant from the point of view of the legal system. Reference avoids conflicts between the rules of the referring system and the rules of the system to which reference is made, because the content of the referring system is adapted to the content of the referred system. Private International Law provides many examples of this, because it contains meta-rules that determine which national legal system provides the applicable rules. For example, the judgment whether a couple has divorced is given in country A on the basis of the rules of country B, the validity of which is from the perspective of country A a matter of fact. These rules are not incorporated in some international set of object-level rules, and neither is there an independent international system. As a consequence, the rules of the national systems determine the outcomes of cases, without a potential conflict with rules of an international system. In this way, rule conflicts can be avoided. In case of reference, the content of a foreign system is treated by the own legal system as a matter of fact that co-determines the application of the domestic law. In case of incorporation, meanwhile, foreign law becomes part of domestic law. The typical example of this phenomenon is the incorporation of international law in a national legal system in so-called ‘monist’ legal systems. The Dutch legal system nicely illustrates incorporation. Provisions from international treaties ratified by the Netherlands and rules created by international organizations in which the Netherlands participate (in particular the European Union) automatically become part of the Dutch legal system (Art. 93 Grondwet). The foreign rules are not foreign anymore, except in the sense that they were not created by native Dutch legislative 15  Technically speaking, derogation of a rule can be construed in two ways. The one is that an exception is made to the rule. Exceptions are not limited to rule conflicts, but can be made in any case when decisive reasons are available against applying an applicable rule. The other way to construe derogation is to assume that the derogated rule is temporarily not valid. Because only valid rules can be applicable, derogation thus construed makes the rule inapplicable.

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bodies. However, they are part of the Dutch legal system to the same extent as home-made rules. Strictly speaking, incorporation is not a technique to deal with conflicts between rules of different systems, but a way to ensure that only one legal system is relevant.16 If EU regulations become automatically part of the Dutch national law, there is no need any more to pay attention to EU law, because the relevant rules are already part of Dutch national law. In the case of the EU one may even ask whether there exists such a thing as the EU legal system, because arguably the EU only provides organs which can create (uniform) law that becomes part of the national legal system of the Member States. If all counties would have monist systems with regard to the relation between laws of domestic and laws of non-domestic origin, the same might be said about the provisions of human rights treaties.17 These treaties would then create uniform human rights in different legal systems and it might be argued then that there is no separate international human rights system. However, theoretically it is imaginable that some legal system incorporates part of a foreign legal system, while that foreign system has independent existence. The situation is then comparable to one country that uses the national currency of some other country. If ‘foreign’ rules are incorporated in a national legal system they are not foreign rules anymore but merely rules with a foreign origin. Such rules may still conflict with rules of a national origin, or with other rules of foreign origin. However, because of the incorporation, such conflicts are not conflicts between legal systems anymore. What is avoided by incorporation is not a conflict of rules, but a conflict between legal systems.18 If there is still a conflict of rules, the techniques used within a single legal system to deal with conflicts, such as making exceptions, can be used to deal with possible conflicts between rules from national and international sources. 9.  Limitation of Rule-Creating Power A common way to avoid inconsistencies within a single legal system is to avoid rule conflicts by preventing conflicting rules from entering into existence at all. 16  This holds at least from the perspective of the incorporating system. However, the mere incorporation of rules of international law into a national legal system does not make any statement about the place of the incorporated rules in the hierarchy of norms of that legal system. International law will hold itself to be above the constitution, while national law might give the incorporated rules a different status. This brings us back to the issue of subscripting, whereby the national legal system holds that it is the only relevant system because it has incorporated rules of international law, while international law might nevertheless claim relevance. 17  Since not all countries use a monist system, this exercise is quite theoretical. However, it is useful to see what the effects of incorporation might be. 18  As a matter of fact, incorporation makes more rule conflicts possible, because rules from different systems can only lead to conflicts of compliance, while rules that belong to the same system can also lead to conflicts of imposition.

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A national legislator for instance might make an exception to the general right of free speech for cases of hate speech. This will not allow a local legislator to make an exception to the exception for hate speech against people of a particular origin, such as French-speaking people from Walloon. If a local legislator nevertheless attempted to do so, its rules would simply not be recognized as valid law: the local legislator does not have the power to make rules that conflict with the ‘higher’ rules of the national legislator. This limitation of power avoids conflicting rules. With regard to international law, however, limitations of power occur less frequently. This is because such limitations suggest an overarching organization of the distribution of rule creating power that can divest certain actors of their ability to create rules. Such organization is absent in the international plane. As mentioned in the introduction, rule creation in international law is decentralized and tends towards anarchy as even the importance of the doctrine of the sources of law seems to be decreasing. Instead of limitation of power, international law usually creates prohibitions, which can be violated.19 The typical sanction is not invalidity, but the need to make some sort of compensating behavior, which may range from monetary compensation to restitution.20 This is different when it comes to European Union law, which ‘has as a corollary the impossibility, for the Member State, to give preference to a unilateral and subsequent measure against a legal order accepted by them’ (Case 6/64, Costa v ENEL, ECR 585).21

III.  Exceptions To Rules In the previous section we have seen that selecting which rules are applicable to a case can avoid rule conflicts, and that there are a number of logical techniques available to aid in the selection of rules, from scope limitations to derogation, interpretation, incorporation, reference and limitations of rule-creating powers. However, it is clear that even with these techniques to avoid conflict, rule conflicts nevertheless occur. Then it is desirable to make an exception to one of the conflicting rules.22 In this section we will take a closer look to rule exceptions.

19  This emphasis on prohibition, rather than lack of competence, partially explains why the Lotus-principle – that States are allowed to do what was not explicitly prohibited – belongs to the foundations of public international law. 20  Cf. Chapter II of the Draft Articles on the Responsibility of States for Internationally Wrongful Acts. 21  Another exception may be the invalidity of soft law, when it does not complement, but contradicts hard law. The precise nature of soft law and its relation to hard law are too complicated, however, to deal with here. 22  Theoretically it is possible to live with institutional legal facts that seem incompatible, and with rules that prescribe actions that cannot be combined. But that would not be desirable.

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1.  Applicability and Application An exception occurs if a rule that is applicable to a case is nevertheless not applied to that case, and does not generate its normal legal consequences. Applicability and application are in this connection somewhat technical notions with a precise meaning. Both applicability and application concern a relation between a rule and a particular case. If a rule is applied to a case, this means that the rule attaches its consequences to this case. Such a consequence may be that an agent, for instance a State, has the competence to perform some juridical act such as concluding a treaty. It may also be that an agent such as an IGO becomes liable for damages, for instance because it violated an international obligation. Normally a rule will be applied to a case if and only if it is applicable to that case. Applicability is determined by three factors: 1. a rule must exist, or – which boils down to the same thing – it must be valid; 2. the case must fall within the – territorial, temporal and personal – scope of the rule; and 3. the case must satisfy the conditions of the rule. The conditions of a rule are given with the rule formulation, which expresses the conditions and conclusion of the rule. For example, Article 36 of the UN General Assembly Resolution 56/83 creates a rule that defines a State’s liability for particular damage, and gives as conditions for this liability that there was an internationally wrongful act, that a State was responsible for this act, that the damage was caused by this act, and that the damage was not (yet) made good by restauration. If a rule is not applicable to a case, but nevertheless applied, this is most often a case of rule application by analogy. We will not pay attention to this possibility here.23 If a rule is applicable to a case, but nevertheless not applied, an exception is made to the rule. 2.  Are Exceptions Unavoidable? The idea that legal rules are open to exceptions is somewhat controversial. That has to do with a certain ambiguity in the notion of a legal rule. A legal rule may be seen as something that flows directly from a legal source, such as a treaty, legislation, international custom, or case law.24 It may also be seen as a general connection between operative legal facts and legal consequences. These two are not identical, as may be illustrated by a simple example. The interested reader may consult Hage 1997, p. 118 – 121. if a rule ‘flows directly’ from a source, there is a need for an interpretive step that translates the words of the source into the rule formulation, that is the conditions and the conclusion of the rule. The possibility to combine rules into a derived rule goes a step further than this relatively straightforward interpretation. 23 

24  Even

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Under the UN Charter, the use of force is prohibited. However, the Security Council may authorize military intervention in cases of threats to international peace and security. If we have a case in which there is a threat to international peace and security and the Security Council authorizes a military intervention, the two rules seem to conflict. Since the second rule is a lex specialis with regard to the main rule it would normally prevail over it, and application of the second rule would make an exception to the first rule. However, it is also possible to combine the two original rules into a ‘derived rule’ without exceptions, and this derived rule would read that the use of force between States is prohibited unless the Security Council has authorized such use because there is a threat to international peace and security.25 This derived rule has the absence of the exception as one of its conditions, and it would not even be applicable if the Security Council has authorized the use of force. Since exceptions are only possible to rules that are applicable, this new derived rule would not suffer from an exception in case of authorized use of force. Let us have a more systematic look at this phenomenon of ‘derived rules’.26 If a rule is applicable to a case this normally means that the rule is applied to that case and attaches its legal consequences to it. This is so normal that the logic of rule application seems to be nothing else than an ordinary syllogistic argument (Alexy 1983, 273 – 283; MacCormick 1978, 19 – 53). The facts of a case are subsumed under a general rule, and the conclusion that describes the legal consequences of the case follows deductively. This deductive application of rules seems so natural that it requires explanation that exceptions to rules are possible. If a rule seems to have an exception, why not say that the rule was not formulated properly, and that it actually has an additional condition namely that the exceptional circumstances are absent? 3.  Case – Legal Consequence Pairs The insight that rules can have exceptions can be reconciled with the impression that rules can be applied in deductive arguments by means of so-called ‘case-legal consequence pairs’ (CLCPs) (Hage 2005, 27). CLCPs describe the effects of rules such as the prohibition of the use of force and the permission of military action when authorized by the UN Security Council. The two inconsistent rules are combined into a single ‘rule’ that leads to a single consistent result. We use quotation marks here to indicate that this ‘rule’ differs from the two rules that were used to construct it. Both the rule prohibiting the use of force and the rule permitting it in cases of Security Council authorization are directly based on an official legal source, in this case the UN Charter. The derived ‘rule’, however, cannot be traced 25 

Actually, we used this ‘derived rule’ in an example in section 2.4. The question whether it is possible to derive rules (the more often used tem is ‘norms’) from other rules is highly debated. For an overview, see Navarro/Rodriguez 2014, chapter 2. 26 

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back directly to such a source, but is the result of combining the two original rules in light of their apparent purposes, thereby creating a CLCP. It is possible to characterize a legal system as defined by an exhaustive set of such CLCPs: for every kind of case (abstract case) that has legal consequences, there exists a CLCP that gives the characteristics of the kind of case and the legal consequences attached to it. These CLCPs are the outcome of the original rules (including rights and legal principles or incorporated or referred rules) of the system, interpretation and solutions of potential rule conflicts by means of prevalence (such as lex superior) or any other technique the system in question employs to resolve rule conflicts. The CLCPs are constructed in such a way that no particular case can fall under two different abstract cases to which incompatible consequences are attached. For example, there will be a case for ‘military action without Security Council author­ ization’ and one for ‘military action with Security Council authorization’, but not one for military action in general, because the latter might give a different legal consequence in a concrete case of military action with Security Council authorization. Understanding a legal system as an exhaustive set of CLCPs, it is not possible that a case has inconsistent legal consequences. Imminent inconsistencies are filtered out in the step from the original (conflicting!) rules to the CLCP. Moreover, there are no exceptions to CLCPs. If there seems to be an exception, this means that the CLCP was formulated too broadly: there should be two different CLCPs, one for the normal cases and one for the exceptional cases. If a legal system is seen as an exhaustive set of CLCPs, exceptions to rules only play a role in this step from the original rules based on legal sources to the derived ‘rules’ – the CLCPs – that define the outcome of all the interacting original rules. It is this step that requires a non-deductive logic. The derivation of the legal consequences of a case by applying the relevant CLCP to that case can be purely deductive, because all exceptions have already been filtered out in constructing the CLCP. When we discuss exceptions to rules, we are not necessarily talking about the immediate application of rules to cases; we may also be talking about the construction of CLCPs which can in turn be used for legal justification is a deductively valid manner. 4.  Burden of Proof It is possible to characterize a legal systems by means of an exhaustive set of CLCPs, but is this also desirable? One factor that should play a role in answering this question is whether exceptions to rules have the same function as negative rule conditions. If their function is the same, the existence of exceptions should not impede the reformulation of a legal system as a set of CLCPs. However, if exceptions have a function that exceeds that of negative rule conditions, things become different.

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As a matter of fact, exceptions do have a role that exceeds that of negative rule conditions. However, this function can only be recognized if we stop treating rules as a kind of premises in deductive arguments, and start to treat them as tools in the production of arguments in legal dialogues.27 In such a dialogue a party who wants to justify a claim can adduce a rule supporting that claim and facts that satisfy the conditions of this rule. If this happens and the opponent in the dialogue does not react, the claim counts as justified. If an exception should be made to the rule, the opponent in the dialogue must claim this, and justify the claim by providing reasons for making the exception. This means that the opponent who wants to invoke the exception, has the burden of proof for this exception. The burden of proof for the applicability of the main rule rests on the person who uses the rule in justifying the main claim. In other words, the invocation of an exception goes hand in hand with a shift in the burden of proof. Such a shift would not take place if the exception would merely be a negative rule condition, since the burden of proof for the conditions of a rule, including the negative ones, rests with the dialogue party who invokes this rule.28 Because exceptions fulfill a different function than negative rule conditions, it is not desirable to represent a legal systems as an exhaustive set of CLCPs, at least not if the function of exceptions as distributor of the burden of proof is relevant. 5.  The Logic of Exceptions There must be a reason for making an exception to a rule; the exception itself is the outcome of an argument on whether the rule should be applied, and not an independent reason against application. It is, for instance, not possible to say that State A violated WTO law, but should not be sanctioned because there is an exception to the violated rule, even though there are no reasons for making such an exception. Precisely what counts as a reason to make an exception to a rule is not a matter of logic or even legal theory; it is a matter of substantive law. To find out what these reasons are in a particular legal domain such as international law, one should study the domain in question to discover which reasons are recognized as reasons to make exceptions to rules. However, it is possible to say a little bit more in general: reasons for exceptions that are generally recognized are that application of a 27  This step towards seeing legal rules as tools in the construction of legal dialogues was originally inspired by the work of the so-called ‘Erlanger Schule’ (Lorenzen/Lorenz 1978). It was introduced in legal theory through the work of Alexy (1983) and in legal logic through the work of Gordon (1995). For an overview, see Hage 2005, p. 227 – 264. 28  This is almost true by definition, since a negative rule condition that must be proven by the opponent of the rule’s application will count as an exception to the rule. We encounter here a second definition of an exception to a rule, namely as a negative condition for the application of the rule for which the burden of proof rests on the party which does not want the rule to be applied.

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rule would be against the purpose of the rule, and that application of a rule would lead to a conflict with another rule which is also applicable. Here we will pay no additional attention to conflict with the rule’s purpose as a reason for making an exception to a rule. If the rule conflicts with another applicable legal rule, the rule conflict itself will normally be treated as a reason to make an exception to one of the conflicting rules. The ‘logic’ of exceptions to rules works as follows. If a rule is applicable to a case, this is a contributory29 reason to apply the rule, and to attach the rule’s conclusion as a legal consequence to the case. Normally, there are no reasons against applying an applicable rule, and then the applicability of the rule suffices as reason to actually apply the rule, and to make it attach its consequences to the case. If, for example, the United States violated an international obligation and are responsible for this violation, and if damage was caused by this act and the United States did not yet compensate that damage, these facts together constitute a reason to apply the rule of Article 36 of the UN General Assembly Resolution 56/83 to the effect that the United States must compensate this damage. Sometimes, there are contributory reasons against applying an applicable rule. If there are both contributory reasons for and against applying a rule to a case, these reasons must be ‘balanced’. This ‘balancing’ is little more than taking a decision which reasons outweigh the other reasons.30 If the ‘balancing’ of reasons leads to the conclusion that an applicable rule should not be applied, we say that there is an exception to the rule. This exception is in this case nothing else than the outcome of ‘balancing’ the reasons for and against application of the rule. If in a particular case there is an exception to a rule that is applicable to that case, this rule should not be applied, and its consequences are not attached to the case. Furthermore, if a similar case arises later, the exception should hold in that case as well, or an argument needs to be made why this is not the case.31 6.  Prevalence between Rules Since it is not desirable that the rules of a legal system attach incompatible legal consequences to a case, the possibility that this might occur is a reason not to apply one of two rules that are in conflict. This immediately raises the question which rule to apply and which rule to discard. In other words, it becomes necessary to make a choice as to which rule prevails over the other. Again, this is not a choice that logic is suited to make by itself, but logic can provide the techniques to deal 29  A contributory reason is a reason that may have to be balanced against other reasons. For an elaborate discussion, see Dancy 2004, chapter 2. The logic of contributory rules is described in Hage 1997, p. 130 – 158. 30  Such a decision may itself be the result of an argument or the balancing of reasons. The reasoning involved in balancing reasons is discussed in Hage 2005, p. 122 – 129. 31  There may, for example, be an exception to the rule that supported the exception in first instance.

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with prevalence between rules and the implications this has for avoiding actual rule conflicts. The relevant argument in this connection goes as follows: If two rules are applicable to a case, and their application would result in incompatible legal consequences, the rules are in conflict in this case. Such a conflict is a contributory reason against the application of one of the two rules. The fact that application of both rules would lead to an inconsistency is a stronger reason against application than the applicability of both rules is as reason for their application. The intermediate conclusion is that one of the two conflicting rules should not be applied. Making a choice as to which one is a matter of prevalence: the rule that prevails over the other should be applied. Several contributory reasons can be - and in fact are - recognized in this connection.32 One option is that the rule that better fits in the overall legal system prevails over the less fitting rule (coherence). Another option is that the rule that was made by the ‘higher’ authority prevails over the rule made by the lower authority (lex superior). Equally, the more specific rule could prevail over the more general rule (lex specialis), or the more recent rule over the older one (lex posterior). Taking the lex posterior rule even one step further is the technique of implied repeal, whereby it is presumed that if the later rule conflicts with the earlier rule, the later rule not only prevails, but the earlier rule is in fact repealed. However, if one of the ‘conflicting’ rules counts as repealed, there is no real conflict, since the repealed rules does not exist anymore and can for that reason not be applicable.

IV. Conclusion The development of the internet, the rise of transnational law, the co-existence of different legal traditions and sub-traditions, and globalization all mean that the opportunities for conflicts between rules increase. International law is not excluded from this development, and is in fact in many ways prone to such rule conflicts. A conflict of rules occurs when it is possible that two or more rules attach incompatible legal consequences to a case. Such conflicts can be conflicts of imposition, where two rules impose incompatible facts upon the world, or they can be conflicts of compliance, where two rules demand incompatible behavior from one and the same agent. These conflicts can occur between rules of the same system, but equally between rules of different (legal) systems. To deal with these conflicts, it is often necessary to make exceptions to one or more of the rules that are involved in the conflicts. One major purpose of this contribution is to investigate which techniques logic has on offer to deal with conflicts between rules and the exceptions that are needed in that connection. Logic cannot and should not dictate a particular way of dealing with rule conflicts, but it can be of help by providing a conceptual framework that clearly defines when a rule conflict occurs, and which techniques are available to deal with it. Moreover, 32 

The following is a non-exhaustive list.

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it can help us understand why the view that rules are without exceptions can be very attractive. A second major purpose of the present contribution is to see what logic can offer us as techniques to avoid rule conflicts. If only one of two conflicting rules is applicable to a case, there is no conflict. Subscripting rules from different normative systems, the use of scope conditions, interpretation, changing background conditions, derogation, incorporation, reference and limitations of the power to create rules are all discussed as techniques to prevent conflicts. It is important to emphasize, however, that although logic can offer us techniques to avoid and to handle conflicts of rules, it cannot make the decisions for us. The knowledge which techniques are available only gives us an indication of what is possible. Next to that we need a view on what is desirable, and this view requires the study of law, politics, international relations and morality.

References Alexy, R.: Theorie der juristischen Argumentation, 7. Aufl., Frankfurt a. M.: Suhrkamp 1983. Arend, Anthony Clark: Legal rules and international society. Oxford: Oxford University Press 1999. Barth, E. M./Krabbe, E. C. W.: From Axiom to Dialogue, Berlin: Walter de Gruyter 1982. Dancy, Jonathan: Ethics Without Principles, Oxford: Clarendon Press 2004. Franck, Thomas M.: The power of legitimacy among nations. Oxford: Oxford University Press 1990. General Assembly A/CN.4/L.682: ‘Fragmentation of international law: difficulties arising from the diversification and expansion of international law, Report of the Study Group of the International Law Commission, finalized by M. Koskenniemi (2006) (Koskenniemi 2006). Gordon, Th. F.: The Pleadings Game. An Artificial Intelligence Model of Procedural Justice, Dordrecht: Kluwer 1995. Hage, Jaap C.: Reasoning with Rules, Dordrecht: Kluwer 1997. – ‘Rule Consistency’, Law and Philosophy 19 (2000), pp. 369 – 390. – Studies in Legal Logic, Dordrecht: Springer 2005. Koskenniemi, M./Leino, P.: ‘Fragmentation of international law? Postmodern anxieties.’ Leiden Journal of International Law, 15 (2002), 553 – 579. Lorenzen, P./Lorenz, K.: Dialogische Logik, Darmstadt: Wissenschafliche Buchgesellschaft 1978. MacCormick, Neil: Legal Reasoning and Legal Theory, Oxford: University Press 1978. Navarro, Pablo E./Rodríguez, Jorge L.: Deontic Logic and Legal Systems, Cambridge: Cambridge University Press 2014. Prakken, Henry: Logical Tools for Modelling Legal Argument. A Study of Defeasible Reasoning in Law, Dordrecht: Kluwer 1997.

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Prakken, Henry/Sartor, Giovanni (eds.): Logical Models of Legal Argumentation, Dordrecht: Kluwer 1997. Raz, Joseph: The Authority of Law, Oxford: Clarendon Press 1979. Sartor, G.: Legal Reasoning, A Cognitive approach to the Law, Dordrecht: Springer 2005. Schauer, F.: Playing by the Rules, Oxford: Clarendon Press 1991. Thompson, M.: Life and action, Cambridge: Harvard University Press 2008. Waddington, L./Visser, Laura: ‘Temporary Special Measures under the Women’s Convention and Positive Action under EU Law: Mutually Compatible or Irreconcilable?’ in I. Westendorp (ed.), The Women’s Convention Turned 30: Achievements, Setbacks, and Prospects, Cambridge: Intersentia 2012.

Logic and Criminal Law1 By Jan C. Joerden Jan C. Joerden

In the context of Criminal Law, the usage of logical instruments has proven successful, in particular when structuring individual areas of concern. In this essay, only few selected fundamental issues in which logic can contribute to solving criminal legal problems can be presented. For a greater amount of detail, please refer to further relevant literature.2

I. Propositional Logic 1. Dyadic Case-systems Modern propositional logic traces back to Ludwig Wittgenstein, who was the first to compile a complete table of all 16 propositional logical operations in his paper Tractatus logico philosophicus3 (tab. 1). Table 1: Wittgenstein’s Truth Table x

y

1

2

3

4

5

6

7

8

9

10

11 12 13

14

15 16

T

T

T

T

T

T

T

T

T

T

F

F

F

F

F

F

F

T

F

T

T

T

T

F

F

F

F

T

T

T

T

F

F

F

F

F

T

T

T

F

F

T

T

F

F

T

T

F

F

T

T

F

F

F

F

T

F

T

F

T

F

T

F

T

F

T

F

T

F

T

F

F

This so-called Wittgenstein’s truth table is based on a binary logic, that uses only the two logical values “true” and “false”.4 At the same time, it is a two-digit (dyadic) table, because only two propositions (x and y) are connected to each 1  For translating this contribution into the English language and his valuable advice, I am especially grateful to my former research assistant Dr. Johannes Bochmann. 2 E.g. Rödig (1969); Klug (1982); Hruschka (1988); Joerden (2010); Philipps (2012), each containing further references. 3  Wittgenstein (1921), No. 5.101. 4  There are also multi-valued logics, that are however, in the end, based on Wittgenstein’s systematics and merely expand and develop his ideas further. For Criminal Legal doctrine, these different logics have not led to any further developments in solving problematic cases yet.

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other.5 The usual interpretation6 of the individual columns in fig. 1 can be found in tab. 2. Table 2:

Interpretation of the dyadic truth functors Column Matrix Symbol Name 1111

2

1110

3

1101

4

1100

5

1011

6

1010

7

1001

8

1000

9

0111

10

0110

11

0101

12

0100

13

0011

14

0010

15

0001

16

0000

┬

tautology

everything (is always true)

˅

∟

prependence

∟

postpendence

˄

disjunction

at least one (not none)

←

replication

→

implication

the latter not without the former at least the former (no matter whether or not the latter) the former not without the latter

↔

equivalence

at least the latter (no matter whether or not the former) not one alone (either both or none)

conjunction

both

exclusion

not more than one (not both)

/

∟

exactly one of both (either the former or the latter) in no case the latter (no matter whether post-nonpendence or not the former) post-section the former without the latter in no case the former (no matter pre-nonpendence whether or not the latter)

⤙

pre-section

the latter without the former

rejection

none (both not)

antilogy

nothing (is true in no case)

⤚ ⤙ ∟

1

Textual Interpretation

⤚ †

┴

contravalence

In the criminal legal context, it has proven convenient to interpret the signs “T” for “true” and “F” for “false” as possibility of a truth value and therefore replace them with (+) and (–) signs, respectively, with (+) symbolizing “possible” and (–) symbolizing “impossible”. By means of Wittgenstein’s truth table in this reinterpreted form, different criminal legal issues can be systematized in such a manner, that their respective surrounding dyadic case-systems are displayed. Dyadic case-systems herein refers to those groups of cases, that result from a corresponding interpretation of Wittgenstein’s truth table if judgments not only referring to one single criminally legally relevant situation, but to two situations are examined; what exactly is meant by this will be exemplified in the following. 5  If three propositions are connected to each other, this results in a triadic table with 256 columns. 6  Taken from Bocheński/Menne (1983), p. 35.

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Such an approach makes it possible to develop solution strategies for the relevant criminal legal issues. In doing so, it is not the goal to decide criminal legal cases, so-to-speak, with the help of logical instruments. This is impossible not only because, in general, several legal evaluations are necessary that cannot be replaced with a purely logical tool-set which merely can depict the formal side of a problem. However, with this method, it is possible to display why certain suggestions of a solultion face concerns, namely if they are not able to lead to a consistent solution for all cases in such a case-system. Additionally, this method of generating case-systems makes it possible to compare the structures of indeed different criminal legal issues by presenting them using the same systematics and thus being able to examine solution strategies with regard to their consistency with each other as well as concerning necessary differences. Criminal legal issues that can be presented in such a way are, among others, the following:7 (1) The cases in which an offender envisages that by his concrete action he will commit not only one offence but two offences. In doing so, it is possible that he wants to commit both offences together simultaneously (dolus cumulativus); but it is also possible that he wants to commit only either one or the other offence (dolus alternativus). Dealing with the latter, it is problematic which form of intent the offender must be attributed (cf. in greater detail section I.2. below). (2) At the end of a criminal trial, it is often the case that after hearing the evidence the judge has the impression that the defendant has committed not only one offence but rather two offences. In this process, it is possible that the judge is sure that the defendant committed both offences; in such a case he will convict the defendant for both offences. However, it is also possible that he believes the defendant has committed either one or the other offence. Then the question is, how to deal with such a case in light of the principle in dubio pro reo. German criminal judicature suggests, as a rule, the defendant’s aquittal regarding both offences. Only by way of exception, that is, if both offences are similar, the defendant can be convicted of “offence A or offence B” (so-called conviction in the alternative [“Wahlfeststellung”]). These cases, too, belong to a dyadic case-system that furthermore includes the case of the so-called finding of postpendence [“Postpendenzfeststellung”] which is recognized in the Federal Court of Justice’s judicature. This term itself already states the obvious, namely, that this is based on a constellation in Wittgenstein’s truth table. It therefore immediately becomes plausible that it is necessary here to use the structures of propositional logic to present the decision in such constellations of cases. (3) Furthermore, the criminal legal issue of conflict of duties [Pflichtenkollision] or alternative duties can be structured and illustrated by means of a dyadic case-system, because here, too, a “two-digit” systematics is in place, in which the addressee is under two duties but can only fulfil one or the other. At the heart of 7 

Cf. in more detail Joerden (1986) and (2010), pp. 5 et seq. with further references.

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clarifying the criminal legal issues connected to this situation is the rule ultra posse nemo obligatur that must be applied to the different constellations of cases of this case-system in the adequate manner. (4) For attributing criminal legal responsibility, it is of essential importance to ascertain a causal connection between a deprecated “result” (i. e. the death of another person) and a person P’s action. Without such a causal connection, P cannot be held responsible for this result. Difficulties in evaluating this may arise if not only one person was involved in bringing about the respective result, but rather two persons’ actions affected the result. If both actions are necessary in order to explain the result, both persons caused the result (so-called cumulative causation). The problematic case, however, is that of so-called causal over-determination, in which the result can be explained completely by the actions of one of both persons although, at least seemingly, both persons played a part (so-called alternative causation). Additionally, further criminal legal issues can be identified, that can be structured and illustrated as dyadic case-systems. These cannot be elaborated upon at this point.8 But, in order to illustrate the above-mentioned issue (1), a summarizing overview of a chain of arguments to solve, in particular the underlying criminal legal issue of dolus alternativus, that is committed to propositional logical systematics, is outlined. 2. For Example: The Issue of dolus alternativus9 Usually, the offender in Criminal Law, at the time of his act, imagines that he will commit one offence. If, for example, A intentionally hits B’s arm, he imagines circum­stances that will amount to committing the crime of “causing bodily harm” (Körper­verletzung, sec. 223 German Criminal Code). Other crimes and their committal are out of the question, here. However, there are indeed constellations in which the offender A, at the time of his act, envisages not only the committal of one crime but of two or perhaps even more crimes. For reasons of clarity, I will limit my argumentation to constellations dealing with the committal of exactly two crimes. Take, for example, the following case: A fires a single shot with his shotgun, imaging that this one shot will hit B as well as C lethally. In other words, he imagines that his one act results in circumstances that amount to committing the crime of murder10 (sec. 212 German Criminal Code) twice, more precisely: cumulatively, i. e. at the same time by the same act. If in such cases the question arises, how intent is to be attributed, there is no serious problem in Criminal Law. A is simply attributed two intents; in this example: Cf. ibid., pp. 107 et seq.; Philipps (1974). Part I.2. is a revised and expanded version of a lecture I have given at the University of Bielefeld and that has been published in Pływaczewski (2017). 10  Translation as follows: Totschlag (sec. 212 German Criminal Code) = “Murder”. – Mord (sec. 211 German Criminal Code) = “Murder under specific aggravating circumstances“. 8  9 

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two intents of murder. His culpability then further depends on whether or not he has succeeded in carrying out his intent. If he lethally hits B and C, he must be convicted for two crimes of murder in concurrence of (same) offences (sec. 52 German Criminal Code). If he only hits one of the victims, he is guilty of one murder and one attempted murder. And if he missed completely, he is criminally liable only for two attempts of murder. Therefore, the general rules of attribution in Criminal Law are not problematic in constellations of dolus cumulativus. The matter is different, though, in the contro­ver­sial cases of alternative intent, or dolus alternativus. Here again, the offender ima­gines the committal of two crimes, this time, however, not cumulatively but alter­na­tively. Take, for example, the following case: Skyjacker S wants to hijack a plane on a do­mes­tic flight and divert it to another country. While he is threatening the pilot P and the co-pilot C in order to force them to change course to this end, both P and C – after activating the auto-pilot – suddenly rise from their seats and approach S wanting to overpower him. S, therefore, shoots at both pilots, expecting that he will hit either P or C lethally. He completely rules out that his one shot could kill both P and C. In fact, he does not even want this to happen, as the aeroplane would have no competent guidance and would not be able to land safely, costing his (S’s) own life. In this case, it is not as simple as in the dolus cumulativus constellation above to just attribute two intents of murder to S, because S excludes the possibility of killing both persons (pilot and co-pilot). He rather wants to kill only one of the two. Of course, things can turn out differently than he had imagined. For example, P and C could coincidentally stand behind each other while S fires and his shot could happen to kill both pilots – contrary to S’s expectation. It might also be that S misses, thus causing neither P’s nor C’s death. Therefore, we must deal with the following four variants of the case: (1) P and C are killed; (2) Only P is killed, C survives; (3) Only C is killed, P survives; (4) P and C survive. What intent should be attributed in dolus alternativus cases and each of their four variants is controversial. Two main groups of opinions can be distinguished, that I will refer to here as “first thesis” and “second thesis”. The first thesis demands that the offender should be attributed two intents in these cases. According to the second thesis, on the other hand, only one intent may be attributed to the offender, because he only wanted to commit one offence at the most. a) First Thesis: Two Intents must be Attributed Let us, at first, examine the first thesis, according to which two intents must be attributed to the offender. In the above-mentioned example of the skyjacker, this would mean that in variant (1), i. e. if P and C are both killed, the offender is guilty of two murders. In variant (2), if only P but not C is killed, he will be punished for one accomplished murder and one attempted murder. Accordingly, in variant (3), i. e. if only C dies. Finally, in variant (4), S is guilty of two attempted murders. All

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this is consequence of the thesis that in dolus alternativus cases two intents must be attributed. That something can’t be right about this thesis can be seen by comparing it to the parallel case in which the offender acts with dolus cumulativus. For in both cases two intents are attributed, so that the evaluation results in the four depicted dolus alternativus variants would be exactly identical to those in dolus cumulativus cases. This is not very plausible, not least because the offender in the dolus cumulativus case wants to shoot dead two persons (B and C), whereas in the dolus alternativus case he only wants to kill one of two persons (either P or C). The opinion in (German) legal literature11 that wants to attribute two intents in cases of dolus alternativus sees this issue, too, and suggests that in contrast to dolus cumulativus cases, in cases of dolus alternativus only two “conditional intents” (dolus eventualis) should be attributed. This is argued to be justified because the offender (e. g., in the above-mentioned skyjacker case), after all, considered it possible that he kills P and also considered it possible that he kills C. And in order to attribute dolus eventualis it is sufficient, according to the prevailing view, that the offender considers the committal of the elements of crime to be possible and approves of the criminal result. However, this argument is not convincing, because it does not take into account the “mutual conditionality” of both dolus eventualis within the dolus alternativus. Insofar as the offender in the skyjacker case considers it possible to kill P, he rules out that he will also kill C and vice versa. Accordingly, even by attributing two dolus eventualis, the objection cannot be escaped that an offender acting with dolus alternativus wants to kill only one of the two victims and not both – in fact, he does not even believe the latter to be possible. This becomes strikingly clear in the skyjacker case if the skyjacker’s interests are looked at more closely: It may be that S approves of P being killed and also approves of the fact that (instead) C might be killed. By no means, however, does he approve of P and C being killed, because he himself would not survive due to the lack of competent personnel able to safely land the aeroplane. It can, therefore, be concluded that the suggestion to attribute two intents in dolus alternativus cases is not convincing because doing so would level out the difference to dolus cumulativus without any justification. b) Second Thesis: Only one Intent must be Attributed Accordingly, the opposing view to the first thesis discussed so far seems to be preferable. This second thesis demands that in dolus alternativus cases only one of both possible intents must be attributed to the offender, in order to avoid an unjustified equal treatment with dolus cumulativus cases. With this, the question 11 

Cf. references for this position in Joerden (2010), pp. 33 et seq.

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immediately arises, which of the two intents should be considered. This question is relatively simple to answer if two homogeneous intents are concerned – as is the case of the skyjacker. With this, I mean intents directed at the same crime; in the skyjacker case: murder according to sec. 212 German Criminal Code (to the disad­ vantage of the pilot P on the one hand, and to the disadvantage of the co-pilot C on the other). In such a case, which of the intents to commit murder is attributed is irrelevant for the criminal legal result. In contrast, things become complicated as soon as dolus alternativus cases are dealt with, in which both crimes envisaged by the offender are evaluated diversely by Criminal Law. Take the following example as a starting point: The house owner H, who is extremely sensitive to noise, yet again hears a disturbing noise coming from the shrubs in his neighbour’s garden. As he happens to carry his shotgun, he angrily shoots at the shrubs, imagining that in doing so he will kill either his neighbour’s son or his neighbour’s dog. While shooting, H excludes the possibility that both (son and dog) might be in the shrubs and could be hit lethally. Once again, four variants of this case are easily conceivable: (1) Coincidentally, the neighbour’s son and dog are both sitting in the shrubs and are killed by the shot; (2) only the neighbour’s son is killed, the dog is not present and thus survives; (3) only the dog is killed, but not the son; and (4) the sound in the shrubs was caused by neither the neighbour’s son nor his dog, because they are both not there; accordingly they both stay alive. This case shows that there are dolus alternativus cases in which the alternatives differ significantly regarding their criminal legal judgment. Namely, this case is concerned with murder according to sec. 212 German Criminal Code regarding the death of the neighbour’s son, on the one hand. On the other hand, this case deals with mere criminal damage (to property) according to sec. 303 German Criminal Code as far as the killing of the neighbour’s dog is concerned. Regarding their criminal legal evaluation, both crimes differ significantly. While murder requires a minimum penalty of 5 years imprisonment under sec. 212 German Criminal Code, criminal damage under sec. 303 German Criminal Code is punishable with a maximum punishment of only 2 years imprisonment. So the question arises for the second thesis on dolus alternativus in all its severity: Which intent should be attributed if this must be only one of both possible intents, as this thesis stipulates? Should it be the intent to murder or the intent to cause criminal damage? To answer this questions, three different suggestions (referred to as “sub-theses” here) have been put forward. c) First Sub-Thesis: Intent Attributed Depending on the Criminal Result The first sub-thesis on the thesis that only one intent must be ascribed, aims at attributing only the intent to commit the crime that’s criminal results have occurred, more precisely: the crime that’s actus reus requirements are met.12 This means that 12 Cf.

ibid.

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in variant (2) of the case, i. e. only the neighbour’s son is killed, the intent to murder is attributed to H. He is, therefore, punished for intentional, accomplished murder. However, if only the neighbour’s dog is killed, as is the case in variant (3), the intent to cause criminal damage is attributed to the offender, accordingly making him guilty only of intentional, accomplished criminal damage. This last result appears to be problematic if only because the fact that H at least considered the possibility that his neighbour’s son might be killed is discounted completely. But even these evaluation issues left aside, this sub-thesis is not convincing from a systematic point of view, too. For it cannot state how to decide in variant (1), i. e. the case in which both victims, the neighbour’s son and dog, are killed. Because, if on the one hand, only one intent should be ascribed, this intent, however, being dependent on which criminal result occurred, the issue cannot be resolved, which intent to ascribe if both criminal results have occurred, as is the case in variant (1). Likewise, in the case’s variant (4) there is no decisive criterion because neither the neighbour’s son nor his dog was killed. Should this, then, be an attempted murder, attempted criminal damage, or no attempt at all? However, that this sub-thesis is not convincing is not only because there are no decision-making criteria for variants (1) and (4). Furthermore, it is a mistake to make questions of subjective attribution depend on the fulfilment of the objective elements of that crime (actus reus). The subjective elements of crime (roughly: mens rea) are taken from the offender’s world of imagination, i. e. his mental state, whereas the objective elements of crime represent the objective world. Both can match, namely in cases of intentionally accomplished crimes, but do not have to match, as is the case if the offender is mistaken; a negative mistake (ignorance) may lead to a negligent crime, whereas a positive mistake (erroneous assumption of facts) may lead to an attempted offence. In any case, objective and subjective worlds do not depend upon one another in the sense that one is determined by the other. Likewise, the attribution of results in the objective and in the subjective level must not be made dependent on one another. d) Second Sub-Thesis: Intent Attributed only Regarding the more Lenient Accu­sa­tion If, accordingly, the first sub-thesis must be ruled out because it is not suitable to solve the issue, two sub-theses on the second thesis remain, that one and only one intent must be attributed in dolus alternativus cases. One of these two sub-theses now claims that the intent must always be based on the more lenient criminal accusation (“second sub-thesis”),13 while the other remaining sub-thesis (“third sub-thesis”) suggests to always refer to the more severe criminal accusation.14 In the case of the noise-sensitive house owner, the sub-thesis that always bases intent on the more lenient accusation (in this case: criminal damage), would reach 13 Cf. 14 Cf.

ibid. ibid.

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the following conclusions in the case’s four variants: In variant (1), in which the neighbour’s son and dog are killed, one would have to assume accomplished criminal damage; the son’s killing could only be considered as negligent manslaughter under sec. 222 German Criminal Code. In variant (2), in which only the neighbour’s son is killed, the offender could only be punished for attempted criminal damage and for negligent manslaughter, at most, regarding the neighbour’s son. In variant (3), in which only the dog is killed, the offender could only be punished for accomplished intentional criminal damage. And in variant (4), in which none of both objects is hit, he is only punishable for attempted criminal damage. e) Third Sub-Thesis: Intent Attributed only Regarding the more Severe Accusation According to the other remaining sub-thesis, that attributes only the intent meaning the more severe criminal accusation, these results would follow: In variant (1), in which both the son and the dog are killed, H must be punished for intentional, accomplished murder; in structure, he has also committed “negligent criminal damage”, however – at least in German Law – this is not a crime. In variant (2), in which only the neighbour’s son is killed, the offender is punished for intentional, accomplished murder. In variant (3), in which only the dog is killed, H would be criminally liable for attempted murder; so far as it is a criminal offence negligent criminal damage would also have to be considered. Finally, in variant (4), in which neither the neighbour’s son nor his dog are killed, H would have to be punished for attempted murder. f) Decision between Second Sub-Thesis and Third Sub-Thesis Now, the question has to be answered, which of these two remaining sub-theses is preferable: The one that bases intent on the more lenient accusation, or the other one, that prefers the more severe criminal accusation? In order to answer this question, some systematic efforts are necessary. In a first step, I will go back to the level that I mentioned at the very beginning of my remarks, in which the offender’s mental state is directed at only one crime; I shall refer to this level as the “monadic level”, as the offender’s mental state is, so to speak, one-digit (= monadic), simply because it is directed at only one actus reus. Later on, I shall use the term “dyadic level” to refer to an offender’s two-digit mental state, in other words: cases in which the offender envisages two actus reus. But first, let us turn to the monadic level of the offender’s mental state. g) Monadic Level of Attribution of Intent Here, at least three constellations15 can be distinguished from one another (cf. tab. 3). 15 

Constellation 4 is not of importance here, because it represents the contradiction.

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Table 3

Table for the Monadic Level Circumstances A

1

2

3

4

Present

+

+

−

−

Not present

+

−

+

−

1. The offender considers it possible that he will fulfil the objective elements of the crime A by his act; but he also considers it possible that he will fail in doing this. 2. The offender considers it possible that he will fulfil the objective elements of the crime A by his act; and he believes it is impossible that he will not be successful in doing this. 3. The offender considers it possible that he will not fulfil the circumstances of the crime A; and he believes it is impossible that he will succeed in doing this. Obviously, constellation 2 represents a case of dolus directus, in which the offender is sure that he will fulfil all elements of a crime. For here the offender believes that it is possible that circumstances of crime A will be present (i. e. the criminal result will occur), while at the same time he believes it is impossible that this will not be the case. All in all, this means that he is sure that the criminal result will occur.16 Accordingly, constellation 3 represents non-intent, because the offender is sure that he will not fulfil the elements of crime. In such a case, the offender can be accused of a negligent crime, if any. By contrast, the constellation 1 is of particular interest in the present context. In this case, the offender believes on the one hand it is possible that the elements of crime will be fulfilled, and on the other hand that it is just as possible that this will not be the case. So this is a case in which the offender considers it merely possible that he will fulfil the elements of crime A; he is not sure of it, because he also considers the opposite (i. e. non-fulfilment of the elements of crime A) to be possible. Under the condition that the requirement regarding an additional voluntative component of intent, that is deemed necessary by many scholars, is met, this is a case of dolus eventualis. Now, it is worth noting that the resulting criminal evaluation of constellation 1 is (at least under German Law) equal to that of constellation 2. For in both constellations 1 and 2 intent is attributed to the offender: in one case dolus eventualis 16  At this point, the common differentiation between acting with 1st degree dolus directus (i. e. with direct intent) and with 2nd degree dolus directus (i. e. knowingly) may be set aside, because only the cognitive, and not the voluntative, element of intent is of interest here.

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(constellation 1), in the other case dolus directus (constellation 2). However, at the same time, constellation 1 represents a constellation of doubt. In this case, the offender is not sure what will happen, he is rather in doubt as to whether or not the criminally relevant circumstances will be present. Thus, the constellation of dolus eventualis is a constellation of the offender’s doubt regarding the criminally relevant facts. And German Criminal Law reacts to these doubts by attributing intent to the offender, despite the fact that from a logical point of view the attribution of non-intent, i. e. an equalisation with constellation 3, would have been imaginable, too. The material reason for this attribution of intent (dolus eventualis) in constellation 1 is that the offender’s doubts are what he is charged with. Whoever is in doubt as to whether or not his acts will fulfil the elements of a crime, must inform himself of what is actually the case. If he acts nonetheless, without having cleared up his doubts, he is liable as if he had known that he will fulfil the elements of crime: intent is attributed. This approach regarding attribution of intent is, therefore, structurally different from the way doubts regarding fact-finding at a trial are dealt with in Criminal Law. As is known, in such cases the rule in dubio pro reo (“when in doubt, for the accused”) applies. That doubts arising within the Criminal Procedure are dealt with in favour of the accused, is based on the presumption of innocence, a constitutional guarantee, and on the fact that the duty to explore and prove the facts is on the State and not the accused. Concerning the attribution of intent, this is different; any doubts the offender may have regarding the circumstances of his actions are to his own disadvantage, because he could have cleared them up before acting. Now, the ground is laid for an answer to the question which of both remaining sub-theses regarding dolus alternativus is correct; the one that takes the more lenient, or the more severe accusation as a basis. One simply must take a look at the structure of dolus alternativus once again: This, too, is a structure of doubt. Now, however, no longer the doubt as to whether or not one situation A will or will not occur (dolus eventualis), but the doubt as to whether situation A or situation B is (or will be) present. h) Dyadic Level of Attribution of Intent The best way to clarify this, is to compile a table that includes all possible constellations of the offender’s mental state regarding two criminally relevant situations or sets of circumstances. Because such a table records two-digit, i. e. dyadic, mental states, it can be referred to as “table for the dyadic level”. Such a table (tab. 4) contains exactly 16 different constellations, and is based on a representation of Wittgenstein’s above mentioned truth table.17 17 Cf. fig. 1, regarding our topic here in a slightly transformed version, cf. Joerden (2010), p. 50.

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Table 4

Table for the Dyadic Level Circumstances A Circumstances B 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Present

Present

+ + + + + + + + −

− − − − − − −

Present

Not present

+ + + + − − − − +

+ + + − − − −

Not present

Present

+ + − − + + − − +

+ − − + + − −

Not present

Not present

+ − + − + − + − +

− + − + − + −

But for our question here, it is not necessary to look at all of these 16 constellations. It is enough to emphasize two of them, constellation 8, a case of dolus cumulativus, and constellation 10, a case of dolus alternativus, which are as follows regarding the offender’s mental state: 1. Dolus cumulativus (constellation 8): The offender is sure that he will not only commit crime A, but also crime B, whilst he excludes that he will commit none of these crimes nor only one of them. 2. Dolus alternativus (constellation 10): The offender believes that he will commit one out of two possible crimes A or B, and he excludes that he will commit both of them (by the same act) or none of them. Constellation 8 represents a case of dolus cumulativus, because here the offender is sure that he will commit both crimes A and B, as he rules out all other possibilities. Here, he must be attributed two dolus directus. The contestable dolus alternativus case in question here is found in constellation 10, because it represents an either-or-connection between crime A and crime B. For here, the offender rules out that both crimes A and B will be committed, as he believes it is possible that he will commit either crime A or B, respectively, alone, i. e. without also committing the other crime. So the decisive element is that the offender does not even consider it possible that he could commit both crimes together. At the same time, this makes clear that dolus alternativus cases are also constellations of doubt, more precisely: the offender’s doubt, which one of the two crimes A and B he will commit. Insofar, this situation is comparable to the dolus eventualis case, in which the offender is in doubt as to whether or not he will commit the crime in question. The only difference is that in dolus alternativus cases the offender’s doubt relates to two different crimes: Either he will commit crime A or crime B, but not both at the same time. Against the background of these structural similarities between dolus eventualis and dolus alternativus, precisely: regarding the offender’s doubt, it becomes even clearer now, that the offender must not be attributed two intents in dolus alterna-

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tivus cases; only one intent may be ascribed. And because the offender himself is responsible for his doubt, this attribution must not be based on the more lenient accusation but on the more severe accusation. This corresponds with dolus eventualis cases, in which Criminal Law deals with the offender’s doubts by basing its evaluation on the more severe perspective, namely by evaluating dolus eventualis and dolus directus equally, and considering both as forms of intent. With that said, the last question is now answered, which of the three sub-theses on the second thesis (i. e. the thesis, that in dolus alternativus cases only one intent must be attributed) is preferable: It is the (second) sub-thesis that holds the attribution of intent regard the more severe criminal accusation to be correct. 3. Checking the Reasoning in Judgments The systematics of propositional logic can also be utilized to check the arguments and reasoning found in court judgments. Due to the fact that such judgments often must include value decisions that can be systematized logically only to a limited extent,18 the use of this method is limited in this area. At least the courts’ errors of reasoning can be identified if the judgment is thoroughly redacted.19 As a violation of the general rules of logic [“Verstoß gegen Denkgesetze”] is a fundamental error and an absolute ground of appeal, this approach is indeed practically relevant in criminal proceedings.

II. Class Logic In Criminal Law, class logic, too, has proven to be helpful.20 This is particularly true for issues dealing with the theory of so-called concurrence. This means cases in which two different offences are committed by one and the same act. For example, if a person P, by firing one and the same shot, both kills a person (murder under sec. 212 German Criminal Code) and destroys a window pane (criminal damage under sec. 303 German Criminal Code). The question then arises, of which of the two offences (or, perhaps indeed of both offences) the accused must be convicted. This issue can be presented using logical instruments by asking what norm-logical relationship can actually exist between two rules, i. e. the law on offences A and B. If all cases covered by one rule are symbolized by a circle, with each point within the circle’s area representing one of the rule’s cases, exactly four different constellations can be determined:

Cf., however, the interesting suggestions on this matter found in Alexy (2003). Alexy (1980); Herberger/Simon (1980), pp. 77 et seq.; Joerden (2010), pp. 111 et seq., 351 et seq.; each containing further references on legal fallacies and to relevant literature. 20  Cf., among others, Klug (1956); Hruschka (1983) and (1988), pp. 387 et seq.; Seier (1983); Joerden (2010), pp. 127 et seq. 18 

19 Cf.

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(1) Identity between offence A and offence B, i. e. every case that is covered by offence A is also a case of offence B and vice versa (cf. fig. 1). A=B Figure 1: Identity

For the issues of concurrence, this case is not of much interest, because an identical doubling of offences within the same legal order practically does not exist.21 If anything, this constellation may be of interest in the field of Comparative Law, if it can be established that an offence in one jurisdiction has the exact same scope as another offence in another jurisdiction. (2) Heterogenity between offence A and offence B, i. e. every case of offence A cannot at the same time be a case of offence B and vice versa. Put otherwise: There is no common case of offences A and B (cf. fig. 2).



A

B

Figure 2: Heterogenity

From a criminal legal point of view such an exclusive relationship exists, e. g. between fraud under sec. 263 German Criminal Code and theft under sec. 242 German Criminal Code, at least regarding the same object. For the same object cannot be obtained by a disposal of property due to an error (sec. 263 German Criminal Code) and a removal (sec. 242 German Criminal Code) at the same time. Therefore, no issue of concurrence arises in this constellation, because it is never possible that one case falls within the scope of both offences, and thus no concurrence of offences exists. (3) Subordination between offence A and offence B, i. e. every case of offence B is also one of offence A, but not vice versa (cf. fig. 3). A B Figure 3: Subordination

21  There is one exception in the area of justification grounds in German Law: In sec. 227 German Civil Code and sec. 32 German Criminal Code (self-defence), the scope of both rules is practically identical.

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From a criminal legal point of view, this is the case of speciality. The issue of concurrence for the overlapping area, i. e. cases that cover both offence A and offence B, is solved in such a way that the judgment is based only on the more specific offence B according to the rule lex specialis derogat legi generali. There can be more specific offences that lead to a higher sentence (aggravated offence) or to a mitigated sentence (privileged offence). In both cases, the respective basic offence (in this case: offence A) is superseded. This is true, e. g. for the relationship between sec. 223 German Criminal Code (causing bodily harm) and sec. 224 German Criminal Code (causing bodily harm by dangerous means) (aggravated offence), as well as the relationship between sec. 212 German Criminal Code (murder) and sec. 216 German Criminal Code (killing at the request of the victim) (privileged offence). (4) Interference between offence A and offence B. This means, that there are cases which are only covered by offence A, cases that are only covered by offence B, as well as cases that fall within the scope of both offences (cf. fig. 4). A B Figure 4: Interference

One example for this constellation is murder according to sec. 212 German Criminal Code as offence A and criminal damage according to sec. 303 German Criminal Code as offence B. For there are cases that are murder without at the same time being criminal damage, there are cases that are criminal damage without at the same time being murder, and there are cases that are murder and criminal damage at the same time (e. g. X kills Y by a gunshot through Y’s window). A case falling within the overlapping area of offences A and B raises an issue of concurrence, because it is unclear of which offence the accused is to be convicted and according to which offence he must be sentenced. Two possibilities are conceivable: (a) A conviction of both offences A and B takes place; this is called concurrence of offences [“Idealkonkurrenz”] or unity of crime [“Tateinheit”], cf. sec. 52 German Criminal Code. (b) A conviction only of one of the two offences takes place, because the other offence appears to be relatively insignificant (as is the case with murder on the one hand and criminal damage on the other); this is called subsidiarity of the insignificant offence to the other offence that does not stand back. Then, a further differentiation can be made between express subsidiarity, if subsidiarity is explicitly mandated by the law (cf., for example, sec. 246 German Criminal Code) and implicit subsidiarity, where there is no such mandate in the written law. The advantage of such a complete table of all possible relationships between two rules, namely offence A and offence B, lies in the fact that one can be sure that there can be no further concurrent relationships between two offences and there are no more than the two relationships already mentioned. Insomuch as further con-

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current relationships are postulated (e. g., in German Criminal Law the notion of “consumption” [“Konsumtion”]) it would have to be proven to what extent they are not already included in the above-mentioned systematics, or even merely represent a specific sub-case of one of the mentioned concurrence relationships.

III. Logic of Relations In the most simple case of a relation, the relationship between two relata A and B is established, e. g. by the relation “is standing next to”, as is used in the sentence “A is standing next to B”. But also, the relation “is as big as”, e. g. in the sentence “A is as big as B”, is two-digital, as well as the relation “father of” in the sentence “A is the father of B”22. However, there are also three-digit relations (e. g. in the sentence “A is standing between B and C”) and even more-digit relations. But, in the following, only two-digit relations are of interest. It is notable, now, that relations have formal properties which make them comparable to each other despite the fact that their content may vary significantly. Three aspects can be distinguished: reflexivity, symmetry and transitivity. Within the aspect of reflexivity a relation R is labelled reflective if the following is always true for all relata A: ARA. This means, A is always in the relation R to itself, e. g. in the relation “is identical with”. For “A is always identical with A” (i. e. with itself). On the other hand, a relation R is irreflective, if ARA is true for no relatum A; e. g. the relation “bigger than” is irreflective, because “A is never bigger than A”. Finally, a relation R is partimreflective, if ARA is true for some but not for all relata. A partimreflective relation is “provider of”. Because there are some persons, e. g. A, that are “self-providers”23 (meaning: ARA), and others, e. g. B, that are not, thus meaning BRB is not true for them. Regarding the aspect of symmetry, for symmetrical relations R the following is always true: ARB→BRA. Such a relation is, so-to-speak, reversible, as e. g. the relation “is equal to”. For if it is true that “A is equal to B” then it is also always true that “B is equal to A”. In contrast, a relation is asymmetrical if the conclusion ­A RB→BRA is not valid in any case. The relation “taller than”, e. g., is asymmetrical, because if “A is taller than B” is true, it can never be the case that simultaneously “B is taller than A”. Finally, a relation is partimsymmetrical if there are some relata for which ARB→BRA is true and some cases where it is not. For instance, the relation “brother of” is partimsymmetrical. For there are cases in which ARB→BRA is true, i. e. that “A is the brother of B” and “B is the brother of A”; but there are also cases in which this is not true, e.g. if “A is the brother of B” but the reverse is not true because B is A’s sister. Regarding the aspect of transitivity, a relation R is transitive if the following is always true: [ARB and BRC]→ARC. Such a transitive relation is, for instance, 22  23 

In more standard English: “A is B’s father”. In the sense of “self-supporters”.

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“ancestor of”. For if “A is the ancestor of B” and “B is the ancestor of C”, then “A is also the ancestor of C”. If this conclusion, however, is never true, the relation is called intransitive. For if “A is the father of B” and “B is the father of C” then it is never true that “A is the father of C”, because he is his grandfather. Finally, a relation is partimtransitive if the above-mentioned conclusion of transitivity is true only in some but not in all cases. For example, the relation “friend of” is partimtransitive. For if “A is a friend of B” and “B is a friend of C” then it may be that “A is a friend of C”, however, this is not always the case. For ascribing criminal responsibility, the connection of cause and effect between a (deprecated) result and the acts of a person who is supposed to be held responsible for this result is of particular importance. In other words, there must be a cause-effect relation between the offender’s actions and the result of this action that is ascribed to him. This relation is firstly irreflective because no situation is its own cause (“nihil est causa sui”)24. For, not least because cause and effect are chronologically separate, no cause can cause itself. Secondly, the relation “cause of” is asymmetrical, because no cause-effect relation is reversible. This, again, is due to the chronology of events from a cause to its effect. If “A is the cause of B” then it cannot be that “B is the cause of A”. Additionally, the relation “cause of” is transitive. For if “A is the cause of B” and “B is the cause of C” then “A is also the cause of C”; causa causae est etiam causa cau­sati25. The sentence causa causae est etiam causa causati (“the cause of the cause is also the cause of the thing caused”) regarding transitivity of the cause-effect relation is frequently used in the relevant literature even since scholasticism. However, it is not self-evident, because the term “cause” also could have been formed in an intransitive manner (analogously to family relations). Then, only the final cause before a result would be considered to be the cause, while the cause of the cause could be referred to as the “cause-cause”, or analogously to family relations: the “grand-cause”, and the cause before that “grand-cause” in the chain of causation would be the “great-grand-cause” etc. For family relations (father, grandfather, great-grandfather etc.) this makes sense, because these relations do not deal with ascribing responsibility and people can essentially not be classified as mere “causes”26. In contrast, if the relation “cause of” were to be seen as intransitive even in the context of ascribing responsibility, only the bullet that hit the victim would be “responsible” for killing a person by a gun-shot, but not the person who pulled the trigger, thus causing the cartridge to explode and bringing the bullet on its way towards the victim.27 If the Nicholas of Amiens (1721); in greater detail on him cf. Joerden (1988), pp. 17 et seq. with further references. 25 Ibid. 26  The German word for cause makes this even clearer. “Cause” in German means “Ursache”. The etymological origin of this term, which is “Ur-Sache” can be translated as “original thing”. 27  Cf. also Hale (1736), p. 428: „But if a man receives a wound, which is not in itself mortal, but either for want of helpful applications, or neglect thereof, it turns to a gangrene, 24 Cf.

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relation is transitive, on the other hand, the person who fired the gun can be held responsible as a cause of the victim’s death, too. In German Criminal Law, this connection is referred to as “theory of equivalence” [“Äquivalenztheorie”] because in the context of ascribing responsibility, all causes are “equivalent”, no matter how remote from the final effect they may be in the chain of causation. There are a number of further implications for Criminal Law from these mentioned formal properties of the cause-effect relation “cause of” that cannot be traced in detail at this point.28 Additionally, the formal relational properties can also be made useful for analyzing further criminally legally relevant relations, for instance the relations “abettor of”, “aider of”, “danger that” and “receiver (of stolen goods) of” and chains of relations formed from these (and other) relations (“chain of abettors” [“Ketten­an­stiftung”], “chain of aiders” [“Kettenbeihilfe”], “danger chain” [“Gefahrenketten”] etc.). Once again, I refer to the relevant literature.29

IV. Further Fields of Logic and Outlook Apart from the possibilities to use logical instruments from the fields of propositional logic, class logic and relational logic to analyze the structures of criminal legal30 terms and dogmatics, which have been illustrated here in a more detailed manner, instruments from other areas of logic can also be utilized. So far, this has been proven for the fields of combinatorics31, deontic logic32, logic of action and omission33, syllogistics34, fuzzy logic35 and predicate logic36. Additionally, paradoxical structures37 are of interest for Criminal Law. or a fever, and that gangrene or fever be the immediate cause of his death, yet this is murder or manslaughter in him, that gave the stroke or wound, for that wound, tho it were not the immediate cause of his death, yet, if it were the mediate cause thereof, and the fever or gangrene was the immediate cause of his death, yet the wound was the cause of the gangrene or fe­ver, and so consequently is causa causati.“ 28 Cf. Joerden (1988), passim and (2010), pp. 255 et seq. 29  Ibid.; as well as Herberger/Simon (1980), pp. 146 et seq.; Philipps (1981); Kaufmann (1987). 30  And other fields relevant to Criminal Law, such as Legal Philosophy. On system formation in law in general, cf. Schuhr (2006). 31  Cf., e. g., Hruschka (1979) and (1988); Lugert (1991); Joerden (2010), pp. 157 et seq. with further references. 32  Cf., e. g., Hruschka/Joerden (1987); Joerden (2010), pp. 195 et seq. with further references. 33 Cf. Joerden (2010), pp. 293 et seq. with further references. 34  Cf., regarding attempts to reconstruct legal argumentation by the so-called “judiciary syllogism” [Justiz-Syllogismus] Neumann (1986), pp. 16 et seq.; Hilgendorf (1991); Bung (2005); Joerden (2010), pp. 327 et seq., 336 et seq. 35  Cf., in particular, Philipps (1993) and (1995); summarizing Joerden (2010), pp. 371 et seq. 36  Herberger/Simon (1980), pp. 89 et seq. 37  Cf., e. g., Fletcher (1984); Joerden (2010), pp. 379 et seq.

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Therefore, it can be concluded that a logical analysis of Criminal Law – if undertaken correctly – can indeed provide helpful suggestions to systematize and solve certain issues.

References Alexy, Robert: “Die logische Analyse juristischer Entscheidungen”, Archiv für Rechts- und Sozial­philosophie, Beiheft n.F., Nr. 14 (1980), 181 et seq. – “Die Gewichtsformel”, in: Gedächtnisschrift für J. Sonnenschein, Berlin 2003, pp. 771 et seq. Bocheński, I. M./Menne, Albert: Grundriß der formalen Logik, Paderborn 1983. Bung, Jochen: “Der Syllogismus als Modell der Rechtsbegründung”, in: E. Schweighofer/ D. Lieb­wald/S. Augeneder/T. Menzel (eds.), Effizienz von e-Lösungen in Staat und Gesellschaft, Stuttgart 2005, 71 et seq. Fletcher, George P.: “Paradoxes in Legal Thought”, Columbia Law Review 85 (1984), 601 et seq. Hale, Sir Matthew: The History of the Pleas of the Crown, London 1736. Herberger, Maximilian/Simon, Dieter: Wissenschaftstheorie für Juristen, Frankfurt a. M. 1980. Hilgendorf, Eric: Argumentation in der Jurisprudenz. Zur Rezeption von analytischer Philosophie und kritischer Theorie in der Grundlagenforschung der Jurisprudenz, Berlin 1991. Hruschka, Joachim: “Rettungspflichten in Notstandssituationen”, Juristische Schulung 1979, 385 et seq. – “Pflichtenkollisionen und Pflichtenkonkurrenzen”, Festschrift für K. Larenz zum 80. Geb., Munich 1983, 257 et seq. – Strafrecht nach logisch-analytischer Methode, 2nd edition, Berlin 1988. Hruschka, Joachim/Joerden, Jan C.: “Supererogation: Vom deontologischen Sechseck zum deonto­lo­gischen Zehn­eck. Zugleich ein Beitrag zur strafrechtlichen Grundlagenforschung”, Archiv für Rechts- und Sozialphilosophie 73 (1987), 93 et seq. Joerden, Jan C.: Dyadische Fallsysteme im Strafrecht, Berlin 1986. – Strukturen des strafrechtlichen Verantwortlichkeitsbegriffs: Relationen und ihre Verkettungen, Berlin 1988. – “Interessenabwägung im rechtfertigenden Notstand bei mehr als einem Eingriffs­opfer”, Goltdammer’s Archiv 1993, 245 et seq. – Logik im Recht, 2nd edition, Heidelberg 2010. Kaufmann, Arthur: “Vorüberlegungen zu einer Juristischen Logik und Ontologie der Relationen: Grund­legung einer personalen Rechtstheorie”, Rechtstheorie 17 (1987), 257 et seq. Klug, Ulrich: “Zum Begriff der Gesetzeskonkurrenz”, Zeitschrift für die gesamte Straf­ rechts­­wissen­schaft 68 (1956), 399 et seq. – Juristische Logik, 4th edition, Heidelberg 1982.

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Lugert, Georg: Zu den erhöht Gefahrtragungspflichtigen im differenzierten Notstand, Berlin 1991. Neumann, Ulfrid: Juristische Argumentationslehre, Darmstadt 1986. Nicholas of Amiens: “De arte seu articulis catholicae fidei, libri V”, in: Bernard Pez, Thesaurus anecdotorum novissimus, Tomus I, Augsburg 1721 (wrongly published under the name Alanus de Insulis). Philipps, Lothar: “Täter und Teilnehmer – Versuch und Irrtum. Ein Modell für die rechts­ wissen­schaft­liche Analyse”, Rechtstheorie 5 (1974), 129 et seq. – “Über Relationen – Im Rechtsleben und in der Normlogik”, Rechtstheorie, Beiheft 3 (1981), 123 et seq. – “Unbestimmte Rechts­­begriffe und Fuzzy Logic. Ein Versuch zur Bestimmung der Wartezeit nach Verkehrsunfällen (§ 142 Abs. 2 StGB)”, Festschrift für Arthur Kaufmann, Heidelberg 1993, 265 et seq. – “Eine Theorie der unscharfen Subsumtion. Die Subsumtionsschwelle im Lichte der Fuzzy Logic”, Archiv für Rechts- und Sozialphilosophie 81 (1995), 405 et seq. – Endliche Rechtsbegriffe mit unendlichen Grenzen. Rechtslogische Aufsätze, Bern 2012. Pływaczewski, Emil W.: Current problems of the penal law and criminology. Aktuelle Probleme des Strafrechts und der Kriminologie, 7th edition, Warsaw 2017. Rödig, Jürgen: Die Denkform der Alternative in der Jurisprudenz, Heidelberg 1969. Schuhr, Jan C.: Rechtsdogmatik als Wissenschaft. Rechtliche Theorien und Modelle, Berlin 2006. Seier, Jürgen: “Die Gesetzeseinheit und ihre Rechtsfolgen”, Jura 1983, 225 et seq. Wittgenstein, Ludwig: Tractatus logico-philosophicus (1921), 16th edition, Frankfurt a. M. 1982.

Logic and the Analysis of Legal Arguments in Public International Law By Gabriel M. Lentner Gabriel M. Lentner

I. Introduction What makes a good international legal argument? In the Max Planck Encyclopedia of Public International Law, Martti Koskenniemi writes in his entry on the “Methodology of International Law” that “international law is argumentative practice”.1 Arguments seek to persuade target audiences such as courts, governments, scholars, lawyers, etc. Under this view, methodology of international law is understood as “being about criteria that legal arguments ought typically to fulfill in different contexts – including the academic context – in order to seem plausible.”2 What these criteria actually are, is still uncertain.3 Koskenniemi (2014), para. 1. Similarly, Kratochwil, p. 238; Cass, p. 359 f. Koskenniemi (2014), para. 1. For Koskenniemi, a good (and therefore persuasive) argument is one that appears both normative and concrete in the sense he has elaborated in his famous dissertation From Apology to Utopia, Koskenniemi (2006). 3  Illustrative for an apparent lack of established criteria is a recent article on what makes a good legal argument in international law, see e.g. Venzke It must be noted however that the use of ‘valid’ argument in this article has to be distinguished from validity in a technical sense. Validity in logic refers to the logical form of deductive arguments. Validity is concerned only with the ‘inferential correctness’ of legal reasoning. Here, validity is concerned with answering the question whether – given the premises – the argument supports the conclusion. In deductive arguments, the truth of the premises guarantees or necessitates the truth of the conclusion, whereas in inductive and abductive arguments, the truth of the premises makes the truth of the conclusion (only) more or less likely. 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 with respect to deductive arguments, and their epistemic warrant the premises provide for the conclusion, see Lentner, Krimphove (2015b), 399 ff. See also Douven, ‘Abduction’, in: E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (spring edn, 2011), available at: http://plato.stanford. edu/archives/spr2011/entries/abduction/ (accessed 21 April 2014); Brewer (2011), p. 177 f. See further on the limits of logic for legal reasoning, Krimphove (2013). Such an approach could be viewed as an epistemic turn from the text back to the argument see Gabriel (2013), p. 141. See also David Kennedy, who demonstrates in his book on expertise that “[t]he most accomplished experts are not surprised – or troubled – by the uncertainty of their expertise. Often they seem emboldened. People make strong arguments but seem to have lost confidence in the determinacy of their analytics. The odd thing is that it does not seem to matter. 1  2 

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Against this backdrop, this contribution proposes logical criteria to evaluate the (epistemic) strengths and weaknesses of international legal arguments.4 In doing so, the first section will lay the groundwork for the application of logical tools for the analysis of legal arguments by looking at the concept of legal methodology in international law. Next, it introduces the concept of argument and will demonstrate that any argument takes the form of one (or several) of the four modes of logical inferences based on the ‘logocratic method’ as developed by Professor Scott ­Brewer. What follows is a demonstration of typical arguments in international law and evaluation criteria for these four modes of logical inferences that is, deduction, induction, abduction and analogy. The last section will conclude.

II.  Methodology in International Law Before introducing the concept of argument adopted by the ‘logocratic method’, it is important to locate its place in the canon of methodology of international law. As a general definition, “[m]ethodology seeks to define the means of acquiring scientific knowledge.”5 Methodology is determined by the subject of scientific inquiry.6 In other words, the methodology applied depends on the goal or aim of the scientific inquiry. The goal of this study, and legal science7 in general as opposed to political science,8 is to cognize the law.9 Legal science is often described as a normative science. It is not. Law itself is normative because it prescribes what has to be, but legal science, “like any other science, aims at the acquisition of knowledge. Its subject is the study of rules and, generally, of the legal phenomenon, but it is not a normative science.”10 Indeed, the uncertainty and ambivalence of professional knowledge may be the subtle secret of its success. What stabilizes their argumentative practices seems to be the argumentative practice itself: a collective sensibility about what would ‘go too far’ or fall outside the horizon of plausible expert argument. Within those boundaries, a potentially infinite terrain of dispute opens up, stabilized by commonsense wisdom about the world and the field of knowledge.” Kennedy, p. 9 f. 4 This follows the ‘logocratic method’ as developed by Prof. Scott Brewer, see e.g. Brewer (1996); Brewer (2011). See also Brewer in this volume. 5  Dominicé, p. 354 f. See also Zippelius, p. 1; Schüle, p. 3. 6  Zippelius, p. 1. 7  In Anglo-American legal systems, there used to be conceptual difficulties in classifying law as a science because of common law’s development through case-law. By contrast, the European-Continental legal systems considered law to be a science. For the development of the law as science in the Middle Ages and afterwards in Europe see Berman/ Reid, Charles J. Jr. 8  Kelsen (1934), p. 1. 9  Kelsen (1920), p. iv; Kelsen (1960), iii-iv, 72 – 78. 10  Dominicé, p. 354 f. This analytical distinction is important to distinguish legal science from normative reasoning adopted in the field of law and economics (see esp Georgako-

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Then, if the study of law is conceived in this sense as legal science, it needs to create a single scientific theory that governs the law. In analogy to the natural sciences, a theory of law must meet two requirements.11 First, it must describe accurately all relevant events without using any random elements and it must predict accurately all relevant future events.12 The emergence of such a new theory is not always simple. The primary theory appears to be inconclusive after some time, and exceptions arise that the theory cannot explain. As a result, amendments or changes are introduced in the primary theory to account for the exceptions. When the theory can no longer explain the exceptions, it is replaced by a new one. The new theory may also turn out to be inconclusive, and must therefore be amended, changed, or replaced.13 Indeed international legal theory is developing in the same way.14 All this is based on a definition of law.15 The nature of international law as law is of course not uncontested.16 For the purposes of this contribution, a legal-positivist approach is adopted.17 A strict positivist approach abstracts itself from ethical thinking to the point where “law does not cease to be law even if all were to agree that it was immoral.”18 In the positivist tradition, this contribution deals with the poulos, p. 11 ff., arguing that formal logic fails in normative reasoning, and that law and economics approach “is the greatest innovation in legal thinking at least since the code of Hammurabi” (at 3) arguing that the economic analysis of law is scientific. (at 3 – 8). How­ ever, the economic analysis of law takes the position that the proper ideal of the legal system is the promotion of social welfare, that is, the maximization of the satisfaction of individual’s preferences. In this way it is different from legal science that seeks to cognize the law as it is, and not how it should be. 11  Making this analogy see Hallevy, p. 2. 12  Hawking, p. 18. 13  Hallevy, p. 2. 14  See on this development what Malcolm Shaw describes as ‘New approaches’ in international law, see Shaw, pp. 39 ff. See also the doctrinal history of the international legal argument in Koskenniemi (2005), pp. 71 ff. See also Orford. 15  For an overview on the legal-philosophical debate of the definition of law in general, see e.g. Koller, pp. 19 ff. 16  See e.g. Hart, H. L. A, pp. 214 ff. See already Jellinek, who wrote in 1880: „In keiner juristischen Disciplin kommt es so häufig zu einer Erörterung der Grundbegriffe, wie im Völkerrecht. Von den Vertretern der anderen Fächer der Rechtswissenschaft oft nicht also ebenbürtig betrachtet, von Zeit zu Zeit in seiner juristischen Existenz negiert und in die Staatenmoral oder die Politik oder sonst eine zweifelhafte wissenschaftliche Kategorie verwiesen, muss es stets um sein wissenschaftliches Dasein ringen und stets darauf bedacht sein, gegnerische Argumente durch den Nachweis zu entkräftigen, dass es auf demselben Fundamente ruhe, wie Staats-, Process-, Straf- und Privatrecht.” (Jellinek, Die rechtliche Natur der Staatenverträge, 1880, 1) cited from Ago, p. 857. 17  Recognizing that legal positivism offers a useful tool for cognition of the existence of valid rules in international law see d’Aspremont, p. 370 For a brief overview of Positive Law and Natural Law see Shaw, pp. 35 ff.; Ago, p. 873. 18  Mégret, p. 68.

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law as it is and not with its actual or desired role in the international play of powers.19 Such an approach is justified on grounds of the conviction that in a deeply divided international society, “what is needed is an international law that can be determined through recognized professional procedures, distinct from the political or moral values that it may, more or less accidentally, embody.”20 A strict analytical distinction between law and politics is therefore employed. At the same time however, this study does acknowledge the political dimension of all legal interpretation and analysis.21 Nevertheless, international law is understood as the norms and rules originating from the sources of international law as authoritatively listed in Article 38(1) of the Statute of the International Court of Justice.22 A methodology of international law is therefore the method used to determine the existence and content of norms of international law stemming from the sources of international law.23 There is no generally accepted definition of the methodology of international law.24 What is generally accepted in regard to international treaties is that the methods used for the legal analysis in international law are provided for in Article 31(1) of the Vienna Convention on the Law of Treaties (VCLT)25. This provision, reflecting customary international law,26 provides the rules for interpretation together with Articles 32 and 33 VCLT.27 Additionally, Art 38(1)(d) of the Statute of the ICJ contemplates the use of doctrine and judicial decisions as subsidiary means for the determination of rules of law.28 The scientific value and reliability of doctrine for the elucidation of rules of international law is of course very variable,29 and should thus be carefully evaluated. Kelsen (1950), preface. Mégret, p. 68. 21  On this point (in the tradition of critical legal studies) see e.g. Buckel/Fischer-Lescano, pp. 85 ff.; Buckel. 22  Aust, p. 5; Shaw, p. 50. This list is of course not complete and it is generally accepted that unilateral acts of states and decisions of international organizations are additional sources of international law, see Pellet, para 90. For a comprehensive account of the history of Article 38 of the ICJ Statute see Fitzmaurice forthcoming, in: Samantha Besson/Jean d’Aspremont (eds): The Oxford Handbook of Sources of International Law (Oxford University Press 2017). 23  Dominicé, pp. 354 f. 24  Dominicé, pp. 354 f. 25  Vienna Convention on the Law of Treaties (adopted 23 May 1969, entered into force 27 January 1980) UNTS I-18232 (VCLT). 26  The ICJ has confirmed the status of Articles 31 and 32 as part of customary international law in e.g. Sovereignty over Pulau Ligitan and Pulau Sipadan (Indonesial Malaysia) (Judgment) ICJ Rep 2002, 625 (17 December 2002) para 37. 27  Nouwen, Sahra M. H., p. 29. 28  Article 38(1)(d) provides „subject to the provisions of Article 59 [no binding precedents], judicial decisions and the teachings of the most highly qualified publicists of the various nations, as subsidiary means for the determination of rules of law.“ It is not a ‘source’ of international law properly speaking, see Pellet, para 176 19 

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However, exactly how doctrine and judicial decisions are to be evaluated is unclear. This is where this article sees its contribution: it seeks to establish logical criteria for the evaluation of the strengths and weaknesses of international legal argument since any legal argument is also an argument in a logical sense. 29

III.  The Concept of Argument – the Logocratic Method Arguments in international legal decisions, as well as in doctrine, can be viewed as the application of different modes of logical inference.30 In fact, as Brewer notes “[l]aw, considered as an intellectual discipline, consists of certain methods of argument”.31 As with all arguments, legal arguments draw conclusions from premises.32 More precisely, an argument may be defined as “a connected series of sentences, statements, or propositions (called “premises”) that are intended to give reasons of some kind for a sentence, statement, or proposition (called the “conclusion”).”33 For the purposes of this contribution, logic is then defined as the study of the different modes of logical inference that different kinds of (legal) arguments display. An argument’s mode of logical inference (i.e. its logical form) is then the evidential relation34 between the argument’s premises and its conclusion.35

Pellet, para 338. It is widely recognized that the language of judicial decisions is mainly the language of logic, see Holmes, ‘The path of the law’, 10 Harvard L Rev (1896 – 1897) 457, at 465; for an interesting account on the role of logic in the life of the law, see Brewer, ‘Traversing Holmes’ Path toward a Jurisprudence of Logical Form’, in St. J. Burton (ed.), The Path of the Law and its Influence: The Legacy of Oliver Wendell Holmes, Jr (2000) 94. On the question of the applicability of logic in international law see Krimphove (2015), 430 ff.; Lentner, Krimphove (2015a), 399 ff. 31  Brewer (1996), p. 925. 32  Note that Aristotle, the founder of the theory of argument, conceived an argument as „the science of establishing conclusions“, see Horovitz, p. 1. 33  Sinnott-Armstrong/Fogelin, p. 3. See also the similar definition adopted by Scott Brewer: “[a]n argument is a set of propositions (one or more), called ‘premises’, that is offer­ ed (or can be taken) to support another set of propositions (one or more), called ‘conclusions’.” Brewer (2011), p. 175. 34  As Brewer notes: “The definition of ‘logic’ just offered calls for a distinction between empirical and non-empirical evidentiary arguments. Under this definition of ‘logic’, every argument is evidentiary because in every argument premises are offered as providing some degree of evidentiary support for conclusions. In a modus ponens argument ‘If P then Q and P, therefore Q’, for example, premises ‘P’ and ‘Q’, taken together, provide evidential support for conclusion ‘Q’ under this definition of ‘logic’, but it is not empirical evidential support – although a modus ponens can of course be used to establish empirical propositions.” Brewer Handout S. 2. 35  See also Skyrms’ definition of logic: “Logic is the study of the strength of the evidential link between the premises and conclusions of arguments.” Skyrms, p. 15. 29 

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This contribution is premised on two methodological hypotheses of the ‘logocratic method’ that is applied here to arguments in international law. The first methodological hypothesis is that every identifiable argument in international law has a (implicit) logical form. As will be demonstrated, in addition to analogy, the methods usually associated with natural and demonstrative sciences are in fact important in legal argument as well (such as deduction, induction and abduction).36 Second, every underlying evidential claim is an enthymeme that can be translated into an argument that represents its logical form.37 The four modes of logical inference to be presented here are distinguished from one another by the nature and structure of the support their premises provide for their conclusions. Once the logical form of an argument is identified, it can be evaluated on the basis of the degree of evidential warrant the truth of the premises provide for the truth of the conclusion. In deductive arguments, the most prominent example is that of the legal syllogism, the truth of the premises guarantees or necessitates the truth of the conclusion. However, with respect to inductive, abductive or analogical arguments, the truth of the premises makes the truth of the conclusion (only) more or less likely.38 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. The subsequent analysis departs from previous accounts of logic in legal reasoning in that it does not seek to analyse legal reasoning with the tools of logic, but that it employs the tools of logic in order to evaluate the strengths and weaknesses of arguments. This is done premised on the recognition of the limits of logic in law.39 For present purposes, it is important to note that in the argumentative practice of international law, it is these modes of logical inference which are being applied and handled naturally, often without acknowledging its inherent logical structure. However, all reasoning in judicial decisions, submissions, legal briefs, and academic writing, apply these modes of logical inference.40 Thus, considerations of formal logic merit a closer look at these arguments. Another aim of such approach is to make explicit all the assumptions used in our natural way of arguing.41 Indeed, the implicit and seemingly natural application of logic in judicial decisions brings with it the fact that most legal arguments in international law do not Brewer (1996), p. 926. Brewer (2011), p. 185. There exists disagreement in this respect 38  Douven, ‘Abduction’, in E. N. Zalta (ed), The Stanford Encyclopedia of Philosophy (spring edn, 2011), available at: http://plato.stanford.edu/archives/spr2011/entries/abduction/; Brewer (2011), p. 177 f. 39  See exensively Krimphove (2013). See also Larenz, p. 154; Alexy, p. 17 f. 40  Indeed as S. Brewer demonstrates, deduction, induction and abduction play a vital role in legal reasoning, see Brewer (1996), p. 926. 41  Alchourrón, p. 333. 36  37 

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strictly follow a formal logical structure. Rather, most legal reasoning is enthymematic. Enthymematic is an argument if the argument’s logical form is not explicitly clear from its original mode of presentation.42 However, even such enthymematic reasoning is, although not explicit, logical reasoning. In fact, all reasoning has a logical form: the argument. And logic, as the early Ludwig Wittgenstein marks the “limit to thinking, or rather – not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought).”43 Such enthymematic reasoning obstructs the inherent logical structure of a given legal argument. Consequently, logical errors or assumptions not sufficiently proven, 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,44 at least as many times as errors in law (if not even more).45 This contribution concedes the fact that the logocratic analyst is required to make an interpretive judgment when making a ‘fair formal representation’ of the argument classifying its logical form and what premises it assumes and how it infers from these premises what conclusion. Logic in this sense is applied as a tool. It lays out the criteria to be employed in order to test the strength of legal arguments in international law. In so doing, this contribution recognizes that the logical strength itself is not the only decisive issue in practice for determining the strength of a particular argument. As Brewer notes, one must take into account the dialectical and rhetorical strength of an argument. 1.  Deductive Arguments In deductive arguments the truth of the premises guarantee the truth of the conclusion.46 In other words, “[i]n a valid deductive argument, it is logically impossible that the premises should all be true while the conclusion is false. That is, the truth of the premises of a valid deductive argument provides incorrigible evidence for the truth of its conclusion.”47 For example, in a legal syllogism, which is the classic form of a deductive argument in law, the truth of the premises P1 and P2 provide

Brewer (2011), p. 179; Schneider, p. 109 f. Wittgenstein, Preface. 44  For violations of the laws of thought see Lentner/Krimphove (2015a). 45  Krimphove (2013), 315 ff. (with further references). For an example of errors in logic in German criminal law see K. Peters, Fehlerquellen im Strafprozeß (1970 – 1974), Vol. 2, 346 (with further references). For examples of errors in logic in international law see Lentner/Krimphove (2015a). 46  Smith, p. 2 f.; Horovitz, p. 3 f. 47  Brewer (2011), p. 177. 42  43 

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incorrigible evidence for the truth of the conclusion h: (an overly simplifying argument taken from international investment law could be: P1: P2: h:

If there is an expropriation then compensation must be paid. There is an expropriation. Therefore, compensation must be paid.

In propositional logic, this argument may be represented as P1: P2: h:

p → q (i.e. If there is an expropriation then compensation must be paid) p (i.e. there is an expropriation) q (compensation must be paid)

This deductive argument (also called modus ponens) is valid, because there is no possible world in which both premises are true but the conclusion is false. In logic, validity can be proven with a truth table of this argument.48 The main criterion for the strength of a deductive argument is therefore its validity. If a deductive argument is not valid, the truth of its premises provides no evidentiary warrant for the conclusion. In other words, an invalid argument does not provide any support for the truth of the conclusion i.e. what is claimed. For example, a common invalid deductive argument is an argument e contrario: It takes the logical form represented in propositional logic of: P1: P2: h:

If p → q not p therefore not q

This is not a valid deductive argument. Consider the following example: If it rains, the street gets wet (If p → q); it does not rain (not p) therefore the street is not wet (not q). However, one can see that even if both premises are true (i.e. that in fact if it rains, the street gets wet and that it actually does not rain, the conclusion that the street is not wet can still be false. For example, someone washes his or her car and the street gets wet, or street cleaning makes the street wet. The conclusion in this example, is false because in these cases the street is in fact wet although the premises are both true. Therefore, this is an invalid deductive argument. Logically, this can be proven by looking at the truth table of this argument. As an example for the practice of international law, the following argument e contrario was rejected by an ICSID tribunal in Plama v. Bulgaria: If a dispute resolution clause is explicitly excluded from MFN then the dispute resolution provision cannot be incorporated from another treaty; MFN is not explicitly excluded, therefore the dispute resolution clause can be incorporated from another treaty.49 48 

The truthtable for this argument: p T T F F

q T F T F

p→q T F T T

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This argument equally can be represented as an invalid deductive argument: 49

P1: P2: h:

If p → q not p therefore not q

However, validity is not the only criteria for the strength and weaknesses of a deductive argument. The strength of a (valid) deductive argument relies entirely on the truth of its premises. If only one of the premises of a deductive argument is not true, the truth of the conclusion is undermined. Indeed, in most cases, the validity of the legal syllogism will not present problems but whether a particular legal rule, is indeed the case (i.e. is true) or whether the facts are indeed taken to be true (this is mostly a question of evidence and the burden of proof) might be disputed. The truth of the premises of such a deductive argument must then be established by several other arguments that could take the form of another mode of logical inferences. These further arguments may then be evaluated in accordance with the following criteria that will be established below for inductive, abductive and analogical arguments. 2.  Inductive Arguments In inductive arguments, “the premises provide probabilistic evidential warrant for the conclusion (with probability less than 1).”50 Inductive arguments have two main forms: inductive generalization and indicative specification. In an inductive generalization, the observation of particular instances (the premises) are generalized in its conclusion. As Brewer notes “inductive arguments are arguments about evidence and the hypotheses the evidence is said to support. Thus, the premises of an inductive argument are evidentiary propositions and the conclusion is a hypothesis that the evidence is offered to support.”51 In other words from the premises a1, a2 , …, an are all Fs that are also G, one infers a general law or principle that all Fs are G.52 The second main form of inductive arguments is inductive specification. Inductive specification is defined as an argument that “offers a conclusion about one individual, based on a generalization about the classes to which that individual

International Centre for Settlement of Investment Disputes, § 203. Brewer (2011), p. 177 (emphasis in the original). See also Hawthorne, James, “Inductive Logic”, The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/win2014/entries/logic-inductive/; Horovitz, p. 4. 51  Brewer (2011), p. 189 f. 52  Vickers, John, “The Problem of Induction”, The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/ spr2016/entries/induction-problem/. 49 

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belongs.”53 Specification has also been called inductive analogy.54 A typical use of such argument is in evidence.55 When the International Court of Justice (ICJ) is identifying a rule of customary international law, for example, it adopts an argument by inductive generalization.56 In the Gulf of Maine case the ICJ even expressly stated that “customary international law […] comprises a set of customary rules whose presence in the opinio juris of States can be tested by induction based on the analysis of a sufficiently extensive and convincing practice and not by deduction from preconceived ideas.”57 In the actual practice of identifying customary international law, the ICJ does not employ a complete analysis of all relevant instances of state practice and opinio juris. In the Belgium v. Senegal Case, for example, it simply held: “In the Court’s opinion, the prohibition of torture is part of customary international law and it has become a peremptory norm (jus cogens). That prohibition is grounded in a widespread international practice and on the opinio juris of States. It appears in numerous international instruments of universal application (in particular the Universal Declaration of Human Rights of 1948, the 1949 Geneva Conventions for the protection of war victims; the International Covenant on Civil and Political Rights of 1966; General Assembly resolution 3452/30 of 9 December 1975 on the Protection of All Persons from Being Subjected to Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment), and it has been introduced into the domestic law of almost all States; finally, acts of torture are regularly denounced within national and international fora.”58

While the ICJ cites the international instruments mentioned, it does not provide any reference to domestic law or instances where “acts of torture are regularly denounced within national and international fora.” Strictly speaking, this is therefore merely an assertion rather than an argument. Evaluation An inductive argument is cogent (i.e. having the probability of truth) when its premises are true, relevant to the conclusion and the truth of the premises give good reason to accept the truth of the conclusion. The following evaluation criteria are typically important for the strength of an inductive argument. It is, however, not a comprehensive analysis of criteria for the evaluation of inductive arguments.59 Brewer (2011), p. 190. Stephen Barker refers to this as ‘inductive analogy’, see Barker, p. 260. 55  Brewer (2011), p. 190. 56  On this see e.g. Schüle, p. 19 f.; Visscher, p. 16; Bleckmann, p. 505; see also Talmon, p. 421, with further references. 57  International Court of Justice (12 Oktober 1984), § 111. On the actual practice of the ICJ in determining customary international law rules see particularly Talmon, p. 417 ff. 58  International Court of Justice (20 Juli 2012), § 99. 59 For an overview of the application of inductive probabilities to the evaluation of scientific hypotheses and Bayesian estimation and convergence for enumerative inductions 53 

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First, the larger the sample size relative to the population the stronger the induction. For example, when identifying customary international law, the higher the number of instances of state practice, the stronger the induction.60 In the argument presented by the ICJ above lists all major international human rights treaties that prohibit torture and this part of the argument is therefore strong. Second, the more representative the sample, the stronger the induction. For example, in identifying a rule of customary international law, the state practice and opinio juris of states should be representative of the international community and not only Western Europe, for instance. Furthermore, the sample should vary as widely and in as many different but relevant dimensions as possible. Aside from the use of inductive arguments for questions of customary international law and evidence, legal arguments in international law regularly rely on a particular type of inductive arguments. The argument by authority (and this includes expert opinion61) is an inductive argument (inductive specification). For exsee e.g. Hawthorne, James, “Inductive Logic”, The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), Edward N. Zalta (ed.), URL = . 60  See however the qualification of practice in the Nicaragua case before the ICJ, in which the court held that “In order to deduce the existence of customary rules, the Court deems it sufficient that the conduct of States should in general be consistent with such a rule; and that instances of State conduct inconsistent with a given rule should generally have been treated as breaches of that rule, not as indications of the recognition of a new rule.” International Court of Justice (27 Juni 1986), p. 98. 61  The appeal to expert opinion itself raises the problem that has already been addressed in antiquity by the argument attributed to Anacharsis of Scythia: “Who is to be the judge of skill? Presumably, either the expert or the nonexpert. But it cannot be the nonexpert, for he does not know hwat constitutes skill (otherwise he would be an expert). Nor can it be the expert, because that would make him a party to the dispute, and hence untrustworthy to be a judge in his own case. Therefore, nobody can be the judge of skills.” Sextus Empiricus, Against the Logicians, cited in Walton (1997), preface. See also Peirce. Also making this point see Brewer (1998), who argues that “First, the Article argues that in order to avoid making an epistemically arbitrary choice about which of the competing scientific experts ought to be believed, a person must understand (in a special sense discussed in the text) the cognitive aims and methods of science. But nonexpert judges and juries lack just that kind of understanding, which is why they rely instead on other indicia of expertise, such as credentials, reputation, and demeanor. Second, nonexpert judges’ and juries’ lack of understanding of the cognitive aims and methods of science and their reliance on such indicia of expertise as credentials, reputation, and demeanor to choose between competing scientific experts thus yield only epistemically arbitrary judgments. Third, the conclusions that nonexpert judges and juries ultimately reach by relying significantly on expert scientific testimony are often also epistemically arbitrary and are therefore not justified from a legal point of view. Fourth, I identify - and begin the process of explicating - an emerging norm that belongs in the family of rule-of-law values: the norm I call intellectual due process.” Brewer (1998), p. 1539. As two examples of employing an appropriate distinction between between the roles of scientific and legal reasoning, see European Communities – Measures Prohibiting the Importation and Marketing of Seal Products – Report of the Appellate Body (EC – Seal

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ample, because one commentator is correct in the legal analysis of one question, she is therefore also likely to be correct in the legal analysis of another question. Criteria for the evaluation of arguments by authority include questions such as: Is the authority qualified? Is the authority within his or her area of expertise? Is the authority unbiased in providing an opinion? Has the authority performed competently for others? How long has the authority been practicing in his or her area of expertise? What has the authority accomplished in his or her field? In any case, the argument by authority in law should, in principal, be evaluated on the merits of the articulated argument that is presented by the authority itself on the basis of the logocratic method as proposed here. 3.  Abduction (Inference to the Best Explanation) Abduction or inference to the best explanation (IBE) involves an “inference to an explanation of some fact or set of facts. In this argument, a statement of the phenomenon (or phenomena) to be explained and the putative explanation both appear as premises of the argument and the explanation itself is the argument’s conclusion.”62 In abductive arguments the premises of IBEs provide probabilistic warrant for the truth of their conclusions63 (probability less than 1).64 Abduction is widely used in evidence but also in international legal arguments when the opinio juris of states is deduced from certain conduct or voting in international fora, for example. Abductive arguments are also used when arguing about mind states, including intent (e.g. the intent of treaty drafters) and object and purpose (used in teleological interpretation of international treaties). Evaluation As a basic rule, the conclusion (i.e. the hypothesis) of an IBE explains the truth of the premise; if the hypothesis were false, the premise would be more puzzling Products – AB Report), 22 May 2014, WT/DS400/AB/R and WT/DS401/AB/R; Whaling in the Antarctic (Australia v. Japan; New Zealand Intervening), Judgment, 31 March 2014, ICJ Reports (2014) 226. On this point see Sykes, p. 497 ff..; see also Malintoppi, p. 430 ff.. 62  Brewer (2011), p. 178; see also Douven, Igor, “Abduction”, The Stanford Encyclopedia of Philosophy (Spring 2011 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/ archives/spr2011/entries/abduction/; see also Walton (2016), p. 35 ff. 63  Generally on IBE, see e.g. Lipton. For the argument that IBE is not admissible in a scientific methodology see Ritchie, p. 94 ff.; for an excellent rebuttal of Ritchie’s argument see Caro, p. 28 ff. 64  See however Brewer how argues that “Unlike many students of IBE, including Peirce, I believe that some IBE explanations could fairly be represented as valid deductive infer­ ence. For example, explain how a pawn in chess can appear on the same column as a pawn on the same ‘team’. (Peirce and many others think they all instantiate the fallacy of affirming the consequence.) Thus, in my view, sometimes the premises of IBEs provide incorrigible evidence for the truth of their conclusions.” Brewer (2011), p. 178.

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(the IBE should explain the phenomenon and the all of the phenomenon). The more plausible the hypothesis, the stronger the inference. Similarly, the greater the explanatory power of the conclusion, the stronger the inference (i.e. the same kind of explanation can be used successfully over a wide range of cases). However, it must be noted that these two criteria might be in conflict. For example, a hypothesis with greater explanatory power might be less plausible. In the practice of evidence, the hypothesis should be tested by searching for confirming and disconfirming evidence, whereas disconfirming evidence is more powerful than confirming evidence. A well-known example of an IBE is illustrated in the Corfu-Channel case, in which the ICJ recognized indirect evidence to be admissible.65 While commentators criticized the court for not elaborating on how it arrived at this conclusion, the question of admission of indirect evidence as such is essentially a legal question.66 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.”67 This statement is – logically speaking – not correct. 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 explanation (i.e.) 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. 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.”68 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. Another example for the use of IBE is the evidentiary standard with regard to the proof of the subjective element (e.g. the intent to destroy a protected group in the crime of genocide) adopted by the International Criminal Tribunal for the former Yugoslavia (ICTY). Here the evidentiary standard is carefully elaborated in the Karadzic case adopting a rather high evidentiary standard: “When the Prosecution relied upon proof of a certain fact such as, for example, the state of mind of an Accused by inference, the Chamber considered whether that inference was the only reasonable inference that could have been made based on that evidence. Where that inference was not the only reasonable inference, it found that the Prosecution had not proved its case.”69 […] Corfu Channel Case, ICJ Reports (1949) 18. For the lack of space the issue of evidentiary questions and logic cannot be discussed further; on this see e.g. Brewer (2011), 175 ff. 67  Corfu Channel Case, ICJ Reports (1949) 18, emphasis added. 68  Corfu Channel Case, ICJ Reports (1949) 18, emphasis in the original. 69  International Criminal Tribunal for the former Yugoslavia, § 10. 65 

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Circumstantial evidence is evidence of a number of different circumstances surrounding an event from which a fact at issue may be reasonably inferred. Where an inference is drawn from circumstantial evidence to establish a fact on which a conviction relies, that inference must be the only reasonable one that could be drawn from the evidence presented.”70

In practice the most important task for the reasoner in abductive arguments is then to search for evidence both confirming and disconfirming the explanation (i.e. conclusion). 4. Analogy An analogical argument can be defined in the following way: “In an analogical argument, one reasons that because two or more items share some characteristics, one can infer that they share an additional characteristic that is of particular interest to the reasoner.”71 Scott Brewer has convincingly established that analogical reasoning can be represented in logical form: “[analogical] reasoning is best reconstructed as a patterned sequence of reasoning steps that have three analytically distinct components. These are to be understood as three individually necessary and jointly sufficient conditions. First, there is abduction in a context of doubt about the extension of some predicate or the meaning of some text; probably the most typical “contexts of doubt” in legal arguments are instances in which a legal concept or term is actively vague - that is, instances in which a judge or lawyer is undecided about whether to apply the concept to a given object or event. Having found or been confronted with several examples, the reasoner (say, a judge) seeks to “discover” a rule-like sorting of these examples [i.e. the analogy warranting rule or AWR]; Second, there is a confirmation or disconfirmation of the AWR that the reasoner has “discovered” in the first step. This step involves the testing of the “abduced” AWR for its ability to satisfy several requirements […]. The AWR is what the exemplary reasoner ultimately settles on, after it passes the test of confirmation, in the belief that the AWR effects an acceptable sorting of the examples that the reasoner is considering. To determine whether the AWR does effect an acceptable sorting, the reasoner must measure the AWR against a separate set of explanatory and justificatory propositions; these I refer to as “analogy-warranting rationales.” […] The reasoning device used for confirmation or disconfirmation is “reflective adjustment” in which three distinct types of “holistic” adjustment are possible. One is between the AWR and the chosen examples (exemplary propositions) the AWR sorts; another is between the AWR and the analogy-warranting rationales that explain and justify it; a third is between the analogy-warranting rationales and the chosen examples. Third, in the final step of exemplary reasoning, the reasoner applies the AWR discovered in the first step and confirmed in the second step to the particular example or examples

70  71 

International Criminal Tribunal for the former Yugoslavia, § 14. Brewer (2011), p. 178 f.

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(exemplary propositions) that originally triggered the exemplary reasoning process – the example sub judice, as it were.”72

In this way, analogical arguments in international law can be analyzed based on the logocratic method. Consider the following example of the logical form of an analogical argument in which the shared characteristics are F and G and the inferred characteristic is H. Y has F and G (target premise); X has F and G (source premise); X also has H (source premise); AWR: if anything that has F and G also has H, then everything that has F and G also has H; Therefore, Y has H.

Applied to an argument in international law, consider the question whether the delegation of jurisdictional authority of the UN Security Council to the ICC involving non-State Parties to the ICC is within its competences under the UN Charter. The following analogical argument is taken from the literature that affirms such competence based on the argument that such delegation of jurisdiction is analogous to the establishment of the so-called ad hoc tribunals of the International Criminal Tribunal for the former Yugoslavia (ICTY) and Rwanda (ICTR) by the Security Council, which was held to be within the competences of the SC in the famous Tadic case and accepted in doctrine.73 Simplifying this legal issue for present purposes one could establish the following argument. First, the reasoned identifies as relevant shared characteristics that the measure was adopted under Chapter VII of the UN Charter to secure international peace and security (F) and that in both cases the Security Council delegated powers it possesses but cannot itself exercise (i.e. exercising criminal jurisdiction) (G). In other words, the source premise i.e. the establishment of the ad hoc tribunals has F and G and also the target premise i.e. the SC referral also has F and G. The inferred characteristic is that the SC’s measure is legal (H) i.e. in the source premise F and G also has H (i.e. the measure is legal). The analogy warranting rule could be that if anything that has F and G also has H then everything that has F and G also has H. The analogy warranting rational could be that the SC must be entitled to adopt measures necessary for the maintenance of international peace and security. Applying the AWR to the target premise means Y also has H.

Brewer (1996), p. 962 f. [emphasis in the original] Decision on the Defence Motion for Interlocutory Appeal on Jurisdiction, Tadic (ICTY-IT-94-l-A), Appeals Chamber, 2 October 1995; Decision on the Defence Motion on Jurisdiction, Kanyabashi (ICTR-96 – 15-T), Trial Chamber 2, 18 June 1997; Decision on Preliminary Motions, Milosevic (ICTY-IT-99 – 37-PT), Trial Chamber, 8 November 2001; Schabas, p. 294; Cassese, p. 494. 72 

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Evaluation For an analogy to be strong there must be sufficient warrant for the analogy warranting rule (AWR) and the analogy warranting rationale (AWRa).74 The arguments to provide support to the AWR and AWRa may then be abductive or inductive arguments, which must then be assessed based on the criteria established above. The strength of this argument can then be tested on the basis of the AWR. Is there sufficient warrant to support this AWR? Is there sufficient warrant to support this AWRa? There are several arguments that could be brought against this AWR because of two main differences between the SC referral and the establishment of the ICTY. First, almost all the features of the ICTY (as well as those of the ICTR) concerning the election of judges, the jurisdiction of the Tribunals and the requirements of State cooperation were unlike the provisions of the proposed ICC. Second, the ICC is a separate international organization and not a subsidiary organ established by the SC. Therefore, the analogical argument presented is not strong.

IV. Conclusion This contribution demonstrated that formal logic is a useful tool to evaluate the strengths and weaknesses of international legal arguments. Applying the ‘logocratic method’ to the analysis of arguments of international law appears to be able to establish objective criteria for the evaluation of arguments. This evaluation requires the following steps: First, identify the argument. Second, represent the natural language argument in logical form. Third, confirm the first step. Fourth, make a judgment about the mode of logical inference of that argument (i.e. is it deductive, inductive, abductive or analogical). And finally, assess whether the argument has the characteristic strengths or weaknesses that that argument in that mode of inference has when it is strongest. Additionally, but beyond the scope of this contribution, the so established logical strength of an argument is, of course, only part of a comprehensive analysis of the persuasiveness of an argument: arguments must also be assessed on their dialectical and rhetorical strength.

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Hawking, Stephen: A brief history of time. From the big bang to black holes, London 1989. Horovitz, Joseph: Law and Logic. A critical account of legal argument, New York 1972. Kelsen, Hans: Das Problem der Souveränität und die Theorie des Völkerrechts. Beitrag zu einer reinen Rechtslehre 1920. – Reine Rechtslehre. Einleitung in die rechtswissenschaftliche Problematik, Leipzig/Wien 1934. – The law of the United Nations. A critical analysis of its fundamental problems, London 1950. – Reine Rechtslehre, 2. Aufl. 1960. Kennedy, David: A world of struggle. How power, law, and expertise shape global political economy, Princeton 2016. Koller, Peter: Theorie des Rechts. Eine Einführung, 2. Aufl., Wien/Köln/Weimar 1997. Koskenniemi, Martti: From apology to Utopia. The structure of international legal argument: reissue with a new epilogue, Cambridge 2005. – From Apology to Utopia. The Structure of International Legal Argument, Cambridge 2006. – Methodology of International Law, in: Wolfrum, Rüdiger (Hrsg.): Max Planck Encyclopedia of Public International Law, Oxford 2014. Kratochwil, Friedrich V.: Rules, Norms, and Decisions. On the conditions of practical and legal reasoning in international relations and domestic affairs, Cambridge 1989. Krimphove, Dieter: Grenzen der Logik, in: Rechtstheorie, Heft 3, 2013, pp. 315 ff. – Logik in Völkerrechtlichen Entscheidungen, in: Archiv für Rechts- und Sozialphilosophie, Heft 3, 2015, p. 428 ff. Larenz, Karl: Methodenlehre der Rechtswissenschaft, 3. Aufl., Berlin/Heidelberg/New York 1975. Lentner, Gabriel M./Krimphove, Dieter: Logic as an Inherent Principle of International Law an its Consequences for International Adjudication, in: Schwaighofer, Erich/Kummer, Franz/Hötzendorfer, Walter (Ed.): Tagungsband des 18. Internationalen Rechtsinformatik-Symposions IRIS 2015, Wien 2015a, p. 399 ff. – Logic as an Inherent Principle of International Law and its Consequences for International Adjudication, in: Schweighofer, Erich/Kummer, Franz/Hötzendorfer Walter (Ed.): Tagungsband des 18. Internationalen Rechtsinformatik Symposions IRIS 2015 2015b, pp. 399 ff. Lipton, Peter: Inference to the best explanation, 2. Aufl., London/New York 2004. Malintoppi, Loretta: Fact Finding and Evidence Before the International Court of Justice (Notably in Scientific-Related Disputes)Etablissement des faits et question de la preuve devant la cour internationale de justice (notamment dans le cadre de différends liés à des questions scientifiques), in: Journal of International Dispute Settlement, Heft 2, 2016, pp. 421 ff. Mégret, Frédéric: International law as law, in: Crawford, James/Koskenniemi, Martti (Ed.): The Cambridge companion to international law, Cambridge, New York 2012. Nouwen, Sahra M. H.: Complementarity in the line of fire. The Catalysing Effect of the International Criminal Court in Uganda and Sudan, Cambridge 2013.

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Orford, Anne: Scientific Reason and the Discipline of International Law, in: European Journal of International Law, Heft 2, 2014, pp. 369 ff. Peirce, Charles Sanders: The Fixation of Belief, in: Popular Science Monthly, 1877, pp. 1 ff. Pellet, Alain: Article 38, in: Zimmermann, Andreas/Tomuschat, Christian/Oellers-Frahm, Karin/Tams, Christian J. (Ed.): The Statute of the International Court of Justice. A commentary, 2. Aufl., Oxford 2012. Ritchie, Jack: Understanding naturalism, Stocksfield [England] 2008. Schabas, William: The International Criminal Court. A commentary on the Rome Statute, Oxford 2010. Schneider, Egon: Logik für Juristen. Die Grundlagen der Denklehre und der Rechtsanwen­ dung, 4. Aufl., München 1995. Schüle, Adolf: Methoden der Völkerrechtswissenschaft, in:  Schüle, Adolf/Gamillschegg, Franz/Möller, Hans/Bülck, Hartwig (Ed.): Verhandlungen der Tagung der Gesellschaft in Frankfurt am Main am 9. und 10. April 1959, Heidelberg 1959. Schüle, Adolf/Gamillschegg, Franz/Möller, Hans/Bülck, Hartwig (Ed.): Verhandlungen der Tagung der Gesellschaft in Frankfurt am Main am 9. und 10. April 1959, Heidelberg 1959. Schwaighofer, Erich/Kummer, Franz/Hötzendorfer, Walter (Ed.): Tagungsband des 18. Internationalen Rechtsinformatik-Symposions IRIS 2015, Wien 2015. – Tagungsband des 18. Internationalen Rechtsinformatik Symposions IRIS 2015 2015. Shaw, Malcolm N.: International law, 7. Aufl., Cambridge 2014. Sinnott-Armstrong, Walter/Fogelin, Robert J.: Understanding Arguments. An Introduction to Informal Logic, 8. Aufl., Australia, Belmont, CA 2010. Skyrms, Brian: Choice and Chance: An Introduction to Inductive Logic, 4. Aufl., Stamford 1976. Smith, Peter: An introduction to formal logic, Cambridge, UK/New York 2003. Sykes, Katie: The Appeal to Science and the Formation of Global Animal Law, in: European Journal of International Law, Heft 2, 2016, pp. 497 ff. Talmon, Stefan: Determining Customary International Law. The ICJ’s Methodology between Induction, Deduction and Assertion, in: European Journal of International Law, Heft 2, 2015, pp. 417 ff. Venzke, Ingo: What Makes for a Valid Legal Argument?, in: Leiden Journal of International Law, Heft 4, 2014, pp. 811 ff. Visscher, Charles de: Problèmes d’interprétation judiciaire en droit international public, Pa­ ris 1963. Walton, Douglas N.: Appeal to expert opinion. Arguments from authority, University Park, Pa. 1997. – Argument evaluation and evidence, Cham 2016. Wittgenstein, Ludwig: Tractatus Logico-Philosophicus 1921. Wolfrum, Rüdiger (Ed.): Max Planck Encyclopedia of Public International Law, Oxford 2014. Zimmermann, Andreas/Tomuschat, Christian/Oellers-Frahm, Karin/Tams, Christian J. (Ed.): The Statute of the International Court of Justice. A commentary, 2. Aufl., Oxford 2012. Zippelius, Reinhold: Juristische Methodenlehre, 11. Aufl., München 2012.

Meaning Negotiation in Legal Interpretation By Antonino Rotolo

I. Introduction Meaning negotiation is a process in which the object of negotiation is the meaning of a set of terms1. When this happens in the law, the object of negotiation is typically the meaning of terms occurring in one or more legal provisions relevant for the parties involved in a dispute: the parties in the interaction may typically have a common interest in achieving at least a partial agreement in regard to the interpretation of a given legal provision, although they also have conflict of interests in other respects. Parties can thus make an attempt to converge into a legal solution, which requires to agree on the same legal definitions. Negotiating the meaning of a set of legal terms basically means to propose definitions and to accept and/or to reject them. This may require parties to revise their own concepts or those that have been anyway adopted in previous steps of the process. In this chapter we will examine only some types of disagreements, which concern the coherence of the interpretation of terms occurring in legal provisions when the goals assigned to such provisions are considered. Indeed, norms can often be viewed as plans which aim at achieving the social goals shared by the members of a society. However, the legislator could try to specify all the circumstances which a norm applies to and all the exceptional contexts where it does not apply, but, as well known for instance in the planning community of AI, complete and universal plans rarely are a practicable strategy. It is more feasible to produce a partial plan and revise it when part of it becomes unfeasible. In the same way as replanning allows us to revise plans while keeping fixed original goals, legal interpretation of terms allows norms to be adapted after their creation to the unforeseen situations in order to achieve the social goal they have been planned for. Thus, the research questions of this chapter are: 1. How to logically model the interpretation mechanism of law that adjusts concepts to concrete cases, so to design more flexible systems regulated by norms? 2. How to model negotiation processes on top of this interpretation mechanism of the law?

1

Burato, p. 3.

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In earlier work2, we developed modal extensions of Defeasible Logic (DL, henceforth)3 and we conceptually used the well-known distinction of constitutive (or counts-as) and regulative norms.The idea was that interpreting norms may require to revise theories of constitutive rules that characterize the concepts occurring in legal rules. This revision is goal driven: the goals of legal norms and the terms occurring in them must be aligned in order to ensure that the application of norms in fact promote those goals. The revision is based on the idea that legal concepts can be inferentially characterized by arbitrarily large and connected theories of constitutive rules, and so, when we broaden or narrow the scope of legal concepts we are doing nothing but changing (revising or contracting) those theories. The advantages of this approach are thus that it allows us to make these interpretive arguments more transparent and to show interesting connections with techniques from the domain of revision theory. Our earlier analysis is extended in two respects: – instead of resorting to quite cumbersome proof-theoretic machineries, here we rethink the revision procedures in an argumentation setting; – we explain how the above mentioned argumentation setting can be used to run legal dialogues and negotiations.

In this chapter we confine our attention to two types of revision: the case when the applicability scope of any legal rule is restricted or broadened and the negotiation mechanism focuses on such restrictions or broadening. The layout of the chapter is as follows. Section 2 briefly recalls the main idea of we developed elsewhere and provides an informal background. Section 3 presents a variant of DL, which is the logical framework we use to revise theories: we first study the proof theory; this choice allows us to easily develop an argumentation semantics for that logic. With this done, we provide a first definition of applicability restriction and expansion (Section 4). Some technical discussion about possible alternatives and results are then offered in Section 5. All operations determine the possibility that different revision outcomes are obtained: we outline some criteria that can be used to choose the best theory among these outcomes (Section 6) and how legal negotiations can be developed accordingly, having as object the narrowing or broadening of the applicability conditions of norms.

II. The Background As well known, norms have a conditional structure such as b1 ; . . . ; bn ) OBL l (if b1 ; . . . ; bn hold, then l is obligatory); an agent is compliant with respect to this norm if l is obtained whenever b1 ; . . . ; bn is derived. Due to the complexities and dynamics of the world, norms cannot take into account all the possible conditions 2 3

Boella et al. (2009); Boella et al. (2010). Governatori / Rotolo.

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where they should or should not be applied, giving rise to the so called “penumbra”4. After all, not only the world changes, giving rise to circumstances unexpected to the legislator who introduced the norm, but even the ontology of reality can change with respect to the one constructed by the law to describe the applicability conditions of this norm. Normative systems regulating real societies have two mechanisms to cope with this problem. First they distinguish legal rules (obligations, prohibitions and permissions) from constitutive rules. While the former, which are changed only by the legislative system, specify the ideal behaviour, the latter ones provide, by means of counts-as definitions, an ontology of institutional concepts. The applicability conditions of legal rules very often refer to these institutional concepts, rather than to the so called brute facts. Second, the judicial system, at the moment in which a case concerning a violation is discussed in court, is empowered to interpret, i.e., to change norms, under some restrictions not to go beyond the purpose from which the legal rules stem. The distinction between legal and constitutive rules (ontology vs norms) suggests that legal interpretation does not amount to revising norms, but to interpreting legal concepts, i.e., to revising constitutive rules. The ontology of legal concepts is built via constitutive rules having the so-called counts-as form5: r : a1 ; . . . ; an ) c b. For example, a bicycle is considered as a vehicle by the following constitutive rule: r0 : Bike ) c Vehicle. Constitutive rules have a defeasible character, for example, a bicycle for children cannot be considered as a vehicle: r1 : Bike; ForChildren c :Vehicle, where r1  r0 . As usual in DL, our language includes (1) a superiority relation  that establishes the relative strength of rules and is used to solve conflicts, (2) special rules marked with , called defeaters, which are not meant to derive conclusions, but to provide reasons against the opposite. The set of legal rules is kept to be fixed: any judge during the interpretation process can argue about their applicability conditions but cannot either add new rules nor cancel them. Only legislators have the power to change legal rules. As said, legal rules have the form r : b1 ; . . . ; bn ) OBL l, for example: r2 : Vehicle; Park ) OBL :Enter. This rule reads as follows: if we have a vehicle and we are in a park, then it is (defeasibly) forbidden to enter. Finally, as usually assumed in legal theory6, we assign goals to legal rules. In the social delegation cycle7 norms are planned starting from goals shared by the community of agents. However, such goals play also another role: they pose the limits 4 5 6 7

Sartor (2005). Searle. Sartor (2005). Boella / Torre.

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within which the interpretation process of the judicial systems must stay when interpreting norms. Note that the goal alone is not sufficient to specify a norm, since there could be many ways to achieve that goal and some guidance should be given to the citizens. Thus, the norm works like a partial plan the legislator sets up in advance. The judicial system is left with the task of dynamically adapting the applicability of the regulative norm by revising the constitutive norms referring to its applicability conditions, in order to fulfil the goal of the norm also under unforeseen circumstances. We define a set G of goals and a function G which maps legal rules into elements of G. For example, if G ðr2 Þ ¼ road safety, this means that the goal of the rule prohibiting to enter into parks is to promote road safety. Checking legal compliance requires to establish if a legal rule r : b1 ; . . . ; bn ) OBL l is violated by a fact or action l happened under some circumstances H. Let us assume that r states that :l ought to be the case. However, l is not necessarily a violation, because we also have to check whether H, via the constitutive rules, matches with the applicability conditions b1 ; . . . ; bn of r. In easy cases, these match and l directly amounts to a violation. However, jurists argue that we have cases where this does not hold, as for example when there is a discrepancy between the literal meaning of b1 ; . . . ; bn and the goal assigned to the rule r by the legislator. If so, even though H matches with b1 ; . . . ; bn , we do not have a violation because H should not match with b1 ; . . . ; bn . A non-literal interpretation of b1 ; . . . ; bn would exclude H as a circumstance falling within the scope of r, since the goal of the norm would be achieved anyway: lex magis dixit quam voluit, the law said more than what the legislator was meaning to say. Analogously, not all cases in which H mismatches with b1 ; . . . ; bn are not violations. We could have that lex minus dixit quam voluit, the law said less than what the legislator was meaning to say: here a non-literal, goal-based interpretation of r would lead to broaden its applicability scope to match H, thus making the agent a violator. In this chapter we provide details only for the case when “the law said more than what the legislator was meaning to say”. Here is an example illustrating the main idea. Example 1 Suppose Mary enters a park with her bike, thus apparently violating rule r2 above about vehicles' circulation. Police stops her when she is still on her bike in the park and fines her. Mary thinks this is unreasonable and sues the municipality because she thinks that here the category “vehicle” should not cover bikes. The conceptual domain T of the normative system, corresponding to a set of constitutive rules, allows us to derive that any bike a is indeed a vehicle. The goal of the norm r2 is reducing pollution G ðr2 Þ ¼ :pollution. In court, the judge has to establish if Mary violated r2 or not. If T is the case, the judge could argue that r2 clearly applies to Mary: T ¼ fr0 : Bike )c Vehicle; r3 : 2 wheels; Transport; :Engine )c Bikeg

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But suppose that the judge can show that, if Mary’s case fulfils the applicability conditions of r2 (Mary’s bike is a vehicle) then a goal which is incompatible with the goal assigned to r2 would be promoted. Since G ðr2 Þ ¼ :pollution, prohibiting to circulate with bikes in parks would encourage people to get around parks by car and then walk. This would be against the goal of r2 and so the judge has good reasons to exclude that bikes are vehicles when r2 should be applied. Accordingly, when arguing in this way, the judge may interpret r2 by reducing its applicability conditions as far as Mary’s case is concerned. He thus contracts T in order to obtain in T that Mary’s bike is not a vehicle in the context of the current situation, by adding a defeater r4 blocking the Vehicle conclusion: r4 : Bike; Park c :Vehicle and by stating that r4 is stronger than r0 : ¼ fr4  r0 g.

III. The Logical Framework 1. Proof Theory The following framework is an extension of DL; such an extension slightly revises [3]’s one and is in line with works such as Governatori/Rotolo8. While countsas rules do not prove modalised literals, the system develops a constructive account of those modalities that rather correspond to obligations and goals: rules for these concepts are thus meant to devise suitable logical conditions for introducing modalities. For example, while a counts-as rule such as a1 ; . . . ; an ) c b, if applicable, will basically support the conclusion of b, rules such as a1 ; . . . ; an ) OBL b and d1 ; . . . ; dn ) Goal e if applicable, will allow for deriving OBLb and Goale, meaning the former that b is obligatory, the latter that e is a goal promoted by the facts used to derive it. In our language, for X 2 fc; OBL; Goalg, strict rules have the form 1 ; . . . ; n !X . Defeasible rules have the form 1 ; . . . ; n )X . A rule of the form 1 ; . . . ; n X is a defeater. Accordingly, the mode denoted by X determines the type of conclusion one can obtain, and the three types of rules establish the strength of the relationship. Strict rules provide the strongest connection between a set of premises and their conclusion: whenever the premises are deemed as indisputable so is the conclusion; then we have defeasible rules: a defeasible rule, given the premises, allows us to derive the conclusion unless there is evidence for its contrary; finally we have defeaters. A defeater suggests that there is a connection between its premises and the conclusion, but this connection is not strong enough to warrant the conclusion on its own; on the other hand a defeater shows that there is some evidence for the conclusion, thus it can be used to defeat rules for the opposite conclusion. Definition 1 (Language). Let PROP be a set of propositional atoms, MOD ¼ fc; OBL; Goalg, and Lbl be a set of labels. The sets defined below are the smallest sets closed under the given construction conditions: 8

Governatori/Rotolo (2008a); Governatori/Rotolo (2008b).

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Literals Lit ¼ PROP [ f:pjp 2 PROPg

If q is a literal,  q denotes the complementary literal (if q is a positive literal or goal p then  q is :p; and if q is :p, then  q is p); Modal literals ModLit ¼ fXl; :Xljl 2 Lit; X 2 fOBL; Goalgg

Rules Rul ¼ ðRulXs [ Rulcs Þ [ ðRulXd [ Rulcd Þ [ ðRulXdft [ Rulcdft Þ; where X 2 fOBL; Goalg, such that RulX s ¼ fr : a1 ; . . . ; an !X bjr 2 Lbl; a1 ; . . . ; an  Lit [ ModLit; b 2 Litg Rulcs ¼ fr : a1 ; . . . ; an !c bjr 2 Lbl; a1 ; . . . ; an  Lit; b 2 Litg RulX d ¼ fr : a1 ; . . . ; an )X bjr 2 Lbl; a1 ; . . . ; an  Lit [ ModLit; b 2 Litg Rulcd ¼ fr : a1 ; . . . ; an )c bjr 2 Lbl; a1 ; . . . ; an  Lit; b 2 Litg RulX dft ¼ fr : a1 ; . . . ; an

X bjr

2 Lbl; a1 ; . . . ; an  Lit [ ModLit; b 2 Litg

Rulcdft

X bjr

2 Lbl; a1 ; . . . ; an  Lit; b 2 Litg

¼ fr : a1 ; . . . ; an

We use AðrÞ to denote the set of antecedents of the rule r, and CðrÞ to denote its consequent. Other obvious abbreviations are, for example, Rul½bŠ to denote the set of rules whose consequent is b and Rulc ¼ fr : a1 ; . . . ; an ,!c bj,! 2 f!; );

gg

Rulsd ¼ fr : a1 ; . . . ; an ,!X bjX 2 MOD; ,! 2 f!; )gg Ruls ½bŠ ¼ fa1 ; . . . ; an !X bjX 2 MODg

A normative theory is the knowledge base which is used to reason about the applicability of legal rules included in the theory itself. Definition 2 (Normative Theory). A normative theory is a structure D ¼ ðF; Rc ; R ; RGoal ; Þ, where OBL

– F  Lit [ ModLit is a finite set of facts; – Rc  Rulc is a finite (non-empty) set of counts-as rules, – ROBL  RulOBL is a finite set of obligation rules, – RGoal  RulGoal is a finite set of goal rules, –  is an acyclic relation (called superiority relation) defined over ðRc  Rc Þ[ ðROBL  ROBL Þ [ ðRGoal  RGoal Þ.

Proofs are sequences of literals and modal literals together with the so-called proof tags þ
,
, þ@ and @. If X 2 fc; OBL; Goalg, given a normative theory D, þ
X q means that literal q is provable in D with the mode X using only facts

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and strict rules,
X q means that it has been proved in D that q is not definitely provable in D with the mode X , þ@ X q means that q is defeasibly provable in D with the mode X , and @ X q means that it has been proved in D that q is not defeasibly provable in D with the mode X . Definition 3. Given a normative theory D, a proof in D is a linear derivation, i.e, a sequence of labelled formulas of the type þ
X q,
X q, þ@ X q and @ X q, where the proof conditions defined in the rest of this section hold. Definition 4. Let D be a normative theory. Let # 2 f
; @g and X 2 fOBL, Goalg, and P ¼ ðPð1Þ; . . . ; PðnÞÞ be a proof in D. A literal/modal literal q is #-provable in P if there is a line PðmÞ, 1  m  n, of P such that either 1. q is a literal and PðmÞ ¼ þ#c q or 2. q is a modal literal Xp and PðmÞ ¼ þ#X p or 3. q is a modal literal :Xp and PðmÞ ¼

#X p.

A literal q is #-rejected in P if there is a line PðmÞ of P such that 1. q is a literal and PðmÞ ¼

#c q or

2. q is a modal literal Xp and PðmÞ ¼

#X p or

3. q is a modal literal :Xp and PðmÞ ¼ þ#X p. The definition of
X describes just forward (monotonic) chaining of strict rules 9: þ
X : ¼ If Pðn þ 1Þ ¼ þ
X q then ð1Þ q 2 F if X ¼ c or Xq 2 F; or ð2Þ 9r 2 RXs ½qŠ : 8a 2 AðrÞa is
‑provable:

To show that a literal q is defeasibly provable with the mode X we have two choices: (1) We show that q is already definitely provable; or (2) we need to argue using the defeasible part of a normative theory D. For this second case, some (sub) conditions must be satisfied. First, we need to consider possible reasoning chains in support of  q with the mode X , and show that  q is not definitely provable with that mode (2.1 below). Second, we require that there must be a strict or defeasible rule with mode X for q which can be applied (2.2 below). Third, we must consider the set of all rules which are not known to be inapplicable and which permit to get  q with the mode X (2.3 below). Essentially, each such a rule s attacks the conclusion q. For q to be provable, s must be counterattacked by a rule t for q with the following properties: (i) t must be applicable, and (ii) t must prevail over s. Thus each attack on the conclusion q must be counterattacked by a stronger rule. In other words, r and the rules t form a team (for q) that defeats the rules s. 9 For space reasons, in the remainder we present only the proof conditions for þ
and þ@. Conditions for the negative tags are obtained using the so-called principle of strong negation and the notion of #-rejected Governatori/Rotolo (2008a).

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þ@ X : If P ðn þ 1Þ ¼ þ@ X q then ð1Þ þ
X q 2 P ð1::nÞ or ð2Þð2:1Þ


X  q 2 P ð1::nÞ and

ð2:2Þ 9r 2 RX sd ½qŠ such that 8a 2 AðrÞ a is @ -provable, and ð2:3Þ 8s 2 RX ½ qŠ either 9a 2 AðsÞ such that a is @ -rejected, or ð2:3:1Þ 9t 2 RX ½qŠ such that 8a 2 AðrÞ a is @ -provable and ts

Definition 5. Given a normative theory D, D ‘ #X l, where # 2 f
; @g and X 2 fc; O; Gg, iff there is a proof P ¼ ðPð1Þ; . . . ; PðnÞÞ in D such that PðnÞ ¼ #X l. Definition 6. Given a normative theory D, the universe of D (U D ) is the set of all the atoms occurring in D. The extension of D (E D ), is defined as follows10: þ ED ¼ ð
þ D ;
D ; @ D ; @D Þ

where for X 2 fOBL; Goalg X c
þ D ¼ fXl : D ‘ þ
lg [ fl : D ‘ þ
lg; X
D ¼ fXl : D ‘
lg [ fl : D ‘
c lg;

@Dþ ¼ fXl : D ‘ þ@ X lg [ fl : D ‘ þ@ c lg; @D ¼ fXl : D ‘ @ X lg [ fl : D ‘ @ c lg:

It is worth noting that the logic enjoys the following properties. Proposition 1. Let D be a normative theory where the transitive closure of  is acyclic. For every # 2 f
; @g; X 2 fc; OBL; Goalg: – it is not possible that both D ‘ þ#X p and D ‘

#X p;

– D ‘ þ@ X p and D ‘ þ@ X  p iff D ‘ þ
X p and D ‘ þ
X  p.

Proof. The proof is a trivial variation of the ones for Theorems 1 and 2 in Governatori/Rotolo11. Proposition 1 shows the soundness of the logic: it is not possible to derive a tagged conclusion and its opposite, and that we cannot defeasibly prove both p and its complementary unless the definite part of the theory proves them; this means that inconsistency can be derived only if the theory we started with is inconsistent, and even in this case the logic does not collapse to the trivial extensions (i.e., everything is provable). Theorem 1. For every normative theory D, the extension E D can be computed in time linear to the size of the theory, i.e., OðjU D j  jRjÞ. Proof. The proof comes directly from the result provided in Governatori/Rotolo12. In fact, the current logic is structurally similar to those presented there. 10 11

þ When clear from the context, we will omit the subscript D in
þ D ;
D ; @D ; @ . Governatori/Rotolo (2008b).

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2. The Argumentation Semantics Let us now provide an argumentation semantics based on Governatori et al.13 for the logic presented in the previous section. Definition 7 (Argument and Supportive Argument). An argument A for a conclusion p generated from a normative theory D ¼ ðF; Rc ; ROBL ; RGoal ; Þ is a (possibly infinite) tree with the following structure: 1. all nodes are labeled by elements h 2 Lit [ ModLit; 2. the root is labeled by p; 3. if h1 ; . . . ; hn label the children of h then, either (a) if h 2 Lit then there is a rule r in Rc with body b1 ; . . . ; bn (where h1 ¼ b1 ; . . . ; hn ¼ bn ) and head q (where h ¼ q), or (b) if h ¼ Xl 2 ModLit then there is a rule r in RX with body b1 ; . . . ; bn (where h1 ¼ b1 ; . . . ; hn ¼ bn ) and head q (where h ¼ q), such that all arcs connecting h1 ; . . . hn to h are labeled by the rule r; 4. if a rule r labeling an arc is a defeater, then h ¼ p is the root of the argument; 5. the leaf nodes are labeled by either elements of F or by modal literals having the form :Xl. Some auxiliary terminology: – The nodes labeled by modal literals having the form :Xl are called open nodes. – A supportive argument is a finite argument in which no defeater is used. – An argument is positive iff no defeater is used in it. – A strict argument is an argument in which only strict rules are used. – An argument that is not strict is called defeasible. – A constitutive argument is an argument where all the used rules are constitutive rules. A goal argument is an argument supporting a goal conclusion.

Definition 8 (Top subargument of an argument). Let A any argument with height j  1 for any literal p. The top subargument At of A is the top subargument of A with height 1. Let us use RðA t Þ to denote the rule associated with the arcs arriving at the root of A t . In characterizing the argumentation semantics for our logic we can disregard the superiority relation to keep the discussion and the technicalities simple. This restriction does not affect the generality of the approach: in Governatori/Rotolo14 we gave 12 13 14

Governatori/Rotolo (2008b); Governatori/Rotolo (2008a). Governatori et al. (2004). Governatori/Rotolo (2008a).

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a modular transformation that empties the superiority relation while maintaining the same conclusions in the language of the original theory. (The logic of Governatori/ Rotolo15 is structurally identical to the one presented here; the only difference is that we have here a different set of modalities.) Definition 9. Let l 2 Lit [ ModLit. The set ComplðlÞ of complementary literals of l is defined as follows: – if l ¼ p 2 Lit then ComplðlÞ ¼ f:pg; – if l ¼ Xp 2 ModLit then ComplðlÞ ¼ f:Xp; X  pg.

Definition 10 (Attack). An argument Ai attacks an argument A j iff there is a literal/modal literal l such that 1. h ¼ l, where h is a node in Ai ; 2. l 2 ComplðmÞ, where h0 ¼ m such that h0 is a node in A j . A set of arguments S attacks an argument A j if there is an argument A i in S that attacks Aj . Definition 11 (Support and Undercut). A set of arguments S supports an argument A if every proper subargument of A is in S. An argument Ai is undercut by a set of arguments S if S supports an argument A j attacking a proper subargument of A i . Definition 12 (Acceptable and Rejected Aruments). An argument A for l is acceptable w.r.t a set of arguments S if A is finite and every argument attacking A is undercut by S. An argument A is rejected by sets of arguments S and T when 1. a proper subargument As of A is in S, or 2. As is attacked by an argument supported by T. Definition 13 (Rejected Arguments and Rejected Literal/Modal Literal). Let D be a normative theory and T a set of arguments. We define RD i ðT Þ as follows. – RD0 ðTÞ ¼ ;; – RDiþ1 ðTÞ ¼ fA 2 ArgsD jA is rejected by RDi ðTÞ and Tg.

The setS of rejected arguments in a normative theory D w.r.t. T is D D RArgsD ¼ 1 i¼1 Ri . An argument is rejected if it is rejected w.r.t. JArgs . A literal/modal literal l is rejected by T if there is no supportive argument for l in ArgsD RArgsD ðT Þ. A literal/modal literal l is rejected if it is rejected by JArgsD.

15

Governatori/Rotolo (2008a).

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Definition 14 (Grounded Arguments). Let D ¼ ðF; Rc ; ROBL ; RGoal ; Þ be a normative theory. An argument A 2 ArgsD is grounded iff, for each leaf node h in it, either h 2 F or, if h ¼ :Xp then Xp is rejected. Definition 15 (Justified Argument and Justified Literal/Modal Literal). Given any normative theory D, let ArgsD be the set of arguments that can be generated from D. We define JiD as follows. – J0D ¼ ;; D – Jiþ1 ¼ fA 2 ArgsD jA is acceptable w:r:t: JiD and is groundedg.

The set of justified arguments in a normative theory D is JArgsD ¼

S1

D i¼1 Ji .

A literal/modal literal l is justified if it is a conclusion of a supportive argument in JArgsD . Theorem 2 (Characterization of the Logic in Argumentation Semantics). Let D be a normative theory, X 2 fOBL; Goalg, and l 2 Lit [ ModLit. 1. D ‘ þ
X p iff there is a strict supportive argument for l ¼ Xp in ArgsD . 2. D ‘ þ
c p iff there is a strict supportive argument for l ¼ p in ArgsD . 3. D ‘


X p iff there is no (finite or infinite) strict argument for l ¼ Xp in ArgsD .

4. D ‘


c p iff there is no (finite or infinite) strict argument for l ¼ p in ArgsD .

5. D ‘ þ@ X p iff l ¼ Xp is justified. 6. D ‘ þ@ c p iff l ¼ p is justified. 7. D ‘

@ X p iff ¼ Xp is rejected by JArgsD.

8. D ‘

@ c p iff l ¼ p is rejected by JArgsD.

Proof (Sketch). The proof for points 1 – 4 is a trivial extension of the one for Proposition 5 in Governatori et al.16. The proof for points 5 – 8 by induction of the length of derivation in the logic, is a variation of the one for Theorem 17 in Governatori et al.17. In both cases, the addition of modal operators does not technically make things harder, but only requires to also consider when modal literals are obtained with rules for X 2 fOBL; Goalg. The only significant difference is that supportive arguments that make use of rules with negative modal literals like :Xl in their antecedents require that Xp is rejected, a case which is covered in Definition 15 by requiring that all justified arguments be grounded.

16 17

Governatori et al. (2004). Governatori et al. (2004).

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IV. The Revision of Norm Applicability In Section 2 we have recalled the basic ideas presented in Boella et al.18 and have informally illustrated how to revise legal concepts in order to make legal rules applicable or to block their applicability. Here, we focus on the operations of contraction and expansion. We first show how to reframe the operation in Boella et al.19 by making use of the argumentation semantics presented in Section 3.2. This requires to preliminarily introduce some notions which we will use in the remainder (extended normative theory, goal demotion and promotion). Definition 16 (Extended Normative Theory). An extended normative theory is a structure hðF; Rc ; ROBL ; RGoal ; Þ; G; G ; >i, where – ðF; Rc ; ROBL ; RGoal ; Þ is a normative theory; – G  Lit is a set of goals; – G : ROBL 7!G is a function assigning a goal to each obligation rule; – > is a partial order over G defining the relative importance of the rule goals.

Definition 17 (Goal Demotion and Promotion). Let hðF; Rc ; ROBL ; RGoal ; Þ; G; G ; >i be an extended normative theory. Let H ¼ f  Lit [ ModLit be a set of facts, r : b1 ; . . . ; bn ,!OBL l 2 ROBL be a regulative legal rule, and g the goal of r. sd H demotes the goal g iff – there is no justified argument for Goal:g if H \ F ¼ ;; – there is at least one justified argument for Goal:g if H  F.

H promotes the goal g iff – there is no justified argument for Goal g if H \ F ¼ ;; – there is at least one justified argument for Goal g if H  F.

When H ¼ F we say that the extended normative theory promotes or demotes any given goal g. The procedure for contracting the theories that characterize legal concepts can be framed in general as follows. Definition 18 (Applicability Contraction). Let D ¼ ðF; Rc ; ROBL ; RGoal ; Þ a normative theory and ExðDÞ ¼ hðF; Rc ; ROBL ; RGoal ; Þ; G; G ; >i be an extended normative theory obtained from D such that r : b1 ; . . . ; bn ,!OBL l 2 ROBL sd , g is the goal of r, and H ¼ ff1 ; . . . ; fm g  F. If 1. there exists at least one justified argument A whose top subargument A t is such that RðA t Þ ¼ r; and

18 19

Boella et al. (2009); Boella et al. (2010). Boella et al. (2009); Boella et al. (2010).

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2. either (a) H [ f:lg and H [ flg demote g and there exists any bk , 1  k  n, such that bk is a node in each justified argument C for Goal:g when either H [ f:lg  F or H [ flg  F; or (b) H [ f:lg promotes g and H [ flg demotes g, and there exists any bk , 1  k  n, such that bk is a node in each justified argument C for Goal g when H [ f:lg  F, or bk is a node in each justified argument C 0 for Goal:g when H [ l  F; or (c) H [ f:lg and H [ flg promote g and there exists a bk , 1  k  n, such that bk is a node in each justified argument C for Goalg when either H [ f:lg  F or H [ flg  F; then the contraction of the applicability conditions of r with respect to the case H denoted by RH r ðExðDÞÞ20 amounts to revising Rc and  in hðF; Rc ; ROBL ; RGoal ; Þ; G; G ; >i as follows: R0c ¼ Rc [ fr : f1 ; . . . ; fm

c

 bk g

0 ¼ [fr  tj8t 2 Rc ½bk Šg

The normative theory ðF; Rc ; ROBL ; RGoal ; Þ in the resulting extended normative theory is denoted by D0 and is such that 0

3. for any other goal g 0 , there is no argument A 2 JArgsD for Goal:g 0 when H  F, where – g 6> g 0 , and 0

– g 0 ¼ G ðzÞ where z 2 ROBL and there exists at least one argument B 2 JArgsD sd t whose top subargument B is such that RðB t Þ ¼ z when H  F.

Remark 1. We have three situations in which the applicability conditions of a regulative legal rule should be intuitively restricted (sub-conditions (a), (b), and (c) under point 2 above). First, we have that the goal of r is demoted not only by :l but also by complying with the regulative legal rule; moreover, there exists at least one of the antecedents of the legal rule which is used in all goal arguments, in which either l or :l occur, to prove :g (the goal violation of the legal rule). Thus, we have reasons to block the constitutive rules supporting this antecedent. Second, we have that the violation of r (:l) unexpectedly promotes the goal g of this rule, while compliance (l) doesn’t; moreover, there exists at least one of the antecedents of the legal rule which is used in all goal arguments, in which l occurs, to support g (the goal promotion of the legal rule), while an antecedent is used in all goal arguments, in which :l occurs, to support :g (the goal demotion of the legal 20 When H is omitted it means that the operation is done considering the set F of all facts. The same applies also for the subsequent expansion operation of Definition 19.

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rule). Thus, we have reasons to block the constitutive rules supporting such antecedents. Finally, we have that the goal of the norm is promoted independently from the fulfillment or violation of the norm. The resulting revision is subject to the final constraint that no other goal g0 of any applicable regulative rule would be demoted if g 0 is at least as important as g. Notice that the operation of contraction is technically done by changing Rc and . This revision is supposed to remove any bk from the extension of the normative theory D0 when f1 ; . . . ; fm are the case. Definition 19 (Applicability Expansion). Let D ¼ ðF; Rc ; ROBL ; RGoal ; Þ a normative theory and ExðDÞ ¼ hðF; Rc ; ROBL ; RGoal ; Þ; G; G ; >i be an extended normative theory obtained from D such that r : b1 ; . . . ; bn ,!OBL l 2 ROBL sd , g is the goal of r, and H ¼ ff1 ; . . . ; fm g  F. If 1. there exists a subset fbk ; . . . ; bkþj g  AðrÞ of all the applicability conditions of r for which there is no positive constitutive argument built using H and Rc ; 2. H [ f:lg demotes g; 3. H [ flg promotes g; 4. there exist the non-positive constitutive arguments C k ; . . . ; C kþj built using H and Rc for bk ; . . . bkþj ; such that each element of H occurs in each of such arguments; then the expansion of the applicability conditions of r with respect to the case H dec c OBL noted by RH ; RGoal ; Þ; þr ðExðDÞÞ amounts to revising R and  in hðF; R ; R G; G ; >i as follows: for each argument C h among C k ; . . . ; C kþj , there is a defeater r0 : d 1 ; . . . ; dn e occurring in C h such that R0c ¼ Rc

fr0 : d 1 ; . . . ; dn

eg [ fr0 : d 1 ; . . . ; dn ) eg

0 ¼  [fr  tj8t 2 Rc ½eŠg

The normative theory ðF; Rc ; ROBL ; RGoal ; Þ in the resulting extended normative theory is denoted by D0 and is such that 0

5. for any other goal g 0 , there is no argument A 2 JArgsD for Goal:g 0 when H  F, where – g 6> g 0 , and 0

– g 0 ¼ G ðzÞ where z 2 ROBL and there exists at least one argument B 2 JArgsD sd t whose top subargument B is such that RðB t Þ ¼ z when H  F.

Remark 2. This definition considers the situation where a regulative legal rule r is only partially applicable since some of the conditions cannot be matched by the facts H (1). However, in this situation, not respecting r (i.e., :l) leads to demoting the goal g of this rule (2). This would be avoided by complying with r, i.e., by

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achieving l (3). Moreover, the constitutive rules suggest that some elements of the context could be interpreted as the missing applicability conditions of the rule r (4). Thus, the theory should be expanded by transforming some defeater rules, among the constitutive rules, into standard rules. The resulting theory is however subject to the final constraint that no other more important goal g0 of any norm would be demoted.

V. Refining the Argumentation Model: The Case of Contraction In comparison to Boella et al.21, the operations presented in the previous section have the advantage of being much less cumbersome, since they make use of a more intuitive framework that looks also more natural in an argumentative domain like legal reasoning. However, the model can be further refined. We will only focus here on the case of contraction. If so, we see two main limits: (i) Definition 18 only works with defeasible arguments, i.e., when any literal b to be contracted occurs in @Dþ ; with strict arguments (when b 2
þ D ), no contraction is possible; (i) Definition 18 does not cover the case where the contraction of the literal is not made by directly attacking the rules supporting it, but by attacking proper subarguments. 1. Contraction Operation: Refinements In this section we present simple operations extending what we have recalled in the previous section. Such extensions aim at solving the problems mentioned above under points i and ii. However, the cost for this solution is that we no longer satisfy some standard postulates of AGM revision theory22. In particular, AGM postulates for minimal change can be problematic; let us define the contraction Dp of conclusion p as Dp X and consider the following two postulates that reframe in our setting two well-known AGM postulates (see Billington et al.23), where ] 2 f
; @g and Dþ p is the expansion operation as proposed in Billington et al.24: D D If p 62 ]þ D then Ep ¼ E

If p 2

21 22 23 24

]þ D

then


þ D


þ ðD

þ p Þp

Boella et al. (2010); Boella et al. (2009). Alchourrón. Billington et al. Billington et al.

þ and @Dþ  @ðD

þ p Þp

(]-Vacuity) (]-Recovery)

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The operations that we are going to present do not enjoy in general these properties: an extensive discussion of the topic and some more refined operations of contraction can be found in Governatori et al.25 Let us consider the first problem: what to do when there is a strict supportive argument for the literal b? Since strict rules cannot be defeated, the only solution is rule removal. Definition 20 (Rule Removal). Let D ¼ ðF; Rc ; ROBL ; RGoal ; Þ be a normative theory. Let A 1 ; . . . A n the strict arguments in ArgsD supporting p. The normative theory Dp X is equal to D except for Rc X , which is defined as follows: – Rc X ¼ Rc

X and

– X ¼ w1 ; . . . ; wm is the smallest set of strict rules in Rc where, for each k 2 f1; . . . ; ng, there is at least a wj 2 X such that wj occurs in Ak .

Example 2. Consider the following normative theory D: F ¼ fa; bg Rc ¼ fr1 : a !c :c; r2 : d )c c; r3 : b !c d; r4 : d; a !c :cg ROBL ¼ fr4 : :c )OBL lg RGoal ¼ f )Goal gg ¼ ;

Suppose we want to contract :c, which is in
þ of the extension of D and triggers r4 . In this normative theory we have only two strict arguments for :c: llA 1 ¼ a !c :c

A 2 ¼ b !c d; a !c :c

Since the two arguments do not share any rule, we have necessarily to remove at least two rules. An option that satisfies Definition 20 is the removal of r1 and r4 , but also the removal of r3 would be acceptable. Notice that Definition 20 allows us to change arguments in a very flexible way, as it permits to contract a literal by removing rules that do not directly support it. This may be needed in the law. For instance, suppose we have the following rules r1 : Embryo !c Alive

r2 : Alive !c Person

r3 : Person; Kill !c Homicide

and we want that killing an embryo does not amount to a homicide. Perhaps, it would be better to remove r1 or r2 rather than denying that killing a person is not a homicide (removing r3 ).

25

Governatori et al. (2013).

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Similar considerations can be applied to the contraction of defeasible conclusions, which is introduced, following Billington et al.26, in Definition 18. The contraction operation described there works in such a way that any p is removed from the defeasible extension of the normative theory when some facts hold. Even in this case, the operation directly affects the defeasible rules that prove p, but a more flexible contraction operation can be introduced. Definition 21 (Defeasible Contraction). Let D ¼ ðF; Rc ; ROBL ; RGoal ; Þ be a normative theory. Let A 1 ; . . . An be the arguments in JArgsD for p. The theory D[p ¼ ðF; R0c ; ROBL ; RGoal ; 0 Þ is such that (i) R0c ¼ Rc [ fs : 0

c

 qg [ ft :

c

 xg,

c

(ii)  ¼ ½frk  sjrk 2 R ½ Cðsފ; rk occurs in A k 8k 2 f1; . . . ; ngg [ fw  t j for each argument B where all the subarguments of B are in JArgsD except the top subargument B t and CðRðB t ÞÞ ¼ x, either x ¼ p or RðB t Þ occurs in Ak 8k 2 f1; . . . ; nggŠ. Remark 3. The apparent complexity of Definition 21 depends on the fact that, removing p from @Dþ without possibly affecting the rules in Rcd ½pŠ must take into account that the fact blocking some other literals that are used to argue in favor of p may trigger in turn some rules proving p, like in the following set of rules: Rc ¼ fr1 :)c a; r2 : a )c b; r3 : b )c p; r4 : a )c c; r5 :)c :c; r6 : :c )c pg

Here, if we only add a defeater like s : c :a, we remove a from @Dþ , which occurred in all justified arguments for p, but in doing this rule r4 is no longer applicable and thus we trigger r5 and r6 , once again having p in the defeasible extension.

VI. Meaning Negotiations and Arguments to the Best Theory Definition 18 does not guarantee to get one resulting normative theory: we may have to explore if there are counterarguments for each antecedent of the norm at hand. A fortiori this applies as well to Definitions 20 and 21: here we may have cases where more results are available for revising the given theories of constitutive rules in order to align concepts with the goals of regulative legal rules: Proposition 2. The restricting procedures based on Definitions 18, 20, and 21 lead to more than one outcome. This fact raises the question of how to choose among different theory revisions. This problem can take the form of a dialectical process where an exchange of arguments and counter-arguments are meant to establish which is the best theory supporting or excluding the contraction of the applicability conditions of a given legal 26

Billington et al.

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Antonino Rotolo

rule27. In general, some criteria can be proposed, such as inclusiveness, simplicity, minimal change, and theory connectedness28. Let us just consider two of them. Minimal change In the previous sections we have mentioned that some AGM criteria of minimal change can be re-framed in our logic setting. In our framework, minimal change still amounts to minimizing the changes of the theory extension. However, since the contraction is made by adding defeaters and by removing strict rules, one may state that the minimal change should be rather obtained by keeping the set of rules as close as possible to the original one. This idea is well-known in revision theory but is overlooked in rule-based defeasible systems. Notice that the second option (minimal rule change) is independent of the facts of the normative theory, whereas the other (minimal extension change) is context-dependent, since different facts may fire different rules. Obviously, these two options do not always lead to the same results: suppose the facts include a and consider Rc ¼ fr : a ) b; s : b ) e; t : b ) d; z : b ) eg

If we want to block e (we want to restrict the interpretation of a concept), we have two options: add either two defeaters to override respectively s and z, or only one defeater that overrides r. The first option is better in terms of minimizing the change of conclusions (we only drop e), while the second one is better, as only one defeater is added (but two conclusions are dropped: b and e). Theory connectedness This can be roughly measured by the number of links (based on sharing common literals) that connect each concept with the others. Intuitively, this is a desirable property, since it reflects the systematic character of legal systems. Consider, for instance, the following two sets of rules: Rc ¼ fr1 : Embryo !c Alive; r2 : Alive; Kill !c Homicide; r3 : Person !c Aliveg ROBL ¼ fr4 : Homicide )OBL Punishedg

Since all counts-as rules are strict, what we can do is only to remove rules. Suppose we want to prevent the situation where one is punished because she “killed” an embryo. We have two options here: either (a) remove r1 or (b) remove r2 . Option (b) is less satisfactory in this specific example: the impact on the theory is greater, as rule 2 is more connected to the other rules than r1 . We could just notice that an argumentation framework for norm applicability can be based on the following intuitions. Let us assume to work using theory connectedness as the only criterion for preferring theories. Definition 22 (Norm argument). Let A be any extended normative theory and r be an obligation rule in it: by A r and Aþr we mean, respectively, that 9b 2 AðrÞ such that A ‘ @ c b and that 8b 2 AðrÞ we have A ‘ þ@ c b. We call 27 28

Prakken / Sartor. Rotolo / Roversi.

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A r a norm argument against r and Aþr a norm argument for r. If Ar is a norm argument, then Rr ðA r Þ is a norm argument. Definition 23 (Norm attack). A norm argument B r attacks a norm argument A x with respect to rule r iff, either29 – x ¼ r , Ar demotes the goal g, B r ¼ Rr ðAr Þ, and B r promotes the goal g; or – x ¼ r , Ar promotes the goal g, B r ¼ Rr ðA r Þ, B r promotes the goal g, and B r is at least theory connected as Ar ; or – x ¼ r , Ar promotes the goal g, B r ¼ Rr ðA r Þ, B r promotes the goal g, and B r is more theory connected than Ar .

Let us now move to meaning negotiations. Following Wooldridge / Parsons; Veenen / Prakken30, these negotiations can be viewed as dialogues involving two parties that run according to a general negotiation protocol. Such a protocol can be rather complex, but if meaning negotiations are concerned, it is in fact identical to the one formulated for any other type of negotiations: what is distinctive is rather the object of the dialogue moves. For this reason, we will not present an explicit and complete definition of the protocol: the interested reader is referred, e.g., to Veenen/Prakken31, [Definitions 1,3, and 4]. For our purposes, it is enough to work on the basic intuition behind the idea of meaning negotiation. A meaning negotiation takes place between two players, one of whom starts with either an offer or a request, given an initial set of norm arguments based on a given extended normative theory (see Definition 22), which is shared by both players. The players then take turns after each utterance, selecting their replies as intuitively specified in Definition 24 below. The initial move is the request of one player, the proponent, to make applicable (or inapplicable) a certain norm r in the extended normative theory if r is initially inapplicable (resp., applicable) in the theory. The other player, the opponent, can reply by offering a solution, i.e., by presenting a norm argument supporting the request. Then, the negotiation carries on by using the initial set of norm arguments shared by the players or by revising norm arguments used in the previous steps of the dialogues. As the definition below states, a negotiation terminates when an agent accepts an offer or withdraws from the negotiation. Finally, moves may not be repeated by the same player 32. Definition 24 (Speech acts and replies in meaning negotiations; cf. 133). The following are the acts and the corresponding replies or effects for any step n in a 29 Notice that R r can denote any contraction operation among those outlined in Definitions 18, 20, and 21. 30 Wooldridge / Parsons; Veenen / Prakken. 31 Veenen/Prakken. 32 Veenen/Prakken, p. 3. 33 Boella/Torre.

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meaning negotiation dialogue. Let 1  j  n and A rj be a norm argument belonging to the initial set of norm arguments shared by the players or anyway occurring in at least one previous step n m (1 < m < n) of the dialogue: Acts at step n

1

Replies at step n

n

1 ¼ requestðA0rj Þ

n ¼ offerðRrj ðArj ÞÞ

n

1 ¼ offerðRrj ðArj ÞÞ

n ¼ offerðR0rj ðArj ÞÞ : R0rj ðA rj Þ attacks Rrj ðArj Þ; or n ¼ acceptðRrj ðA rj ÞÞ; or n ¼ rejectðRrj ðArj ÞÞ if 9n n

m:

m ¼ A and A attacks Rrj ðArj Þ; or

n ¼ withdraw n

n ¼ offerðR0rj ðArj ÞÞ : 8n

1 ¼ rejectðA rj Þ

m ¼ B where

B attacks Arj ; R0rj ðA rj Þ attacks B or Arj demotes the goal of rj ; or n ¼ withdraw n

1 ¼ acceptðArj Þ

n ¼ end of negotiation

n

1 ¼ withdraw

n ¼ end of negotiation

As recalled in Veenen/Prakken34, in order “to ensure that the offers exchanged during a negotiation and its outcome are related to an initial request”, it is required to add the following rule to the protocol: – If requestðA 0rj Þ is the initial request of a dialogue then for any move offerðB Þ in the dialogue B ¼ Arj .

Example 3. Suppose we consider an extended normative theory A where the set of facts and rules is the following: F ¼ fEmbryo; Killg Rc ¼ fr1 : Embryo !c Alive; r2 : Alive; Kill !c Homicide; r3 : Person !c Aliveg ROBL ¼ fr4 : Homicide )OBL Punishedg

For the sake of illustration, assume for simplicity that the goal assigned to r4 is human well-being. Clearly, we have the following justified constitutive argument in A: Embryo ! AliveAlive; Kill ! Homicide

34

Veenen/Prakken, p. 3.

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Hence, the players share this set of initial norm argument: fAþr4 g. Assume that the extended theory, which thus makes r4 applicable, demotes the goal well-being. The proponent’s first move is: 1. requestðA0 r4 Þ The opponent replies as follows: 2. offerðR

r4 ðA þr4 ÞÞ

which removes from Rc the rule r2 (see Definition 20). Assume that the resulting theory demotes the goal well-being, hence the proponent reply is 3. rejectðR

r4 ðA þr4 ÞÞ

The opponent now offers the following: 4. offerðR0 r4 ðA þr4 ÞÞ which removes r1 thus promoting the goal well-being and obtaining a more connected theory. The proponent thus 5. acceptðR0 r4 ðA þr4 ÞÞ and so the negotiation ends.

Summary In this chapter we proposed a framework for reconstructing the arguments supporting the restrictive and extensive interpretations of legal provisions. The contribution is based on the idea that the interpretation of legal concepts may require to change the constitutive rules defining them. Indeed, if our ontology does not classify, for example, a bike as a vehicle, but we have reasons that this is the case, then this implicitly leads to conclude that the ontology must be revised and that a bike, at least in the contexts under consideration, is a vehicle. The revision procedures presented in this chapter are driven and constrained by considering the goal of the regulative legal rules in which these concepts occur. The framework has been the applied to model meta-argumentation over the legal meaning of terms occurring within legal provisions and used to show how negotiations may take place in this context and be formally captured.

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References Alchourrón, Carlos E. / Gärdenfors, Peter / Makinson, David: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50 (2): 510– 530, 1985. Billington, David / Antoniou, Grigoris / Governatori, Guido / Maher, Michael J.: Revising nonmonotonic belief sets: The case of defeasible logic. In Proc. KI-99, Springer, Berlin, 1999. Boella, Guido / Governatori, Guido / Rotolo, Antonino / Torre, Leendert van der: Lex minus dixit quam voluit, lex magis dixit quam voluit: A formal study on legal compliance and interpretation. In Proc. AICOL 2009, pages 162–183, Springer, Berlin, 2010. – A logical understanding of legal interpretation. In KR 2010, AAAI Press, Menlo Park, 2010. Boella, Guido / Torre, Leendert van der: Norm negotiation in multiagent systems. Int. Journal Coop. Inf. Syst., 16 (1): 97–122, 2007. Burato, Elisa: Meaning Negotiation in Multiple Agent System: an Automated Reasoning Approach. PhD thesis, University of Verona, 2010. Governatori, Guido / Maher, Michael J. / Billington, David / Antoniou, Grigoris: Argumentation semantics for defeasible logics. Journal of Logic and Computation, 14: 675–702, 2004. Governatori, Guido / Rotolo, Antonino: BIO logical agents: Norms, beliefs, intentions in defeasible logic. Autonomous Agents and Multi-Agent Systems, 17 (1): 36–69, 2008. – A computational framework for institutional agency. Artif. Intell. Law, 16 (1): 25–52, 2008. Governatori, Guido / Rotolo, Antonino / Olivieri, Francesco / Scannapieco, Simone: Legal contractions: a logical analysis. In Proc. ICAIL 2013, pages 63–72, ACM, New York, 2013. Prakken, Henry / Sartor, Giovanni: The three faces of defeasibility in the law. Ratio Juris, 17: 118–139, 2004. Rotolo, Antonino / Roversi, Corrado: Constitutive rules and coherence in legal argumentation: The case of extensive and restrictive interpretation. In Legal Argumentation Theory, Dordrecht, 2012. Springer. Sartor, Giovanni: Legal reasoning: A cognitive approach to the law. Springer, Dordrecht, 2005. Searle, John R.: The Construction of Social Reality. The Free Press, New York, 1996. Veenen, Jelle van / Prakken, Henry: A protocol for arguing about rejections in negotiation. In Proc. ArgMAS 2005, pages 138–153, Springer, Berlin, 2005. Wooldridge, Michael / Parsons, Simon: Languages for negotiation. In Proc. ECAI 2000, pages 393–400, IOS Press, Amsterdam, 2000.

Paradigms for Automatization of Logic and Legal Reasoning By Tanel Kerikmäe and Sandra Särav Tanel Kerikmäe and Sandra Särav

I. Introduction Technology is one of the most prevalently discussed topics today – philosophically, economically, socially and, of course, legally. The debates can be divided into endless categories representing controversial stands. In the context of this contribution, the authors analyse certain confluences between legal logic and information technology, with special considerations on the following two questions: a) Can information technology, contributing to legal science and politics and drawing its course of action out of augmented logic, help towards a more just, impartial and fair legal administration and decision-making system? b) How can the digital and technological developments (mainly Artificial Intelligence) impact or change legal reasoning? It is debatable whether technologies can actually replace human reasoning. According to Walker that is because “[l]egal reasoning tends to be dynamic and probabilistic in nature,” and that logic in law is based on “default reasoning” that is strongly dependent on revisions on occurrence of new evidence or reanalysing old evidence.1 Considering Bergman’s viewpoint, our society is not yet prepared for the technology revolution, since “it is often unclear exactly what the new technology is and where it might go.”2 Nevertheless, certain technological revolutions have been taking place in the field of legal reasoning. There are, of course, and always will be dissenting opinions, and the authors will subsequently present a handful of such. In case of conservative-minded lawyers3, it can be presumed that the automatized logic in legal science and practice receives severe criticism. According to Menne – “the logical formation of legal science is more easily possible than the au1  Walker 2010. Legal Reasoning and the Need for Empirical Research. In Hosftrahorizons. Accessible at: http://people.hofstra.edu/vern_r_walker/LLT/LLTLabHofstraHori zonsFall2010.pdf 2  Bergman, p. 171. 3  Hereby the authors do not refer to the UK’s Society of Conservative Lawyers, but a group of lawyers at a larger scale in the meaning of conservatism as political and social philosophy as opposed to liberalism and more liberal-minded legal professionals.

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tomatization of legal decisions”4 mainly due to the uniqueness of the circumstances versus abstractness of the normative system. Nevertheless, the so-called AI-lawyers, or more specifically, augmented intelligence tools for legal research, have become rather fashionable (IBM Watson and ROSS). E-Identities and e-contracts drafted by artificial intelligence are expected to reduce redundant bureaucracy. On the other hand, the ordained digital society leading to dehumanisation cannot imitate cordial “default reasoning.”5 Bearing various contentious discussions in mind, the current chapter focuses on the relevant references to info-technological theories and presents the approaches taken in relation to such field. This is done by identifying the statements of legal scholars and evidence of debateable triumphs and relative failures in the use of the computed legal reasoning practice so far. More specifically, the research is divided into subsequent subchapters. Firstly, section II, presents the general introduction to the information and communication technology revolution in the field of law. This section includes the evaluation of hindrances of regulation with respect to the Fourth Industrial Revolution in technology, focusing on the intricacy of comprehending the abstract ways of automatized technological systems. Section III gives an insight on legal practice and management software products and portrays the expectations which are set for artificial intelligence and intelligence augmentation systems in a contemporary IT-infused society; it also ponders upon the likelihood of such systems displacing human legal reasoning. In section IV and V, the authors ratiocinate over confrontation of lawyers versus computers from the perspective of prevailing consciousness (IV) and morality (V) as, perhaps, peremptory plea for avoiding over-automatization in order not to let technology rule over human-drafted law and not vice versa. In conclusion, the authors reach the opinion (as expected) that technology and automatization should and could contribute to better structuring of legal knowledge and reasoning, but cannot and ought not substitute the humane default reasoning, as portrayed by the various contemplations and contradictions of “traditional” and new-era philosophers and practitioners.

II.  Are Robots Purely Autistic Positivists? Moritz Schlick, Ernest Mach, Ludwig Wittgenstein, Bertrand Russel and Auguste Comte were the fathers of (logical) positivism and were not lawyers, but physicists, mathematicians, sociologists. Yet they had the same platform of thinking as legal philosophers John Austin, Jeremy Bentham, Hans Kelsen, H.L.A Hart and Joseph Raz. Although Green believes that the association between logical positivism and legal positivism is arbitrary,6 the main thesis of logical positivism – “verifiability” – may not make sense when analysing the essence of e-Regulation Menne, p. 135. See the discussion on dehumanisation of law in Kerikmäe and Rull 2016. 6  Leslie (2009). 4  5 

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as a distinct area of law, and therefore, the so-called realistic approach may be helpful. The Information and Communication Technology (ICT) experts-driven “digital by default” refers to the statements of Sayer: “the world exists independently of our knowledge of it” and “the process of developing knowledge is not continuous or discontinuous” as interpreted by Ahmad H Juma’h.7 Positivism in general, as the main direction of methodology, has often assumed to be coupled with an understanding of law. For example, Keat states that: “for the positivist, it is the aim of science to provide us with predictive/explanatory knowledge” and the “scientific theories are to be seen, primarily, as sets of highly general, law-like statements.”8At the same time, comparative and teleological methods in legal science, provide a solid ground to assume that in legal research, a creation, application and interpretation of a legal norm is related to numerous societal variables. Although law may reflect a positivist model, automatization of decision-making is exceptionally complex and insecure. Is the Fourth Industrial Revolution (or Industry 4.0) – offering breakthroughs in artificial intelligence, robotics, the Internet of Things, and the Internet of Systems as thoroughly discussed by Prof. Schwab9 something dissimilar from the previous three industrial revolutions? Schwab believes it is fundamentally different, and proposes that if the previous revolution liberated humankind from animal power, built mass production means and gave way to digital capabilities, the current, industry 4.0, challenges the idea of what it means to be a human being in itself. He sees the fourth revolution as having created new technologies that combine the biological, physical and digital worlds, whilst impacting all disciplines, industries and economies.10 The authors of this paper also believe that with the revolutionary nature of an automatization-driven economy and unforeseen expansion of information society, social interactions will be changed like never before. The problematic aspect of regulating fourth revolution technologies, is that they are programmed, leading to the inescapable fact that a human cannot dissect the programmed/automatized technological system through the use of legal norms. This, in turn, similarly to what Schwab has written, means that perhaps the automatized “minds” themselves can regulate equal technologies.11 Sayer, p. 96. Keat, p. 3. 9  Schwab (2016). 10 Ibid. 11  Here an example is the regulation of driverless cars in Europe. Self-driving cars are on the market, however, there is no targeted legislation or a proposal for legislation. A Parliament report from 2016, proposes that „full automation is expected to be feasible on a large scale in a farther time horizon (more than 20 years).“ Report available at: http://www. europarl.europa.eu/RegData/etudes/STUD/2016/573434/IPOL_STU(2016)573434_EN.pdf. The current UN regulation (UN Regulation No. 79. In 2014) sets limit to driverless cars to conditions below 10 km/h. There are negotiations ongoing to overturn this limitation but the amendments are not expected to be passed before the end of 2017. 7  8 

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Realists argue that “reality is layered and some of the layers are not available to sense perception.”12 May this be the case with digital innovations, where future perspectives can only vaguely be predictable? The central idea of law-making is to have regulations which control certain conduct in reasonable abstractness, peering into the future, anticipating the possible conflicts, rights and duties that do not appear today while not hindering prospective process.

III.  Artificial Intelligence as an Agent for Systematisation or for Applying Law? As concluded by Huhn, “All rules of law may be stated in the following hypothetical form: If certain facts are true, then a certain legal conclusion follows.”13 Artificial Intelligence (AI) seems to be a proper tool for finding conclusions to the specified facts. Before making premature assumptions of Artificial Intelligence in legal reasoning, we have to be familiar with the main classical criticism in the area. One convenient example is an essay written by pioneers in the field, Buchanan and Headrick in 1970; in this particular decade, there was an attempt to conduct research on, and subsequently implement “thinking” machines to the decision-making process (see, for example the “Taxman” project14). The authors present the essential problem that follows from the different mentality of separate professional circles in the interest field. They claim that “lawyers have viewed the computer as, at most, a storehouse from which cases and statutes might be retrieved by skillfully designed indexing systems,”15 as the computer scientists have been convinced that the lawyers need computers to get quick and right answers.16 This understanding leads to the presumption that the legal professionals would rather see themselves as authors of unique arguments, which are only partially derived from the (computed) databases or archives. This dichotomy is exposed by Habermas who has claimed that stereotype engineers carry the purposive-rational action, that is, “can intend the use of appropriate instruments; the behaviour is then guided by technical rules”17. Habermas refers to Kaufmann who distinguishes between theoretical laws (based on idealising assumptions) and empirical laws.18 Another dichotomy is presented by Sunstein more than 30 years later, suggesting that computers and AI cannot reason by analogy “because they are unable to engage in the crucial task of identifying the normative principle that links or sep-

Juma’h, p. 98. Huhn, p. 17. 14  McCarty (1977). 15  Buchanan/Headrick, p. 40. 16 Ibid. 17  Habermas, p. 44. 18 Ibid. 12  13 

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arates the cases.”19 The common expectation of AI’s role in being involved in the legal reasoning is what Sunstein calls “analogizers in law” whose task is to find “relevant similarities to the case at hand” as the basis of the successful operation would be the identification of “a principle that justifies a claim of similarity or difference.”20 Today, we are faced with an overflow of so-called “Law Practice Management Software Products”21 that vary on the basis of used software techniques, such as streamlines, clouding, built-in reminder- and billing systems and calendars, but also by governing specific fields of law.22 However, the main discourse of the efficacy of the AI in legal reasoning has remained the same. As explained by Cross, who introduces one of the flagships software of London based firm Hodge Jones & Allen, “A more sophisticated use of AI is in providing strategic guidance. By instantly trawling through records of past cases, a system can find the optimum percentage at which an increased offer would lead to a settlement.”23 Probably the most famous software among others is the well-known IBM Watson.24 It uses natural language processing and machine learning techniques, and analyses unstructured data by extracting key information from all documents available. However, the IBM Watson has a variety of applications beyond the field of law and is not strictly speaking artificial intelligence, but rather a form of intelligence augmentation (IA),25 i.e., an intelligence system intended to supplement human actions through computer-man interaction, with the decision-making aspect remaining in the hands of the man.26 Here, parallels can be drawn with what effect calculators at first had on engineering and architectural professions.27Ergo, in legal practice and science, IBM Watson contributes to faster and time efficient research by absorbing, gathering and analysing data based on the inserted inquiry, with its intelligence being limited to action on command. More legal profession-oriented is the so-called artificially intelligent lawyer (the authors would consider it as intel19 

Sunstein, p. 2.

20 Ibid. 21 

See examples from: http://www.capterra.com/law-practice-management-software/. See for example automatisation of copyright law with the ‟Copyright Reform Observatory,” in Täks, et al. 2015. 23  Cross, Michael 2015. “Role of artificial intelligence in law.” Accessed July 16, 2016. http://raconteur.net/business/time-for-technology-to-take-over/. 24  See the description and official website at: http://www.ibm.com/watson/. 25  The conceptual framework for augmenting human intellect was initially introduced in the early 1960s by Engelbart (1962), where it was referred to as increasing the human intellectual capacity to approach and solve particular problems. See his original work: Augmenting Human Intellect: A Conceptual Framework at: http://www.dougengelbart.org/pubs/ augment-3906.html/.Engelbart’s work has been customised to contemporary human-computer interface by Cambridge and MIT scholars’ joint work: Xia/Maes (2013). 26  O’Grady (2015). 27 Ibid. 22 

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ligence augmenting lawyer), ROSS28 which is built upon IBM Watson, performing research based on direct queries and delivering prompt results, whilst also being a self-learning system. Just as is the case with the Watson programme, it is a supporting system, leaving the default legal reasoning to the commander. Lippe and Katz, however, say that “many imagine Watson might displace lawyers for legal reasoning. We believe that systems like Watson are very unlikely to displace the reasoning processes of lawyers.”29 The authors of this given article do not support the latter claim, especially considering that in cases of the IBM Watson or the ROSS, we are referring to intelligence augmentation (IA), as opposed to artificial intelligence (AI). However, software systems like the aforementioned are useful tools in the process of systematising legal order. Although, it is doubtful whether computers are able to substitute legal decision-makers, they are able to structure the legal knowledge by: a) clarifying the sources of legal norms, and their hierarchical order, i.e., finding any inconsistencies in the law; b) analysing lawyers’ arguments from the perspective of presented values and principles, and, using the big data method, thus moving closer the system of weighty and valid values; c) analysing textual interpretation methods and their applicability in practice; d) categorising case law and picking up elements from the reasoning behind the decisions, that were influenced by extra-legal elements; e) being “fact-determiners”30 when processing digital(ly) legal documents. We tend to assume, that the computerised brain is not (yet) ready for composing arguments and remains unyielding in nature. This main obstacle of having AI (or IA) as a leading stakeholder in a legal decision-making process is not a question of inability of computers nor engineers, but lawyers who hold different perceptions of what law and legal society must and ought to be. It seems that the digital reality and flirting with the theories of AI have revitalised the ancient antagonism between positivism and natural law. Flavius, when writing his “The Battle for Legal Science” in 1906, emphasised that the “resurrection of natural law in renewed form” would lead to a more motivated, objective, foreseeable law and what is probably the most relevant in the context of the current paper – any judgement i.e., the legal decision should, by Flavius, “be a strictly scientific achievement.”31 This creates a temptation to tie the digital innovation, based on science, info technology to be(come) a tool for better adjudication and interpretation processes. 28 

See more about the ROSS at its official website at: http://www.rossintelligence.com/. Lippe, Paul/Katz, Daniel Martin 2014. “10 predictions about how IBM’s Watson will impact the legal profession.” Accessed August 12, 2016.http://www.abajournal.com/legal rebels/article/10_predictions_about_how_ibms_watson_will_impact/. 30  A term, used by Dewitz more than two decades ago. See: Dewitz (1995). 31  Flavius, p. 2026. 29 

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Why, then, has the creation of an ideal digital judge still failed (or has not found sufficient support)? The authors believe that the main reason can be discovered due to the intrinsic systematic incompleteness of law and legal systems and the unwillingness of lawyers to be subordinated to mechanical and transparent technology that would most likely not perceive law as a “living phenomenon”. Concurrently with the digitally divided regions, there may exist different approaches or attitudes of distinct professions, for e.g., prosecutor, advocate, corporate lawyer, in the utilisation of AI. This would lead to even more large-scale digital gaps in terms of equality of arms – even if using “dialogical reason-based logic”, introduced by Leenes, the idea of two equally equipped automatized systems opposing themselves in a legal dispute, may theoretically work in light of Leenes’ “dialogical reason-based logic”32 but could be inadmissible in most of the conservative legal societies. Evidently, it is not only subjective resistance by legal practitioners but also legislators. Prakken and Sartor33 convince their audience on a so-called reverse effect – by the authors, even “legislators can never fully predict in which circumstances the law has to be applied” – they also refer to abstractness, general exception categories that can be interpreted “in concrete cases, which creates uncertainty and room for disagreement.”34 One of the interesting cases of automatization of legal techniques is the attempt of Australians to apply uniform evidence law that foresees mechanical approach. – Dahdal analyses discussions on the human factor i.e., “judicial discretion” (in the context of applying this Act) which is hidden behind the legal term “sufficient relevancy” and is, therefore dependent from natural logic, establishing therefore not an isolated set of norms but (only) “emerging clarity” and “solid foundation” for more consistent system of evidence legislation.35 Prakken and Sartor directly refer to: a) orientation of law to the uncertain future; and b) its institutional nature, which ties legal reasoning to the contexts (addressees, producers, appliers, enforcers of the norms).36 The first “problem” is acceptable as a presumption that no one can foresee tomorrow’s world. It is even more evident in relation to digitalisation and the info-technological era, as innovations are derived from inventions which cannot be foreseen. The second aspect is supported, for instance, by Edwards, who, convincingly recounts that law is closely related to culture i.e., myths, metaphors and narratives: “because narrative’s power in the sacred domain of legal authority is so effectively hidden, the law needs a well-honed narrative sensibility, including a sensibility to the role of myth and metaphor in law’s stories.”37 Although the comLeenes (1993). For previous studies, see also: Hage (2000). Prakken/Sartor (2015). 34  Ibid., p. 215. 35  Dahdal, p. 10. 36  Prakken/Sartor, p. 215. 37  Edwards, p. 916. 32  33 

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puter written novel recently did almost win the Nikkei Hoshi Shinichi Literary Award,38 it might be assumed that the methods of constructing sci-fi are not as full of assumptions and as multi-layered as the legal world. Besides, art based on certain principles, is always trying to challenge the same principles in creating a new quality and, the most relevant, free art is not looking for a right answer, the truth, but is rather tempted to question the values that are prevailing. Poscher, who is seeking reasons(s) why the legal interpretation is seldom foreseeable, states that law cannot be more concrete than the ambiguous life itself and finds that complicated i.e., “hard cases” that are “law’s borderline phenomena” cannot have predictable, mechanic judgements or legal decisions39 but are rather dependent on the decision-maker. Prakken and Sartor propose to use AI to elaborate a model that “prescribes sequences of actions which must be followed to achieve a certain effect”40. These determined “procedures” can be “logically specified” to promote, for example, determined regulation areas or areas related to e-technologies, such as e-commerce but also e-governance and e-democracy in wider perspective.41 Can we also assume, that creating a highly operational model of procedural requirements and/or sequences with the help of AI can be preferably used in the fields that are regulating technological solutions? The procedural law dealing with digital phenomena can be perceived as law of limitations to the judicial system rather than to the policy makers who are much more interested in the material law, i.e., extending the scope of permissible activities, services and products. This fits also with a widely used approach of digital or Boolean logic (named after computer pioneer George Boole42) that can be divided into two categories: combinational and sequential. Although operators AND, OR, NOT and XOR are clearly too simplified for hard cases or constructing legal argument (with the answers TRUE and FALSE) the procedural law can be well tested with the rules that require limitations. The current trend in the discussion on how to identify elements of legal argument is focusing on finding more effective logical processing tools. Prof. Walker’s Research Laboratory for Law, Logic & Technology at Hofstra University dedicates its research to the problematics of “how to extract argumentation-relevant information automatically from a corpus of legal decision documents, and how to build new arguments using that information.”43Ashley and Walker propose that developing the automatization of natural language processing tools may well lead to the construction of evidence-based legal arguments and 38  Oulton, Emma 2016. “A Computer Wrote a Novel – and Nearly Won a Literally Prize for it.” Accessed July 21, 2016.http://www.bustle.com/articles/149887-a-computer-wrote-anovel-and-nearly-won-a-literary-prize-for-it/. http://www.bustle.com/articles/149887-a-com puter-wrote-a-novel-and-nearly-won-a-literary-prize-for-it. 39  Poscher, p. 19. 40  Prakken/Sartor, p. 241. 41 Ibid. 42  See about Boole at: https://www.britannica.com/biography/George-Boole. 43  Ashley/Walker, p. 1.

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they refer to the IBM Watson architecture (DeepQA) that, according to them “uses refined techniques for machine learning from unstructured sources annotated in syntactic and domain-general semantic terms.”44 The authors refer to the term “evidentiary assertions” which means that a fact “is attached to the appropriate terminal rule condition, and the supporting evidentiary reasoning is attached to the finding”. Ashley and Walker are applying the assertions with plausibility-values of “highly plausible” “very plausible”/“slightly plausible”/“undecided”/“slightly implausible”/“very implausible”/“highly implausible.””45 In order for legal (e-)services to thrive and abandon “archaic” modus vivendi, former Estonian Chancellor of Justice introduced the start-up Avokaado, that enables the clients to create draft standardised legal documents, such as contracts, online. He claims that the purpose is to make commonplace forms, which are more easily accessible and affordable.46 Teder, a sworn advocate, founder and partner of Teder law firm, reckons that the field of legal services is a late bloomer in terms of adapting innovations. He insists that “[i]t is no longer acceptable to charge a ‘tailor made’ price for a standard solution,” and thinks that the field of legal services will change dramatically over the course of few years.47 Sometimes it seems, that there is a kind of an “arms race” amongst leading law firms in producing more effective software, whereas the aim is to sell one’s product to competitors, not to disburden one’s colleagues. Concurrently, lawyers themselves are not particularly thrilled about the recent innovative dependency on the digital world and even discuss the “vacation from technology” or “being unplugged”, yet usually find that it would in lieu be beneficially possible to reduce overload or minimise the impact of technology, than to ignore it.48 The structure of diverse categories of data through different models of logic most likely defines the future of research and practice in the field. Only a few software developers have attempted to create (though not in the field of law) tools for strategic aid; an example of the latter could be Neota’s technology “calculating rental values and assessing the risk profile”49 based on using big data rather than legal norms and case-law. 44 

Ibid., p. 2.

45 Ibid. 46  See: „Former Estonian Chancellor of Justice established Law Firm Teder.“The Baltic Course, 06. 01. 2016. Available in English online at: http://www.baltic-course.com/eng/markets_and_companies/?doc=115102/. 47 Ibid. 48  Listen, for example, podcast of The Kennedy-Mighell Report at Legal Talk Network, available at: http://legaltalknetwork.com/podcasts/kennedy-mighell-report/2016/08/takingbreak-technology/. 49  See the press release of software provider HighQ,: “Now that’s witchcraft”: HighQ announces strategic partnership with Neota Logic”, available at http://www.legaltechnolo gy.com/latest-news/highq-announces-integration-with-neota-logic/.

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IV.  Interdisciplinary Empiricism as a Potential Core Element for the Emerging Principles of Digital Law Why are we thinking and discussing the probability to use digital means in legal space? Naturally, due to the cost benefits50 (less time and human resources), avoiding extra-legal elements in the process of securing rule of law (politics, ideologies) and also better predictability (legal certainty) of legal decisions. Computers were created first for calculating, not for operating social processes. There have been further attempts to reduce the gap between law and information technology by using the hard sciences’ methods in solving social problems. One of the most remarkable examples here is titled Quantum Social Science (QSS). Wayne, the father of this theoretical approach, starts with the platform that contemporary social scientists “have constantly debated whether social science could ever become a scientific theory like physics” and offers QSS as a tool to match hard sciences with social sciences such a legal science51 with an example of how the theory would work in the case of the US Constitution. Wayne uses the term “design flaw”, and demonstrates, for example, that gun violence is caused by the intrinsic flaw of the Second Amendment (right to bear arms). The ambitious theory of QSS comprises the following physics laws of social sciences: a) law of indeterminacy; b) law of prediction; c) law of choice; d) law of information; and e) law of equilibrium. Wayne believes that “the correct formulation of physics laws of social science is the most important achievement of quantum social science.”52 Utopian as it may seem, the theory of QSS could take us closer to solving dichotomy between AI and argumentum ad homini insofar as the purpose of the QSS is not to analyse something which is not directly designed by humans. It is believed that this theory leads us to a closer understanding that digital legal space should strongly consider identifying principles and values that have proved their consistency in societal relations. Very often, the AI and law disputes are related to the inhumane character of too standardised legal implementation. At the same time, the purification of the law and its implementation have been approaches seeking a certain Deus ex Machina that, have been, traditionally after a collapse of justice, revitalising attempts of human conscience. This is portrayed in the 41st conference of the International Law Association, held in 1946, in Cambridge. After the atrocities of World War II, Van Hamel believed that “the object of the work of every lawyer is to find means of controlling this mysterious machinery which we call the human soul, of keeping it on a right track at the right speed.”53 Thus, in fulfilling this task, it seems probable that lawyers could be assisted by computers. Humans may “Doing more with less” as stated by Puron-Cid (2013), p. S46. Wayne, p. 3. 52  Wayne. p. 8. 53  Report of the Forty-first Conference [of the International Law Association] Held at Cambridge in the Old Schools, August 19th to 24th 1946. International Law Association, 1948. 50  51 

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be slower system-thinkers, and lawyers are often accused of being callous, but then can the robots have a conscience at all? According to Smith, human “consciousness functions like a meta-representational system“54 which can be seen as the main difference between (legal) reasoning of the human being and a machine. Computing or automatization of any system of symbols is directed towards having the best solution and adequate action. The discussions reflected above indicate that the AI is rather focused on the question as to “what” rather than “how”55. Let us assume that the consciousness is one of the prerequisites for legal reasoning – is it not then all about reductionism that would fit well to the homo faber with the computerised brain? Once again, the questions arises as to whether the scope of regulation in the field of e-services and applications is based on limitations. Ideally, law should be a living instrument but it is often treated as a hermeneutic system that legalises something only by licensed professionals who adopt or apply the norms in their seemingly tautological world. The approach of limitations is, therefore, in place if the purpose of legal interpretation is to avoid influences of this tautological world from “outer space” such as reinterpretations by politicians, businessmen or any other interest groups. Pursuant to Cohen, “if we cannot be like the gods, knowing the absolute difference between good and evil, we can at least have the knowledge of our limitations…”56 Perhaps the confrontation of lawyers versus computers is based on conservative legal education. Sandgren states: “lawyers’ one sided training in the legal method makes them poorly equipped to use other methods and creates a mental block against the use of such methods.”57 He then explains the multidisciplinary approach through empiricism and social roles such as employer, employee, customer, woman, and refugee. In the context of digitalisation and rapid development of technology, there should not be only different disciplines involved (i.e. IT engineers and architects, policy makers, customers, and lawyers) but also the groups of stakeholders directly related to the application of the new digital technologies. Going even further, empiricism can be a useful factor also from “dark side”, and so experience of hackers, criminals and terrorists should also be used when strengthening the efficacy of legal regulations. As Sandgren suggests: “empirical material can also contribute to a shift of perspective within the law”58. The methods that he recommends59 i.e., practice, contracts as empirical materials, soft-law, statistics, observation, media and surveys are nothing new per se but could be innovative for lawyers in the context of digitalisation. Smith (1998), p. 281. Poole/Mackworth (2010), part 1. 4. 3. “Reasoning and Acting.” Full text available at: http://artint.info/html/ArtInt.html/. 56  Cohen (1932), p. 11217. 57  Sandgren (2000), p. 448. 58  Ibid., p. 456. 59  Ibid., pp. 465 – 466. 54 

55 See

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V. Situational Logic and Morality as Promoters of Regulating e-Technology: Do we Need Samaritan IV? Knepper supported the adequacy of Karl R. Popper’s approach to relay one model of situational logics to any social problem, be it an economically-related matter or any other (Popper’s situational analysis).60 E-regulation and economic developments (such as e-services, digital market) are closely interconnected and interdependent. Would Popper’s methodology be applied in the current context? User-centricity, one of the proposed prerequisites for a legal regulator (when deciding to legalise technological innovativeness) is clearly referring to the behavioural aspect (market reactions), and, therefore leads to the situational logic in case of customer. In legal science, it is called utilitarianism or rational behaviour. – Knepper who leans on Nobel-prize winning scholar, Becker,61 states that “people decide whether or not to engage in criminal activity by comparing the benefits and costs of criminal and legitimate activities.”62 Crime is often explained by weighing the risks and benefits or awards to be received. Of course, the social and economic environment may heavily influence the decision, as can be seen in the case of poor people who commit crimes more often. But there are also several new factors that are different when comparing the tendency to use old-fashioned/digital means in comparison with the tendency of using legal/illegal behaviour (which may, of course be conducted also in digital world as cybercrime, for example). Therefore, the criticism of Popper’s theory should be taken seriously. As Popper says, “elements of a social situation define the appropriate line of action, and given the rationality postulate, the theory predicts that actors will adopt this line of action.”63 Although Popper is relying on rationality or rational choice, it cannot be defined or predetermined. One illustrative paradox could be the domain of intellectual property which can have very different cost-benefit balance through the eyes of the possessor of rights and the market. The technology neutrality principle64 can be tested by the assumption that law must be moral. The social approach proposed by Tamanaha reminds us that morality of law is relative as “law is a form of concentrated social power that claims to be moral.”65 Could morality be a tool for a rational social model that Popper was looking for? Positive law as such is not inherently moral per se. The problem here, as worded by Tamanaha is the following: “Any assertion that law is moral must be followed immediately by a reminder that law is a form of concentrated social power that Knepper (2007). Becker (1976). 62  Knepper (2007), p. 33. 63  Hedström/Swedberg/Udéhn, p. 356. 64  There is no one definition to “technology neutrality“ principle. By and large it means „a principle of good regulation in Internet, telecoms and data protection regulation.” See, for instance: Maxwell/Bourreau (2014). 65  Tamanaha, p. 51. 60  61 

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claims to be moral, which doesn’t automatically make it so”66. Mikhail asks directly – “could a computer be programmed to make moral judgments about the cases of intentional harm and unreasonable risk that match those judgments people already make intuitively?”67 Besides his versions of the periodic table of moral elements, Mikhail admits that there are many variables such as neurological activity, reaction-time, etc., (the elements that computers miss and cannot forecast) and his incomplete research can only be used for future research.68 As questioned by scholars of International Humanitarian Law in the context of using autonomously acting technologies during armed conflicts – is the main dilemma “building laws through morals versus having morals interpret the law?” or even “technology rules law versus law rules technology?”69 The symbolic struggles of morality in scientific technology are represented in Mary Shelly’s “Frankenstein” which fictionally reflects how obsession with technology – “infusing life into an inanimate body” – can have moral repercussions and impose a detriment to society. “Frankenstein” though, being still a work of art, cannot be taken as an admonition regarding AI-infused legal tools. Users of AI software in digital assistants (Apple’s Siri, Microsoft’s Cortana), for (legal) unstructured data analysis (ROSS, Avokaado) or similar, do not recognise themselves as living in Orwellian-like dystopian societies, because they consider themselves the masters of the situation, getting blasé about a smart phone’s role or IA created contract in their life, despite knowing that information technology is ubiquitous and has made us dependant on it. Nevertheless, today’s innovators and the predecessors who have inspired them have referred to the effectuation of artificial intelligence as “our greatest existential threat.”70 In 2015, notable AI and technology experts signed an open letter at the International Joint Conference on Artificial Intelligence in Buenos Aires, Argentina.71 Although focusing on morality of AI use in military weapons that may pose fatal threat to all mankind, three signatories of the letter laid down that research priorities calls for conducting thorough research of societal impacts of AI, includ66 Ibid.

Mikhail, p. 27. Ibid., p. 81. 69  Burgess, Laura (2015). “Autonomous Legal Reasoning? Legal and Ethical Issues in the Technologies of Conflict.” IntercrossBlog. Accessed May 28, 2016. http://intercrossblog. icrc.org/blog/048x5za4aqeztdiu3r8f96s8m7lzom/. 70  Elon Musk’s interview for MIT students at the AeroAstro Centennial Symposium, Available at: http://webcast.amps.ms.mit.edu/fall2014/AeroAstro/index-Fri-PM.html/. 71  An Open Letter: RESEARCH PRIORITIES FOR ROBUST AND BENEFICIAL ARTIFICIAL INTELLIGENCE. Signed by, for instance: Stephen Hawking, Director of re­search at the Department of Applied Mathematics and Theoretical Physics at Cambridge, 2012 Fundamental Physics Prize laureate for his work on quantum gravity; Jaan Tallinn, co-founder of Skype, CSER and FLI; Elon Musk, SpaceX, Tesla Motors; Steve Wozniak, co-founder of Apple. Full text and list of signatories. Available at: http://futureoflife.org/ai-open-letter/. 67 

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ing law and ethics research, where enigmatic AI touches upon the field; “[T]he development of systems that embody significant amounts of intelligence and autonomy leads to important legal and ethical questions whose answers affect both producers and consumers of AI technology. These questions span law, public policy, professional ethics, and philosophical ethics, and will require expertise from computer scientists, legal experts, political scientists, and ethicists.”72 It is further noted that with the increase of the role of technology in our daily lives, be it military actions or legal services, we must increasingly be careful that the technology behaves/works as initially intended to. There are several attempts to research moral reasoning of robots73, but the complex research is far from clear conclusions. One can recall the Somerset Maugham prize awarded “The Tin Man” of Michael Frayn74 where the expert of the Institute of the Automation Research, Macintosh, tried to construct moral robots, placing them in a sinking raft with another person and setting the dilemma of saving versus sacrificing. The first test failed, the Robot sacrificed itself whatever was on the sinking raft. The Samaritan II was programmed to sacrifice itself only if another person had the same level of intelligence and in this case, then both of the equal Robots sank. Samaritan III sacrificed itself only for a more intelligent person (by size of its brain). Ideally, lawyers and stakeholders would agree to cooperate only with hypothetical Samaritan IV as an independent agent who would agree with the interpretation methods of humans on “rule-based or precedent-based reasoning”75 and leave the values, morality and ethics (explanations and argumentation) to flesh and blood commanders.

VI. Conclusion Today, the everlasting discussion on the practical options, limits and threats of using automatized logic in legal science and practice, is moving away from science fiction and accommodating itself into research frames. The lawyers’ world is officially welcoming research development but has offered distress as computers may, at least partly, replace them and carefully accuse the engineers of creating positivistic agents that are not capable of evaluating human values, ethics and “living nature” of law. The latter assumption is supported by systems like IBM Watson; although merely a supporting system, leaving the default legal reasoning to the commander, it may, in the course of Schwab’s fourth industrial revolution, contribute to deviations or even certain alienation of human interactions. Therefore, it could be claimed that legal professionals prefer to see themselves as the commanders of Russell/Dewey/Tegmark (2015). For example, by Rennselaer AI and Reasoning Lab within a project “Moral Reason­ ing & Decision-Making: ONR: MURI/Moral Dilemmas.” Available at: http://rair.cogsci.rpi. edu/projects/muri/. 74  Frayn (1965). 75 See: Branting (2000). See also Brozek in this volum. 72 

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such systems, e.g., for purposes of research, and therefore, not granting too much decision-making power to these automatized programmes. As referred to above, there are gradually more Law Practice Management Software Products being generated and sold by IT minded Law firms as service tools. Nevertheless, they can be, at least for now, regarded as intelligence augmentation as opposed to artificial intelligence systems. The latter is also an indication as to why lawyers prefer engineers to create “robotic assistants” instead of artificial lawyers. Inter alia, there is a fear that inhuman machine logic is not based on default reasoning and thus cannot offer a dynamic legal reasoning. However, supporting the “technology neutrality” principle, there is some consensus in the legal society that Artificial Intelligence, using highly operational models of procedural requirements and/or sequences, can preferably be used in fields which are regulating technological solutions. The intelligence augmentation software could indeed contribute to structured data with a higher degree of precision and increase the level of confidence/plausibility, which would alter the way research is conducted. This, in turn, would become potentially a common core of two professional groups – engineers and lawyers; it seems that the trust amongst them can be only achieved if engineers are using methods understandable for social scientists. There are several contradictions in the process. Very often, the AI and law disputes are related to the inhuman character of standardised legal implementation. At the same time, the trimming and purification of the law and its implementation have been approaches seeking a certain Deus ex Machina that, have been, traditionally after a collapse of justice, revitalising attempts of “human conscience”, an element which Robots ironically (yet) lack. The unsolved dilemmas that indicate the different natures of human and artificial intelligence and reasoning, the elaboration of theories and the creation of software, are leading us to the conclusion that: a) AI can be successfully used as creating Agents who, acting in limited environments (databases, certain standard system) assist to categorise, classify, find and link the norms, facts and cases. AI involvement to become analogisers is the borderline issue; b) It is the tendency that independent Artificial Intelligence in natural environments like (legal) society) is not welcomed and severely criticised by societal stakeholders. All in all, we see that although, computers are ‘ridiculed’ in terms of being able to substitute the legal decision-makers, they are able of structuring legal knowledge and regulating technologies such as: clarifying the sources of legal norms, and their hierarchical order; analysing the lawyers’ arguments from the angle of presented values and principles, and, using the big data method,; analysing the textual interpretative methods and their applicability in practice; categorising the cases, ‘hard cases’ and picking up the elements from reasoning influenced by extra-legal elements; and finally, being “fact-determiners” when processing digital(ly) legal documents.

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List of Contributors Matthias Armgardt is Professor of Law and Vice-Rector at the University of Konstanz. Scott Brewer is Professor of Law at Harvard Law School, Director of the Logocratic Academy, and co-founder and co-chairman of the European University Institute-Harvard Law School Summer School on Law and Logic. Bartosz Brozek is Professor of Law and Philosophy at the Jagiellonian University and the Deputy-Director of the Copernicus Center for Interdisciplinary Studies in Krakow. Michael S. Green is Woodbridge Professor of Law and Cabell Research Professor of Law at William & Mary Law School. Jaap Hage is Professor of Jurisprudence at Maastricht University. Jan C Joerden is Professor of Criminal Law and Legal Philosophy at the European University Viadrina Frankfurt (Oder). Tanel Kerikmäe is Professor of Law at Tallinn University of Technology (Tallinn Tech). Dieter Krimphove is Professor of Law at the University of Paderborn and Visiting Professor at Danube University Krems. Gabriel M. Lentner is Postdoctoral Fellow at Danube University Krems and TTLF Fellow at Stanford Law School. Antonino Rotolo is Professor of Law and Vice-Rector at the University of Bologna. Sandra Särav is a Research Fellow at Tallinn University of Technology (Tallinn Tech). Antonia Waltermann is a Research Fellow at Maastricht University.