On the Logical Analysis of Judicial Decisions

International Journal for the Semiotics of Law V/14 [1992]

ON THE LOGICAL ANALYSIS OF JUDICIAL DECISIONS

by

MAARTEN HENKET Utrecht University

1. Introduction

The subject of this contribution is, as the title indicates, the logical analysis of judicial decisions. The term "logical" refers to formal deductive logic. 1

Whenever arguments are offered for a judicial decision, they usually refer to the "facts of the case" and the "applicable rule or principle". In as far as the judge suggests that the decision follows inescapably from given facts and a given rule or principle, his argumentation is misleading. This much seems to be uncontroversial, at least on the level of theoretical reflection. Legal theoreticians agree about the existence of a certain room for choice and interpretation regarding the facts and the rules or principles of a case, and about the interdependence of these two. As far as the applied rule or principle is concerned, this is not some clearly defined entity, lying in store for the judge, but has to be chosen and interpreted against the background of the facts of the case. 2

1 The terms "logic" and "formal logic" do not have fixed meanings. Perelman. for example, emphasizes that "legal logic" is not formal (Ch. Perelman, Logique Juridique (Paris: Dalloz, 1976), passim). For Horovitz, formal logic encompasses what he calls inductive logic (J. Horovitz, Law and Logic (Wien/New York: Springer, 1972), 78). In American literature especially, logic covers about the whole area of argumentation theory.

2 To avoid misunderstandings, let me state clearly at this point that I do not want to take position as to the nature of the rules that judges appeal to. For example, I do not wish to affirm or deny that the rule phrased in a particular judicial opinion can derive any justificatory power from the fact that it is identical or similar in words to a rule given by a historical legislator. This, I think, is a matter of what Wr6blewski has called external justification. My essay is about internal justification. (See J. Wr6blewski, "Justifi- cation of Legal Decisions", in Revue Internationale de Philosophie 127/128 (1979), 127ff.)

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This should be taken into account in analyzing a judicial decision and judging its quality. Like the judge himself, the critical analyst of the judge's decision should not ascribe a fixed meaning to rules and principles, apart from the facts of the case. This is not only true for the conceptual terms in the rule or principle, but a l so - and this takes us to the subject of this article m for its logical aspects.

In jurisprudential literature, legal rules and principles are commonly analyzed as (material) implications. 3 In this article, I shall defend the view that a legal rule or principle serving as a premise in a judicial decision should very often not be interpreted as a material implication, but as a replication or as an equivalence. In any case, I shall argue, it is wrong to use the material implication as the standard interpretation of the legal rule. I shall adstruct this thesis in section 2, with the help of the example of the argument form e contrario ("by contrast").

Anyone who rejects the implication as the standard interpretation of the legal rule must reject the modus ponens as the standard argument form of judicial argumentation. I shall clarify this in section 3. In section 4, I shall argue that the logical analysis of the rule in a judicial decision, just like any other kind of analysis, should take place against the background of the facts of the case. Finally, in section 5, I shall try to show the relationship between the logical analysis of the rule on the one hand, and the function of the logical

3 In addition to the literature referred to in the text, I mention P.W. Brouwer: Samenhang in recht, (Groningen: Wolters Noordhoff, 1990), 221; M.A. Loth: Recht en taaI, een kleine methodologie (Arnhem: Gouda Quint, 1984), 157; O. Weinberger: Rechtslogik (Berlin: Duncker und Humblot, 1989, 2nd imp.), 224, 251-253; R. Zippelius: Einfiihrung in die juristische Methodenlehre (Mfinchen: C.H. Beck, 1971), 121ff. Soeteman seems to hold a nuanced view: A. Soeteman: Norm en Logica (Zwolle: Tjeenk Willink, 1981), 355-56; so does perhaps Tammelo (cf. note 14 below). Klug and Koch/Rfissmann explicitly mention other interpretations besides the material implication (cf. U. Klug: ]uristische Logik (3d imp, Berlin: Springer, 1966), 128-129; H.J. Koch and H. Rfissmann, Juristische Begrandungslehre (Mfinchen: C.H. Beck, 1982), 78ff). R6dig rejects the material implication as standard interpretation: J. R6dig: "Logische Untersuchungen zur Makrostruktur rechtlicher Kodifikate", in Studien zu einer Theorie der Gesetzgebung, ed. J. R6dig (Berlin/Heidelberg: Springer, 1976), 592-611; his argument however does not regard the separate rule but the regulation as a whole (the "rechtliche Kodifikat").

ON THE LOGICAL ANALYSIS OF JUDICIAL DECISIONS 155

analysis of judicial decisions on the other. In this article I shall use propositional logic. This logical sys-

tem is a popular analytical instrument, and it only demands com- paratively little technical knowledge and skill, both on the part of the analyst and on the part of the reader who wants to examine the results of the analysis.

It is implied in what follows that there is room for deductive logic in law. This is of course highly controversial. A defense of my position would be beyond the scope of this article. Let me just indicate that I would draw most of my arguments from Weinberger. 4

2. The Logical Interpretation of the Legal Norm

In a much quoted article, the Dutch author Nieuwenhuis argues that the e contrario inference is a "classical non-sequitur", and that its use can only be defended on other than logical grounds#

To illustrate his point, Nieuwenhuis uses an example from Dutch law, based on section 1843 of the Dutch civil code. This section reads as follows (my translation, M.H.):

The mandatory who has given proper notice of his mandate to those with whom he acts in that quality, is not liable beyond the limits of his mandate (..3.

The Dutch Supreme Court, arguing e contrario on the basis of this section, has inferred that a mandatory who has not given proper notice of his mandate, is liable beyond the limits of his mandate. According to Nieuwenhuis this inference is logically invalid. I do not agree, and I shall explain why.

Section 1843 can be rewritten as "if p then q": "If the mandatory (...) has given proper notice (...) then he is not liable." But what is the meaning of this "if"? There are three possibilities: "always if", "only if" and "always and only if." In the first meaning, "if p then q" is a sufficient condition, in logical terms a (material) implication. In the second meaning, it is a necessary condition, a (material)

4 See especially O. Weinberger, "'Is' and 'Ought' Reconsidered", in Archly flit Rechts- und Soziaphilosophie LXX/4 (I989), 455-474. 5 J.H. Nieuwenhuis: "Legitimatie en heuristiek van her rechterlijk oordeel", in Rechtsgeleerd Magazijn Themis (1976), 494-515.

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replication. 6 In the third meaning it is a necessary and sufficient condition, a (material) equivalence. Nieuwenhuis does not state explicitly which of the three possible meanings he attaches to "'if ... then". However, his choice can be derived from the following passage (my translation, M.H.):

What the logician can't bring off, the jurist manages to do without blinking: the inference from "if p then q" to "if not-p then not-q"7

The meaning of "if" in this passage can not be "only if", nor "always and only if", for in both cases the logician would not have any trouble with this inference. So, for Nieuwenhuis's argument to make sense, he must intend "if" to be interpreted as an implication; "always if p, then q."

Let us now take a closer look at section 1843. Is it arguable to interpret this provision, contrary to Nieuwenhuis, as "only the mandatory who has given notice ... is not liable ..."? I think it is. For, had the legislator wished to include other mandatories in this exemption, the following formulation would have been sufficient and, indeed, more appropriate: "The mandatory is not liable beyond the limits of his mandate." In view of the formulation chosen by the legislator, I am of the opinion that section 1843 should not be interpreted as a material implication, but as a replication or an equivalence. 8 In both these interpretations, the derivation of the conclusion "if not-p then not-q" is logically valid.

The question as to when an e contrario inference is allowed should in my opinion be addressed as follows. Reasoning e contrario from a certain rule goes hand in hand with interpreting that rule either as a replication or as an equivalence. Whoever is reasoning e contrario cannot interpret the relevant rule as an implication. Or, to put it the other way round, whoever wants to interpret a rule as an implication can't defend an e contrario inference from that rule

6 The name "replication" (for the necessary condition) is less commonly accepted than the names "implication" (for the sufficient condition) and "equivalence" (for the necessary and sufficient condition). The following symbol for the necessary condition, however, is generally used: p (~ q.

7 Supra n. 5. at 506. 8 Of these two possible interpretations, the equivalence is the more plausible one in my opinion. This, however, is not relevant to my main argument.


without implicitly contradicting himself. The right interpretation of a legal ru le - implication, replica-

tion or equivalence - - is not a matter of logic. This question does not differ in essence from other questions of interpretation. The choice will be determined by looking for the meaning, the purpose, that is best defensible juristically. For some rules, the answer will be sim- ple, such as rules that are explicitly formulated as definitions. In other cases, opinions as to the right interpretation may legitimately differ. Nevertheless, one must be aware of the possibility that some rules should not be interpreted as implications. As I just argued, section 1843 of the Dutch civil code is an example of such a rule.

3. The Limits of the Modus Ponens

3.1 Denying the Antecedent

Whoever interprets the rule or principle in a judicial decision as a material implication, interprets the decision as a modus ponens. This classical argument form looks as follows:

p ~ q (material implication) p (antecedent)

q (consequent)

Traditionally, a discussion of this logically valid argument form is followed by a discussion of two logically invalid forms or fallacies that are misleadingly similar to the valid modus ponens. They are commonly called denying the antecedent and affirming the consequent. These invalid argument forms look like this:

p - )q

q (the consequent, "q", is affirmed)

P

P~q not p (the antecedent, "p", is denied)

not q

Nieuwenhuis, in the article quoted above, rightly calls this second form a classical non-sequitur which "any school child can expose".

It should be realized, however, that affirming the consequent ('q') or denying the antecedent ("not p") only leads to an invalid argument if the first premise ("if p then q") is a material implication.

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If, on the contrary, the first premise is a replication or an equivalence, affirming the consequent and denying the antecedent lead to two perfectly valid argument forms. The outcome for legal reasoning is that it depends upon the logical interpretation of a legal rule which inferences can validly be based on it. The following two argument forms are perfectly valid in propositional logic, even though they both contain the denial of the antecedent:

p (--) q (equivalence)

not p

not q

p 4-- q (replication)

not p

not q

Each of these two argument forms can be used for reasoning e contrario. The logical validity of this form of reasoning depends upon the right interpretation (either as equivalence or as replication) of the legal rule that is used as a premise. 9

3.2 Validating an Invalid Argument Form

There are other possible strategies for making the e contrario inference into a valid argument form. In a recent publication, Kap- tein proceeds as follows. 1 He begins by interpreting the legal rule in the e contrario reasoning as a material implication, he then admits that the result is "in itself" an instance of the fallacy "denying the antecedent", and he finally saves the e contrario by adding an extra premise: the material implication "if q, then p." With the inclusion of this extra premise, the logically valid form of the e contrario inference is then presented as follows:

P~q

9 Klug expresses the same opinion (supra n. 3, at 128). He adds that the intention of the historical legislator should prevail in case of doubt (at 129). In this respect, 1 do not agree with him, as ! hope to make clear later in the article. 10 H. Kaptein, "Logica in rechtspraak, in her bijzonder in analogie- en a contrarioredeneringen: vroom bedrog?", in F.H. van Eemeren and E.T. Fe- teris, eds., ]uridische argumentatie in analyse (Groningen: Wolters No- ordhoff, 1991), 75-90.


not p

q--cp

not q

Essentially, Kaptein uses the extra premise to transform the legal norm from a material implication into an equivalence. 11 He justifies the extra premise by an appeal to the closed character of the legal system: "legally speaking, not every premise is acceptable. "m

I agree, of course, with Kaptein's result, but the route he choses in order to get there is winding and dangerous. In the first place, Kaptein begins his analysis by presenting the judicial argument as a modus ponens and the e contrario inference as logically invalid33 He thereby adds fuel to the view that the material implication is the standard interpretation of any legal rule (except perhaps those rules that are unequivocally definitions). As I argued in section 2, this is a mistake.

In the second place, Kaptein brings up some quite heavy artillery to save the e contrario inference from invalidity: he invokes the closed character of the legal system to justify his added premise. To readers who do not readily accept that the legal system is closed, Kaptein's argument therefore will not be convincing. In other words, Kaptein's cannon may backfire. As I have tried to show, the case for the e contrario inference can be won without recourse to such dangerous weaponry.

My conclusions so far can be summarized as follows. The material implication should not be considered the standard interpretation of the legal rule. Each case should be examined upon its merits, and quite often the equivalence or the replication should be pre- ferred. Accordingly, the modus ponens should not be considered the standard argument form of judicial decisions.

So far I have neglected almost completely the factual context of the case. In the following section I intend to make up for this. I shall argue that a logical analysis of the rule that serves as a premise in a judicial decision should, like any other kind of analysis, take into account the facts of the case at hand.

11 "p ---) q" together with "q --) p" adds up to "p +-, q." 12 Supra n.10, at 80. 13 Supra n.10, at 76.

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4. The Factual Context and the Analysis of the Rule

Logical analysis can be used on any text in which conclusions are based upon arguments. Before the actual logical "calculation" can take place, the argumentation must be interpreted. What this means varies between various types of texts. To confine ourselves to two types of legal argumentation, there is an important difference between jurisprudence and judicial opinions.

In jurisprudential texts, the subject is more or less abstract. The. subject is not, say, whether X, who admittedly has hidden Y from the police, should go to jail, but whether it is a criminal offence to help suspects against the authorities. Consequently, argumentation in such texts is of a general nature, and should be interpreted accordingly.

On the other hand, the judge who writes a judicial opinion argues in a concrete procedural setting and about a concrete factual case. The analyst who wants to judge the argumentative quality of such an opinion should take this into consideration. As I noticed before, legal theorists nowadays generally recognise that the meaning of a rule in a concrete case is dependent on the facts. Two points, however, have not received much attention so far. Firstly, the facts may affect not only the meaning of the conceptual terms in the rule but also its logical status. Secondly, not only the facts of the case but also the concrete procedural setting should be taken into consideration. Let me illustrate these points.

My first example is taken from criminal law. Section 307 of the Dutch criminal code reads as follows (my translation, M.H.):

He to whose fault the death of another person is attributable, shall be punished with a maximum of nine months imprisonment or a fine of the fourth category.

If we look at this provision apart from a concrete procedure, it clearly should be interpreted as a sufficient, not as a necessary condition. The intention clearly is not to reserve this particular maximum penalty exclusively for this particular criminal offence. But in a concrete trial where the defendant is charged with this particular offence, the provision quoted above becomes a replication, a necessary condition: only if someone else's death is attributable to the defendant's fault can he be punished. And if nothing special happens (the defendant does not, for example, plead the statute of


limitation or self defence), the provision counts as an equivalence in the context of that particular setting. ~4

I now take an example from civil law. In many countries, a contract is voidable if one of the parties is an infant. Taken by itself, this rule contains a sufficient condition for a contract to be voidable, not a necessary one. Contracts may be voidable for all sorts of reasons. Now suppose someone asks the judge to nullify a specific contract on the ground of infancy, and the defendant's only defense is a denial of plaintiff's infancy. In that case, the rule can be interpreted as a necessary condition: if the judge concludes that the plaintiff was not an infant at the time of the agreement, he will rule for the defendant. It would be absurd to label his reasoning logically invalid. The law may know other grounds for nullifying contracts, like for example undue influence, but they do not belong to the context of the case at hand and do not have to be taken into consideration by the judge, not even tacitly.

The context of a case is partly determined by the facts and other arguments brought forward by the parties, and these are thereby in the end relevant for the meaning of the rule or principle in that particular case. In a concrete judicial opinion, eventualities which are not pertinent to the case do not have to be considered. In a civil case, the judge restricts himself to the questions that keep the parties di- vided; a criminal judge does not cross the boundaries set out in the charge. This should have its consequences for any critical analysis of the judicial argumentation, including a logical analysis of the applied rule.

One and the same rule or principle may legitimately be used as a basis for an inference e contrario in one case, and for a reasoning by analogy in the next. In my approach this does not present a problem: in the context of the first case, the rule boils down to a replication or an equivalence, in the context of the second case to an implication.

This approach to the analysis of rules in concrete cases is con- nected with what I see as the main function of logical analysis. In the next section I shall explain what I mean by that.

14 In his Modern Logic in the Service of Law (Wien/New York: Springer, 1978), 77, I. Tammelo makes the same point. Nevertheless, he seems to regard the material implication as the standard interpretation of the legal norm. I conclude this from the fact that in his examples and exercises he uses almost exclusively material implications.

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5. Deducing From or Tracing Back To?

The task of the logical analyst is usually seen as checking, firstly, whether the premises are consistent among themselves and, secondly, whether the conclusion can be validly deduced from the premises. In this view, the analist of a judicial opinion first makes a list of the premises, one by one (the facts of the case and the rule or principle that is invoked). Having done that, he checks their con- sistency. If he does not find any inconsistencies, he adds the conclusion (the decision), and then checks whether the totality of premises plus conclusion corresponds with a valid argument form.

I think this is an unfortunate way of presenting the matter. In the first place, it suggests to the lawyer (logicians know better) that logic and judicial creativity don't go together. In the second place, it suggests to the logician (jurisprudents know better) that the meaning of the factual premises can be established apart from the meaning of the normative premises and vice versa. Whereas it is commonplace in jurisprudence that the interpretation of the rule and the qualifi- cation of the facts go hand in hand, this connection tends to be over- looked in the context of logical analysis. In the third place, the approach just sketched leads to a black or white answer "valid" or "not valid", which has a misleading look of objectivity and inescapabil- ity, and which diverts the attention from what matters most: the degree of juridical acceptability. 15

A judge who is justifying his decision is not deducing it from legal rules and so-called facts. He is tracing back the decision, regardless how he found it, to grounds that can support it. The usual terminol- ogy - - "deducing", "following from," etc. - - tends to send us barking up the wrong tree. A judicial opinion is not an account of the judge's quest for the right decision but a justification of the result as

15 An exponent of this approach is Boukema, as the following quotations illustrate (from H.J.M. Boukema,"A Logical Scrutiny of the Van Duyn Case", in Legal Issues of European Integration (1987/2), 83-100): "... sometimes legal reasoning is complicated to the extent that even the finest 'feeling' for logic is not enough to determine whether that reasoning is logically sound ..." and "... modern (or symbolic) logic contains an instrumentarium without which contemporary tasks of ethics and law cannot be performed in intellectual integrity."


juristically acceptable. 16 And the critical analyst should take it as such. With regard to logic, this approach is in line with the origi- nal function of logic. Logic was not invented to deduce conclusions from given premises but to find premises for given conclusions. 17 Given a certain conclusion and a set of possible premises, logic enables us to point out those premises to which the conclusion can, and those to which it can not be traced back.

The logical analyst who shares this view will approach a judicial opinion as follows. He simply assumes that the argumentation given by the judge for his decision is deductively valid. Starting from the decision, he then will interpret the arguments given (factual and normative) in such a way that the result is indeed logically valid. The outcome of his analysis will be something like this: "Given this decision, the judge has interpreted the rule as follows ...". Sometimes there will be more than one possibility. Here the logical analysis ends. Next comes an investigation regarding the juridical acceptability of the judge's interpretation. That, however, is not a logical investigation. It does not end in a verdict "valid" or "not valid", but in a judgement about the juridical quality of the opinion. An example of this approach can be found in section 2 above. On the assumption that Nieuwenhuis's reasoning is logically valid, it is determined that he interprets section 1843 of the Dutch civil code as an implication. This interpretation is then criticized.

Only if it should be impossible to reconstruct a certain judicial argumentation in a meaningful way as valid, the verdict "not valid" would be appropriate. However, as long as judicial opinions are written in human language, such a verdict will always be open to attack. TM To borrow Perelman's term, such a verdict is not a logical

16 I hold this to be the case not only for opinions of civil law judges but for common law opinions as well. Despite appearances, caused by their narra- tive style, common law opinions are, I think, not a faithful account of a heu- ristic process, but a justification. Their quality does not depend on whether or not they contain the real reasons the judge had for deciding as he did. 17 See Ernst Kapp, Greek Foundations of Traditional Logic (New York: Columbia University Press, 1942), especially chapter 1.

18 I know two publicized formal-logical analyses of judicial opinions that end in the verdict "logically incorrect". Both are, I think, open to criticism. The first can be found in H.J.M. Boukema, "A Logical Scrutiny of the Van Duyn Case", in Legal Issues of European Integration (1987/2), 83-100.

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but a quasi-logical argument against the opinion so labeled. 19

Conclusion

Three steps can be distinguished in this essay. Firstly, it is argued that the material implication should not be regarded, as is often done, as the logical standard interpretation of legal rules and principles. Even if we do not take into consideration the context of a particular case, countless rules should be interpreted as an equivalence or as a replication. This implies that the modus ponens should be rejected as the standard form of legal reasoning.

Secondly, it is argued that the logical analyst, just like any other analyst, should take into account the context of the case if he analyses a judicial opinion. The judge uses that context in determin- ing the meaning of the rule he applies; how then could it be justifi- ably passed over in analyzing his argumentation? This means, among other things, that the logical status of one and the same rule may vary from one case to the next.

Finally, this approach to logical analysis is linked to a view on the function of deduction, more specifically deduction in judicial opinions. It is argued that deduction is not so much the derivation of conclusions from given premises but rather the justification of a given conclusion by tracing it back to premises. If a judicial opinion is analyzed critically~ the emphasis should be on the juridical acceptability of the premises. This is best accomplished by starting from the assumption that the judge's reasoning is logically valid, and working backward from the conclusion to the premises.

Boukema's conclusion that the premises are contradictory seems based on a mistaken interpretation- and consequently a mistaken formal recon- struction- of the judge's argumentation. The second can be found on p. 62 of I. Tammelo, G. Moens and P. Brouwer. "De tegenformulemethode en haar rechtslogische toepassingen", in Rechtsfilosofie en Rechtstheorie (1981). 55-65. These authors admit that different interpretations may lead to different results (p. 59). Here too, l think a different reading of the text is possible and defensible, whereby the incorrectness is avoided,

Unfortunately, an adequate foundation for my critique would go far beyond the spacial limits of a note. 19 See Perelman's taxonomy of argument forms in, e.g., Ch. Perelman and L. Olbrechts-Tyteca, The New Rhetoric. A Treatise on Argumentation (Notre Dame: University of Notre Dame Press, 1971), (2d imp.).

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On the Logical Analysis of Judicial Decisions