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Pravno sklepanje in argumentacija

Analogy and Balancing

A Reply to David Duarte
Bartosz Brożek
p. 163–170
Analogno sklepanje in tehtanje [sl]


The goal of the paper is to reply to David Duarte’s critique of the partial reducibility thesisa claim I defended in one of my books that analogy is partly reducible to the balancing of legal principles. In the first part of the paper I sketch the framework against which the thesis was formulated, i.e. Robert Alexy’s theory of legal reasoning. In the second part I attempt to rebut Duarte’s objections, pointing out that they do not take into account the Alexian background of my considerations. Finally, I suggest that some aspects of my theory of analogical reasoning are independent of its theoretical background and may be of value for any conceptualization of analogy in the law.

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1 Partial Reducibility Thesis and the Alexian Framework

1In Brożek 2008 I suggested that within the context of Robert Alexy’s conception of legal reasoning analogy may be partially reduced to the balancing of legal principles. The procedure looks roughly as follows:

2(1) One encounters a problematic case, i.e. a case for which there is no directly applicable legal rule.
(2) One identifies cases
prima facie similar (or similar1) to the given one, for which there exist definite solutions, i.e. for which there are directly applicable legal rules.
(3) One identifies principles standing behind (backing) the legal rules that govern the
prima facie similar cases.
(4) Through the balancing of principles, one decides which of the principles should govern the case at hand. (This also establishes which of the
prima facie similar cases is relevantly similar or similar2 to the case at hand.)
(5) The course of action dictated by the prevailing principle(s) is the decision in the case at hand.

3In this way, I argued, one is able to solve the most pressing problem for any account of analogical reasoning in the law: that of relevant similarity. Usually, it is quite easy to determine a number of already solved legal cases which are similar in one way or another to the case at hand. The hard problem is to decide which of those cases is relevantly similar, i.e. which is to serve as the basis for the analogical decision. By transforming this problem into the balancing of principles, I believe to have replaced an unfamiliar procedure (e.g., choosing the ‘prevailing factor’ which the case at hand shares with one of the prima facie similar cases) with a familiar one (i.e. balancing of legal principles; of course, it is familiar for those who know Alexy’s view of legal reasoning and agree with it). This means that analogy can be divided into two phases. The first phase consists in identifying cases which are prima facie similar to the unregulated case. It is purely heuristic it may be dispensed with (as when one resolves the problematic case without contemplating any similar cases, but instead directly looks for the applicable principles). The second phase, in turn, is justification-generating and consists in balancing of the legal principles which govern the prima facie similar cases. More importantly, in the paper I claimed that what makes analogy “work” at least in the general case is that, given a problematic case, there usually is more than one case prima facie similar to the contemplated case. Of course, there are instances in which analogy operates with only one prima facie similar case. However, this is or so I argued not typical. In order to fully appreciated the mechanism of analogical reasoning, one needs to recognize its dialectical dimension. It is that dimension that makes analogy rational, as it is what enables balancing to enter the stage.

4 Before I examine David Duarte’s objections against this view of analogy, and the partial reducibility thesis, it is necessary to devote a few words to the Alexian framework which served as the background for my analyses. Following in the footsteps of Ronald Dworkin, Alexy distinguishes rules and principles:

Principles are norms which require that something be realized to the greatest extent possible given the legal and factual possibilities. Principles are optimization requirements, characterized 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. (Alexy 2002: 47)

5Rules, on the other hand, “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” (Alexy 2002: 48).

6 When one accepts the thesis that any legal system is made of rules and principles (I have my doubts regarding the distinction in question; see Brożek 2012), important theoretical consequences follow. It is best to grasp them by imagining a legal system which consists solely of principles, i.e. “optimization requirements” such as “The environment should be protected by the law” or “Everyone has freedom of movement”. In such a case, the application of law would become very complex, as for (presumably) every case the judge would have to carry out a balancing procedure (i.e., for any case there would be principles leading to contradictory conclusions). This is the reason why the legislator introduces legal rules, which are applied via simple modus ponens. But it is necessary to notice that legal rules are already a result of weighing some principles, although not in relation to a particular case, but to a class of cases. Thus, the legal rule “Vehicles are not allowed into the park” is an outcome of the balancing procedure undertaken during the legislative process in which such principles as “The environment should be protected by the law” and “Everyone has freedom of movement” are weighed against each other to produce a legal rule governing a generic case. Moreover, since the legislative process cannot take into account all the possible circumstances in which the question arises of whether a vehicle (say, an ambulance carrying a seriously injured person) can enter the park, it is still possible that the application of the rule may be blocked by another principle (say, “Human life should be protected by the law”). However, Alexy emphasizes that such an occurrence is rare, since for a principle to prevail over a legal rule requires that the principle outweighs not only the principle backing the rule, but also the so-called formal principles, such as “Rules passed by an authority acting within its jurisdiction are to be followed” or “One should not depart from established practice without a good reason” (Alexy 2002: 58). This changes little, however, when it comes to characterizing the relationship between rules and principles: the latter are logically prior to the former in the sense that each rule is an outcome of balancing some principles (for a class of cases). It is possible to imagine a legal system consisting solely of principles, while it is impossible to imagine a legal system consisting only of rules (this thesis follows from Alexy’s insistence that legal discourse is firmly embedded in the general practical discourse, cf. Brożek 2007: 160–189). One further consequence of Alexy’s view of the legal system is that there are no genuine gaps in the law (and here I concur with Duarte’s conclusion; cf. Duarte 2015: 7). The only kind of “gap” one can speak of is a situation when there is no legal rule governing the given case; however, there always are principles which are applicable to any given circumstances.

2 Duarte’s Objections

7 Let me now turn to examine David Duarte’s objections to the partial reducibility thesis. First, he claims that it may be difficult to pinpoint the principles standing behind the legal rule governing the prima facie similar cases; further, he observes that there may be more than one such principle. For example, the rule forbidding cars to enter the park may be backed by both the principle pertaining to the protection of the environment, and the principle pertaining to the safety in public places. Duarte’s first worry is genuine, but it is an objection against Alexy’s theory of legal reasoning in general, and not the partial reducibility thesis. Alexy clearly claims that it is possible to identify principles “standing behind” the given legal rule. It is required, inter alia, when one decides a conflict between a legal rule and a legal principle. In such a case, one weighs, on the one hand, the conflicting principle, and on the other, the principles standing behind the formulation of the rule (together with the formal principles). I believe that Alexy’s reply to this problem would be quite straightforward: in order to identify legal principles supporting the given legal rule one makes recourse to common sense, but also to the general legal provisions of the legal act in which the rule is expressed, as well as the documents produced during the legislative process and doctrinal theories. Duarte’s second worry that there may be more than one principle standing behind the given rule, which would make it necessary to pick one of them for the process of balancing has been identified and answered directly by Alexy. In Alexy 2007 he elaborates his conception of the Weight Formula in such a way that enables the simultaneous balancing of several principles.

8 Second, Duarte claims that balancing as used in analogy is only a façade: what really goes on, is the

determining of the meta-factor: among the factors selected by the principles chosen, balancing just decides which one of them prevails. Under the cover of balancing, proper analogy is performed. (Duarte 2015: 5)

9I read Duarte as saying the following: each two cases are similar and dissimilar in an endless number of ways. For example, cars and bicycles may be compared according to an infinite number of factors: price, speed, metal texture, comfort, beauty, how it pleases John, etc. (Duarte 2015: 2). Analogical reasoning aims at identifying a criterion which would determine which of the possible comparison factors should be taken into account to establish relevant similarity between two cases, and thus resolve the case at hand. Further, Duarte seems to claim that the selection of this meta-factor is the essence of analogical reasoning. It follows that the use of the process of balancing I suggested for establishing relevant similarity between cases is just the determination of the meta-factor “in disguise”. What really happens, is the selection of the relevant factor; and the selection is described “as if” it concerned something completely different. I believe that Duarte misses an important point here. The very reason for introducing the partial reducibility thesis was to dispense with all the talk about factors and meta-factors, as such idiom is simply misleading. It is visible already at the surface level of Duarte’s argument: when he compares two cases of whether a bicycle can enter the park and whether a car can enter the park he ultimately compares cars and bicycles, not cases! Meanwhile, on my account the situation is different. I claim that analogical reasoning is connected to establishing two kinds of similarity. Prima facie similarity between two cases pertains to whether those cases are concerned with the same kind of problem. In its simplest form, a problem may be defined as a pair of contradictory statements (not properties!), e.g. {p, ~p}, where p stands for “may enter the park” (of course, it is possible to provide a more complex and intuitively sound definition of a problem). To say that two cases are prima facie similar means that they pertain to the same kind of problem. Let us observe that this mode of speaking makes it unnecessary to refer to any factors (as understood by Duarte). This is quite fortunate, since when analogy is conceptualized in terms of factors, any two cases are prima facie similar (making the very concept of prima facie similarity useless); but it is not true that any two cases address the same kind of problem. Furthermore, according to the partial reducibility thesis the second stage of analogical reasoning consists of balancing legal principles, which also does not involve factors. Thus, my claim is not that the determination of the meta-factor is done through the balancing of principles, but rather that the very idea of the factor-based mechanism of analogy should be rejected. One further consequence of this theoretical manoeuvre is that analogy understood along the lines of the partial reducibility thesis becomes firmly embedded in a more general conception of justification (i.e., Alexy’s theory of practical discourse). When one sticks to the account of analogy in terms of factors, one is in a more difficult theoretical position regarding the justification force of analogy.

10 Third, Duarte observes that “there is nothing to ensure that those principles [identified by determining the prima facie similar cases] are not irrelevant for the unregulated case, in which case they would be unable to justify any solution (Duarte 2015: 6).” This would be so if the prima facie similar cases were determined on the basis of the similarity of some factors; however, when the prima facie similarity is limited to those cases which address the same kind of problem (as defined above), this objection seems no longer valid: there is no real danger that the legal principles involved in the analogical case would have no relevance for the case at hand.

11 Finally, Duarte claims that “all of the problems with the partial reducibility thesis /…/ are /…/ no more than a consequence of a larger one: analogy and balancing do not match” (Duarte 2015: 6). This point is supposedly justified by the fact that analogy and balancing require “opposite normative circumstances: while analogy depends on the absence of an applicable norm, balancing relies on the applicability of two or more norms” (Duarte 2015: 6). As I tried to show above, this is not true, at least within the framework of the Alexian theory of law and legal reasoning, where a situation in which there is no applicable legal norm (i.e., a rule or a principle) can never take place. The only possibility to trigger analogical reasoning is when the given case is not regulated by a legal rule (there always will be at least one relevant and applicable principle).

3 Conclusion

12Let me reiterate the main points of my argument:

  1. Partial reducibility thesis makes sense only within the framework of the Alexian view of the law (or a similar conception), in which the law consists of both rules and principles, and where there are no genuine gaps in the legal system.

  2. Partial reducibility thesis replaces an unfamiliar and somewhat mysterious process of determining the relevant similarity between cases with the more familiar procedure of balancing principles.

  3. In this setting, analogy is a two-step procedure and consists of the heuristic stage (the identification of prima facie similar cases and the principles that govern them) and the justification-generating stage (balancing of legal principles).

  4. My proposal aims at dispensing with analysing analogy by recourse to factors; instead, I suggest to determine prima facie similarity of cases by referring to the problem involved in the case at hand, and relevant similarity by the process of balancing. This is not intended as another way of saying what the proponents of the factor-based accounts of analogy claim; rather, it is an essentially different conceptualization of analogy.

  5. The important insight of my proposal is that analogy is in the general case dialectical. In a sense, I try to reverse the traditional picture of analogical reasoning. On the traditional view of analogy, when one is dealing with an unregulated case, one is desperately looking for another case which is relevantly similar to the case at hand. What I suggest is that given an unregulated case it is usually easy to identify a number of cases dealing with similar problems, and the hard part is to decide which of these cases is relevantly similar. The existence of various prima facie similar cases makes it possible to contrast and compare various possible solutions to the case at hand, what facilitates the determination of relevant similarity, and hence the solution to the case.

13One final remark: I have repeatedly observed that the partial reducibility thesis is meaningful only against the background of Alexy’s theory of legal reasoning. However, I believe that some aspects of analogical reasoning I have tried to highlight notably those referred to in theses (4) and (5) above are relevant to any theoretical attempt to account for analogy in the law.

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Robert ALEXY, 2002: Theory of Constitutional Rights. Oxford: Oxford University Press.
——, 2007: The Weight Formula.
Studies in the Philosophy of Law. Frontiers of the Economic Analysis of Law. Eds. Jerzy Stelmach, Bartosz Brożek & Woijciech Załuski. Kraków: Jagiellonian University Press. 9–27.

Bartosz BROŻEK, 2007: Rationality and Discourse. Warszawa: Wolters Kluwer.
——, 2008: Analogy in Legal Discourse.
Archiv für Rechts- und Sozialphilosophie 94 (2008) 2. 188–201.
——, 2012: Legal Rules and Principles: a Theory Revisited.
i-Lex, Rivista di Scienze Giuridiche, Scienze Cognitive ed Intelligenza Artificiale (2012) 17. 205–226.

David DUARTE, 2015: Analogy and Balancing: The Partial Reducibility Thesis and Its Problems, Revus. Journal for Constitutional Theory and Philosophy of law (2015) 25. URL: http://; DOI: 10.4000/revus.3244.

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Bibliographical reference

Bartosz Brożek, Analogy and BalancingRevus, 25 | 2015, 163–170.

Electronic reference

Bartosz Brożek, Analogy and BalancingRevus [Online], 25 | 2015, Online since 28 July 2015, connection on 22 October 2021. URL:; DOI:

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About the author

Bartosz Brożek

Professor of Law and Philosophy, Jagiellonian University, Krakow

 Bartosz Brożek
Department for the Philosophy of Law and Legal  Ethics
Jagiellonian University
Bracka Str. 12, 31-005 Krakow


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