“The Weight Formula and Argumentation”, [in:] Law, Rights and Discourse: The Legal Philosophy of Robert Alexy, G. Pavlakos (ed.), Hart Publishing, Oxford 2007, 319-332. more |
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15 The Weight Formula and Argumentation
. BARTOSZ BROZEK *
INTRODUCTION
N THIS CHAPTER I would like to consider the role of Robert Alexy’s ‘weight formula’ (WF) within the framework of his theory of legal argumentation. I will start with a brief overview of the latter, highlighting those aspects thereof which are crucial given the chapter’s aims. Next, the WF will be presented and analysed against the background of another mode of legal reasoning advocated by Alexy, ie the ‘subsumption scheme’ (SS). Finally, I will argue for the necessity of replacing classical logic with so-called defeasible logic as ‘the correct’ form for modelling legal argumentation.
I
ALEXY’S ARGUMENTATION THEORY
Alexy maintains that legal discourse is a special case of general practical discourse (the so-called ‘special case thesis’). Therefore, in order to understand what (rational) legal discourse consists in one has to have a grasp of what general practical discourse amounts to. I shall not go into the details of Alexy’s conception.1 Instead, I will try to sketch the general idea behind it. Painting with a broad brush one can say that any such discourse consists in putting forward arguments backing certain theses and deciding which of the arguments prevails. Therefore, one can distinguish
* Chair of Theory and Philosophy of Law, Jagiellonian University, Kraków. This chapter was written during my stay at the University of Kiel as Alexander von Humboldt fellow. I wish to express my gratitude to Robert Alexy and George Pavlakos for discussing early drafts of the chapter. 1 See R Alexy, A Theory of Legal Argumentation (Oxford, Clarendon Press, 1989).
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(although only conceptually) two ‘stages’ or ‘levels’ of argumentation. The first of them boils down to constructing particular arguments. The second consists in comparing arguments. To the two enumerated stages of argumentation there correspond two sets of rules. As Alexy puts it himself:
[the rules of the first group] are also applicable in the context of monologues, and it can be assumed that no theory of rational practical argumentation or justification can dispense with them. This makes it clear that discourse theory in no way replaces justification by merely producing consensus. It fully embraces those rules of rational argumentation, which are applicable to arguments. Its distinctive feature lies exclusively in the fact that it adds a second level to this one, namely that of rules referring to the procedure of discourse.2
Therefore, a complete theory of general practical discourse must include two sets of rules, namely rules for constructing arguments and rules ‘referring to the procedure of discourse’, ie rules which govern the comparison of arguments. These are precisely those two sets of rules that encapsulate the rationality of discourse. Any discourse that is carried out according to the rules may be deemed rational, and only such a discourse. What follows, an outcome of a discourse that observes all the rules, can also be called rational or justified. It is convenient to quote here some of the rules of general practical discourse, especially those which will be important for the discussion below (I use Alexy’s own numbering from A Theory of Legal Argumentation).3 Of the rules which regulate the construction of arguments one can mention the following: (1.1) No speaker may contradict him or herself. (1.3) Every speaker who applies a predicate F to an object a must be prepared to apply F to every other object which is like a in all relevant respects. Rule (1.1) is of special interest as it constitutes the requirement that all the arguments should be constructed according to the rules of logic.4 Among the rules of general practical discourse of the ‘second stage’ of argumentation the following can be mentioned: (1.4) Different speakers may not use the same expression with different meanings. (2.1) Everyone who can speak may take part in discourse.
2
R Alexy, ‘A Discourse-Theoretical Conception of Practical Reason’ (1992) 5 Ratio Juris
232.
3 All the quoted rules may be found in Alexy, A Theory of Legal Argumentation, above n 1 at parts B and C. 4 See ibid at 188–9.
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The Weight Formula and Argumentation
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(2.2) (a) Everyone may problematise any assertion; (b) Everyone may introduce any assertion into the discourse; (c) Everyone may express his or her attitudes, wishes and needs. (2.3) No speaker may be prevented from exercising the rights laid down in (2.1) and (2.2) by any kind of coercion internal or external to the discourse. In addition, Alexy identifies several rules concerning the allocation of the burden of proof, the so-called justification rules and transition rules (the latter concern transitions from practical discourse to theoretical, linguisticanalytical and discourse-theoretical discourses). Alexy maintains, further, that legal discourse is a special case of general practical discourse. The special case thesis is:
supported on the ground that: (1) legal discussions are concerned with practical questions—that is, what should or may be done or not done; and (2) these questions are discussed under the claim to correctness; … [and] (3) legal discussions do take place under constraints [imposed by the valid law].5
It is the third thesis that distinguishes law from other normative discourses. Therefore, among the ‘special’ legal rules of argumentation there are rules of valid law. Among them one can, as in the case of general practical discourse, distinguish between rules concerning the process of constructing arguments and rules concerning the ‘comparison’ of arguments. The former are, especially, the rules of the so-called internal justification. The simplest form of internal justification has the structure of the SS: (J.1.1) (1) ∀x (Ax → Bx) (2) Ao ———————(3) Bo where (1) is a general legal norm, with A being the conditions of the rule’s application and B the rule’s conclusion. (2), in turn, is a description of the case, ie a statement of facts. Finally, (3) is the legal judgment expressing the solution to the case at hand. Other requirements for constructing arguments include: (J.2.1) At least one universal norm must be adduced in the justification of a legal judgment. (J.2.2) A legal judgment must follow logically from at least one universal norm together with further statements. On the other hand, among the rules of the ‘second stage’ of argumentation the following can be mentioned: (J.8) Determinations of the relative weights of arguments different in form must conform to weighting rules.
5
Ibid at 212–13.
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(J.9) Every possibly proposable argument of such a form that it can be counted as one of the canons of interpretation must be given due consideration. The picture sketched above looks, roughly, like this. Legal discourse consists in putting forward arguments backing certain theses (legal decisions). The arguments must be built according to the first level rules; those rules include, among others, also the logical requirements. In other words, legal arguments must be constructed in compliance with the rules of logic. Then, the arguments which back contradictory (or otherwise incompatible) theses must be compared in order to reach the decision which of the (competing) arguments prevails. This process has to comply with the rules of the second level. A peculiar feature of Alexy’s conception has to be noted here. The rules of the second level are too general to yield a unique decision in every conceivable case. As Alexy puts it himself:
observance of the stated rules and utilization of the described forms of argument do indeed increase the probability of reaching agreement on practical issues, but they do not guarantee that agreement can be reached on every subject nor that any agreement obtained will be final and irreversible.6
Therefore, the rules decide only which theses (legal decisions) are discursively rational. It is not unusual, therefore, for there being a case in which both of the two incompatible outcomes are equally justifiable with regard to the rules of the second level.
In those instances in which two incompatible normative statements or rules can be justified without violating any of the rules of discourse, one can speak of ‘discursive possibility’.7
In other words, the rules of discourse demarcate only what is discursively justifiable (possible) from what is discursively untenable (impossible).
ROLE OF THE WEIGHT FORMULA
Let us now consider the following question: what is the role of the WF within the framework of Alexy’s argumentation theory? We have to begin with a formulation of the WF. Alexy maintains8 that whenever there is a conflict between two legal principles, it should be decided by the following formula:
Ibid at 206. Ibid at 207. 8 See R Alexy, ‘On Balancing and Subsumption: A Structural Comparison’ (2003) 16 Ratio Juris 433.
7 6
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The Weight Formula and Argumentation Ii · W i · R i Ij · W j · R j
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Wi,j =
where Wi,j stands for the concrete weight of the principle Pi relative to the principle Pj, ie 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, ie irrespective of any circumstances. Finally, Ri stands for ‘the reliability of the empirical assumptions concerning what the measure in question means for the non-realization of Pi and the realization of Pj under the circumstances of the concrete case’.9 The principle that has a greater weight prevails in the concrete case over the other principle. The final legal decision is then taken according to what Alexy deems the ‘law of conflicting principles’ (LCP): the circumstances under which one principle takes precedence over another constitute the conditions of a rule which has the same legal consequences as the principle taking precedence.10 In order to illustrate how the WF works let us use a modified version of HLA Hart’s notorious ‘vehicle in the park’ example. The example reads as follows: An ambulance carrying a seriously injured person has to go to a hospital. The shortest way to the hospital is through the park. However, if the ambulance was allowed into the park it would cause serious pollution. The question arises whether the ambulance can enter the park. Be the case as naïve as it may, it constitutes a nice illustration of a conflict between two principles. The principles are: (P1) Human life and health should be protected by the law. (P2) The environment should be protected by the law. The application of (P1) results in allowing the ambulance to enter the park and the application of (P2) bans the entrance. Therefore, the principle (P1) reshaped to fit the example can be formulated as follows:11 (1) ∀x (AHIx → EPx) where AHI stands for ‘is an ambulance carrying a seriously injured person’ and EP for ‘may enter the park’. (P2), in turn, becomes: (2) ∀x (Vx → ¬EPx) where V stands for ‘is a vehicle’. The set of the case’s facts C includes: (3) AHIa (4) Va where a is a name of a specific ambulance.
9 10
Ibid at 446. R Alexy, A Theory of Constitutional Rights (Oxford, Oxford University Press, 2002),
. 11 This transformation is problematic. For a discussion see B Brozek, ‘The Logic of Rules and Principles’ (2005), unpublished manuscript.
54.
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Let us assume, further, that the application of the WF yields the following result: in the described case it is the principle (P1) that takes precedence over (P2). Therefore, according to the LCP the following legal rule should be applied in the case: (5) (AHIa ` Va) → EPa I would like to argue that, within the above sketched framework of Alexy’s argumentation theory, this reconstruction of a conflict between two legal principles is mistaken. We should start with clarifying the role the WF plays within argumentation. There are two interpretations possible. According to the first, the WF serves for ‘producing’ an argument. Therefore it is a device to be used on the first level of argumentation. There is one reason backing this claim. It has to do with the LCP, which states that: the circumstances under which one principle takes precedence over another constitute the conditions of a rule which has the same legal consequences as the principle taking precedence. The LCP together with the WF serve to produce a case-relative legal rule, like: (5) (AHIa ` Va) → EPa This rule, in turn, is used to construct an argument which decides the case. I believe, however, that this interpretation is mistaken. It follows from it that the WF is used before the process of argumentation even starts, what is highly controversial. We are misled here, so I argue, by the wording of the WF and the LCP. Instead of speaking of resolving conflicts between principles, it would be much more convenient to say that the WF decides conflicts between two arguments based on legal principles. This mode of speaking supports the second interpretation, according to which the WF plays its role on the ‘second level’ of argumentation, the one that serves to compare arguments. It is further backed by the fact that both principles which are in conflict when the WF is applied are valid legal norms, so a decision which of two valid norms to apply has to be a result of an argumentation process. The WF, therefore, is not a scheme of constructing arguments. It is a device that serves comparing different, competing arguments. It belongs to the second level of argumentation. Let us recall our example. We have two principles, (P1) and (P2). They have to be compared with the use of the WF for the simple reason that they make it possible to construct two competing arguments, one based on (P1) and the other on (P2). Schematically, we can present it as follows: (ARG1) (1) ∀x (AHIx → EPx) (3) AHIa ———————
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(6) EPa (ARG2) (2) ∀x (Vx → ¬EPx) (4) Va ——————– (7) ¬EPa It has to be stressed that both (ARG1) and (ARG2) have to be constructed according to the rules of logic (rule (1.1)), and they are. Now, the role of the WF is to decide which of the two arguments, (ARG1) or (ARG2), prevails. The WF does it by balancing both principles involved in the formulation of (ARG1) and (AG2) relative to the case at hand. An important problem concerning the role of the WF within legal argumentation is its relation to the rules of discourse. As we said, the WF serves to resolve conflicts between arguments based on principles. Therefore, the urgent question is, whether the outcomes of applying the WF lie within what is characterised by the rules of the second level as discursively possible. If this is the case, then those outcomes (decisions) can count as rational or justified. If not, the WF is useless from the point of view of the theory of legal argumentation. I would like to propose the following solution to this problem. When a conflict of two arguments based on principles occurs, there are two possibilities. It may be the case that one of the arguments is discursively impossible. If so, then there is no need to apply the WF, as the outcome is obvious: it is the discursively rational argument that prevails. Otherwise both arguments are discursively possible and that is when the WF has to be applied. The role of the WF within argumentation should be contrasted with the role of the SS. The SS is a valid form of argument: (SS) (1) ∀x (Ax → Bx) (2) Ao ———————(3) Bo where (1) is a general legal norm, with A being the conditions of the rule’s application and B the rule’s conclusion. In turn, (2) is a description of the case, ie a statement of facts. Finally, (3) is the legal judgment expressing the solution to the case at hand. It is obvious that the SS serves for constructing arguments. Alexy says so literally, formulating the rule of discourse (J.1.1).12 Another point is that, as the WF decides conflicts between two arguments, legal principles (and conflicts between them) cannot be handled with the WF alone: the
12
Ibid.
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arguments based on principles must be constructed as deductive arguments in compliance with rule (1.1). It contradicts what, taken literally, Alexy says. He maintains that legal rules are handled with the SS, while legal principles, with the WF. He goes on to say that:
in both cases a set of premises can be identified from which the result can be inferred. … The relation between those premises and the result is, however, different. The Subsumption Formula represents a scheme which works according to the rules of logic; the Weight Formula represents a scheme which works according to the rules of arithmetic.13
It is clear that the difference between legal rules and principles does not boil down to the fact that rules are handled with the SS scheme and principles with the WF. On the first level of discourse, both arguments based on rules and arguments based on principles must have the form of deductive schemes. The difference lies somewhere else, namely on the second level of argumentation. Conflicts between principles (or, more precisely, of arguments based on principles) and conflicts between a rule and a principle (an argument based on a rule and an argument based on a principle) are decided by the WF. As regards the conflicts of rules, the story is completely different. Precisely speaking, if the validity of a legal rule is established, there can be no argument based on another legal rule incompatible with the argument based on the rule at hand. This is in compliance with what Alexy says:
conflicts of rules are played out at the level of validity; since only valid principles can compete, competitions between principles are played out in the dimension of weight instead.14 LOGIC
In such a setting there immediately occurs a logical problem. If we accept the thesis that the WF decides conflicts between two arguments based on principles, arguments that are both deductively valid, we cannot use the classical logic to deal with the problem. The issue may be illustrated with our earlier example. Recall that on the basis of (P1) and (P2) we constructed the following two arguments: (ARG1) (1) ∀x (AHIx → EPx) (3) AHIa ——————— (6) EPa (ARG2)
13 14
Alexy, above n 8 at 448. Alexy, above n 10 at 50.
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(2) ∀x (Vx → ¬EPx) (4) Va ——————– (7) ¬EPa Having those two arguments we move on to the second ‘level’ of argumentation applying the WF to decide the conflict (and there, naturally, is a conflict, as the conclusion of (ARG1) is contradictory to the conclusion of (ARG2)). The application of the WF leads us to preferring (ARG1) over (ARG2), ie to rejecting the conclusion of (ARG2), ¬EPa. This is, however, highly problematic. If we accept that (ARG2) is a deductive argument which is based on true (or valid) premises, then it is impossible for the conclusion of the argument to be rejected under any circumstances. It is simply the way classical logic works. In order to avoid this problem, a shift to another formalism is needed. The so-called defeasible logics can serve our aims well. Let me present, therefore, a sketch of a simple defeasible formal system. Let us start with a definition of defeasibility:15 a rule of the form A⊃B is defeasible if and only if there are situations in which A is fulfilled but B does not follow. It is easily observable that ⊃ cannot be read as the material implication →, for in such case it is impossible that A→B and A are true and B is not. Let us now describe the formal system.16 Our defeasible logic (DL) operates on two levels. On the first level from a given set of premises arguments are built; on the second level the arguments are compared in order to decide which of them prevails. The conclusion of the ‘best’ argument becomes the conclusion of the given set of premises. The language of DL is the language of the first order predicate logic extended by addition of a new sentential connective, the so-called defeasible implication, for which we will use the symbol ⇒. For defeasible implication there exists the defeasible modus ponens, analogical to that of the material implication: A⇒B A ——B
15 The notion of ‘defeasibility’ was introduced into legal philosophy by HLA Hart in ‘The Ascription of Responsibility and Rights’ in A Flew (ed), Logic and Language (Oxford, Blackwell, 1951). Hart speaks there of defeasibility of legal concepts. Here, a widely accepted rephrasing of Hart’s idea is used: defeasibility is predicated of rules. For more details, see B . Brozek, Defeasibility of Legal Reasoning (Kraków, Zakamycze, 2004). 16 The fundamental ideas of the simple system I present here are those of Prakken’s logic; see H Prakken, Logical Tools for Modelling Legal Argument: Study of Defeasible Reasoning in Law (Dordecht, Kluwer Academic Publishers, 1997). See also J Hage, Reasoning with Rules: An Essay on Legal Reasoning and its Underlying Logic (Dordecht, Kluwer Academic . Publishers, 1997) and Brozek, above n 15.
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The difference between material and defeasible implications is visible only on the second level of DL. The language of DL serves for building arguments. Let us recall our example: (1) AHIx ⇒ EPx (2) Vx ⇒ ¬EPx17 (3) AHIa (4) Va This set of premises enables us to construct two arguments, applying defeasible modus ponens: (ARG1) (1) AHIx ⇒ EPx (3) AHIa ——————— (6) EPa (ARG2) (2) Vx ⇒ ¬EPx (4) Va ——————– (7) ¬EPa The arguments lead to contradictory conclusions. In such a case we have to move to the second level of DL, on which the arguments are compared in order to decide which is ‘better’ and, in consequence, which of the sentences, EPa or ¬EPa, shall be regarded as the conclusion of our set of four premises. On the second level of DL two concepts play a crucial role: attack and defeat. We shall say that an argument A attacks an argument B if the conclusions of both arguments are logically inconsistent.18 In our example it is the case since EPa and ¬EPa are contradictory: consequently, (ARG1) attacks (ARG2). If two arguments attack one another, one has to know how to decide which of the arguments prevails, ie which defeats the other. Various ways of comparing attacking arguments have been developed. The easiest and most flexible is the following. One checks what the defeasible implications that served to build the attacking arguments are. It is assumed that those implications are ordered. In a comparison an argument wins which is built with the use of a defeasible implication that is higher in the ordering. Let us assume that in our example it is the defeasible implication (1) that is higher in the ordering than (2).
Note that material implications have been replaced by defeasible implications. As our presentation is elementary, we apply here a simplified definition of attack. Cf Prakken, above n 16.
18
17
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The conclusion of the argument that prevails in comparison of all attacking arguments built from the given set of premises is the logical conclusion of this set. Therefore, it is EPa that is the logical conclusion of our set of premises (1) to (4). The logical system sketched above can easily be applied to conflicts between legal norms and it is the ordering of defeasible implications that ultimately decides the outcome. In case of a conflict between two rules the ordering can be established in abstracto, ie irrespective of the given legal case. This captures the idea that ‘conflicts of rules are played out at the level of validity’. Conflicts of legal principles or of a principle and a rule are decided relative to the given case. Within the framework of DL, it is the WF that decides the ordering of defeasible implications representing principles. For instance, in the case of our example, where the principle (P1) outweighs the principle (P2), the WF decides the ordering such that (P1)>(P2) (or in other words, (1)>(2)) and, consequently, it is the argument based on (P1) that prevails over the argument based on (P2). In this way the logical mechanism of applying legal rules is the same as in the case of principles, but the difference between the two kinds of legal norms is captured in the way the ordering of defeasible implications is decided. Thus we get exactly what is needed. The arguments based on principles are deductively valid. It is true that the validity in question is a local one, ie the arguments have valid forms and proceed from true premises, but their conclusions do not necessarily belong to the set of the consequences of the given set of premises. The set is decided, ultimately, by comparison of conflicting arguments. In this way the conclusion of (ARG2), ¬EPa, follows deductively from the premises (2) and (4), but nevertheless it is not included in the set of the logical consequences of the set of premises {(1), (2), (3), (4)}. However, unlike in the case of classical logic, DL provides us with a formal mechanism which makes such a situation possible. Moreover, the proposed solution enables us to get rid of the LCP, which was the main source of confusion as to the role the WF plays in argumentation. It is evident from what we said, that the LCP was needed because of the underlying assumption that it is the classical logic that has to be used to formally model legal reasoning. I would like to say, also, that there are some additional reasons justifying the abandoning of the classical logic in favour of DL. One of them concerns the formal mechanisms governing resolution of the conflicts between two legal rules, two principles or a rule and a principle. The use of classical logic in this context requires taking advantage of the notion of revisability, which is acceptable in the case of a conflict between two legal
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rules but is troublesome in the remaining two cases. However, as this problem exceeds the scope of this chapter, I will not pursue it here.19
CONCLUSIONS
The findings of the present chapter may be summarised as follows. The first thesis I defended may be put forward in the following way: (T1) The weight formula plays its role at the second level of argumentation, ie at the level at which arguments are compared. The thesis is backed both by the distinction between two levels of argumentation and by the fact that the very idea of the WF is to settle a controversy, ie the WF cannot be thought of as a device applicable for constructing arguments, or, so to speak, before the argumentation starts. There are several corollaries20 that follow from this: (C1) What the WF ultimately compares are not two principles but two arguments based on principles. (C2) The WF plays an essentially different role within argumentation than the SS; the former is applied on the second level of argumentation, the latter on the first. (C3) The difference between legal rules and principles does not boil down to the fact that rules are ‘handled with’ the SS and principles with the WF. Both rules and principles are used to construct deductively valid arguments. The difference between them lies in the question whether, and in what circumstances, they can face opposing arguments and how such conflicts are decided. (C4) The LCP is misleading. It suggests that the WF plays its role on the first level of argumentation. Therefore, it should be abandoned. The second thesis I advocated reads: (T2) Legal discourse should be modelled with the use of defeasible logic rather than classical logic. This claim is based on the fact that it is impossible to reconcile (T1) and (C1) to (C4) with the classical logic approach. A corollary from (T2) is the following: (C5) A shift from the classical logic to the defeasible logic enables one to abandon the LCP.
. . 19 It is addressed in detail in Brozek, above n 11. See also B Brozek, ‘Revisability vs. Defeasibility’ (2005), unpublished manuscript, for the distinction between revisability and . defeasibility and Brozek, above n 15 for other reasons for preferring defeasible logic over the classical. 20 I allow myself the use of the notion ‘corollary’ somewhat loosely.
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