1The Logic of Legal Requirements. Essays on Defeasibility, edited by Jordi Ferrer Beltrán and Giovanni Battista Ratti, and published by Oxford University Press in 2012, is a very much welcome contribution to one of the most discussed topics in the contemporary legal theory and philosophy. Defeasibility is connected to many essential issues such as the nature of legal reasoning, the structure of legal norms and legal system, the concept of legal validity, as well as the mechanisms and limits of legal interpretation. It suffices to consider this list in order to see that defeasibility constitutes an important topic in any discussion concerning the theoretical reconstruction of legal practice. Moreover, the past two decades have generated substantial literature on the subject, ranging from accounts which fully embrace defeasibility, to very sceptical voices, which question the usefulness of the concept in question.

2 In this context, the collection put together by Ferrer Beltrán and Ratti, containing differentiated, often competing accounts, provides the much-needed panorama of the contemporary discussions of defeasibility. The book is divided into four parts. Part I, including the contributions by Ferrer Beltrán and Ratti themselves, Carlos R. Alchourrón, Juliano S.A. Maranhão, Frederick Schauer, Jorge L. Rodríguez, Giovanni Sartor, and Rafael Hernández Marín, is devoted to the logical and conceptual aspects of defeasibility in the law. Part II, with contributions by Pierluigi Chiassoni, Riccardo Guastini, Brian H. Bix, Daniel Mendonca, and Ricardo Caracciolo, concerns the relationship between defeasibility and the process of legal interpretation. In Part III, devoted to defeasibility in the context of various conceptions of law, one can find papers by José Juan Moreso, Manuel Atienza and Juan Ruiz Manero, Wilfired J. Waluchow, Bruno Celano, Juan Manuel Pérez Bermejo, and María Cristina Redondo. Finally, Part IV, including contributions by Fernando Atria, Richard H. S. Tur, Jonathan R. Nash, and Bruce Chapman, is devoted to defeasibility and adjudication.

4Defeasibility is a fashionable concept, at least in the domain of legal theory. The problem is, however, that it is quite difficult to provide a definition of defeasibility that would be commonly acceptable. Let us illustrate this point. Pierluigi Chiassoni (2012) puts together the following list of phenomena that are referred to as defeasible: (1) facts, (2) beliefs, (3) legal concepts, (4) norm formulations, (5) legal interpretations or meanings, (6) norms, rules or principles, (7) legal reasoning, (8) legal positions, (9) legal arrangements, (10) legal claims, and (11) legal conclusions. To that collection, one can add, at least, (12) properties (Hernández Marín 2012), (13) arguments, and (14) argument-forms (Prakken & Vreeswijk 2002). In the relevant literature, one can also find references to numerous kinds of defeasibility, including ontological, conceptual, epistemic, deontic, and logical (Hage 2005, Brożek 2004). In contrast, Giovanni Sartor and Henry Prakken consider a different aspect of the problem and distinguish between inference-based, process-based, and theory-based defeasibility (Prakken & Sartor 2004). To complicate things even further, defeasibility is often linked with other concepts, such as vagueness, open texture, and revisability (Bix 2012, Brożek 2008).

5In light of the above, it is no surprise that the contributions collected in Ferrer Beltrán and Ratti’s book take quite different definitions of defeasibility as their points of reference. For example, Ferrer Beltrán and Ratti consider, intera alia, the following formulation: “a norm is defeasible when it has the disposition not to be applied even though it is indeed applicable” (Ferrer Beltrán & Ratti 2012: 31). Frederick Schauer, in turn, claims that “the key idea of defeasibility /…/ is the potential for some applier, interpreter, or enforcer of a rule to make an ad hoc or spur-of-the-moment adaptation in order to avoid a suboptimal, inefficient, unfair, unjust, or otherwise unacceptable, rule-generated outcome”, and concludes that “defeasibility is not a property of rules at all, but rather a characteristic of how some decision-making system will choose to treat its rules” (Schauer 2012: 81 & 87). Jorge L. Rodríguez says that “when we express a conditional assertion, we assume the circumstances are normal, but admit that under abnormal circumstances the assertion may become false”, and – transferring this characteristic of defeasibility into the domain of law – claims that “legal rules [are defeasible since they] specify only contributory, yet not sufficient, conditions to derive the normative consequences fixed by legal system” (Rodríguez 2012: 88). Still, Giovanni Sartor defines a defeasible reasoning schema, i.e. such a schema, in which “one should, under certain conditions, refrain from adopting its conclusions though endorsing its premises” (Sartor 2012: 112). Rafael Hernández Marín defines a defeasible property as a property that is “an apparent, but not, or not necessarily, real property” (Hernández Marín 2012: 137). Finally, Riccardo Guastini claims that legal rules are defeasible since “there are fact situations which defeat the rule although they are in no way expressly stated by normative authorities in such a way that the legal obligation settled by the rule does not hold anymore” (Guastini 2012: 183).

6 This complicated, if not chaotic theoretical picture connected to the concept of defeasibility seems to generate more confusion that clarity. My suggestion is that a more structured and useful discussion of defeasibility may result from adopting the following two postulates.

Postulate 1. Defeasibility is primarily a feature of rules. To speak of defeasibility of other entities is to use the term in a derivative sense.

7This postulate is justified by two observations. First, it enables to logically capture the mechanism of defeasibility, since rules can be expressed as some kind of conditionals. Secondly, arguably all other kinds of defeasibility are, ultimately, reducible to defeasibility of (some) rules. For example: concepts may be said to be defeasible when the rules of their application are defeasible; social facts are defeasible since the ‘count-as’ rules that generate them may be defeasible; beliefs are defeasible because they may be represented formally with defeasible rules; legal interpretation may be said to be defeasible because some of the canons of interpretation are defeasible rules; legal reasoning (in general) is defeasible, because it often takes advantage of defeasible rules; legal arguments are defeasible, since they might include defeasible rules; and legal properties may be said to be defeasible since we ascribe them to individuals using some defeasible rules.

Postulate 2. Defeasibility should be regarded as a domain-neutral feature of rules (and, derivatively, of other phenomena).

8I agree with Giovanni Sartor (2012) that the methodologically sound analysis of defeasibility must take it in its most general form, i.e. as a feature of rules (or argument schemata), which are applicable in all kinds of contexts. In other words, I believe that the more general and context-independent concept of defeasibility one has, the better theoretical tool it becomes. On the one hand, defeasibility defined along the lines of Postulate 2 can be applied in different legally-relevant problems (application of law, validity of law, interpretation of law, etc.). On the other hand, if it turns out that defeasibility is useful in non-legal domains (e.g., theoretical reconstructions of morality, language or social ontology), it would constitute an additional argument to take the role of defeasibility in the law seriously, as it would transpire that defeasibility is an important mechanism in quite different attempts to conceptualize our experience.

9In line with the Postulates 1 and 2, we can formulate the following definition:

Defeasibility. A rule of the form A => B is defeasible iff it is possible that although A obtains, B does not follow. (Note that the logical connective ‘=>’ between A and B cannot be the material conditional).

10One of the consequences of adopting the above formulated definition is that defeasibility may be clearly distinguished from other concepts such as vagueness (a predicate P is vague iff there are such objects of which neither P nor ~P can be predicated), open-texture (a predicate P is open-textured iff some changes in reality may make it so that there will emerge objects of which neither P nor ~P can be predicated), and revisability (a rule of the form A => B is revisable if and only if it can be substituted with a rule or a set of rules that would better represent the relevant aspect of experience) (cf. Brożek 2008). The clear distinction between these concepts also has the advantage of opening the way for the discussion how defeasibility is related to vagueness, open texture and revisability (in reference to the last problem, see below).

11The second question I would like to address is how to formally capture defeasibility. There exist three approaches to this question. First, it is claimed that defeasibility may be represented only in a non-monotonic logic (cf. Sartor 2012). Second, some scholars (cf. Alchourrón 2012, Maranhão 2012) argue that what is referred to as “defeasibility” may be formally accounted for without introducing non-monotonicity: what suffices is the classical logic with some suitable belief revision mechanism. The third stance is that defeasibility is not reconstructable logically, and hence should be considered an “extremely confusing” concept (Hernández Marín 2012: 148).

12 I agree with the proponents of the first stance that the only way to formally capture defeasibility is through the utilization of some kind of non-monotonic logic. The reason I reject the combination of the classical logic and belief revision as the formal mechanism behind defeasibility is that it makes it impossible to distinguish defeasibility from revisability, and – as I remarked earlier – I think it is useful to have both concepts. It does not follow, of course, that legal rules (or some other legal phenomena) should be considered both defeasible and revisable. My point is methodological: it is always better to have more formal tools at one’s disposal, and the choice of which of the available tools is best suited for some theoretical purpose is made at the stage of theory-construction.

13 However, the dispute between the defenders of non-monotonic logics and the proponents of the approach to defeasibility based on revision has a more fundamental dimension. Painting with a broad brush, one can describe the philosophical difference between the classical and the non-monotonic logic as formal systems suitable for reconstructing the reasoning of, respectively, perfect and imperfect agents. The classical monotonic logic assumes that the agent has a perfect knowledge of the facts, while the non-monotonic logics are designed to handle situations in which the agent does not have, or – due to some cognitive or physical limitations – cannot have, access to all relevant information (cf. Sartor 2012). Let us consider the famous example:

(Fly) If x is a bird, than x flies.

14The rule (Fly) does not constitute a faithful representation of the world: we know that if x is a penguin or an ostrich, x does not fly. The claim of the proponents of non-monotonic logics is that we nevertheless use rules such as (Fly), because in real-life situations it is often impossible to gather all relevant facts (i.e., to check whether x is not a penguin or an ostrich or has a broken wing, etc.); so, we have no other choice but to make inferences with rues such as (Fly) as long as we do not have evidence contrary to the rule’s conclusion. The defenders of the classical logic disagree. They claim that the accumulation of knowledge consists in constant revisions of the cognitive rules we use. So, as soon as the rule (Fly) turns out false (say, because we have observed a penguin, which is a non-flying bird), we revise it in the following way:

(Fly_Revised_1) If x is a bird and x is not a penguin, than x flies.

15Such revisions are needed whenever an exception to the rule is established, giving more and more complex formulations:

(Fly_Revised_2) If x is a bird and x is not a penguin and x is not an ostrich, and x does not have a broken wing, and …, than x flies.

16Therefore, at the philosophical level the difference between the first two stances (of the proponents of non-monotonic logic on the one hand, and the defenders of the classical logic with belief revision on the other), is how to represent agent’s knowledge. The first camp believes that there is some advantage in leaving the formulation of (Fly) intact (e.g., they claim that the use of such complex rules as (Fly_Revised_2) would be cognitively too demanding); the second camp has a transcendental view of the thinking subject: they disregard some factual limitations of the agent and require her to do everything in her cognitive efforts to approximate the behaviour of a perfect agent. To put it in different terms, if the first camp provides a logical framework for reconstructing the reasoning of a judge, the second camp does the same for a judge Hercules. It is not my claim that one of those two approaches is better than the other. In fact, both are fully legitimate attempts to reconstruct human cognitive efforts, both in theoretical and practical domains. The point is that they are different, just like the concept of defeasibility is different from the concept of revisability.

17 The idea of rendering defeasibility in the law by using non-monotonic logic is also dismissed by the defenders of the third approach (cf. Hernández Marín 2012). The dismissal is based on two claims: that legal logic is impossible and that non-monotonic logic does not encode any consequence relation (the latter position is adopted by other scholars too, in particular Carlos Alchourrón). It so happens that both these claims are based on the same idea pertaining to the nature of logic, i.e. that logic encodes a consequence relation which guarantees the transmission of truth from the premises to the conclusion of a logically valid argument. This idea was made explicit in Alfred Tarski’s (1936) famous essay O pojęciu wynikania logicznego:

A sentence A follows logically from the set of premises г if and only if in every case in which the premises belonging to г are true, A is also true.

18If so, then logical relations obtain only between propositions which may be ascribed truth or falsehood (and since norms are neither true nor false, there is no logic of norms). Moreover, if Tarski’s analysis is sound, then non-monotonic logic is flawed, since truth is a monotonic property (it is hard to imagine that an addition of a new premise would turn some true propositions into false ones). The problem is that Tarski’s view of logical consequence has become a kind of dogma, while it shouldn’t have. To analyse this problem, let me repeat an analogy developed by John Etchemedy. In metamathematics several different formal systems characterizing the class of computable functions have been developed. It turned out that the results provided by the systems are coextensive. It was the basis for the claim (known as Church’s Thesis) that the class of intuitively computable functions is coextensive with the class of computable functions as defined by the systems. The problem with Church’s Thesis is that it hasn’t been proved (and possibly cannot be proved) mathematically (cf. Olszewski, Brożek & Urbańczyk 2014). Now, Etchemedy’s analogy is that a similar problem was faced by the early 20^th Century logicians whose various proof-theoretic or, in other words, syntactic systems were designed to capture the intuitive notion of logical consequence. Etchemedy calls the claim that those systems captured the intuitive notion of consequence, Hilbert’s Thesis. Hilbert’s Thesis has had a different fate to Church’s Thesis. As Etchemedy puts it, it has been replaced by soundness and completeness theorems and the idea of those theorems is ultimately based on Tarski’s analysis of logical consequence (Etchemedy 1990). But what does the 'proof' of Hilbert's Thesis consists in? This is an exercise in the formalist paradigm of doing logic and mathematics. Any soundness and completeness theorems establish certain relations between two mathematical structures; it so happens that some elements of one of these structures (semantics) are informally interpreted as designating truth values. This does not mean, however, that one cannot account for some interesting relations between propositions which have nothing to do with their truth values. This is exactly the case with nonmonotonic logic, which encode a relation of the transmission of justification, not of truth (cf. Hage 1997). To conclude, the rejection of non-monotonic logic as “confused” or “not a logic at all” has nothing to do with its comprehensiveness, but rather is based on some philosophical choices related to the question what is the nature of logic.

19 The final question I would like to comment on is whether there is defeasibility in the law. This question can be interpreted in two ways: either as inquiring into the possibility of reconstructing legal phenomena with the utilization of the mechanism of defeasibility, or as demanding the answer, whether defeasibility is an inherent feature of the law. On the first reading, the question is trivial: yes, it is possible, and many theories of law utilizing the concept of defeasibility have in fact been developed. On the second reading the question is ill-stated, as it assumes that there exists some nature of law – independent of our theories – which can (and should) be theoretically captured. To put it differently: there is no unique, ultimate theory of law. What we can do is to develop different, often competing views of legal phenomena, and the only way to decide which is better is to compare them against some chosen criteria (e.g., some practical ends). From this point of view, defeasibility – similarly to revisability – is just one tool we have at our disposal when attempting to reconstruct the investigated legal issues. Thus, ultimately, the use of defeasibility (and non-monotonic logic) to model some phenomena is a theoretical choice; whether the choice is justified, can be assessed only by comparing the resulting model with some alternatives.

20 I do not want to suggest that the conceptual framework I sketched above is the only theoretical option. I believe, however, that it has the advantage of providing clear conceptual distinctions, and hence paves the way to a more balanced discussion pertaining to the relationship between law and defeasibility. Defeasibility is a formal mechanism which may – but also may not – be used to model legal phenomena. The utilization of defeasibility remains our theoretical choice, which hangs together with other theoretical choices we make (e.g., the view on the nature of logic), as well as our practical ends. Still, the concept of defeasibility is theoretically very fruitful, as illustrated by the engaging and multi-faceted contributions collected in Ferrer Beltrán and Ratti’s book.