The debate between Bulygin and Kelsen on the validity and efficacy of law

José Renato Gaziero Cella

Doutor em Filosofia e Teoria do Direito pela Universidade Federal de Santa Catarina - UFSC (2008);
Mestre em Direito do Estado pela Universidade Federal do Paraná - UFPR (2001), mestrado financiado
por meio de bolsa de estudos fornecida pela CAPES; Pesquisador da Universidad de Zaragoza - Espanha,
com financiamento da CAPES (2007-2008 e 2013) e da Agência Espanhola de Cooperação Internacional para
o Desenvolvimento - AECID (2009-2012); Professor Adjunto dos Cursos de Graduação e Pós-Graduação (Mestrado)
em Direito da Faculdade Meridional - IMED e Professor Adjunto do Curso de Graduação em Direito da Pontifícia Universidade Católica do Paraná - PUCPR.
Atua na Linha de Pesquisa “Fundamentos Normativos da Democracia e da Sustentabilidade”, na área do Direito, com ênfase em Direito Eletrônico;
Inteligência Artificial e Lógica Jurídica; Governança Eletrônica e Democracia Digital; Filosofia do Direito.

E-mail: <[email protected]>.

Marlus Heriberto Arns de Oliveira

Doutorando em Direito na Pontifícia Universidade Católica do Paraná – PUCPR; Mestre em Direito
pela Pontifícia Universidade Católica do Paraná – PUCPR; Advogado.
E-mail: <[email protected]>.

Abstract

Eugenio Bulygin, in one of his first published work, dated 1965 (Der Begriff der Wirkamkeit), considers the concept of effectiveness, in which it develops a critique of the theory of Alf Ross and, in order to clarify this criticism, reflects on the design of Hans Kelsen on the effectiveness of Law. From that moment it gave a true debate between Bulygin and Ross, but it was not news, by the year 2002, nearly 20 years after the death of Kelsen (1881-1973), any response to this Bulygin respect of that article 1965 until the Hans Kelsen Institute of Vienna located a manuscript, probably written between 1967 and 1970, in which Kelsen polemic with Bulygin on the subject of the validity and effectiveness of the Law, so that only recently Bulygin could present its rejoinder the debate in question. The article addresses this debate between Bulygin and Kelsen, where it comes to issues such as the justification of the judgment and logic deductibility of legal rules; the idea of judicial competence; applicability; the distinction between legal system and order. Anyway, we have from this debate an important key to the refinement of the pure theory of Law, their logical relations, their intangible basic premises as legal positivism, ethical skepticism, the separation between “is” (Sein) and “ougth” (Sollen) and neutrality scientific.

Keywords: Controversy Bulygin-Kelsen on Validity and Effectiveness. Legal positivism. Ethical skepticism. Deductibility Logic of Legal Standards.

1 Introduction

Eugenio Bulygin, in one of his first published work, dated 1965 (Der Begriff der Wirkamkeit), reflects on the concept of effectiveness, in which it develops a critique of the theory of Alf Ross, and in order to clarify this criticism, reflects on the concept of Hans Kelsen on the effectiveness of law.

From that moment it gave an effective debate between Bulygin and Ross, but it had no news until 2002, almost 20 years after the death of Kelsen (1881-1973), any response to this Bulygin respect of that Article 1965 until the Hans Kelsen Institute of Vienna located a manuscript, probably written between 1967 and 1970 in which Kelsen polemic with Bulygin on the subject of the validity and effectiveness of the right, so that only recently Bulygin was able to present its rejoinder the debate in question.

The article addresses this debate between Bulygin and Kelsen, where it comes to issues such as the justification of the judgment and logic deductibility of legal rules; the idea of judicial competence; the applicability; the distinction between legal system and order.

Anyway, we have from this debate an important key to the refinement of pure theory of law, their logical relationships, their intangible basic premises as legal positivism, ethical skepticism, the separation between being and duty and neutrality scientific.

2 Assumptions Intangibles in the Thought of Eugenio Bulygin

There are no moral truths.

This is one of the main hypotheses that Bulygin holds for the refinement of the postulates of the Pure Theory of Law.

If there were moral truths to determine human conduct, the rules of positive law would be superfluous:

If one could be aware of absolutely just order whose existence is postulated by the doctrine of natural law, positive law would be superfluous, or rather meaningless. Faced with the existence of a just ordering of society, intelligible in nature, reason or divine will, the activity of legislators would amount to a foolish attempt to create artificial lighting in full sun (KELSEN, 1998, p. 18-19).

The separation between law and morality resulting from the relativity of the latter is a characteristic of legal positivism cut in the twentieth century. Gustav Radbruch, who became one of the staunchest advocates of legal positivism during the 1930s, gave clear preference to the right in case of conflict with the law, “... it is more important to the existence of the legal order that their justice, since justice is the second major mission of the law, the first being, legal certainty, peace” (RADBRUCH, 1930, p. 34).

The reason can lead to knowledge of the truth? The skeptical response, which denies such a possibility to reason, although present from classical antiquity, is accentuated greatly from the twentieth century.

According to Aristotle, philosophy is born from terror caused concerning the events in the world (ARISTOTLE, 2002 A 2, 982-29 - B 22, p. 11), the unpredictable, the unknown future. At first man creates the myth so that he realizes the existing chaos, seeking a sense of order. But the myths survive from beliefs that can easily be destroyed and don’t have the radicalism that philosophy, from its beginning, proposed to seek, that is “the idea of a knowledge that is irrefutable; and that is irrefutable not because society and individuals have faith in it or live without doubt it, but because he himself is able to refute all of his opponents. The idea of knowledge that can’t be denied nor by men nor by gods, nor by changing times and customs. An absolute knowledge, definitive, incontrovertible, necessary, undoubted” (SEVERINO, 1986, p. 29).

Through episteme, predicting and anticipating the becoming of life, man is freed from terror, making predictable what was unpredictable. The episteme appears as the great remedy against the terror of life.

It is precisely against the idea of philosophy as episteme that since ancient times through the Middle Ages and the modernity that will react the contemporary thinkers, among them the nihilism of Nietzsche seems to be the most radical.

Nihilism is precisely the refusal of response to the metaphysical whys because it realizes that there is no end to be achieved.

Indeed, the dogmatic attempts to establish knowledge were shattered. Dogmatic were accused of absolutism, fundamentacionists, objectivist. In contrast skeptics and their relativism gain new life and start to recover all their millenary tradition.

The thought of Kelsen, for example, in line with the relativism of skeptics, extracts the idea that science should be neutral, which leads to the search for a methodological purity that is based on the absence of value judgments.

But as adds Bulygin (KELSEN; BULYGIN; WALTER, 2005, p. 99), Kelsen is well aware of the dangers that threaten his theory, considering that “a positivist theory of law is faced with the task of looking for, between two extremes, both unsustainable, the right middle way. One extreme is the view that between the validity, as they should, and effectiveness, as a fact, there is no connection; that the validity of law is entirely independent of its effectiveness. The other extreme is the view that the validity of law is identical to its effectiveness” (KELSEN, 1960, p. 215).

In order to move away from both extremes that reputs unsustainable - natural law, for which the validity of the law has nothing to do with its effectiveness; and legal realism, for which the validity of the right coincides with its effectiveness - Kelsen proposes the thesis of separation, which says there is no conceptual relationship between law and morality; and the theory of normativity, which states the separation between law and the facts, since the law consists on rules irreducible into facts.

Not a few authors tried to point out the failure of Kelsen in seeking the middle path he desired. Mario G. Losano, for example, discusses the basic norm is not a norm in the Kelsen’s sense, a fact that, according to this author, would be directly linked to the limits of the pure theory of law:

Hans Kelsen says that the pure theory of law has as its object the normativity and not the value; and with that argument refutes the criticisms that were directed by natural law theories. But if we cover back all hierarchical structure of the rules that delegate validity to each other, we arrive at the fundamental norm, that is, to that underlying the kelsenian construction: it is the first source to validate the entire legal system. Kelsen himself, however, must admit that this is not a rule of law in the sense defined by the pure theory of law. For this, in fact, are legal only the norms laid by the legislator; the fundamental norm, in contrast, “must be assumed, because can not be put by an authority whose competence should rest on an even higher standard.” The word game does not solve the underlying problem: the fundamental rule is not a positive rule of law, it is something that the jurist accepts based on his evaluation of justice or opportunity, thar is, based on a choice that, for Kelsen is because it is unscientific therefore irrational (or rather subjective). If, however, the basic norm is a gnoseological expedient to foreclose on unitary system the various normative levels, we face a theoretical element (belonging to the world of nature, of “being”) that determines the existence of a standard (belonging to the world of law, “should be”); passage that Hans Kelsen considers incompatible with the premise of methodological purity. However, responding to his opponents, ... Kelsen will point without hesitation to the Pillars of Hercules of all legal theory, the extreme law boundary, beyond which opens a different world: “The problem of natural law is the eternal problem of what is behind the positive law. And those looking for an answer find - I fear - not the absolute truth of a metaphysical nor the absolute justice of a natural right. Who lifts that veil without closing his eyes sees himself fixed by the bulging eyes of Gorgon’s power” (LOSANO, 1996, p. XIX-XX).

In that same critical line is Celano’s thought (1999), according to whom both, the thesis of separation as the thesis of normativity, result unsustainable inside the pure theory.

Bulygin, in turn, acknowledges that there is no doubt that many of kelsenian formulations are, in fact, incompatible with his normative positivism, reason why his proposal is to reconstruct the pure theory of law, the assumption of its defense, including against Kelsen in the points where his claims result incompatible with the following theses, which are postulated as intangible:

a) legal positivism, ie, all law is positive law.

b) moral skepticism, ie, no norms are “true”, norms generally and moral norms in particular are neither true nor false.

c) separation of “is” (Sein) and “ougth” (Sollen), ie, if something is, it does not follow that it outh to be, and, vice versa, if something ougth to be, it does not follow that it is.

d) value-free legal science, ie, legal science consists in describing the positive law, not in evaluating it, evaluating positive legal system as just or injust is a matter of politics, not science.

(KELSEN; BULYGIN; WALTER, 2005, p. 101-102).

Having as intangibles the premises above, Bulygin try to refine the pure theory of law in retlation to the question of the validity and effectiveness, allowing him to save the theory of the criticisms made by Losano, Celano and, especially, traps that Kelsen armed to himself.

3 Proposals for Reconstruction of the Pure Theory of Law of Eugenio Bulygin

The most important conclusions Bulygin came to in refinement of the Pure Theory of Law (cf. KELSEN; BULIGYN; WALTER, 2005, p. 117-118) are that the term validity is ambiguous in Kelsen. A distinction must be made at least for two very different concepts listed with this label: belonging and obligation.

Membership is a descriptive concept. The statement belonging to the N standard of S system expresses a true or false proposition.

Mandatory is a normative concept. The N statement is binding rule expresses a standard that is neither true nor false.

If membership is interpreted as existence of a rule, then it is necessary to distinguish between system and order. A regulatory system is a set of standards relating to a temporary time. A policy is a set order (timing) of regulatory systems. This forces to distinguish between membership of a rule to a system and a system belonging to an order.

Given the ambiguity of the term validity, the problem of the relationship between validity and effectiveness must be treated separately; between belonging and effectiveness there is no connection.

For the definition of ownership, the assumption of the basic rule is completely unnecessary. Only for validity as a binding force Kelsen needs the basic norm.

The concept of binding force is interpreted by many authors (Ross, Raz, Nino, Losano, Celano) as a moral duty to obey the law, which is incompatible with positivism of Kelsen.

The obligation can be interpreted as a legal obligation, for which Bulygin proposes the term applicability. A standard is applicable when a positive legal norm (called standard application) establishes the duty (or faculty) of the judge to apply to a particular case.

Applicability may not be confused with belonging. Judges may be required or permitted to implement rules that do not belong to their system or even their legal order.

The analysis of the formal structure of both concepts shows that applicability is very different from the obligation, as understood by Kelsen. His definition of relative mandatory presupposes the absolute obligation, which leads to the assumption of the basic rule. The hypothesis of this basic rule is unnecessary for applicability.

4 Logical Relations and Law

Does the judge create law?

Theorists of law, to answer that question, traditionally have two extreme and conflicting opinions, one of which emphasizes the role of standards and limits the judicial decision to a mechanical operation, which called Bulygin judicial syllogism theory (KELSEN; BULYGIN WALTER, 2005, p. 35).; and another theory denies almost all the importance of standards and emphasizes the creative role of the judge.

According Bulygin had already noticed in 1965 (cf. KELSEN; BULYGIN; WALTER, 2005, p. 36), both concepts share a common mistake not to distinguish the logical and psychological problems:

A legal decision is normatively founded, if it can be logically derived from certain rules (along with descriptive statements of facts). The substantiation or justification legislation is, therefore, a matter of logic. The logical relationship between the rules and the decision is the logical implication; rules involve the decision or (which is the same) decision is deductible by logical laws. Linking the judge to “law and justice” [...] consists precisely in that the judge must justify his decisions by legal standards. In almost all modern legal systems judges are required to base their judgments, that is, to explicitly justify them.

However, this logical relationship between the rules that justify the decision and the latter is confused, often with the causal motivation of the judge. What are the reasons that determine the judge’s decision is a psychological issue that would not affect at all on the grounds of the judgment.

If we consider the difference between logical and psychological problems, it becomes clear that the two theories outlined above are only apparently antagonistic, as they move in different planes (KELSEN; BULYGIN; WALTER, 2005, p. 37-38).

So on the one hand, “the fact that the judgment is deductible from the rules does not follow at all that the activity of the judge is mechanical” (KELSEN; BULYGIN; WALTER, 2005, p. 38), and on the other side the realist critique is wrong to pretend to dissociate the deductive logic of the application of law. The error consists in the fact that realism could not make out what amounts to explain and justify a decision, and also there is a difference between internal justification and external justification. The distinction between explanation and justification is brought by Manuel Atienza (1993, p. 125):

To clarify the first couple of concepts [explain and justify], you can use a distinction that comes from the philosophy of science, between the context of discovery and context of justification of scientific theories. So, on the one hand the activity consisting of discover or enunciate a theory and, according to popular opinion, it is unsuitable for a logical analysis; all that suits here is to show how it is generated and developed the scientific knowledge, which is a task for the sociologist and historian of science. But on the other hand, it is the consistent procedure to justify or validate the theory, that is, comparing it with the facts in order to show its validity; the latter task requires an analysis of (though not only logical) logical type and is governed by the rules of the scientific method (which, therefore, do not apply in the context of discovery).

That is, the distinction can be used in the field of application of the law, and so there is possible to conclude that one thing is the process by which a given premise or conclusion is established, which is very different from the procedure that involves justifying the aforementioned premise or conclusion.

It should be noted that, generally, the courts do not have to explain the reasons why they decided this or that way, having barely justify their decisions.1

Therefore, in view of the distinction it is easy to verify the misunderstanding incurred realistic theories that reduce validity and efficiency, so that for them the decision making process of the courts is not made according to a logic model.2

The second aspect that realistic theories did not take into account was the fact of not having perceived, as is mentioned above, that there is a difference between internal justification and external justification.

The internal justification is the way that goes from the normative premise (major premise), which must generally be subsumed the phatic premise (minor premise) until a valid conclusion is deducted.3

No legal decision may dispense with that kind of justification.

Well, the internal justification is only sufficient when neither the rule nor the verification of the facts raise a reasonable doubt.

It happens that in many cases the establishing of normative premise and / or phatic premise involves a problematic issue, making necessary the use of additional arguments for the premises that are to be used, those arguments will probably not be purely deductive. That kind of argument is what is called external justification.

In this line of reasoning, Bulygin shows that the conclusions reached by the two opposing positions - syllogism legal theory and legal realism - are not incompatible, but often they are regarded as conflicting, and even contradictory opinions:

It is a very widespread and entrenched prejudice among jurists that relates the logical relationship of foundation with the doctrine of the mechanical activity of the judge. Both supporters and opponents of the theory of the syllogism often make the same mistake, arguing as follows: “the sentence is deductible from the rules, therefore, the judge is an automaton” or “the judge is not a automaton, therefore, the judgment is not deductible from the rules.” (KELSEN; BULYGIN; WALTER, 2005, p. 38, note 31).

Indeed, “the knowledge of the factors that motivate the judge is of great importance for practical lawyer who seeks to influence the judge and predict the sentence; knowledge of standards is essential for the judge or the lawyer who tries to justify or criticize the sentence” (KELSEN; BULYGIN; WALTER, 2005, p. 39).

5 Applicability and Logic

There are cases in which the choice of assumptions that are subject to deduction may lead to different results, a fact which is inconsistent with classical logic and requires the use of some other underlying logic, since there is an underlying logic behind any reasoning even applied intuitively.

Bulygin, in addressing the normative concept of validity, presents the idea of applicability so that “avoid both the overlap between binding and legal duties, such as moral connotation. The normative validity can be seen as a legal duty and not a moral one [...]. A standard is applicable when a judge should apply to a particular case” (KELSEN; BULYGIN; WALTER, 2005, p. 110).

Suppose a case where the legal duty to apply points to conflicting solutions together. Imagine prison inmates under custody of any state authority decide to make a hunger strike in order to pressure the government to meet any claim; presume also that these prisoners have expressed the intention to bring the strike to the bitter end, that is, they are ready even to die if their claims are not met.

Consider that are applicable within the meaning of Bulygin, both the right to free expression of thought and to guarantee the right to life, so a dilemma at least three legal duties, affects the judge will be incompatible: a) the administration is obliged and authorized to feed the prisoners by force, although they are in a state of full consciousness and manifest therefore their refusal to respect; b) administration is only allowed to take such a measure when the prisoner has lost consciousness; c) administration is not authorized to take such measures, even in the latter case.

Classical logic does not tolerate contradictions, so that no classical systems have been developed to try to treat cases like the example.

Indeed, one of the recent developments in the field of deontic logic is non-classical formulation and different legal systems with two-dimensional deontic paraconsistent deontic logic operators, that is, moral and legal distinctive operators.

For the formulation of such systems contributed several reasons, including the development of a logic that includes standard and valuation notions and the analysis of purely logical connections between sets of moral, legal and axiological statements, without prejudging relations of another kind that may exist between those sets (cf. VERNENGO, 1989).

Among the systems, it will be displayed just the calculation L1 to formally represent such decisions [L1 system presented here is the system developed by Nicola Grana (1990, p. 74-77). In this work they can be found further details on the various systems of paraconsistent deontic logic and recent developments, as well as the calculation of C1 DA COSTA, that serve as base system].

SYSTEM L1

L1 is built on the calculation C1 from Da Costa [Presented at the end, in the Appendix.] (This is a conservative extension of C1) as propositional calculus standard more Om (required morally) and Oj (required legally) as primitive operators, Fj (prohibited legally), Fm (forbidden morally), Pj (allowed legally), Pm (allowed morally) as derivatives operators and has the following specific assumptions: [Aº abbreviated ¬ (A ^ ¬ A), where ¬ is called weak denial and ~ is called strong denial, equivalent to the negation of classical propositional logic [See Appendix].

DEONTIC POSTULATES

Om (A→B) →(OmA→OmB)

OmA→¬Om¬A

OmA→(OmA)

A/OmA

LEGAL POSTULATES

Oj (A→B) →(OjA→OjB)

OjA→¬Oj¬A

OjA→(OjA)°

A/OjA

MIXED POSTULATES

OjA→OmA

OmA→PjA

THEOREM 1

L1 can be derived:

Where: FmA=def Om¬A

FjA=defOj¬A

~FmA=defOm~A

~FjA=defOj~A

|—PmA→PjA

|—FmA→¬OjA

|—FjA→FmA

|—OjA→PmA

|—Om (OjA→OmA)

|—Oj (OjA→OmA)

THEOREM 2

Are theorems of L1:

T1 OmA→Om(AvB)

T2 OjA→Oj(AvB)

T3 FmA^A°→¬OmA

T4 FjA^A°→¬OjA

T5 OmB→Om(AvB)

T6 OjB→Oj(AvB)

T7 A°→¬(OmA^FmA)

T8 A°→¬(OjA^FjA)

T9 Om~A→~OmA

T10 Oj~A→~OjA

T11 Om(A^B)←→OmA^OmB

T12 Oj(A^B)←→OjA^OjB

T13 OmA^Om~A→OmB

T14 OjA^Oj~A→OjB

T15 ~(OmA^~OmA)

T16 ~(OjA^~OjA)

T17 OmA^Om(A→B) →OmB

T18 OjA^Oj(A→B) →OjB

THEOREM 3

In L1 are not valid the following diagrams:

1. 1- Om¬(A^¬A)
2. 2- Oj¬(A^¬A)
3. 3- Om (A^¬A)→OmB
4. 4- Oj (A^¬A)→OjB
5. 5- OmA^Om¬A→OmB
6. 6- OjA^Oj¬A→OjB
7. 7- FmA^Fm¬A→OmB
8. 8- FjA^Fj¬A→OjB
9. 9- FmA→¬OmA
10. 10- FjA→¬OjA
11. 11- ¬(FmA^PmA)
12. 12- ¬(FjA^PjA)
13. 13- Om (¬A^¬¬A)→OmB
14. 14- Oj (¬A^¬¬A)→OjB
15. 15- FmA^Fm¬A→FmB
16. 16- FjA^Fj¬A→FjB

In justification of the first position (the administration is authorized to feed the prisoners by force, even against their will), they could invoke content of natural law, including the right to life, both ontological terms and legal terms -positive, as superior to any other rights of the human person. Basically that is the plain meaning of the Joint postulate L1, indicated above, OmA→PjA. That postulate does everything moral duty a legal permit, building upon the natural law currents consider moral standards (in this case, the right to life) imply the invalidity of legal rules incompatible with it. In that case, natural law is considered superior to the positive orders revoking the moral autonomy of the individual. So, it would not fit the striker have the right of disposal of his own life even he would be immune to public action of the administration? [A different interpretation of the same premise as well as other systems of deontic paraconsistent logic with moral and legal practitioners, you can find it in Puga, DA COSTA; VERNENGO, 1990, p. 22.].

Highlight the two main characteristics of the L1 system: a) the system does not exclude moral or legally contradictory situations (also called deontic dilemmas [For more details on deontic dilemmas, cf. Puga, 1985]) and; b) for that system, from a contradiction is not possible to derive any proposition, as happens with classical logic, the contradiction becomes trivial system.

The two characteristics are expressed by Theorem 3. The formulas 1, 2, 9, 10, 11 and 12 show the first characteristic, and the remaining formulas show the second characteristic. In general, the classical principle of non-contradiction ¬(A^¬A) is not a valid formula in the system.

So it is possible to say that the underlying judicial assessment of the case of the hunger strikers logic is a system L1. In that system, the solutions 1, 2 and 3, contradictory, can be represented intuitively within the same logical system, without this causing the collapse of the system, mainly the intermediate position 2. standard deontic logic systems, the formulas of Theorem 3 are valid L1, which does not allow the representation and admission of situations and contrary decisions together.

In that system, by allowing any of the three possible solutions, it necessarily should exclude the other two of said system, which does not happen in the case of the adoption of systems of deontic paraconsistent logic, which allowed contradictions without loosing the logical value of inferences (the condition of non-trivial).

Standard deontic logic systems originate, also known paradoxes of the Good Samaritan, of the derivative liability and Ross, among others, to the exclusion situations and contradictory decisions, for example, an action that is mandatory and is not at the same time (OA^O¬A).

Thus, L1 express indirectly, in its set of valid formulas, diagrams of reasoning used by lawyers and various courts, in which the idea of applicability, in the sense defined by Bulygin, may be treated in logical terms. Moreover, the contradictions should not be necessarily excluded from the legal rationality, because contradictions and inconsistencies are not contrary to reason.

Paraconsistent logics, for example, are suitable to serve as the underlying logic of judicial decisions, because “in a given context, the underlying logic is unique” (DA COSTA, 1994, p. 19). The paraconsistent logics have a broader than the domain of classical logic, because they assume that contradictions can be part of rational contexts.

6 Concluding Remarks

Bulygin assumed as intangible assumptions: a) legal positivism, ie, all law is positive law; b) moral skepticism, ie, no norms are “true”, norms generally and moral norms in particular are neither true nor false; c) separation of “is” (Sein) and “ougth” (Sollen), ie, if something is, it does not follow that it outh to be, and, vice versa, if something ougth to be, it does not follow that it is; and d) value-free legal science, ie, legal science consists in describing the positive law, not in evaluating it, evaluating positive legal system as just or injust is a matter of politics, not science.

From these premises, Bulygin reconstructs the pure theory of law, in regard to the issue of validity, it points out that this term is ambiguous in Kelsen. According Bulygin, one can distinguish at least two very different concepts listed with this label: belonging and obligation. Membership is a descriptive concept. The statement belongs to the N standard S system expresses a true or false proposition. Mandatory is a normative concept. N The statement is binding rule expresses a standard that is neither true nor false.

If membership is interpreted as existence of a rule, then it is necessary to distinguish between system and order. A regulatory system is a set of standards relating to a temporary time. A policy is a set order (timing) of regulatory systems. This forces distinguish between membership of a rule to a system and a system belonging to an order.

Given the ambiguity of the term validity, the problem of the relationship between validity and efficacy must be treated separately; between belonging and effectiveness there is no connection.

For the definition of ownership, the assumption of the basic rule is completely unnecessary. Only the validity and enforceability need Kelsen’s basic norm.

The concept of binding is interpreted by many authors (Ross, Raz, Nino, Losano, Celano) as a moral duty to obey the law, which is incompatible with positivism of Kelsen.

But the obligation can be interpreted as a legal obligation, for which Bulygin proposes the term applicability. A standard is applicable when a positive legal norm (called standard application) establishes the duty (or faculty) of the judge to apply to a particular case.

Applicability must not be confused with belonging. Judges may be required or permitted to implement rules that do not belong to their system and not even their legal order.

The analysis of the formal structure of both concepts shows that applicability is very different from the obligation, as understood by Kelsen. His definition of relative mandatory presupposes the absolute obligation, which leads to the assumption of the basic rule. The hypothesis of this basic rule is unnecessary for applicability.

Finally, it was seen that the concept of applicability of Bulygin also allows to verify the logical relationships between legal systems, and even in front of contradictions, non-classical logic, systems example of paraconsistent logic, they can be applied.

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VERNENGO, R.J. Sobre algumas relações lógicas entre sistemas normativos jurídicos e morais. In: Revista Brasileira de Filosofia, XXXVIII, n. 155, São Paulo: 1989.

Appendix

It will be presented, in an abbreviated manner the syntactic part of C1 calculation. Verily these calculations that serve as a basis for paraconsistent systems composing a calculations ranking Cn ,1£n£w, and each one is weaker than its preceding, originally developed by Newton Carneiro Affonso da Costa. The calculations must satisfy the following conditions a) include as maximum as possible schemes and rules of inference of classic calculation b) the principle of non-contradiction (A ^ A) must not be valid; and c) from two contradictory A ^ A must not be possível, in general, deduct an arbitrary formula.

C1 has the following postulates, where A is the abbreviation of (A ^ A):

1- A→(B→A)

2- (A→B)→((A→(B→C))→(A→C)

3- A,A→B/B

4- (A^B)→A

5- (A^B)→B

6- (A→(B→(A^B))

7- A→(AvB)

8- B→(AvB)

9- (A→C)→((B→C)→(AvB→C))

10- Av¬A

11- ¬¬A→A

12- B°→((A→B)→((A→¬B)→¬A))

13- A°^B°→(A→B)°

14- A°^B°→(A^B)°

15- A°^B°→(AvB)°

THEOREM 1

C1 all the rules of classical propositional calculus deduction of Theorem 2 of the book Introduction to Kleene Metamathematics are true, except for the rule of contradiction, that C1 se states:

If G,A|—B°, G,A|—B y G,A|—¬B, then G|—¬A.

THEOREM 2

Among others, the following schemes are not valid in C1

¬A→(A→B),

A→(¬A→B),

(A^¬A)→B,

(A→B)→((A→¬B)→¬A),

(A←→¬A)→B,

¬(A^¬A),

(A→B)→(¬AvB),

(A→B)→(¬B→¬A),

¬A→(A→¬B),

A→(¬A→¬B),

(A^¬A)→¬B,

A→¬¬A,

(A←→¬A)→¬B,

((AvB)^¬A)→B,

A←→¬¬A.

Proof: The following matrices are used, in which the distinguished values are 1 and 2:

A^B:

A	B	1	2	3
1		1	1	3
2		1	1	3
3		3	3	3

AvB:

A	B	1	2	3
1		1	1	1
2		1	1	1
3		1	1	3

A→B:

A	B	1	2	3
1		1	1	3
2		1	1	3
3		1	1	1

¬A:

A	¬A
1	3
2	1
3	1

In C1 the class of propositions is decomposed into two categories: in the class of well behaved, every valid formula in the classical calculation is valid in C1; if A is badly behaved, it may have A^¬A. They are also distinguished two types of denials: strong denial, which has the same properties of classical negation; and weak denial, which supports contradictions. A Depending on the context, it can be used either denial.

Thus, Paraconsistent calculations were not made to eliminate classical logic, but to expand their domains and include it as a special case.

The interested reader is referred for further technical details on the consultation of C1 (DA COSTA, 1993).

O debate entre Bulygin e Kelsen sobre a validade
e a eficácia do direito

Resumo

Eugenio Bulygin, em um de seus primeiros trabalhos publicados, datado de 1965 (Der Begriff der Wirkamkeit), tece considerações sobre o conceito de eficácia, em que se desenvolve uma crítica à teoria da Alf Ross e, com o intuito de aclarar essa crítica, tece considerações sobre a concepção de Hans Kelsen sobre a eficácia do direito. A partir daquele momento se deu um debate efetivo entre Bulygin e Ross, porém não se teve notícia, até o ano de 2002, quase 20 anos após o falecimento de Kelsen (1881-1973), de alguma resposta deste a Bulygin relativamente àquele seu artigo de 1965, até que o Instituto Hans Kelsen de Viena localizou um manuscrito, provavelmente redigido entre 1967 e 1970, em que Kelsen polemiza com Bulygin acerca do tema da validade e eficácia do direito, de maneira que apenas mais recentemente Bulygin pôde apresentar a sua tréplica no debate em questão. O artigo trata desse debate entre Bulygin e Kelsen, em que se trata de temas como a justificação da decisão judicial e a dedutibilidade lógica das normas jurídicas; a ideia de aptidão judicial; a aplicabilidade; a distinção entre sistema e ordem jurídicos. Enfim, tem-se a partir desse debate uma importante chave para o refinamento da teoria pura do direito, de suas relações lógicas, das suas premissas básicas intangíveis como sendo o positivismo jurídico, o ceticismo ético, a separação entre ser e dever e a neutralidade científica.

Palavras-chave: Polêmica Bulygin-Kelsen sobre Validade e Eficácia. Positivismo Jurídico. Ceticismo Ético. Dedutibilidade Lógica das Normas Jurídicas.

Recebido em: 01/09/2015

Aprovado em: 29/10/2015

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