Abstract
The Constitution is considered as an informal axiomatic system. The strategy proposed by the authors rests on the following propositions: (1) axioms are considered as contextual definitions of those concepts by means of which they are formulated; and (2) the main requirement for this type of system is internal consistency. The first proposition is necessary for considering the Constitution as an informal axiomatic system, while the second is sufficient, because the approach proposed, apart from consistency, must certainly consider the requirements for formal axiomatic systems, such as independence and completeness. The authors argue that the Constitution can be compared to axiomatic constructions in modern science in the sense that is given in the research on the logic and methodology of deductive sciences. This analogy is appropriate to the extent to which constitutional provisions are interpreted as the basic elements of the legal system, just as in the formal sciences axioms are regarded as basic principles that define the main features of the formal system. This means that the Constitution itself is seen as coherent, consistent discourse that contextually defines the meaning of the basic terms of the legal system.
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Notes
A similar thesis can be found in an essay by Scott Brewer, “Law, Logic, and Leibniz. A Contemporary Perspective”, especially in the section “Leibniz and Legal Axiomatics: The American (Mis)undersanding”. Brewer argues that “If the law of a country—or a universal ‘natural law’—could be axiomatized, then there would be for law, as for geometry, an effective method of testing the acceptability of any proof that a lawyer or judge offered” (Brewer 2013, p. 201). Moreover we agree with Brewer’s proposition that “logic, including but limited to deductive logic, can be a tool of great value for clarifying, explaining, and articulating law” (Brewer 2013, p. 201). But here we try to prove only that the Constitution can be compared to axiomatic constructions in modern science in the sense that is given in the research on the logic and methodology of deductive sciences, and that it can be considered an informal axiomatic system. For this reason, we do not try to formalize the legal language or to axiomatize the legal system.
The problem of the definition of legal concepts was first conceptualized and thoroughly researched by H. L. A. Hart in his article “Definition and Theory in Jurisprudence”, and later in his book The Concept of Law.
We suppose that internal consistency is the main requirement for the axiomatic system, but it does not imply that other requirements such as completeness and independence are not necessary, rather they are complementary. The requirement of internal consistency is discussed in more detail in the fourth section “The Constitution as a Fictional Discourse: Requirement for Internal Consistency”.
It may seem that the same idea is repeated; however this is not the case. It is on one hand a reference to a consistency of linguistic expressions with content of the law itself. On the other, it is a reference to a consistency of linguistic expressions in the practice of the enforcement of the law.
By lack of “more general provisions” with respect to constitutional provisions, we mean their absence in domestic law itself. Can provisions of international law act as more general provisions? There are conceptions that answer this question affirmatively. However, here we are only interested in the construction and operation of the model of a system of law according to the abovementioned principles and not the issue of co-relation (or the possibility of deduction) of the provisions of international and domestic law.
A, E, I, and O are the designation of categorical propositions: A—universal affirmative, E—universal negative, I—partitive affirmative, and O—partitive negative proposition.
Here and below a symbolic notation of modern formal logic is used, where x is the variable, & and ∼are propositional connectives corresponding to “and” and “not”, and “∃” is an existential quantifier that is read as “there is such…”; parentheses and commas are service symbols.
The square of opposition is a scheme expressing the relationship in terms of truth and falsity between universal affirmative, universal negative, partitive affirmative, and partitive negative propositions, which have one and the same subject and one and the same predicate, and they are denoted by the letters A, E, I, and O.
Other attempts to axiomatize the legal system can be found in works by Alchourron and Bulygin (1971, 1981, pp. 95–124), Wright (1963, 1968) and Ferrajoli (2012). However, these works are mostly about formalization of certain aspects of law with the help of deontic operators. Here we try to prove that the Constitution as an informal axiomatic system is the foundation of the legal system.
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Acknowledgements
We would like to thank Jean Kollantai for her review of style and anonymous reviewers who commented on an earlier version of this paper.
Funding
The work on this paper was supported by the Council for Grants of the President of the Russian Federation for State Support of Young Russian Scientists, Award Number MD-4664.2016.6, and by the Tomsk State University Competitiveness Improvement Programme.
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Ogleznev, V., Surovtsev, V. The Constitution as an Axiomatic System. Axiomathes 28, 219–232 (2018). https://doi.org/10.1007/s10516-017-9359-x
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DOI: https://doi.org/10.1007/s10516-017-9359-x