Paradoxes of Implication and the Issue of Provability
Abstract
Abstract. One of the significant obstacles in the application of logical criteria of argumentation provability is a number of paradoxes associated with the presentation of the logical consequence relation in the form of implicative expressions. However, numerous attempts to solve this problem did not lead to significant positive changes. Therefore, the search for ways of leveling the mentioned paradoxes still does not lose its relevance. In the course of the study, the following methods were used: comparative analysis (to identify common points and differences in approaches to the interpretation and solution of the analyzed problems), inductive generalization (in order to determine the dominant trends in modern studies of the logical foundations of effective construction of legal argumentation), critical analysis (when evaluating common methodological concepts in this field from the point of view of their validity and logical acceptability), logical formalization (for an unequivocally clear presentation of the fundamental foundations of the rationalization of evidential procedures in generalized formulas), logical-semantic analysis (when determining the conditions of relevance for the application of the methodological tools of modern logic in the process of building an argument). The article provides a logical-semantic substantiation of the differences between the functional content of the implication and the relation of logical inference. In view of their substantive differences, potential ways and means of avoiding the difficulties of applying logic in the proof process, caused by paradoxes of implication, are proposed. It has been established that the mentioned paradoxes will not arise if the logical condition for the evidentiality of arguments is not the functional content of the implication, but the criterion of the entry of the domain of definition of the system of given grounds into the domain of definition of a substantiated conclusion. In this case, there will be no collisions between natural and artificial linguistic means of constructing analytical reasoning. In addition, in procedural jurisprudence, it is expedient to evaluate the relationship of logical consequence between the evidence, on the one hand, and the subject of proof, on the other hand, not only in terms of the presence or absence of this relationship (as assumed by classical ambiguous logic), but also from the point of view of the degree of confirmation of what is being proven position with the given evidence (using methods of probabilistic assessment of statements and relationships between them). The proposed approach is aimed at expanding the applied potential of logic as a factor in the rationalization of evidentiary procedures.
Keywords: legal argumentation; logic of argumentation; problem of proof; criteria of proof; logical deduction; paradoxes of implication.
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