In the paper the problem which A. Tarski fairly recognized a priori as infeasible is discussed: about an explication of the intuitive perceptions connected with concept of consequence. Any definition of the relation of consequence bears traits of arbitrariness, and it is connected, first of all with a choice of the language, a corresponding set of logic constants and interpretation of theirs. These logic explications, dealt not with a real discourse, but with its abstract models. Intuitions which stand up for expression «The consent with one statement is necessary attracts the consent with other statement» are not exhausted by the forms presented in the set of the valid arguments of logic. In the paper some philosophical aspects of logic consequence from the point of view of logical pragmatics, important for understanding of the relation of consequence in a natural language are mentioned. The question which is of special interest for me consists in the following: whether figures of speech contain relation of consequence.
Yesenin-Volpin’s theory of modalities eliminates any beliefs from the foundations of mathematics and humanitarian knowledge. Some methods of moral and legal discussions are fuzzy and poorly formalized. The human activities on construction of theories and moral reasoning are submitted to the rules. Both cases include permissions, orders and forbidding different acts. The same act may be allowed in one situation and forbidden in the other situation. Yesenin-Volpin calls the set of orders correlated with suitable situations as “tactics”. He defines hierarchy of tactics which explains the principles of Kant’s autonomic ethics and legislative systems. All rational activities are described by modal words of different groups. Deontic modalities (to be bound, to be permitted, to be forbidden) have no similar axioms for alethic modalities (necessary, possible, impossible). The general meta-theory explains the relations between all kinds of modalities and grounds the construction of any strict mathematic or ethic theory.