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1 | The paper propose a variant of a communicative-pragmatic approach to determining the meaning of proposition, expressed by agents in the discussion. We intend to: 1) to offer an interpretation of the process of persuasion, according to which it can be recognized as successful – even if it pays tribute to the fundamental problem of sign communication and admits that agents in the process of communication transmit only signs to each other, and the meanings of these are inaccessible to the interlocutor; 2) to show that popular contemporary approaches (Pragma-dialectical approach, AGM-approach, DBR-approach, etc.) to the process of persuasion do not offer this kind of interpretation the process of persuasion; 3) to establish precise and verifiable conditions which are necessary and sufficient to admit the process of persuasion in our interpretation as successful. Our approach uses contemporary approaches to the interpretation of the meaning of the proposition (first of all, the mental holism – M. Harrell, N. Blok, etc.), and also extrapolates actual structuralist approaches to the understanding of mathematical objects in the philosophy of mathematics (D. Hilbert, M. Resnik, S. Shapiro) on sign communication in a situation of persuasive argumentation. We reject the solution to the problem of sign communication, which in fact consists that it is quite possible to transfer visual images regardless of their content or meaning, which implies that the communication of agents is still possible through the transmission of such images. This solution, in fact, suggests discussing unsigned rather than signed communication, but, first, the transfer of beliefs as linguistically expressed objects is not possible in this case, and, second, there are strong arguments in favor of the fact that even the content-free objects of different agents are different, which also makes transfer impossible. We determine the rhetorical meaning of the proposition expressed by agents in the discussion. Such a meaning is also a proposition, the antecedent of which is a complete description of the agent's belief system, and the consequent is the original proposition. We also admit the persuasion process as rhetorically successful if, at the end of this process, the audience cannot object to the persuader's thesis, on the assumption that the persuader attaches some (at least rhetorical) significance to his or her suggestions and those of the audience. The fact that the rhetorical meaning does not depend on the meaning attributed to their words by the interlocutors themselves, allows us to show that, despite of the problem of sign communication the persuader can have a rhetorical success. Since our approach is focused solely on rhetorical success in the process of persuasion through sign communication, our interpretation of the process of persuasion has a communicative and pragmatic character. As befits a pragmatic approach to the persuasion process, our approach does not require the persuader to express only those proposition that he himself understands and considers to be true, and those arguments that he himself understands, considers its as correct and acceptable. Keywords: argumentation theory, argumentative belief, change of beliefs, meaning of beliefs, communication, pragmatics, mental holism, structuralism in the philosophy of mathematics, formalism in the philosophy of mathematics | 991 |