Unclosed questions in non-classical logic (in memory of Professor D. V. Pivovarov)

Abstract

As a methodological tool of sorts in the memorial paper makes use of reconstruction of professor Pivovarov’s talks, which often displayed genuine, persevering and always critical interest in non-classical logic. The questions at hand are the question of scientific status and philosophical consistency of deuniverslization of classical logic. The various types of logical systems, whose co-existence was brought about during the XX century, has become an actual phenomenon, insistently calling for a broader philosophical, scientific, and even cultural reflection on the nature of contemporary logic as a body of knowledge. Among the questions three touch upon the problem of the status of non-classical logic, considered as the part of humanities: Should non-classical logic be taken as a response to mathematical logic’s absolute «inhumanity»? Mathematization of logic is related to another crisis of the foundations of mathematics – could one imply the crisis of ultimate methodological principles of social studies and humanities to be the reason for deuniversalization of classical logic? Does non-classical logic fit the natural reasonings? Three other questions address the philosophy of logic: Does contemporary logic – whether classical or not – build upon mathematics still belong to philosophy? Is there distinctive philosophy of non-classical logic yet? Could non-classical logic still serve as the normative discipline, as the «canon of thinking»? The very character of the questions doesn’t lead to any closed, definitive answers. Be that as it may and, having the current scientific studies philosophically reflecting on the logical pluralism backing us up, we aim here at a coherent and a consistent examination of philosophical aspects and problems of non-classical logic. The examination resulted in formulating several key results: non-classical logic’s development effectively was a response to semantic and metatheoretical problems of mathematical logic, that was coming to be, but a kind of «humanistic» aspect is the fundamental non-elimination of the subject in the semantics of the corresponding intensional logics; the actuel stance is supported that various types of reasoning do not correspond to the subject of logic, but can be (and traditionally are) objects of application of various logics as intellectual tools; extrological stimulations and especially intrological resources of logical investigations affect significantly the current understanding of philosophical nature of logic; the question of alterations of ontological and epistemological premises, which underlie the various logical systems – an essential one for the philosophy of logic – is reformulated as in effect being the question of correctness and efficiency of some particular tools in the logical arsenal; logical analysis in general is to be methodologically receptive to different contexts, their specifics in order to avoid destructive conflicts, threatening to eliminate the uniqueness of said contexts. The author voices a hope, that the critical assessment of the results presented as to their being valuable and sound will make the work a proper incentive for perspective and productive discussion of diversity of logic.

Keywords

• logical pluralism
• deuniversalization of classical logic
• ontological and epistemological premises of logical systems
• non-classical logics