The Nature of Logical Knowledge and Foundations of Logical Systems

Abstract

In this paper, I address a wide range of problems related to the nature of apodictic knowledge and foundations of logic. In so doing, a primary focus is on ideal entities and connections, forming a ground for logical systems. The core component of the conception presented is a so called ‘generalized approach to semantics formation’, which presupposes that (i) every statement can be associated with a pair of sets representing ‘extension’ and ‘anti-extension’ of a statement, correspondingly; (ii) these sets consists of differently interpreted possible worlds. A variation of requirements for relations between these sets opens possibility to define logical consequence in a different way that, in turn, results in a variety of logical systems. An important consequence of a generalized approach is an identification of two types of epistemological presuppositions: those connected with conceptual apparatus of cognitive agent, and ontological commitments. The final section contains a discussion of perspective for logic and possible transformations of its subject-matter and methods. DOI: 10.21146/2074-1472-2017-23-1-105-120