From Philosophy to Theory of Information

摘要

This is an attempt to develop a systematic formal theory of information based on philosophical foundations adequate for the broad context of pre-systematic concept of information. The existing formalisms, in particular that commonly called information theory, consider only some aspects of information, such as its measure. In spite of spectacular successes of Shannon’s entropy and its generalizations, the quantitative description did not help in the development of the formal description of the concept of information itself. In this paper, the brief review of the contexts in which the term information is being used is followed by similarly brief presentation of philosophical foundations incorporating such aspects of information as its selective and structural manifestations, information integration and semantics of information presented in more extensive form in other publications of the author. Finally, based on these foundations, a mathematical formalism is proposed with an explanation of its relationship to the philosophical concepts associated with information. The formalism utilizing mathematical concepts from the theory of closure spaces and associated with them complete lattices of closed subsets playing the role of generalized logic of information is taking into consideration the selective and structural manifestations of information. Since the original source of inspiration in the development of the formalism was in quantum logics, an outline of concepts in this domain is included in the appendix.