Problems of Information in Dialectical Materialism (Translated from English)

The article introduces a complete translation of Professor P. P. Kirschermann's "Problems of Information in Dialectical Materialism". It was originally published in the respectable sovietological journal "Studies in Soviet Thought" in 1968. Professor P. P. Kirschermann's article is a preview of his monograph "Information und Widerspiegelung. Zu Problemen der Kybernetik und des Diamats", published in 1969. Its English translation appeared a year later and was published by D. Reidel Publishing Company as "Information and Reflection: On Some Problems of Cybernetics and how Contemporary Dialectical Materialism Copes with Them". Professor P. P. Kirschenmann worked under the guidance of the famous Polish philosopher J. M. Bochenski in the framework of a special program implemented by the Institute for Eastern European Studies at the University of Fribourg, Switzerland. In his article, he identified the main features of dialectical and materialistic reflection of information and demonstrated their connection with the fundamental principles of the dialectical materialism. Professor P. P. Kirschenmann focused on the existence of internal collisions, which impeded the implementation of a consistent conceptualization of information. This critical understanding of the dialectical and materialistic philosophy of information is of significant interest for several reasons. First of all, it proves the involvement of dialectical and materialist philosophy in the context of European thought of the XX century. In addition, it demonstrates the relevance of P. P. Kirschenmann's provisions for modern domestic contexts of the philosophy of information.

Functional equations with division and regular operations

Functional equations are equations in which the unknown (or unknowns) are functions. We consider equations of generalized associativity, mediality (bisymmetry, entropy), paramediality, transitivity as well as the generalized Kolmogoroff equation. Their usefulness was proved in applications both in mathematics and in other disciplines, particularly in economics and social sciences (see J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948) 392–400; J. Aczél, Remarques algebriques sur la solution donner par M. Frechet a l’equation de Kolmogoroff, Pupl. Math. Debrecen 4 (1955) 33–42; J. Aczél, A Short Course on Functional Equations Based Upon Recent Applications to the Social and Behavioral Sciences, Theory and decision library, Series B: Mathematical and statistical methods (D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1987); J. Aczél, Lectures on Functional Equations and Their Applications (Supplemented by the author, ed. H. Oser) (Dover Publications, Mineola, New York, 2006); J. Aczél, V. D. Belousov and M. Hosszu, Generalized associativity and bisymmetry on quasigroups, Acta Math. Acad. Sci. Hungar. 11 (1960) 127–136; J. Aczél and J. Dhombres, Functional Equations in Several Variables (Cambridge University Press, New York, 1991); J. Aczél and T. L. Saaty, Procedures for synthesizing ratio judgements, J. Math. Psych. 27(1) (1983) 93–102). We use unifying approach to solve these equations for division and regular operations generalizing the classical quasigroup case.