Antagonistic log-pairs in the social sciences and the humanities

The starting point of this research is the law of unity and struggle of opposites, that is, the first law of dialectics, along with V.I. Arnold's thesis on the role of logarithms in economics. A new interpretation of the first law of dialectics is suggested in terms of the technical terminology of the kabbalah: The world is the pairing and straining of opposites. The main objective of this study is an introduction of the mathematical notion of antagonistic log pair to scientific circulation and filling the notion with more subjective contents by a philosophical apparatus in the social sciences, the humanities, and the complex sciences. An antagonistic log pair is defined to be a pair (x, y) of antagonistically contradicting entities (in the philosophical sense), the second of which is proportional to a logarithmic function of the first, where the base of logarithm is arbitrarily chosen in the interval (0, 1) and fixed. In the social sciences, the humanities, and the complex sciences, six antagonistic log pairs, covering a whole range of socio-economic phenomena and laws, are identified as follows: (efficiency, deficiency), (reliability, entropy), (quality, variability), (quality, loss), (share of delays, deadline), (share of pensioners, retirement age). A comprehensive analysis of the log pairs is provided. The dialectical struggle of opposites between the components of the log pairs is carried out by an intermediary. The intermediary for the dialectic struggle may be the whole society or the classes, strata or groups within a society, such as social classes (e.g. comparing “upper” and “working” classes), personnel of companies, market players, or the participants of business processes. Multiplication of the first components of log pairs corresponds to addition of the second components; for example, the overall efficiency of a logistics chain is equal to the product of the efficiencies of its links while its total deficiency is equal to the sum of the deficiencies of its links. The unity of opposites is seen as the equivalence of two dual problems of optimal control: Maximizing efficiency is equivalent to minimizing deficiency (with limitations on resources). All the identified log pairs are discussed along similar lines. For example, the log pair (quality, loss) leads to a philosophical justification for the economic definition of quality improvement (especially useful for service businesses): Quality improvement is equivalent to loss reduction. A definition of quality is provided by the following formula: Quality = a constant b raised to the power equal to the variability, where the base (b) can be fixed arbitrarily in between 0 and 1. This article is absolutely unbiased scientific research having nothing to do with Realpolitik.