The ninth issue:
Gregory Palamas and Our Knowledge of God
Although Gregory wrote very little about this, he acknowledged that natural reason can lead us from the orderliness of the physical world to the existence of God; in this, he followed the tradition of Athanasius and other Greek fathers. Unlike Aquinas, he did not seek to present the argument as deductive; in fact his argument is inductive, and of the same kind as – we now realize – scientists and historians use when they argue from phenomena to their explanatory cause. Gregory wrote hardly anything about how one could obtain knowledge of the truths of the Christian revelation by arguments from non-question-begging premises; but in his conversations with the Turks he showed that he believed that there are good arguments of this kind. Almost all of Gregory`s writing about knowledge of God concerned how one could obtain this by direct access in prayer; this access, he held, is open especially to monks, but to a considerable degree also to all Christians who follow the divine commandments.
Philosophical Problems of Foundations of Logic
In the paper the following questions are discussed: (i) What is logical consequence? (ii) What are logical constants (operations)? (iii) What is a logical system? (iv) What is logical pluralism? (v) What is logic? In the conclusion, the main tendencies of development of modern logic are pointed out.
Ordinal Or Cardinal Utility: A Note
Modern microeconomic theory is based on a foundation of ordinal preference relations. Good textbooks stress that cardinal utility functions are artificial constructions of convenience, and that economics does not attribute any meaning to “utils.” However, we argue that despite this official position, in practice mainstream economists rely on techniques that assume the validity of cardinal utility. Doing so has turned mainstream economic theorizing into an exercise of reductionism of objects down to the preferences of ‘ideal type’ subjects.
Continuous Logic and Scheduling in Systems with Indeterminate Processing Times
A general approach to the synthesis of an optimal order of executing jobs in engineering systems with indeterminate (interval) times of job processing is presented. As a mathematical model of the system, a two-stage pipeline is taken whose first and second stages are, respectively, the input of data and its processing, and the corresponding mathematical apparatus is continuous logic and logic determinants.
Interview: Is Russian Mathematics Promising Still?
The interview with Semën Kutateladze, the Russian mathematician who has continued and enriched the scientific tradition of Leonid Kantorovich. He works at the Sobolev Institute of Mathematics of the Russian Academy of Sciences and Novosibirsk State University and known for contributions to functional analysis and its applications to vector lattices and optimization.