В книгу вошли работы Т. П. Григорьевой разных лет в обновленном виде. Автор ставит перед собой задачу показать, как соотносятся западное и восточное знание, опиравшиеся на разные мировоззренческие постулаты. Для специалистов.

Для студентов, аспирантов, преподавателей и исследователей, специализирующихся в области философии и логики, истории русской философии.

I analyze in this article the different ways in which Descartes uses abstraction in the Regulæ, discussing his project of a mathematical physics, the role of the imagination, and the status of numbers. I also try to show that the doctrine of simple natures cannot be well accommodated with the theory of abstraction developed in Rule 14, having instead a greater affinity with Descartes’ later theory of abstraction and exclusion, in which imagination plays no role and everything happens at a (...) strictly intellectual level. This interpretation is supported by the recent discovery of the Cambridge manuscript, which almost certainly records an early stage of composition and in which the doctrine of simple natures is absent, thus being very probably a later development. (shrink)

The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture. One particular motivation for resolving MSC is that (...) it provides grounds for solving the inner model problem which dates back to 1960s. There have been some new partial results on MSC and the methods used to prove the new instances suggest a general program for solving the full conjecture. It is then our goal to communicate the ideas of this program to the community at large. (shrink)

Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216 89–117] and Steel [PFA implies AD L, J. Symbolic Logic70 1255–1296], we show that the failure of square principle at a singular strong limit cardinal implies that there is a nontame mouse. The proof presented is the first inductive step beyond L of the core model induction that is aimed at getting a model of ADℝ + "Θ is regular" from the failure of square at a singular strong (...) limit cardinal or PFA. (shrink)

All arithmetical identities involving 1, addition, multiplication and exponentiation will be true in a 2-element model of Tarski's system if a certain sequence of natural numbers is not bounded. That sequence can be bounded only if the set of Fermat's prime numbers is finite.

All arithmetical identities involving 1, addition, multiplication and exponentiation will be true in a 2-element model of Tarski's system if a certain sequence of natural numbers is not bounded. That sequence can be bounded only if the set of Fermat's prime numbers is finite.

All arithmetical identities involving 1, addition, multiplication and exponentiation are valid in every 2-element HSI-algebra.

We prove that Wilkie's identity holds in those natural HSI-algebras where each element has finite decomposition into components.Further, we construct a bunch of HSI-algebras that satisfy all the identities of the set of positive integers ℕ. Then, based on the constructed algebras, we prove that the identities of ℕ hold in the HSI-algebra of finite posets when the value of each variable is a poset having an isolated point.

The defeat of the USSR and of the world system of socialism, which was of a world-wide significance, raised a key question of its underlying causes. As an answer to that question, it is shown that the defeat was by no way accidental as it was brought forth not only because of mistakes in the application of Marxism but also of significant economic and socio-political fallacies. The key is in the fallacies, which are hidden deeply inside the methodology of Marxism (...) and which therefore went unnoticed by anyone, i.e. in the violation in Marx’s Das Kapital of the requirements of a number of scientific methods that he used. Marx violated the requirements of the main method used in Das Kapital, viz. the method of ascension from the abstract to the concrete (he attributed the function of forecasting the future to that method, even though the method does not have it) as well as the methods of forecast, systems approach and hypothesis. Those methodological fallacies and distortions and their epistemological consequences provide evidence that Marxism is a result of seriously flawed beliefs and it could not avoid failure. Exposure of the above-mentioned fallacies and distortions will help broad masses of people to shed communist illusions and to avoid new social and political upheavals. (shrink)

We show that assuming the determinacy of all games on reals, every set of reals is \ universally baire.

We investigate the indestructibility properties of strongly compact cardinals in universes where strong compactness suffers from identity crisis. We construct an iterative poset that can be used to establish Kimchi–Magidor theorem from (in The independence between the concepts of compactness and supercompactness, circulated manuscript), i.e., that the first n strongly compact cardinals can be the first n measurable cardinals. As an application, we show that the first n strongly compact cardinals can be the first n measurable cardinals while the strong (...) compactness of each strongly compact cardinal is indestructible under Levy collapses (our theorem is actually more general, see Sect. 3). A further application is that the class of strong cardinals can be nonempty yet coincide with the class of strongly compact cardinals while strong compactness of any strongly compact cardinal κ is indestructible under κ-directed closed posets that force GCH at κ. (shrink)

During his Fall 2005 set theory seminar, Woodin asked whether V-supercompactness implies HOD-supercompactness. We show, as he predicted, that that the answer is no.