Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, (...) the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Björling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered. (shrink)

A construction of the real number system based on almost homomorphisms of the integers $\mathbb {Z}$ was proposed by Schanuel, Arthan, and others. We combine such a construction with the ultrapower or limit ultrapower construction to construct the hyperreals out of integers. In fact, any hyperreal field, whose universe is a set, can be obtained by such a one-step construction directly out of integers. Even the maximal (i.e., On -saturated) hyperreal number system described by Kanovei and Reeken (2004) and independently (...) by Ehrlich (2012) can be obtained in this fashion, albeit not in NBG . In NBG , it can be obtained via a one-step construction by means of a definable ultrapower (modulo a suitable definable class ultrafilter). (shrink)

First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.

We classify irreducible actions of connected groups of finite Morley rank on abelian groups of Morley rank 3.

Frankfurt-type cases with covered manipulation received a great attention in the debates about freedom of will and moral responsibility. They pretend to give the refutation of the Principle of Alternative Possibilities and to show that we can intuitively blame or praise an agent who was not able to do otherwise. In this paper, I will try to make explicit some basic intuitions underlying the agent’s responsibility in Frankfurt-type cases, which were surprisingly ignored in the contemporary debates. The key intuition is (...) that the responsibility of the agent in Frankfurt-type cases is always grounded at the point of overcoming the uncertainty preceding action. This overcoming is crucially important for agent’s responsibility and immune to any manipulation of counterfactual intervener. (shrink)

One of the purposes of this paper is to prove a partial Schur-Zassenhaus Theorem for groups of finite Morley rank.Theorem 2.Let G be a solvable group of finite Morley rank. Let π be a set of primes, and let H ⊲ G a normal π-Hall subgroup. Then H has a complement in G.This result has been proved in [1] with the additional assumption thatGis connected, and thought to be generalized in [2] by the authors of the present article. Unfortunately in (...) the last section of the latter paper there is an irrepairable mistake. Here we give a new proof of the Schur-Zassenhaus Theorem using the results of [2] up to the last section and a new result that we are going to state below.The second author has shown in [11] that a nilpotentω-stable group is the central product of a divisible subgroup and a subgroup of bounded exponent, generalizing a well-known result of Angus Macintyre about abelian groups [8]. One could ask a similar question for solvable groups: are they a product of two subgroups, one divisible, one of bounded exponent? One is allowed to be hopeful because of the well-known decomposition of the connected solvable algebraic groups over algebraically closed fields as the product of the unipotent radical and a torus. (shrink)

I. "Filosofskiĭ paroxod": k istorii voprosa -- II. Respressii i permanentnai︠a︡ ėmigrat︠s︡ii︠a︡ -- III. Overkili russkoĭ filosofii -- IV. Postsovetskiĭ period: v poiskakh identichnosti -- V. Vozvrashchenie "filosofskogo paroxoda" (2003) -- VI. "Filosofskie avtobusy" -- VII. Samolet-paroxod-"filosofskiĭ poezd" -- VIII. Afinskiĭ kongress: prikosnovenie k istorii (2013) -- IX. "Uchitʹsi︠a︡ bytʹ chelovekom": XXIV vsemirnyĭ filosofskiĭ kongress -- X. Mezhdu proshlym i budushchim.

A collection of historical essays on human sexuality.

We are old birds, we know which obligations can be accepted and which cannot. Hence the strategy of sustainable development has been assiduously purged of all commitments that might make us look bad not only in two or three years but even in thirty years.

This article discusses the foundation of ideas for Vyacheslav Ivanov’s interpretation of Pushkin’s poem. In The Gypsies, Ivanov sees a conflict between personal freedom and sobornost’ as revealed b...

У статті проаналізовано вчення П'єра Абеляра в частині його впливу на виокремлення світської сфери знання з тотально релігійного середньовічного дискурсу. Схоластична теологія, творцем якої є Абеляр, розглядається автором статті як специфічний результат філософського мислення в граничних екзистенційних обставинах та маркер секулярних зрушень у середньовічній християнській культурі.

The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

This article presents a report of the Fourth Immanuel Kant International Summer School devoted to Kant’s doctrine of war and peace (24-31 July 2022), organised by the Academia Kantiana of the Immanuel Kant Baltic Federal University with the support of the “Petersburg Dialog” Forum. The lectures of the School’s scientific supervisor, Alexei N. Krouglov, address a wide range of topics: the sources of Kant’s doctrine on war and peace, Kant’s political views and their inherent contradictions, analysis of Kant’s treatise on (...) perpetual peace, as well as its early reception and current discussions. The conference of young scholars heard 22 papers whose content is reviewed here. Among the topics were the cultural, social and intellectual conditions in which the treatise on perpetual peace appeared, its influence on the creation of the League of Nations, the UN and the EU; intersections with twentieth-century philosophical projects were also covered. Some original interpretations were offered. (shrink)

This publication aims to analyze the economic, social, and cultural phenomena that first appeared in the "era of revolutions" that occurred in the nineteenth to early twentieth centuries. The modern European trend toward tolerance, which is the basis of current social and cultural changes, including in our country, has specific intellectual grounds. The subject of the study was the ideosphere of the nineteenth and early twentieth centuries, including philosophical, economic, and psychological concepts that gave rise to modern trends in these (...) areas. The result of this study was the determination of the reasons that caused the change of the ideological paradigm in Europe. The novelty of the research lies in the fact that, for the first time, the intellectual foundations of the formation of tolerance as an actual socio-cultural phenomenon are analyzed. This article consistently proves that among the first such grounds, it is possible to determine the emergence of machine production and, as a result, the appearance of a mass person with a culture corresponding to them, performing a compensatory and entertaining function. The most important cultural foundation is mainly the intellectual "background" created by the teachings of Friedrich Nietzsche, Karl Marx, and Sigmund Freud. The ideas of Anglo-American pragmatism played a significant role in forming a new morality, which included the denial of religion and its values, giving it a utilitarian character. During the subsequent historical period and at present, these views have become the basis for the creation of the so-called "individual faith," in which religion ceases to be the guide of human life but only serves the needs of the individual. The desacralization of religion leads to the study of different aspects of sexuality, which opens up the possibility for modern thinking about gender. The concept of "natural law" should also be attributed to the intellectual factors of the formation of modern European tolerance. (shrink)

People often use indirect speech, for example, when trying to bribe a police officer by asking whether there might be “a way to take care of things without all the paperwork.” Recent game theoretic accounts suggest that a speaker uses indirect speech to reduce public accountability for socially risky behaviors. The present studies examine a secondary function of indirect speech use: increasing the perceived moral permissibility of an action. Participants report that indirect speech is associated with reduced accountability for unethical (...) behavior, as well as increased moral permissibility and increased likelihood of unethical behavior. Importantly, moral permissibility was a stronger mediator of the effect of indirect speech on likelihood of action, for judgments of one's own versus others' unethical action. In sum, the motorist who bribes the police officer with winks and nudges may not only avoid public punishment but also maintain the sense that his actions are morally permissible. (shrink)

One of the main trends of modern society is a marked increase of the theoretical interest to the sphere of mythology and the theory of myth. And in light of globalization approaches explicitly focus on the impact study of the regional aspects of social phenomena. In this regard, in regional studies of mythology appear attempts seen the myth city's as a socially formalized knowledge about the city or region, a strong regulatory and mobilization element in society, which is capable of (...) forming a regional entity and identity. A problem is in that every city has the own myths and specific municipal culture. It can be one of reasons of conflicts at co-operation of townspeople of different regions because all of us are inclined to identify itself with a sub-group on the sign of place of inhabitation, line of business or the world view. Thus, at all cities have different myths and symbols. We are inclined to see our city as city of the chosen townspeople, while other cities and regions are inhabited by demons and monsters. The article suggests to consider the city like a self-valuable phenomenon. The article submitted to scientific use of the term "the myth city's" which, the author's perspective is not identical to the concept of "myths of the city" and "Mythology of the city." also authors conducted analysis the history of the formation of the Donetsk's myth, identified the main stages of its formation, and conducted explication of its meaningful and functional characteristics. (shrink)