ABSTRACTIn his Lectures on Aesthetics, Hegel reasons that comedy responds to the fact that democratic ideals become a subject for a joke when enacted: progressive values such as free speech enable...

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)

У статті оцінюється значення онтологічної та метафізичної проблематики у сучасному філософському дискурсі, критично аналізується концепція монографії Андрія Баумейстера «Буття і благо» та пропонується інтерпретація буття як ствердження реальності в соціально детермінованій дії.

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)

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)

Recently, we have faced the outbreak of the coronavirus disease 2019 in the world, which has attracted the attention of all people. Stress has become a word familiar to all people. The stressors of life are relatively clear and some of them cannot be eliminated by humans. One of the stressors in the life of humans is the COVID-19 pandemic. Doctors believe that the virus is controllable but its prevalence is quicker and deadlier than other viruses. In addition, the virus (...) puts the elderly and those with underlying diseases at extreme risk. Therefore, more care is seriously required to protect members of society. However, this psychological imbalance caused by the virus is associated with stress and anxiety. Lack of proper management of this stress will be associated with emotional impacts, physiological impacts, cognitive impacts and behavioural impact.Contribution: Given the importance of this topic, this study aimed to evaluate the relationship between religious beliefs and coping with COVID-19-related stress amongst Muslim students in three cities of Russia – Ingushetia, Chechnya and the Republic of Dagestan – in 2020. Data were collected using questionnaires, the validity and reliability of which were previously confirmed. According to the results, religious beliefs had an impact on stress coping by p = 0.657. In other words, students’ ability to cope with stress improved by 0.657 units, with each unit of enhancement in their religious beliefs. (shrink)

In the article, the authors have raised an urgent topic related to the provision of state support for rural areas. Attention is focused on the deficit of most of the budgets of both the municipal and regional levels, which does not contribute to the development of the infrastructure of the territories. In addition, the low investment attractiveness does not allow relying on private capital. The authors are confident in the rationality of the development of public-private partnership, as the most optimal (...) form of relationship between private capital and public authorities. (shrink)

This paper examines the controversy between Franz von Baader and Schelling as it takes place in Schelling’s lecture course Das System der Weltalter. This particular instance of their disagreement involves Schelling criticising Baader for his notion of the biblical Elohim as divine proxies. The paper first provides a background to Baader-Schelling philosophical feud before examining Schelling’s remarks against Baader in the System der Weltalter. Then, Baader’s writings on Elohim are looked into in the light of their connection to Baader’s conception (...) of creation as falling-away and Baader’s source for interpreting Elohim as proxies, including Saint Martin and Kabbalah. Thereafter, Schelling’s criticism of Baader is analysed and interpreted in the context of the System der Weltalter. The paper aims to achieve several things: to show the presence of distorted kabbalistic influence in Baader and its discussion in Schelling; to revise Koslowski’s view on Baader’s creation narrative by pointing out how Baader’s Elohim/divine proxies function to form a rather dualistic relation between God and creation; and to interpret Schelling’s convoluted and difficult reply to Baader displaying that at stake between the two thinkers were questions of God’s ineffability and freedom as well as God’s involvement into creation. (shrink)

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to (...) teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms. (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)

Abstract:The lack of extant contemporary comparanda obscures the workings of iambic trimeter in Senecan tragedy. This article offers a quantitative analysis of the reception of Senecan trimeter in four early works of Italian Humanist Tragedy, which illuminates the creative possibilities afforded by the basic structure of the meter and identifies specific features important to questions of style and semantics. Our analysis demonstrates, among other things, that both Seneca and the Humanist tragedians use clusters of resolution in conjunction with antilabe as (...) a literary device to convey high emotion. (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.

The purpose of the study is an institutional view of the state and modern Russia, as opposed to the civilizational and formational worldview. It allows you to switch public and scientific consciousness from a statocentric to a sociocentric worldview, in its own way reveals the correlation of the categories of people, society and the state in the political universe. As a result, the history of political society appears to be a socio-dialectical sequence of public legal structures built by historically changeable (...) political norms. The analysis of institutional transitions and political norms allows us to assert that modern society, including the Russian one, is rationally moving towards a libertarian institution, i.e. to co-governance of citizens equal in law. (shrink)