The author of the article studies the creative legacy of Yuriy Mamleev, trying to establish the correlation between of his philosophical and fiction writings. The conventional editorial distinction between philosophical and literary texts as different and autonomous categories is rejected. Instead of the idea, that philosophical and fictional aspects of texts by Mamleev are inextricably linked, it is claimed that they should be considered together. In the author’s opinion, these texts present different perspectives and implementations of his oeuvre that contains (...) the rational dimension and on the other hand – irrational dimension of artistic images and obscure allusions. Mamleev’s writings considered by means of 5 crucial “metathemes”: Аbyss and the “Ultimate relationships” concerned with it, the Mystery which has two levels – one cognizable and the another – uncoognizable in principal, the “root of self-being” and metaphysic of “I”, death and immortality, Russia and the Russian soul which are existed between West and East with special historical and cosmological mission. It is concluded that these 5 metathemes pervade all Mamleev’s texts and comprise his spiritual search. The characters of Mamleev’s fiction are mostly people of post-Soviet world, who ask questions with no set answers to become acquainted with the secrets of being. At the same time they are concerned with their own existence, their self destiny. Their actions are extraordinary and illogical. Supposedly Mamleev’s artistic images not only correspond with his philosophical ideas, for instance – utrism or the “Ultimate relationships”, but also reveal them from unexpected perspective. The author determines that distinction between philosophy and literature of Mamleev is incorrect, as these areas are conflated. Any distinction of this kind will ruin the logic of Mamleev’s thinking and outlook. Thus, metaphysical realism can be viewed as the crossing, distinction blurring area, productive and creative transgression. Or as the situation when philosophy is more than it is itself. (shrink)

The article dealt with the question of the ratio of Yuri Mamleev’s I-utrism to Tradition. The problem is in the contradiction between two positions, which Mamleev notes in different places of “The Destiny of Being” – a view of the I-utrism as a new approach within the framework of Tradition, and as going beyond it with the introduction of extraneous elements. Based on the connection between the I-utrism and the “Last Doctrine”, which clearly lies outside the Tradition, the author of (...) the article concludes that the I-utrism should not be considered as a new approach within the framework of the Tradition, but as an autonomous construction to it. According to the author, the I-utrism due to its own radicalism contains two key problems that lead not only to a break with Tradition but also to a violation of the inner integrity of Mamleev’s philosophy itself. These two problems are defined as the radicalization of the Vedanta formula “Atman = Brahman” and the absence of the figure of the Other. I-utrism forms unified I, which the author of the article proposes to call “I-total”, because it displaces everything but itself, including the classical concept of the Absolute. Hence the lack of a topos for Mamleev’s concepts such as “Abyss” and “Eternal Russia”. It is compounded by the prevention of the metaphysical event of the Other, which is especially important for the idea of a metaphysical and mysterious Russia that requires intersubjectivity. In the process of analyzing these problems and issues, the article compares the philosophical positions of Stirner and Mamleev, as well as addresses the topic of demonic I-utrism. After all, the author concludes that the I-utrism needs to be revised and softened. This would allow it to exist organically in the overall picture of Mamleev’s worldview and not lose touch with Tradition despite the inevitable exit from it. (shrink)

The article examines the role and place of the Mystery within the structure of Mamleev’s metaphysics. The author of the article implicates the concept of “chaosmos’’, introduced by James Joyce in the experimental novel “Finnegans Wake”, to the Mamleev’s Universe. This leads to the transformation of the formula “chaos – osmosis – cosmos”, actualized by postmodern discourse, into the formula “Chaos – Osmosis – Cosmos”. Chaos here is Sacred Chaos, being one of the metaphysical manifestations of Eternal Russia. Osmosis appears (...) to be an antinomic Russian life, which combines the incompatible, and sets itself fundamentally impossible tasks. The Сosmos brings us to the tradition of Russian cosmism with its problem of microcosm and macrocosm conformity. The author of the article points out that the all-pervading and unifying element of Mamleev’s chaos is the Mystery. It is one of the five key metathemes of Mamleev’s oeuvre. The particularity of the Mystery is that it provides a link between other metathemes: utrism “I”, Death, the Abyss and Russia. In the plane of utrism “I” the Mystery is seen as the mystery of man. The Mystery is related to Death by the person’s interest of his own destiny and finiteness. The problem of overcoming death and the passion for eternal life are the central themes that concern almost all the heroes of Mamleev’s novels and short stories. For Mamleev they are the source of values aimed at the human need to achieve a higher “I”. The connection between the Mystery and the Abyss, as well as the connection between the Mystery and Russia are the strongest and the most important for Mamleev. Consideration of these connections prompts the author to conclude that Yuri Mamleev describes such dimensions of the Mystery, which go beyond the categories “unfathomable-to-us” and “unfathomable-in-itself”, introduced by S. Frank. This requires the introduction of new concepts that would bring out the essence of Mamleev’s innovations. The author of the article proposes to consider the Abyss as a “Last Mystery” by the fact it is transcendent to the transcendents themselves, that is it goes beyond the Absolute, as well as to consider Eternal Russia as a Russia-Mystery on the grounds that Mamleev gives it the status of the third metaphysical Beginning, along with the Absolute and the Abyss. (shrink)

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.

We exploit properties of certain directed graphs, obtained from the families of sets with special effective enumeration properties, to generalize several results in computable model theory to higher levels of the hyperarithmetical hierarchy. Families of sets with such enumeration features were previously built by Selivanov, Goncharov, and Wehner. For a computable successor ordinal α, we transform a countable directed graph into a structure such that has a isomorphic copy if and only if has a computable isomorphic copy.A computable structure (...) is categorical if for all computable isomorphic copies of , there is an isomorphism from onto , which is . We prove that for every computable successor ordinal α, there is a computable, categorical structure, which is not relatively categorical. This generalizes the result of Goncharov that there is a computable, computably categorical structure, which is not relatively computably categorical.An additional relation R on the domain of a computable structure is intrinsically on if in all computable isomorphic copies of , the image of R is . We prove that for every computable successor ordinal α, there is an intrinsically relation on a computable structure, which not relatively intrinsically . This generalizes the result of Manasse that there is an intrinsically computably enumerable relation on a computable structure, which is not relatively intrinsically computably enumerable.The dimension of a structure is the number of computable isomorphic copies, up to isomorphisms. We prove that for every computable successor ordinal α and every n≥1, there is a computable structure with dimension n. This generalizes the result of Goncharov that there is a structure of computable dimension n for every n≥1.Finally, we prove that for every computable successor ordinal α, there is a countable structure with isomorphic copies in just the Turing degrees of sets X such that relative to X is not . In particular, for every finite n, there is a structure with isomorphic copies in exactly the non- Turing degrees. This generalizes the result obtained by Wehner, and independently by Slaman, that there is a structure with isomorphic copies in exactly the nonzero Turing degrees. (shrink)

This article devoted to study of the issues of formation and functioning of national political elites in the context of globalization processes. According to the author, processes of globalization, socio-political, public-legal, and financial-economic development in national societies and States led to the formation of the national political elites in a single global governing elite in the face of the global Manager class, which, in turn, forms the main approaches, requirements and principles that underlie the formation and functioning of national political (...) elites. However, all this leads to the fact that global and national management of the elite are unable on the one hand, to quickly solve global problems facing humanity, and on the other hand, to ensure the progressive development of humanity as a whole, resulting in the creation and development of a revolutionary situation in the national and international scale. The only alternative to the existing trends of the formation and development of national political elites in anti-state and anti-social manner, which inevitably can lead humankind to destruction or self-destruction, is the growing activity of civil society to the state of leveling of power and influence of the global ruling elite in the face of the global Manager class. In the present work, a number of scientific methods of research were used, in particular: comparison; hermeneutic analysis; socio-phenomenological approach. (shrink)

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

Let ???? be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of ???? in which the image of R (¬R, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on ???? and R, a necessary and sufficient condition for the existence of a computable copy ℬ of ???? in which the image of R (¬R, resp.) (...) is simple (immune, resp.). (shrink)

This research partially answers the question raised by Goncharov about the size of the class of positive elements of a Roger's semilattice. We introduce a notion of effective infinity of classes of computable enumerations. Then, using finite injury priority method, we prove five theorems which give sufficient conditions to be effectively infinite for classes of all enumerations without repetitions, positive undecidable enumerations, negative undecidable enumerations and all computable enumerations of a family of r.e. sets. These theorems permit to strengthen (...) the results of Pour-El, Pour-El and Howard, Ershov and Khutoretskii about existence of enumerations without repetitions and positive undecidable enumerations. (shrink)

The paper enters into a polemical dialogue with the american theorist Jodi Dean and her attempts to critically examine the blogosphere through the prism of psychoanalysis. To this end, the text analyses whether user-generated content on the internet can produce meaningful and epistemologically sustainable “social enclaves”, informal communities and institutions, or whether it operates more as a series of recursive and increasingly meaningless quasi-messages. While attempting to consider blogging as both a constructive practice and a pathology, the text develops the (...) hypothesis that in special cases one can conceptually speak of “epistemic inflation”, a phenomenon that can manifest itself at the personal as well as the social, economic and/or political level. Furthermore, the paper briefly introduces the ideas, history and one of the key concepts of the influential british theory-fiction collective, CCRU (Cybernetic Culture Research Unit). (shrink)

In the paper A. I. Malcev's problem on the characterization of axioms for classes with strong homomorphisms is being solved.

The Hanf number for a set S of sentences in \ is the least infinite cardinal \ such that for all \, if \ has models in all infinite cardinalities less than \, then it has models of all infinite cardinalities. Friedman asked what is the Hanf number for Scott sentences of computable structures. We show that the value is \. The same argument proves that \ is the Hanf number for Scott sentences of hyperarithmetical structures.

Computable structures of Scott rank ${\omega_1^{CK}}$ are an important boundary case for structural complexity. While every countable structure is determined, up to isomorphism, by a sentence of ${\mathcal{L}_{\omega_1 \omega}}$ , this sentence may not be computable. We give examples, in several familiar classes of structures, of computable structures with Scott rank ${\omega_1^{CK}}$ whose computable infinitary theories are each ${\aleph_0}$ -categorical. General conditions are given, covering many known methods for constructing computable structures with Scott rank ${\omega_1^{CK}}$ , which guarantee that the (...) resulting structure is a model of an ${\aleph_0}$ -categorical computable infinitary theory. (shrink)

Abraham Robinson’s framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of the Weierstrassian foundations. We propose a view without passing through the lens, by means of proxies for such procedures in the modern theory of infinitesimals. The real accomplishments of calculus and analysis had been based primarily on the elaboration of novel techniques for (...) solving problems rather than a quest for ultimate foundations. It may be hopeless to interpret historical foundations in terms of a punctiform continuum, but arguably it is possible to interpret historical techniques and procedures in terms of modern ones. Our proposed formalisations do not mean that Fermat, Gregory, Leibniz, Euler, and Cauchy were pre-Robinsonians, but rather indicate that Robinson’s framework is more helpful in understanding their procedures than a Weierstrassian framework. (shrink)

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (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)

In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...) Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? As well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s. (shrink)

We show that for every computable limit ordinal α, there is a computable structure A that is $\Delta _\alpha ^0 $ categorical, but not relatively $\Delta _\alpha ^0 $ categorical (equivalently. it does not have a formally $\Sigma _\alpha ^0 $ Scott family). We also show that for every computable limit ordinal a, there is a computable structure A with an additional relation R that is intrinsically $\Sigma _\alpha ^0 $ on A. but not relatively intrinsically $\Sigma _\alpha ^0 $ (...) on A (equivalently, it is not definable by a computable $\Sigma _\alpha $ formula with finitely many parameters). Earlier results in [7], [10], and [8] establish the same facts for computable successor ordinals α. (shrink)

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and (...) clearer system. Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals. (shrink)

The article attempts to analyze the concept of gender, study philosophical preconditions of its emergence and trace the main postmodern aspects of the gender category. It proves that gender research in the postmodern era is not identical to the theories of feminism. It deals with social life of both sexes, their behavior, roles, characteristics, common and different between them, the social relationships of the sexes, considering the world from the standpoint of both socio-gender groups. The article shows that an urgent (...) need for more purposeful development of independent women's research in the developing countries. Such research should holistically reflect and study the lives of women on the basis of the so-called women's rather than universalized man experience. The main idea of this scientific research was to emphasize that the world can be explored not only from a man perspective, but also from the standpoint of woman experience. The level of scientific study of the gender conceptual sphere is clarified, in particular, the gender concept is a multidimensional complex represented in the language, which has a certain ethnocultural specificity. The concept has an unstable structure, which is reflected in the model of the concept developed by us, in which we highlight the root and applications of the concept, the possible movement of features in the relevant semantic directions from and to the root. The unstable structure of the concept is also characteristic of its root: during historical development, the root may change, but the semantic meaning is not lost, but only replaced by synonyms or verbal innovations relevant to today. (shrink)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

When classical scholars use the term ‘spelt’ to translate such words as and in Greek, and far, odor, semen , arinca, and the like in Latin, they seldom realize that all these words denote grains which are nowadays included in the genus wheat. Within this genus a distinction is made between ‘husked’ and ‘naked’ species: naked wheat can be ‘threshed out’ on the threshing-floor, the grain being separated from the chaff and left ready for milling; husked wheat has before (...) milling to undergo a separate hulling operation to free the grain from the husks, or cover glumes, by which it is enclosed and which so tightly adhere to it that the rachis breaks before the grain is freed. The term ‘spelt’, when used in the way described, denotes the husked wheats, while ‘wheat’ is reserved for the translation of the names of the naked species. (shrink)

Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.

In lieu of an abstract, here is a brief excerpt of the content:Human Reproduction: Dominion and LimitsRichard A. McCormick S.J. (bio)The general struggle throughout Christian history has been to seek the proper balance between dominion and limits, intervention and nonintervention, givenness, and creativity. This struggle has worked itself out in six areas that touch human life. In this essay, I will revisit the Catholic tradition’s treatment of these in terms of dominion and limits to see whether we can discern developmental (...) patterns that might suggest an approach to issues pertaining to the sources of life (reproductive ethics) as we move into the next century.1. Abortion. The history of the treatment of abortion in the Catholic tradition is the history of an evaluation. This evaluation was somewhat muddied by [End Page 387] unclarity and inconsistency in the use of terms. Thus, some theologians distinguished three types of abortion: prevention of conception, abortion of an inanimate fetus, and abortion of an animated fetus. Others regarded all interventions into the life-giving process as homicides. Still others argued that termination of a nonanimated fetus was justified to save the life of the mother. And still others said such termination was anticipated homicide or the misuse of semen conceptum.Such unclarities and qualifications eventually vanished and produced an evaluation of fetal life that yielded to very few competing interests, what John Noonan (1970) referred to as “an almost absolute value.” There was some dominion or control, but the limits became increasingly clear and powerful.2. Individual and corporate self-defense. Augustine disallowed lethal individual or personal self-defense, but established the first elementary rules for war. Aquinas allowed both. Vitoria, Suarez, and others refined the criteria justifying war (jus ad bellum) and listed them as three: recovery of property, resistance to aggression, and vindication of injuries (injustices). Pius XII narrowed these to a single reason: national self-defense. The Challenge of Peace (NCCB 1983) moves away from the licitness of nuclear war and nuclear deterrence even for self-defense. Once again, the limits to the dominion over life in war grow stronger and more powerful even as the weapons of such dominion grow more powerful.3. Capital punishment. Over the centuries, Christian thinkers, such as Thomas Aquinas, permitted the use of capital punishment. Three justifications were proposed to found this right of the state: retribution, deterrence, and reform. In the past decades, however, these justifications have been seriously questioned. Both the American and Philippine bishops’ conferences have rejected all use of capital punishment. Most recently John Paul II (1995, n. 56, p. 709) adduces defense of society as the only possible justification for it and sees such cases as “very rare if not practically non-existent.”4. The preservation of life. The theme of a balance between dominion and limits is perhaps nowhere clearer than in the Catholic approach to life preservation. Catholic tradition does not accept our culture’s rejection of death. Rather it asserts that the facts that we are pilgrims, that Christ has overcome death and lives, and that we also will live with him yield a general value judgment on the meaning and value of life as we now live it: Life is a basic good but not an absolute one. It is basic because, as the Congregation for the Doctrine of the Faith (1980, p. 511) worded it, it is the “necessary source and condition of every human activity and of all society.” It is not absolute because there are higher goods for which life can be sacrificed—e.g., the glory of God, salvation of souls, service of one’s brethren, and the like. Thus in John (15:13): “There is no greater love than this: to lay down one’s life for one’s friends. John Paul II (1995, n. 47, p. 706) briefly summarizes this in Evangelium Vitae: “The life of the body in its earthly state is not an absolute good for the believer.” This value [End Page 388] judgment has immediate relevance for care of the ill and dying: Not all means must be used to preserve life.Thus the Catholic tradition has moved between two extremes: medico-moral optimism or vitalism (which preserves life with all means, at any cost... (shrink)

Using a sample of 652 college students, we examined several implications of the hypothesis that the shape of the human penis evolved to enable males to substitute their semen for those of their rivals. The incidence of double mating by females appears sufficient to make semen displacement adaptive (e.g., one in four females acknowledge infidelity, one in eight admit having sex with two or more males in a 24-hour period, and one in 12 report involvement in one or (...) more sexual threesomes with two males). We also document several changes in post-ejaculatory behavior (e.g., reduced thrusting, penis withdrawal, loss of an erection) which may have evolved to minimize displacement of the male’s own semen. Consistent with predictions derived from a theoretical model (Gallup and Burch 2006), we discovered that most females report waiting at least 48 hours following an instance of infidelity before resuming sex with their in-pair partners. (shrink)

This article examines how perceptions of what semen is thought to contain affect its value as a marketable product. I explore how donor altruism, intelligence and ethnicity traits thought to be transmitted in sperm are perceived and transacted among representatives of the sperm banking industry, as well as among women who purchase semen for insemination and show how the linkages between the reproductive industry and the sex industry further heighten the commodity-quality of semen donation. I argue that (...) the emphasis placed on altruism, is an attempt to redefine the commodity quality of semen as gift, in order to imbue it with higher emotional and moral value. (shrink)