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)

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 question of the Russian man – his past, present and future – is the central one in the philosophy of history. Unfortunately, at present this area of philosophy is not suffciently developed in Russia. Partly the reason for this situation is the lack of understanding by researchers of the role played by Russian classical literature and its philosophizing writers in historiosophy. The Hunting Sketches, a collection of short stories by I.S. Turgenev, is a work still undervalued, not fully considered (...) not only in details but also in general meanings. And this is understandable because it is the frst systematic encyclopedia of Russian worldview, which is not envisaged by the literary genre. To a certain extent, Turgenev’s line is continued by I. Goncharov, L. Tolstoy, F. Dostoevsky, A. Chekhov. This article examines the philosophical nature of The Hunting Sketches, its structure and content. According to author’s opinion, stories can be divided into ten groups according to their dominant meanings. Thus, in The Hunting Sketches the main Russian types are depicted: “natural man,” rational, submissive, cunning, honest, sensitive, passionate, poetic, homeless, suffering, calmly accepting death, imbued with the immensity of the world. In the image and the comments of the wandering protagonist, Ivan Turgenev reveals his own philosophical credo, which he defnes as a moderate liberalism – freedom of thought and action, without prejudice to others. (shrink)

This article explores the fundamental structure of “man who manages to do without Being” and whose constitution lacks the relation to Being and God. Within synergic anthropology, this phenomenon is...

This paper examines the changing ethical consciousness in Russia since the Bolshevik revolution of 1917 and discusses how this change was reflected in Russian religious philosophy. This process can be characterized by a series of sudden and violent replacements of contradictory ethical models, which, by disorientating the public consciousness, led to the atrophy of the ethical instinct. The last two models in the series correspond to the “anti-ethics” of the 1990s and the “non-ethics” of the third Millennium. The latter model (...) corresponds to the current absence of individual ethical positions and the willingness to adopt any position prescribed by the state. A review of philosophical reflection on this process shows that Russian religious thought did not foresee such an ethical catastrophe. Indeed, although Vladimir Solovyov presented an alarming eschatological foresight of the future, and despite the fact that the collection Landmarks, written in 1907, firmly identified the intelligentsia as a highly destructive agent promoting their own alternative ethics, the optimistic philosophical model nonetheless prevailed. According to this optimistic model, the period of disasters and catastrophes will be followed by a new spiritual reawakening. (shrink)

This article offers a comparative analysis of the Posthuman and the anthropological formation of the Virtual Man as it is presented in synergic anthropology. It reconstructs the ways and strategies...

This article presents a systematic reconstruction of the original ethics created by the tradition of Orthodox hesychasm. Analysis reveals that the tradition has developed two very different kinds o...

The structure of G. V. Florovsky’s concept of neopatristic synthesis is analyzed and reassessed here in light of the current state of philosophy and theology. As a result, the concept receives a ne...

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)

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.

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)

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

By the end of his life Plato had rearranged the theory of ideas into his teaching about ideal numbers, but no written records have been left. The Ideal mathematics of Plato is present in all his dialogues. It can be clearly grasped in relation to the effective use of mathematical modelling. Many problems of mathematical modelling were laid in the foundation of the method by cutting the three-level idealism of Plato to the single-level “ideism” of Aristotle. For a long time, (...) the real, ideal numbers of Plato’s Ideal mathematics eliminates many mathematical problems, extends the capabilities of modelling, and improves mathematics. (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 will study the question about decidability for Boolean algebras with first elementary characteristic one. The main problem is sufficient conditions for decidability of Boolean algebras with recursive representation for extended signature by definable predicates. We will use the base definitions on recursive and constructive models from [2, 4–6, 10, 11] but on Boolean algebras from [1, 8].

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)

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 $\Sigma^0_3$.

At the present time, there are several interpretations and modes of Kant’s transcendental philosophy (TP). Which of these interpretations and modes of transcendentalism most adequately express the spirit of TP, i.e. can claim the title of the transcendental ones? For the explication of the ‘idea of transcendental philosophy’ [KrV, A1], here I distinguish two transcendental shifts: methodological and metaphysical ones, which in their totality predetermine the essence and set the specificity of Kant’s transcendental idealism. The methodological transcendental shift that Kant (...) postulates in his definitions of TP in the Critique of Pure Reason [KrV, A11; B25] represents a shift from studying of objects to the analysis and justification of our mode of cognition of objects. This shift sets a fairly wide range of a la Kantian a priori doctrines and predetermines the transcendental turn (Re–Transcendentalising) of modern philosophy. The metaphysical transcendental shift that can be correlated with “the altered method of our way of thinking [in metaphysics]” [KrV, BXVIII], is associated with the splitting of the “thing” into the actual object (or Kantian thing-in-itself) and object of experience (or Kantian appearance), and involves a transition from the study of thing-in-itself to the analysis of the appearance. More precisely, this shift finds its expression in the transcendental triad “object (thing-in-itself; Ding an sich) – appearance (Erscheinung) – representation (Vorstellung)”, which determines the ‘idea’ (essence) of transcendental idealism/metaphysics. (shrink)

Basil the Great’s theory of time is a fascinating testimony to the metaphysics and philosophy of nature of the fourth century AD. In his treatises Basil sought to tackle such foundational issues of philosophy as God’s being, its hypostatic instantiations, and God’s creative acts. In order to properly address these issues he had to scrutinize the notion of time, thus turning the discussion of time into one of the key philosophical threads of his treatises. Basil’s works unequivocally exhibited his careful (...) approach to and respect for philosophical tradition, along with his innovative brilliance. Moreover, Basil’s oeuvre clearly indicates that he was well acquainted with the then current philosophical literature on the subject. This article aims to shed light on various aspects of Basil’s theory and its conceptual underpinnings. It endeavors to demonstrate that Basil’s theory, at its highest point, cannot be understood apart from its protological and eschatological premises. It also argues that Basil was not merely an eclectic thinker, in that he used various concepts inherited from the late antique philosophical tradition to arrive at a uniquely Christian theological and eschatological synthesis. It concludes with an affirmation of Basil’s theory of time as a valuable extension to our understanding of the topic. (shrink)

Kant’s transcendental philosophy of Kant is the metaphysics of possible experience related to the solution of the [semantic] problem set in his famous letter to M. Hertz (02.21.1772): “What is the ground of the relation of that in us which we call 'representation' to the object?” There are two possible ways to solve it: empiricism and apriorism, – and Kant chooses the second of them, thus making his “Copernican Revolution”. In the Preface to the 2nd ed. Critique Kant correlates his (...) Copernican turn/revolution with "altered method of our way of thinking [in metaphysics]" [BXVIII] and considers it as an analogue of the hypothetico-deductive scientific method of Copernicus – Galileo – Newton. The analysis of structure of the Copernican Revolution shows that it is possible to pick out two vectors: the empirical (from the thing-in-itself to representations) and the noumenal ones (from the transcendental unity of apperception [or transcendental object] to objects of experience). The introduction of an a priori vector (resp. a priori forms) means that Kant's conception is not empirical, but Kant’s keeping empirical vector says that it is compatible with empirical realism [A370–1]. Thus, Kantian transcendentalism is a synthesis of realism (basic level) and transcendental idealism (as a meta-level superstructure above it), whose task is to find out and analyze the transcendental conditions [possibility] of our knowledge of objects. (shrink)

This article aims to shed light on certain aspects of Iamblichus’ theory of time that have not been sufficiently examined to date in the scholarly literature. As of today, there are a mere handful of scholarly works tackling Iamblichus’ solutions to the paradoxes of time in particular, and his contribution to the developments of the Neoplatonic theory of the subject more generally. This article attempts to redress the lack of literature on this topic by examining Iamblichus’ response to Aristotle’s and (...) Pseudo-Archytas’ theories of time. It begins with a brief survey of the philosophical developments that led to and were formative for Iamblichus’ philosophical explorations of the area in question. Then it moves on to provide a detailed account of Iamblichus’ own unique and puzzling theory of time. The author applies the method of comparative analysis, scrutinizing Iamblichus’ solution to the paradoxes of time against the backdrop of Aristotle’s and Pseudo-Archytas’ theories. The author identifies firm scholarly grounds for doing so from within the tradition of Iamblichus studies initiated by the ground-breaking research of Shmuel Sambursky and Salomon Pines and continued, inter alia, in the subtly nuanced analysis of Richard Sorabji and John Dillon. The author concludes that Iamblichus successfully resolved the paradoxes of time and that his conception lent itself to a more effective highlighting of the ordering function of time. (shrink)

In my commentary, I write, firstly, of the dualistic (ambivalent) use of the concept ‘appearance’ by Kant and, secondly, of the need for a semantic (referential) interpretation of the Kantian concept ‘‘appearance’ as opposed to intentional interpretation of R.Aquilla. In his reply to my objections, R. Aquila precisies his initial position and gives additional arguments in it’s favor.

Presented in the “Critique of Pure Reason” transcendental philosophy is the first theory of science,which seeks to identify and study the conditions of the possibility of cognition. Thus, Kant carries out a shift to the study of ‘mode of our cognition’ and TP is a method, where transcendental argumentation acts as its essential basis. The article is devoted to the analysis of the transcendental arguments. In § 2 the background of ТА — transcendental method of Antiquity and Leibniz’s Principle of (...) Sufficient Reason — are analyzed and their comparison with ТА is given. § 3 is devoted to the analysis of TA in the broad and narrow senses; a formal propositional and presupposition models are proposed. In § 4 I discuss the difference between TA and metaphysics’ modes of reasoning. It analyzes the Kant’s main limitations of the use TA shows its connection with the Modern Age and contemporary science. (shrink)

In the course of a close analysis of Kant’s essay in which he gives his original answer to the question, “What is Enlightenment?” I examine the causes and consequences of the theses about Enlightenment which makes a plea for emancipation from the shackles of guardianship, above all by getting rid of one’s own cowardice. In search of an answer to the question, “What is the real reason of self-incurred immaturity?” I consider the bifurcation: Is it all about unjust social institutions (...) established in the interests of the ruling social estates, as the best European brains contended throughout the Enlightenment era, thus anticipating and justifying revolutionary upheavals, or is it within ourselves who have refused to use our reason independently and regularly? — something which Kant unequivocally considers to be everyone’s special kind of guilt. Following Kant, I look for an answer to the question, “Which limits impede Enlightenment, and which limits, far from obstructing it, are bound to promote it?” and reveal the hidden paradox of the Kantian solution: maturity has to be preceded by the granting of freedoms; and the granting of freedoms in turn calls for a mature public. I also ask the question, “Whose yoke is heavier, one’s own or the guardian’s?” and offer my version of an answer. In conclusion, I assemble all parts of the complicated and original formula of the Kantian recipe of Enlightenment. Among other things, I reveal a special type of bonding within the social organism implied by Kant, and that is the requirement to obey those who are not above us in thinking and the right to speak out in public, which ultimately means not only personal maturity, but implies also the maturity of society’s functioning in accordance with the said maxim. (shrink)

Nammalvar, a Tamil poet who lived in IX-X centuries, is revered as one of the great mystics of India. His four poetic works are equated with the sacred hymns and are part of the ritual worship in the temples of South India. Artistic images of Nammalvar formed the basis of the philosophy of Vishishta-Advaita several centuries later. The poem “Thiruviruttam” is considered as his early work, where he combines the canons of ancient Tamil poetry and his devoted love for Vishnu-Tirumal. (...) The study presents a religious and philosophical interpretation of the poem. The secret of the poem is its dualism: external beauty and sacred meaning. There is a spiritual meaning in symbols of Tamil poetry. Nammalvar takes canons of his predecessors, poets of the Sangam era. However, he fills one with new content. The author compares ancient Tamil poetry and the work of Nammalvar. The plot describes the love between God and the soul. The poet reveals several types of bhakti or devoted love. The description of bhakti subsequently formed the basis for the classification of souls in the philosophy of vishishta-advaita. Bhakti leads to the transition to Vaikuntha or the heaven city. Sri Vaishnavism teachers turned the description of relationship soul-Vishnu into a spiritual practice. The artistic images of Nammalvar are compared with Hindu concepts such as transcendence, darshan, divine grace and moksha. In South India “Thiruviruttam” is considered the Tamil Rig Veda. Poem is performed at home, in the temple, during festive processes. It helps to find the roots of Vaishnavism and understand its poetic origin. (shrink)

The Greek Prophetologion manuscript Q12 from the library of the Academy of Sciences in St. Petersburg, copied in 1275, contains some thirty marginal notes written in Alanic, a pre-stage of Ossetic. On leaf 100r, the glossator provided the Greek heading τ παραμο(ν) τς μέ(σο) ν´ (i.e. μεσοπεντηκοστς), ‘Eve of Mid-Pentecost’, with a gloss πητζινάκ χουτζάου πάν which most probably means ‘Pecheneg Sunday’. A Pecheneg festival established after the decisive victory of John II over the Pechenegs is attested by both Nicetas (...) Choniates and Ecloga Basilicorum. It is no wonder that this festival reached distant Alania, since the 12th century was a heyday for the Orthodox Christianity in the Northern Caucasus. The battle took place near Beroea in spring of the “fifth year” of John II's reign. The majority of historians tend to opt for 1122, but we would not exclude 1123 either. Whatever the year, the marginal note from Q12 may help in establishing the day of the battle, which is not mentioned either in Greek or in Scandinavian sources. If the battle of Beroea took place in 1122, it happened either on the 20th–22nd or on the 24th–26th of April. If the battle was fought in 1123, the day of the victory could then be either the 10th–12th or the 14th–16th of May. (shrink)

The presented article compares the points of view on time developed in analytical philosophy and in phenomenology actively developed by B. Russell and L. Tengelyi. The objective of the study coincides with the identifying a common horizon for understanding time in analytical philosophy and phenomenology. This help to clarify the possibilities of productive interaction between analytical philosophy and phenomenology. The author of the article believes that a positive answer to this question can be ensured by a special thought experiment. The (...) experiment involves assessing the perception of time in extreme circumstances in terms of phenomenology and analytical philosophy. (shrink)

Basil the Great’s theory of time is a fascinating testimony to the metaphysics and philosophy of nature of the fourth century AD. In his treatises Basil sought to tackle such foundational issues of philosophy as God’s being, its hypostatic instantiations, and God’s creative acts. In order to properly address these issues he had to scrutinize the notion of time, thus turning the discussion of time into one of the key philosophical threads of his treatises. Basil’s works unequivocally exhibited his careful (...) approach to and respect for philosophical tradition, along with his innovative brilliance. Moreover, Basil’s oeuvre clearly indicates that he was well acquainted with the then current philosophical literature on the subject. This article aims to shed light on various aspects of Basil’s theory and its conceptual underpinnings. It endeavors to demonstrate that Basil’s theory, at its highest point, cannot be understood apart from its protological and eschatological premises. It also argues that Basil was not merely an eclectic thinker, in that he used various concepts inherited from the late antique philosophical tradition to arrive at a uniquely Christian theological and eschatological synthesis. It concludes with an affirmation of Basil’s theory of time as a valuable extension to our understanding of the topic. (shrink)

This article aims to shed light on certain aspects of Iamblichus’ theory of time that have not been sufficiently examined to date in the scholarly literature. As of today, there are a mere handful of scholarly works tackling Iamblichus’ solutions to the paradoxes of time in particular, and his contribution to the developments of the Neoplatonic theory of the subject more generally. This article attempts to redress the lack of literature on this topic by examining Iamblichus’ response to Aristotle’s and (...) Pseudo-Archytas’ theories of time. It begins with a brief survey of the philosophical developments that led to and were formative for Iamblichus’ philosophical explorations of the area in question. Then it moves on to provide a detailed account of Iamblichus’ own unique and puzzling theory of time. The author applies the method of comparative analysis, scrutinizing Iamblichus’ solution to the paradoxes of time against the backdrop of Aristotle’s and Pseudo-Archytas’ theories. The author identifies firm scholarly grounds for doing so from within the tradition of Iamblichus studies initiated by the ground-breaking research of Shmuel Sambursky and Salomon Pines and continued, inter alia, in the subtly nuanced analysis of Richard Sorabji and John Dillon. The author concludes that Iamblichus successfully resolved the paradoxes of time and that his conception lent itself to a more effective highlighting of the ordering function of time. (shrink)

In the “Critique of Pure Reason” and subsequent “Prolegomena to Any Future Metaphysics...”, “Metaphysical Principles of Natural Science”, “Opus Postumum” Kant develops one of the modes of his transcendentalism, the metaphysics of possible experience, whose task is to study the transcendental conditions for the possibility of our (cognition), which, according to Kant, has a priori character. P. Strawson calls this mode of metaphysics ‘ descriptive metaphysics ’ and connects it with the analyzing the ‘conceptual structure’ of our thinking about the (...) world. The contemporary realistic trend (primarily within the framework of the analytical philosophical tradition) in the interpretation of Kant’s transcendental philosophy is associated with the modern theory of “two aspects” (80s of the 20th century), which replaced the classical theory of “two objects/worlds” (compare also with the opposition “ theory of appearance vs. theory of appearances ”). Within the framework of this theory, the Kantian ‘appearance’ receives an objectified status, it is not our mental representation, but corresponds (as its signs) to really existing things, or Kantian ‘objects of experience’. The article traces the formation of the historical and conceptual background of the ‘ metaphysics of experience ’ (H. Paton's original expression). Historically, the metaphysics of experience inherits the neo-Kantian approach to interpreting Kant's transcendentalism as a ‘theory of experience’ (H. Cohen, E. Cassirer), then it develops in logical positivism/empiricism (H. Reichenbach, R. Carnap; further in post-posivivism: the theory of I. Lakatos and T. Kuhn), analytical philosophy of science (W. Sellars, G. Buchdal, H. Putnam), and at present the metaphysics of experience is developing in a number of contemporary works of an analytical orientation (P. Strawson, K. Ameriks, L. Allais and etc.). (shrink)

This paper is dedicated to developing a formalism that takes rejection seriously. Bilateral notation of signed formulas with force indicators is adopted to define signed consequences which can be viewed as the bilateral counterpart of Tarskian consequence relations. Its relation to some other bilateral approaches is discussed. It is shown how David Nelson’s logic N4 can be characterized bilaterally and the corresponding completeness result is proved. Further, bilateral variants of three familiar notions are considered and investigated: that of a fragment, (...) of definitional equivalence, and of a conservative extension. (shrink)