The article stresses that Georgy P. Fedotov's systematic reference to the Bible enabled him in his historical monographs to reconstruct the spiritual reality of past eras and symbolically perceive the present. Fedotov intended to know The Gospel in History, Russian religiosity, exploring it on the material of hagiographies of saints, spiritual poems, folk faith, apocrypha, and prologues. Fedotov considered the history of Russian culture in terms of a "living chain," an integral phenomenon existing due to the Holy Scriptures and Holy (...) Tradition. However, "The sacred tradition of the Church is included in the general stream of historical tradition, all complex, always muddy, human weaving truth and falsehood." Fedotov raised the question of the relationship between scientific criticism and biblical exegetics: how can we reconcile exegetics of sacred texts, which assume that the Bible is an inspired book, and historical criticism, which by its very nature cannot share such a position, being aimed at comprehending objective historical reality? He solved it convincingly practically through hermeneutic religious analysis of hagiographic monuments and spiritual verses. In his Spiritual Poems Fedotov explores folklore material compared to biblical texts, hagiographies, and apocrypha, to comprehend the peculiarity of religious "Weltanschauung" and popular orthodoxy. In spiritual verses, there was a transformation of biblical images under the influence of folk faith with pagan features. In folklore texts, Fedotov reveals how Christ, from savior and redeemer, turns into a king and dreadful judge. The image of the Mother of God merges in the popular consciousness with the image of the mother earth, suffering from people. Eschatological prophecies are based on impressions from icons, frescoes, and lubok pictures. Fedotov's historical monographs illuminate various aspects of Russian religious consciousness regarding Holy Scripture, considering dogmatic biblical exegetics and historical criticism. All the mentioned facts allow us to assert that Fedotov was the leading secular biblical scholar of the Russian diaspora. (shrink)

Xenophanes claimed that God is a ball, which means that he is a perfect body. This idea is well developed in Jagannatha worship, who is a central Deity in Orissa, India. It’s a round form of Krishna, who is usually depicted in a human like form. Jagannatha, his brother Baladeva and sister Subhadra are justified as round forms because of their specific manifestation of ecstasy, that, according to aesthetical theory (rasa tattva) happened to them. Yet there are many other explanations (...) of the Jagannatha’s roundness. Round form personifies unity and diversity principle in Jagannatha worship, whose image was dear in Orissa duringlong historical period to different religious groups: Vaishnavas, Shaivaites, Jains, Buddhists and even some Muslims. Orissa also has a blending of different cultures, sub-cultures and traditions. Even now, it has 62 distinct tribal groups, that makes a largest collection of diverse tribes in a single state. As the legend goes, Jagannatha made His first appearance in the tribe of Savaras thousands of years ago. Up until now, there are cooks in the Jagannatha kitchen that are called sauviras. In worship of Jagannatha we find the model of axiological globalism, when the difference in the vision of the reality does not obscure the interior mood of wholeness, unity. (shrink)

The king therefore went down to the village, since the Wise Men's rule did not permit him to spend more than a day with them, but Iarchas said to the messenger, ‘Damis too we consider worthy of the secrets here, so tell him to come, while you look after the others in the village.’ When Damis had come, the Wise Men formed their usual circle and gave Apollonius permission to put questions. So he asked what they thought the universe consisted (...) of, to which they replied, ‘Elements.’ ‘Four, do you think?’ he said. ‘Not four’, said Iarchas, ‘but five.’ ‘What could a fifth one be’, said Apollonius, ‘besides water, air, earth, and fire?’ ‘Ether’, said Iarchas, ‘which we must consider to be the origin (γένεσιν) of the gods. All that breathes air is mortal, but what breathes ether is immortal and divine.’ Next Apollonius asked which of the elements came into existence first. ‘All came together’, said the other, ‘since a living being is not born one piece at a time.’ ‘Am I to consider the universe living?’, asked Apollonius. ‘Yes, if you reason correctly’, said Iarchas, ‘since itself it gives life to everything.’ ‘Should we then call it female’, asked Apollonius, ‘or of the contrary, male sex?’ ‘Of both’, was the answer, ‘since it has intercourse with itself, and performs both the mother's and the father's role with respect to generation. It feels a desire for itself more intense than that of any two other beings, and this joins and unites it, and there is nothing unreasonable about its coalescence. And just as the action of the hands and feet in a living creature comes from mobility and the intelligence (διὰ τὸν ἐκείνου νοῦν) that causes it, so also we must suppose that, because of the intelligence of the universe (κατὰ τὸν ἐκείνου ϕοιτᾷ νοῦν), its parts accommodate themselves to everything that undergoes birth and conception. For instance, the sufferings resulting from drought arise from the mind of the universe, when justice is banished from mankind and treated with dishonor. And this being guides itself not by one hand alone but by many unseen ones that it uses; though too large to be restrained, it moves obediently and tractably.’The doctrine contained in this extract – the only passage ofThe Life of Apollonius of Tyanatreating matters of ‘cosmogony’ – could be summarized in the six following propositions. First, the universe consists of five, not four elements, the fifth being the ether, the γένεσις θεῶν. Just as mortals breathe air, gods breathe ether. Secondly, there is no ‘primordial element’; all five came into being simultaneously. Thirdly, the universe is a living being. In the fourth place, the universe is both male and female at the same time. In the fifth place, as the universe is androgynous it feels desire (ἔρως) towards itself and it is this desire that makes it whole and united. And finally, the passion of the universe for itself is governed by Intelligence (ἐκείνου νοῦς). (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized functions to solve (...) nonlinear problems on Hilbert spaces. (shrink)

Newtonian and Scr{\"o}dinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. A formula relating the normal probability distribution and the Born rule was also found. Here the dynamical mechanism responsible for the latter formula is proposed and applied to measurements of macroscopic and microscopic systems. A relationship between the (...) classical Brownian motion and the diffusion of state on the space of states is discovered. The role of measuring devices in quantum theory is investigated in the new framework. It is shown that the so-called collapse of the wave function is not measurement specific and does not require a ``concentration" near the eigenstates of the measured observable. Instead, it is explained by the common diffusion of state over the space of states under interaction with the apparatus and the environment. This in turn provides us with a basic reason for the definite position of macroscopic bodies in space. (shrink)

An analogy between the evolution of organisms and some complex computational problems (cryptosystem cracking, determination of the shortest path in a graph) is considered. It is shown that in the absence of a priori information about possible species of organisms such a problem is complex (is rated in the class NP) and cannot be solved in a polynomial number of steps. This conclusion suggests the need for re-examination of evolution mechanisms. Ideas of a deterministic approach to the evolution are discussed.

This article gives a general characteristic of the publications of the Russian philosophers in the oldest Kantian Journal “Kant-Studien”. The study embraces the entire period of the existence of this magazine, from the very beginning down to our days. In general, after compiling all materials related to Russia published in “Kant-Studien”, I became aware of get a picture of a significant presence of Russian philosophers in this periodical. This gives me a good reason to conclude that even if the impact (...) of the Russian philosophical thought on the international Kant studies was not decisive, then, at least, it was tangible. This influence was due to the phenomenon which was later called the “Silver Age of Russian philosophy”, as well as the phenomenon of Russian emigration, arising as a result of wars and revolutions in Russia and the exodus of the Russian philosophers of the West, where one of their main initial shelters was Germany. (shrink)

Some are attracted to the view that repeatable artworks, such as films, novels, plays, symphonies, photographs, and the like, are a particular kind of abstracta—namely, types. This view, however, is not unproblematic. One of the most serious problems it faces is the so-called "creation problem." The core idea behind this problem is that, on the one hand, it seems reasonable to accept the claims that (1) repeatable artworks are types, (2) types cannot be created, and (3) repeatable artworks are created, (...) but, on the other hand, these claims form an inconsistent triad. A popular solution to the creation problem is that (2) can be rejected because the justification for (2) is based on a false assumption—that no type can stand in causal relations. Although this solution looks promising, it can be accepted only if its proponent can refute what might be called the "paraphrasability argument." On this argument, types are not to be regarded as capable of standing in causal relations because any discourse implying the causality of types should be paraphrased into discourse that does not imply this. My aim in this essay is to show that there is good reason to consider the paraphrasability argument sound and, hence, that the foregoing solution to the creation problem fails. (shrink)

A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincare transformations is introduced. For a class of functions in H that are well localized in the time variable the usual formalism of non-relativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; a motion in H becomes (...) the usual Shrodinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical space-time is isometrically embedded into H, Poincare transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincare transformations. (shrink)

In modern philosophy, essentialism is in most cases regarded as an outdated and, in fact, incorrect philosophical trend. And one of the scientists who created such a reputation of essentialism was the famous English philosopher of Austrian origin Karl Popper. The success of his book “The Open Society and its Enemies” led to the fact that in the West essentialism began to be considered not only cognitively untenable, but also suspicious as the theoretical basis of fascism, communism and totalitarianism. In (...) the article, K. Popper’s arguments against essentialism are reviewed all over again, and it is shown that K. Popper’s criticism of essentialism as an anti-scientific and outdated doctrine is not the point of view of the philosophy as a whole, but it is just the position of empirical positivism. Essentialism deals with the reality that lies on the other side of phenomena. And this, according to K. Popper, necessarily leads to “ultimate” definitions. However, in accordance with the doctrine of falsification by K. Popper himself, every scientific conclusion within its expiration date is “ultimate”. The article shows that in reality essentialism did not only play an extraordinary role in the classical metaphysical theory of knowledge, but also continues to do so within the framework of modern ontology. Moreover, in the latter case, he does it with the help of abduction which is a specific form of logical inference generating scientific hypotheses. The existence of abduction in science, which generates new knowledge, suggests that essentialism is not something, at best, tolerable and excusable. This is the main way to development of sciences in general. In all cases, the author of the article considers only logical entities, but not legal, theological or any other. (shrink)

Two aspects of the target article, (1) the extension of the equilibrium point theory to multi-joint movements, and (2) the consequence that the EMG pattern is not directly controlled by the central nervous system (CNS), are discussed in light of the experiments on upper trunk bending in humans. The principle component kinematic analysis and the analysis of the EMG data, obtained under microgravity and additional loading conditions, support the application of Feldman and Levin's for multi-joint pointing movement to equilibrium control (...) during upper trunk movement. (shrink)

According to the orthodox view, photographic artworks are abstract objects. This view, however, has recently been challenged by Christy Mag Uidhir. In his article ‘Photographic Art: An Ontology Fit to Print’, he argues in favour of a nominalist construal of photographic artworks. My goal is to show that Mag Uidhir’s argument is unpersuasive.

1. On the contradictory nature of contemporary linguistic theories and how to change it for the better -- 2. A reference-based approach to describing notional words -- 3. Basic-level concepts as the neurobiological codes for memory -- 4. Elements of a sensory grammar -- 5. On the single structure of lexical meanings of nouns and verbs -- References -- Index.

Conformal group of Minkowski space-time M is considered as a group of bundle automorphisms of a vector bundle U over M. 4-component spin-vectors (4-spinors) are sections of a subbundle of the tangent bundle over U. Isotropic 4-vectors are images of 4-spinors under projection. This leads to a particularly clear interpretation of the spin properties of Nature.

We give an affirmative answer to the following question: Is any Borel subset of a Cantor set C a sum of a countable number of pairwise disjoint h-homogeneous subspaces that are closed in X? It follows that every Borel set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X \subset {\bf R}^n}$$\end{document} can be partitioned into countably many h-homogeneous subspaces that are Gδ-sets in X.

We study uncertainty relations for a general class of canonically conjugate observables. It is known that such variables can be approached within a limiting procedure of the Pegg–Barnett type. We show that uncertainty relations for conjugate observables in terms of generalized entropies can be obtained on the base of genuine finite-dimensional consideration. Due to the Riesz theorem, there exists an inequality between norm-like functionals of two probability distributions in finite dimensions. Using a limiting procedure of the Pegg–Barnett type, we take (...) the infinite-dimensional limit right for this inequality. Hence, uncertainty relations are derived in terms of generalized entropies. In particular, the case of measurements with a finite precision is addressed. It takes into account that in any experiment an accuracy of performed measurements is always limited. (shrink)

The article proposes to consider Hegel's “Science of Logic” as a project, where the most important thing is not to describe the “laws of thinking”, but rather to propose a more precise definition of the theoretical level at which thinking itself becomes the subject of its own description. Thus, on the one hand, Hegel reveals the paradox that lies at the basis of the logic as a philosophical discipline, and on the other, seeks to show the possibility of the existence (...) of the logic in the extreme conditions of this paradox. Within the framework of this approach, logic is inseparable from the theory of knowledge — it is assumed that the configuration or “form” of thinking cannot be “neutral” with respect to its content. Therefore, according to Hegel, in reality there is not the logic of isolated operations occurring in the mind, but the logic of “the object itself”, which shows and directly embodies itself in these operations. At this level, there is no gap between the thinking consciousness and objects of the external world separated from it. We are talking about a special — “pre-ontological” — dimension, where the subject's sensory experience is not yet launched and distinguished, and a subject of the thinking process and thinking itself form a single whole. Such a dimension is developed in the historical experience of philosophical thought, starting from Antiquity, and is captured by Hegel under the name of “Ultimate knowledge”. The article raises the question of why this dimension repeatedly eludes us, acquiring a “semi-mystical” status in the minds of Hegel's interpreters, and yet how it is still possible to infiltrate into it. (shrink)

The article considers the connection between ethics, in particular Kant’s practical philosophy, and economics. The author examines historical reasons for Kant’s ethic not to have become part of the economic discourse and interprets modern business processes from Kant’s perspective. The article aims to demonstrate the possibilities of applying the philosophical instruments of Kant’s morals to concrete economic issues.

The research identifies the amount of headline/article discrepancies in the corpora of western and Russian online articles on sensitive political topics. A quarter of the western headlines and nearly half of the Russian headlines distort the publications they introduce. Language means and manipulative strategies employed by different sides vary considerably. Extensive use of expressive language and style variation are seen as leading causes of distortions in the western corpus. The rich imagery used by the authors forms emotional implicatures that affect (...) the reader’s perception of the issue. In contrast, information substitution, subjective modality and selective citations are identified as major causes of distortions in the Russian corpus. Contributors to Russian news outlets rely on general rather than language manipulation strategies, including frequent use of logical fallacies and wrong generalizations. These techniques establish false logical sequences and wrong causative implicatures that compromise objective reporting. The underlying motives of the journalists’ creating false emotional and causative implicatures in the headlines lies beyond the scope of the study; however, it is assumed that intentional change of the information introduced by the headline could be viewed as a covert misinformation attempt. (shrink)

Gregory Savich Skovoroda (1724-1794) belongs both to the Russian and Ukrainian philosophy. His philosophical doctrine was only revivified at the turn of the 19th-20th centuries, which was caused by the affinity of the philosophical searches of the Silver Age (beginning of the 1890s-1922) with the religious and philosophical doctrine by Gregory Skovoroda. In the history of philosophy, Gregory Skovoroda can be considered «boundary figure» marking transition from the Middle Ages to the culture of the Modernity. The article deals with the (...) thinker’s ethical doctrine, particularly, with two interpretations of nature: essential and voluntary. Moralizing was the main aim and content of the most works by Gregory Skovoroda. Practical philosophy by Gregory Skovoroda immediately sides with his understanding of nature. Volition, wish (desire), affinity, true man are its basic categories. The main aim of Skovoroda’s moralizing is to show the way to the happy life. The essential topic of the Skovoroda’s creative work are concentrated in his ethics: ontology, or doctrine of three worlds (microcosm, macrocosm, symbolic world – the Bible), exegetical method of cognition and symbolism, doctrine of nature and category of affinity, the principle of self-cognition and doctrine of the «true man», doctrine of heart and anthropology, eudemonism and problem of reality of the evil and the good in the world. According to the canons of the symbolism Skovoroda criticizes material, corporeal side of the world and gives preference to its spiritual meaning. Nevertheless, Skovoroda remains a religious thinker in his practical philosophy; he meditates per religious canons. For the 18th century Gregory Skovoroda’s doctrine had been as archaic as it became relevant at the turn of the 19th-20th centuries. (shrink)

In On the Genesis of Thought and Language, linguist Alexey Koshelev explores fundamental questions of how human concepts arise in a child, why concepts appear in a child before words, the genesis of language, and why there are so many languages. Chapter One introduces the fundamental dichotomy "visual (exogenous) vs. functional (endogenous)" cognitive units; these units are used to give non-verbal definitions of mental representations of various objects, actions, and situations. In particular, definitions of such concepts as GLASS, CHAIR, (...) BANANA, TREE, LAKE, RUN, and some others are given. Chapter Two discusses how children form concepts, hierarchical relationships, and propositions (conceptual 'utterances'). It is shown that the initial units of the child's representation of the world are pre-conceptual cognitive units--mental representations of whole situations. In the course of two consecutive cycles in the child's cognitive development, these units transform into (a) primary notions--object and motor concepts, and (b) binary role relationships. Together, they constitute the elementary language of thought which, in the process of thinking, is used to build conceptual structures--propositions. It is further demonstrated that, immediately after the formation of thought, the child begins to develop his native language in which concrete and motor concepts become initial meanings of nouns and verbs, while propositions become the meanings of the child's expressions. The chapter concludes with a contrastive analysis of the proposed approach and Aristotle's and Chomsky's views on thought and language. Chapter Three analyzes how a community's culture affects its language. It is demonstrated that the progress of a community, the main constituent of the civilizational component of its culture, enhances the development of the content component of language by extending the range of its lexical and grammatical meanings. In the context of this analysis, Daniel Everett's (2008) hypothesis that culture affects language structure is discussed. In the subsequent sections, models of the development of human and social activity are offered. These models comprise three components: Activity (main component), Thought, and Language (auxiliary components that ensure the successful realization of activities). The models are illustrated with examples of some concrete societies. (shrink)

The consensus is that repeatable artworks cannot be identified with particular material individuals. A perennial temptation is to identify them with types, broadly construed. Such identification, however, faces the so-called “Creation Problem.” This problem stems from the fact that, on the one hand, it seems reasonable to accept the claims that (1) repeatable artworks are types, (2) types cannot be created, and (3) repeatable artworks are created, but, on the other hand, these claims are mutually inconsistent. A possible solution to (...) the Creation Problem is to argue that claim (2) can be rejected because (a) the only motivation for it is that a type, being abstract, cannot stand in causal relations, but (b) this motivation is ungrounded, since types can, in fact, stand in such relations. Clearly, in order for this solution to be successful, it is necessary to substantiate the possibility of types to be causally efficacious. In this essay, I examine an attempt to do this with the help of Yablo’s principle of proportionality, which has been undertaken by Walters (2013) and, more recently, Juvshik (2018). Although the argument they advance may seem to provide strong support for the causal efficacy of types, I think it actually fails to do this. To explain why this is so, I first show that this argument commits us to the existence of widespread causal overdetermination involving types and then argue that this commitment is both epistemically and ontologically problematic. (shrink)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the (...) perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented. (shrink)

The expression ‘an instance of an artwork’ is often used in philosophical discourse about art. Yet there is no clear account of what exactly this expression means. My goal in this essay is to provide such an account. I begin by expounding and defending a particular definition of the concept of ‘an instance of an artwork’. Next, I elaborate this definition – by providing definitions of the main derivatives of the concept of ‘an instance of an artwork’, namely the concepts (...) of ‘a well-formed instance of an artwork’ and ‘a non-wellformed instance of an artwork’. Finally, I examine the relation of the foregoing definitions to the existence and identity conditions of artworks and make some additional remarks concerning these definitions. (shrink)

Recently, a number of philosophers have defended a novel, materialist view on the nature of musical works—musical perdurantism. According to this view, musical works are a peculiar kind of concreta, namely perduring mereological sums of performances and/or other concrete entities. One problem facing musical perdurantism stems from the thought that if this view is correct, then virtually no musical work can exist in a continuous, non-intermittent fashion. The aim of this paper is to expound this problem and show that it (...) cannot be plausibly solved by a musical perdurantist. (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 106 Heft: 3 Seiten: 518-522.

Name der Zeitschrift: Kant-Studien Jahrgang: 105 Heft: 3 Seiten: 418-420.

My goal is to conceive how the reality would look like for hypothetical creatures that supposedly perceive on time scales much faster or much slower than that of us humans. To attain the goal, I propose modelling in two steps. At step one, we have to single out a unified parameter that sets time scale of perception. Changing substantially the value of the parameter would mean changing scale. I argue that the required parameter is duration of discrete perceptive frames, or (...) snapshots, whose sequencing constitutes perceptive process. I show that different standard durations of perceptive frames is the ground for differences in perceptive time scales of various animals. Abnormally changed duration of perceptive frames is the cause of the effect of distorted subjective time observed by humans under some conditions. Now comes step two of the modelling. By inserting some arbitrary duration of a perceptive frame, we set a hypothetical scale and thus emulate a viewpoint for virtual observation of the reality in a wider or narrower angle of embracing events in time. Like changing lenses of a microscope, viewing reality in different temporal scales makes certain features of reality manifested, others veiled. These are, in particular, features of life. If we observe an object in an inappropriate interval, we may not notice the very essence of a process it is undergoing. (shrink)

There is a widely shared belief in contemporary epistemology that propositional knowledge is incompatible with certain kinds of luck, most of all with so called veritic luck. A subject is veritically lucky in his or her belief that p if this belief is true not due to its foundations (for example, reasons which an agent has to believe that p) but by mere accident. The acceptance of the thesis of incompatibility of knowledge with this kind of luck led to significant (...) modifications of a popular modern epistemological tripartite analysis of propositional knowledge according to which subject knows that p if and only if he or she believes that p is true, p is actually true, and an agent’s belief that p is true is justified. In his famous paper “Is True Justified Belief Knowledge” E. Gettier demonstrated that true justified belief may not be knowledge. The core of the problem is that in the cases described by Gettier and the like an agent’s belief, though justified, is true by accident. This gave rise to a set of theories introducing additional conditions of knowledge which could exclude veritic luck. In this paper the author critically discusses main modifications of the tripartite concept of knowledge aimed at making it independent on veritic luck, and show that they are unable to solve this problem. He agrees with those who think that the very thesis of incompatibility of knowledge with veritic luck is wrong. But he disagrees that all kinds of veritic luck are compatible with knowledge: the author supposes that good veritic luck is compatible with knowledge only when it compensates some negative effect of antecedent bad epistemic luck. According to this view original Gettier examples are not cases of knowledge whereas broken-clocks case and fake-barns case are. This account allows treating many classic cases of dependence of knowledge on luck as cases of knowledge-acquirement, but in the same time it excludes the inclusion into the class of knowledge such intuitively irrelevant outcomes as lucky guess and wishful thinking. (shrink)

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov}, \cite{Kryukov1} is further analyzed. The main subject here is a comparison of the ordinary and the string bases of eigenvectors of a linear operator as introduced in \cite{Kryukov}. It is shown that the string basis of eigenvectors is a natural generalization of its classical counterpart. It is also shown that the developed formalism forces us to consider any Hermitian operator with continuous spectrum as a restriction to a space of square integrable functions (...) of a self-adjoint operator defined on a space of generalized functions. In the formalism functional coordinate transformations preserving the norm of strings are now linear isometries rather than the unitary transformations. (shrink)

This paper is concerned with the logical structure of intuitionistic equality theories. We prove that De Jongh theorem holds for the theory of decidable equality, but uniform De Jongh theorem fails even for the theory of weakly decidable equality. We also show that the theory of weakly decidable equality is the weakest equality theory which enjoys Glivenko theorem.

In the course of the last 20 years, the problem of Kant’s view of races has evolved from a marginal topic to a question which affects his critical philosophy in general, including the anthropology and its influence on contemporary social studies. The goal of our paper is to examine the anthropological role of Kant’s concept of race from the largely overlooked or underestimated perspective of his Lectures on Anthropology. Taking into account the differences between Kant’s approach in the early lectures (...) of the 1770s and early 1780s and the lectures of the late 1780s in the light of the development of the idea of race in Kant’s works, we will demonstrate that several key elements of Kant’s 1780s theory of race presented in his published works can be found in his early lectures. On the other hand, we will prove that Kant gradually abandons racial hierarchies and moral characteristics of races in his anthropological lectures of the late 1780s and in the Anthropology from the Pragmatic Point of View, shifting his focus to more nuanced descriptions of morals of different nations. (shrink)

A classification of the global catastrophic risks of AI is presented, along with a comprehensive list of previously identified risks. This classification allows the identification of several new risks. We show that at each level of AI’s intelligence power, separate types of possible catastrophes dominate. Our classification demonstrates that the field of AI risks is diverse, and includes many scenarios beyond the commonly discussed cases of a paperclip maximizer or robot-caused unemployment. Global catastrophic failure could happen at various levels of (...) AI development, namely, before it starts self-improvement, during its takeoff, when it uses various instruments to escape its initial confinement, or after it successfully takes over the world and starts to implement its goal system, which could be plainly unaligned, or feature-flawed friendliness. AI could also halt at later stages of its development either due to technical glitches or ontological problems. Overall, we identified around several dozen scenarios of AI-driven global catastrophe. The extent of this list illustrates that there is no one simple solution to the problem of AI safety, and that AI safety theory is complex and must be customized for each AI development level. (shrink)

Quantum mechanics is one of the most successful theories of physics. But the creators of quantum mechanics had to reject realism in order to describe some paradoxical quantum phenomena. Einstein considered the rejection of realism unacceptable, since according to his understanding, realism is the presupposition of every kind of physical thinking. The dispute about the permissibility of rejecting realism has largely determined the modern understanding of quantum theory and even led to the emergence new quantum information technologies. Many modern authors (...) are sure that realism can be refute experimentally. Some authors are sure even that real technologies can be created on the basis of this refutation. The well-known GHZ theorem is considered critically in this work the authors of which are sure that realism can be refute experimentally. (shrink)

The article is devoted to the analysis, and introduces the publication, of one of the texts of the documentary complex ‘The Verkhne-Uralsk Political Isolator Notebooks’ – the ‘Theses on Economic Policy’ of 1933. The article (DOI: 10.1163/1569206X-00002252) covers the history of the discovery of this complex of documents reflecting the ideological and political life of imprisoned members of the Opposition of the Bolshevik Leninists (Trotskyists) in the early 1930s, and discusses the context of their creation. On the basis of archival (...) materials, the biography of one of the authors of the Theses – the agricultural economist, and a member of the Siberian opposition centre, F.P. Sasorov – is reconstructed. It is noted that Sasorov held a special position among the Bolshevik Leninists, determined by his economic views. He belonged to the current whose adherents were called ‘neo-Nepists’ by their opponents. This current advocated not just a return to the NEP cancelled by Stalin, but also an expansion of its scope, and this position is presented and argued for in the ‘Theses on Economic Policy’. A comparison of the views of Sasorov and his co-author G.A., stated in the Theses, including on the explanation of the crisis and the liquidation of the NEP, the policy of out-and-out collectivisation and forced industrialisation, with the views of Leon Trotsky, allows us to conclude that the thought of the imprisoned oppositionists developed independently, and not always in accordance with the guidelines of their exiled thought leader. The article also examines the forecasts of the development of the economic and socio-political situation in the USSR presented in the Theses. (shrink)

There is widespread opinion that, notwithstanding deviations, the political life of humanity on a large scale is on the path of progress, and humans are becoming freer and more enlightened with time. I am going to contend with this opinion, namely, with a part of it telling that the prevailing mass of the people strives to achieve more freedom and enlightenment. On the opposite, freedom, individual independence, and political rights are of minor importance to the mass. The ideology of liberalism (...) in its classical form, as created by John Locke, Immanuel Kant, John Stuart Mill and others, yields to the pressure of the ideology of state paternalism. The pressure comes not only from above ; the people also welcome more paternalism. They appear not to value their individual freedom and independence, and they are inclined to give them up voluntarily to some mighty organization such as the state in exchange for care, protection and leadership. Liberalism has played an important role in the development of human civilization and the formation of the Western world, but new ideologies and political practices are pushing it out of people’s minds. For the author, as adherent of classical liberalism, this is unfortunate. However, I wish to treat this issue realistically, even if the facts conflict with my own convictions and desires. (shrink)

The idea that knowledge as an individual mental attitude with certain propositional content is not only true justified belief but a belief the truth of which does not result from any kind of luck, is widely spread in contemporary epistemology. This account is known as anti-luck epistemology. A very popular explanation of the inconsistency of that concept of knowledge with the luck-dependent nature of truth (so called veritic luck taking place when a subject’s belief could not be true if not (...) by mere coincidence) presumes that the status of propositional knowledge crucially depends on the qualities of actions that result in the corresponding belief, or processes backing them, which reflect the socalled intellectual virtues mainly responsible for subject’s relevant competences. This account known as Virtue Epistemology presumes that if a belief is true exclusively or mainly due to its dependence on intellectual virtues, it just cannot be true by luck, hence no place for lucky knowledge. But this thesis is hard to prove given the existence of true virtuous beliefs which could nevertheless be false if not for some lucky (for the knower) accident. This led to an appearance of virtue epistemological theories aimed specifically at an assimilation of such cases. Their authors try to represent the relevant situations as such where the contribution of luck is not crucial whereas the contribution of virtues is crucial. This article provides a critical analysis of the corresponding arguments as part of a more general study of the ability of Virtue Epistemology to provide justification for the thesis of incompatibility of propositional knowledge with veritic luck. It is shown that there are good reasons to doubt that Virtue Epistemology can do this. (shrink)

Within the Hebbian paradigm the mechanism for integrating cell assemblies oscillating with different frequencies remains unclear. We hypothesize that such an integration may occur in cortical “interaction foci” that unite synchronously oscillated assemblies through hard-wired connections, synthesizing the information from various functional systems of the brain.

Quantum observables can be identified with vector fields on the sphere of normalized states. The resulting {\it vector representation} is used in the paper to undertake a simultaneous treatment of macroscopic and microscopic bodies in quantum mechanics. Components of the velocity and acceleration of state under Schr{\"o}dinger evolution are given a clear physical interpretation. Solutions to Schr{\"o}dinger and Newton equations are shown to be related beyond the Ehrenfest results on the motion of averages. A formula relating the normal probability distribution (...) and the Born rule is found. (shrink)

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization (...) H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles. (shrink)

Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory (QT) is indeed a functional tensor theory, i.e., it can be described by functional tensor (...) equations. The main equations of QT are shown to be compatible with the principle of functional relativity. By accepting the principle as a hypothesis, we then explain the origin of physical dimensions, provide a geometric interpretation of Planck’s constant, and find a simple model of the two-slit experiment and the process of measurement. (shrink)