Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define "pressure." The examples illustrate the importance of probabilistic averaging as a method of (...) abstracting away from the messy details of microphenomena, not only in physics, but in other sciences as well. (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)

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)

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the infinite-dimensional counterparts of simple notions such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to the choice of a model. It is also shown that in this formalism a single tensor equation on an infinite-dimensional (...) manifold produces a family of functional equations on different spaces of functions. (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)

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)

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)

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.

Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.

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)

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 paradoxes of the double-slit experiment with an electron are shown to originate in the implicit assumption that the electron is always located in the classical space. It is demonstrated that there exists a natural substitute for this assumption that provides a method of resolving the paradoxes.

The paradoxes of the EPR experiment with two particles are shown to originate in the implicit assumption that the particles are always located in the classical space. There exists a substitute for this assumption that yields a new definition of reality and offers a resolution of the paradoxes.

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)

Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the non-unitary collapse processes are interpreted as isometric functional transformations. Several experiments are analyzed in the new context.

I argue that St. Augustine of Hippo was the first in the history of Christian spirituality who expressed a key tendency of Christian mysticism, which implies a gradual intellectual ascent of the human soul to God, consisting of the three main stages: external, internal, and supernal. In this ascent a Christian mystic proceeds from the knowledge of external beings to self-knowledge, and from his inner self to direct mystical contemplation of God. Similar doctrines may be found in the writings of (...) the Greek Fathers. Although there are many similarities in the overall doctrine and in particular details between them, it does not imply the direct impact of Augustine’s theological thought on the Greek Fathers but rather the influence of the Neoplatonic philosophy on both Western and Eastern Christianity, in particular, of Plotinus’ theory of intellectual cognition. (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)

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)

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)

Some biblical texts suggest that man consists of two parts—body and soul—whereas others seem to indicate instead three parts—body, soul, and spirit. This paper examines how the Church Fathers dealt with this apparent contradiction. It finds that although they generally favor the body-soul dichotomy, they did not see it as contradicting a trichotomous view, for “spirit” can be interpreted in a number of ways: as another term for the soul, or as the lowest imaginative part of the soul, or as (...) its highest rational part, or as the grace of the Holy Spirit. Different approaches can be found in different patristic authors depending on their theological interests and the biblical passages at issue. (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.

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.

The paper considers Plato’s theory of language through the prism of the Timaeus’ metaphysics. It is argued that the apparent contradictions of Plato’s philosophy of language are the consequence of the two-fold nature of language, and that the metaphysical scheme proposed by Plato in the Timaeus can shed a light on his coherent theory of language. The linguo-metaphysical isomorphism of the Timaeus presupposes that (1) words and material elements have their own meaning and nature respectively; (2) they can be reduced (...) to an infinite variety of amorphic sounds and receptacle; (3) the participation in truth is possible only at the level of narrative and universe. According to this scheme the universe (κόσμος), as well as any speech (λόγος), can be explained by the reduction to its constituent elements, but it will be only necessary explanation. Whereas for Plato, the true understanding of cosmos and logos is possible only on the level of the coherent unity of the whole, which represents the ideal paradigm in the best possible way. (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)

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)

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 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)

Composition-nominative logics are program-oriented logics. They are based on algebras of partial predicates which do not have fixed arity. The aim of this work is to present CNL as institutions. Homomorphisms of first-order CNL are introduced, satisfaction condition is proved. Relations with institutions for classical first-order logic are considered. Directions for further investigation are outlined.

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)

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)

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)

The paper discusses Norman Malcolm’s interpretation of Anselm’s ontological argument. Since Malcolm had shown no interest in religious or theological issues prior to publishing his article on that subject in 1960, the analysis takes clue from Malcolm’s earlier writings. By doing so, I revisit the assessment of the ontological argument as fallacious and the tendency to assess Anselm from the traditional framework initiated by Kant. As I demonstrate, Malcolm interpreted Anselm based on the method elaborated during the 1950s. That method (...) involved a synthesis between ordinary language philosophy and common sense philosophy, associated with the late Wittgenstein and Moore respectively. As I further argue, the usual objections to Malcolm’s approach ignore the main line of his reasoning: that Anselm’s ontological argument does not violate ordinary language. Indeed, the two concepts of God as “the greatest of all beings” and of the necessity of God’s existence both perfectly fit in how language works. The “God-talk” is therefore logical only in accordance with Malcoms definition of logical: an explication of the rules of ordinary language, whereas each and every argument against Anselm’s ontological proof violates ordinary language drastically. In his late works on the subject, Malcolm suggested that multiple proofs of God’s existence should be viewed as expressions of a specific philosophic pathology whose underlying drive is a justification of various forms of life. Instead of regarding this idea as “fideistic” (e.g., in K. Nielsen’s work), I propose that the very concept of ordinary language, as Malcolm developed it, makes a treatment of language games along the lines of dependence or independence obsolete. Rather, a crucial issue that Malcolm pushes to investigate is how religious statements correlate with ordinary language. (shrink)

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 is related to the revealing of the intent of Hegel’s “Science of Logic”. As authors take it, there is an attempt to imagine the fundamental level of reasoning, where there is no opposition between cognition and its object. In this dimension there is no need to substantiate compatibility between them — it is a level of primary foundation of knowledge. Consequently, any knowledge at this level may be characterized as “Ultimate”. That being said, place of such knowledge is (...) not taken by several specific statements, but by the certain way of organizing those “mental definitions” that are already used by common human sense. To organize these definitions, to arrange them into consistently deployed sequence of logical notions, there is need to abort the search for the primary foundation for knowledge inherent in philosophy from its very origins. This attempt was reflected in Kant's theory of knowledge, where the problem of the reliability of knowledge was solved due to self-limitation in the process of cognition — it was necessary to stop before a certain line, beyond which thought leaves “the limits of possible experience” and falls into the area of insoluble contradictions (antinomies). Hegel's Logic, which, according to the authors, is in a kind of “symbiosis” with the Kantian program, consists in considering these insoluble contradictions precisely as a “symptom” of achieving the primary foundation of knowledge. It is in the collision with an insoluble contradiction that the definitions are organized in the necessary logical sequence, and that fundamental level is reached where there is no opposition between cognition and its object. (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 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)

Standard semantics of proper names assigns them the function of reference to individual things. This presupposes that to understand the meaning of a proper name is to understand what it denotes in the context of its referential use. But unambiguous identification of the referent of a proper name in its normal (referential) use looks like an unsolvable problem. Senses associated with referential uses of such names don't allow ascribing them singular referents in their contexts; and what concerns contexts themselves, they (...) either don't contain proper referents at all or contain more than one, thus being referentially ambiguous. Some philosophers of language believe that the main problem for the standard semantics of proper names is that they assign them referents of wrong kind: that these, for instance, should be rather abstract entities, i.e. sets, than individual things. In this paper I try to argue that the choice of an alternative semantics for proper names does not solve the main problem with their meanings, i.e. that of their referential ambiguity. On the one hand even in the most transparent contexts there is always available an alternative referent to be assigned to the proper name's use along with some standard or default one; the fact that we prefer some standard interpretation (when we actually do) over alternative ones reflects at best that certain semantic theories contribute more substantially to ordinary communication in comparison with others. This does not yet imply that they better explain meanings of proper names. On the other hand there is also no good explanation of a phenomenon of reference to a particular thing as such: we still don't understand how a name may become referring to one and the same particular thing in many different situations for many different agents of its use etc., and how the thing may literally become a bearer of a name. (shrink)

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)

The article comprises three parts. Part I contains an overview of the areas in the analysis of modern French philosophy that have been of the greatest relevance to Russian researchers over the last years. We conclude that numerous aspects of the French philosophical thought of the twentieth century are well represented in the research of Russian authors, who also point out the emerging trends in its development. Part II deals with the development of analytic philosophy in Russia within the framework (...) of such areas as “critique of bourgeois philosophy”, a purely ideological stand only nominally related to philosophy, logic, and the history of philosophy and theoretical research. Part III contains a periodization of the history of phenomenology in Russia, pointing out the most important achievements of the contemporary Russian scholars of phenomenology as well as their understanding of the essence, the problems, and the aims of phenomenological philosophy. We also indicate the tendencies within the development of the discipline in the Russian Federation. (shrink)

This article examines the views of Latin American philosophers on the process of formation of the Latin American subject of history, its characteristic features, as well as the role of the intellectual in this process. The main objective of this paper is to demonstrate the position of the prominent Argentine philosopher A. A. Roig, and to compare his position with the position of another well-known representative of the philosophy of liberation (E. Dussel). In this paper therefore, Roig's works devoted to (...) the philosophical interpretation of the process of formation and development of Latin American national thought are analyzed. It is established that in the writings of this thinker the activity of Latin American people appears as the activity of a single collective subject of history. During the study, we conclude that both philosophers (Roig and Dussel), come to the same idea in different ways: the intellectual identity of the Latin American collective subject of history is based on the history of interaction between the people of Latin America and Europe, unique in its dramatic nature and same for the entire continent. The work uses mainly the historical and bibliographic method, as well as the method of comparative analysis. (shrink)

The immunoglobulin molecule is a perfect template for the de novo generation of biocatalytic functions. Catalytic antibodies, or abzymes, obtained by the structural mimicking of enzyme active sites have been shown to catalyze numerous chemical reactions. Natural enzyme analogs for some of these reactions have not yet been found or possibly do not exist at all. Nowadays, the dramatic breakthrough in antibody engineering and expression technologies has promoted a considerable expansion of immunoglobulin's medical applications and is offering abzymes a unique (...) chance to become a promising source of high‐precision “catalytic vaccines.” At the same time, the discovery of natural abzymes on the background of autoimmune disease revealed their beneficial and pathogenic roles in the disease progression. Thus, the conflicting Dr. Jekyll and Mr. Hyde protective and destructive essences of catalytic antibodies should be carefully considered in the development of therapeutic abzyme applications. (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)