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.

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)

Obwohl es in der bisherigen Nietzscheforschung detaillierte Untersuchungen separater Aspekte von Nietzsches Homerdeutung während der Leipziger und Baseler Periode gibt, fehlt ein Überblick über die gesamte Perspektive von Nietzsches philologischen und philosophischen Beschäftigungen mit Homer. In diesem Buch wird der gesamte Entwicklungsprozess von Nietzsches Homerinterpretation von den frühen philologischen Schriften und Vorlesungen bis hin zu den spätesten Erwähnungen Homers in den Werken und Nachlassfragmenten von 1888 rekonstruiert. Zugleich widmet der Autor den philosophischen Ansätzen Nietzsches besondere Aufmerksamkeit, u.a. seiner Interpretation der (...) Figur des homerischen Odysseus, seiner Deutung des homerischen Polytheismus sowie dem Gegensatz Homer/Platon. Durch die Untersuchung der philosophischen Dimension der philologischen Kontexte schließt das Buch eine wesentliche Forschungslücke und bereitet die Grundlagen für weitere Interpretationen von Nietzsches Bild der griechischen Archaik. (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)

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)

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.

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)

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)

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)

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 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)

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.

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.

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)

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)

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.

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)

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)

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)

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)

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)

This article focuses on the general theoretical issue of realism versus constructivism in politics, with a case of the present-day Russia as the main and most telling example. We present four assertions that we are going to defend. First, we claim that in the sphere of international relations, political realism of the offensive type, after decades of more tempered USA–USSR relations, is again challenging its opponent: political constructivism. Second, political realism is winning in the sphere of domestic politics and policy (...) in the leading countries as well. Third, we touch upon theoretical issues and discuss the ontological nature of political realism in comparison with political constructivism and the kindred of the latter with normativism, legalism, constitutionalism and liberalism. Political constructivism as a concept is underestimated and rarely used. Our article explicates the concept of political constructivism, which is a novel contribution to political theory and political philosophy. Fourth, we show that political constructivism, being the most advanced achievement of political civilization compared to archaic realism, has not lost the game so far and should be upheld in its battle with the remnants of the wild political past. Sliding back to political realism would turn humankind into another degraded animal species instead of making it the pilot in continuing human progress. (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)

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.