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.

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 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)

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.

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)

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)

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.

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 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)

Name der Zeitschrift: Der Islam Jahrgang: 94 Heft: 2 Seiten: 462-495.

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)

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)

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)

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)

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)

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)

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)

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 consensus is that novels can be fully appreciated only through an experiential engagement with their well-formed instances. But what are the entities that serve as such instances? According to the orthodox view, these entities are primarily inscriptions—concrete texts written or printed on something or displayed on the screen of some electronic device. In this paper, I argue that this view is misguided, since well-formed instances of a novel must manifest certain sonic properties, but such properties cannot be manifested by (...) inscriptions. As an alternative, I put forward the view that the entities that serve as well-formed instances of novels are readings and sums of readings and graphic elements. (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 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)

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)

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)

Cell interdivision periods (IDP) in homogenous cell populations vary stochastically. Another aspect of probabilistic cell behavior is randomness in cell differentiation. These features are suggested to result from competing stochastic events of assembly/disassembly of the transcription pre‐initiation complex (PIC) at gene promoters. The time needed to assemble a proper PIC from different proteins, which must be numerous enough to make their combination gene specific, may be comparable to the IDP. Nascent mRNA visualization at defined genes and inferences from protein level (...) fluctuations in single cells suggest that some genes do operate in this way. The onset of mRNA production by such genes may miss the time windows provided by the cell cycle, resulting in cells differentiating into those in which the respective mRNAs are either present or absent. This creates a way to generate cell phenotype diversity in multicellular organisms. (shrink)

In this paper the questions remaining open about NP-completeness of multiplicative and Horn fragments of the Linear Logic and the Linear Logic with the weakening rule are answered.

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. 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)

Name der Zeitschrift: Internationales Jahrbuch für philosophische Anthropologie Jahrgang: 7 Heft: 1 Seiten: 17-32.

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)

Der vorliegende Beitrag entwickelt Überlegungen zur Geschichte und zum gegenwärtigen Zustand der Psychoanalyse in der Ukraine. Der Autor führt die aktive Entwicklung der Psychoanalyse in den postsowjetischen Ländern sowohl auf wirtschaftliche Gründe – den Zusammenbruch des Gesundheitssystems – als auch auf ideologische Emanzipation zurück. Er beschreibt die Entwicklung der Ukrainischen Psychoanalytischen Gesellschaft (UPG) und die traumatischen Auswirkungen des gegenwärtigen Krieges auf sie, wobei er die verschiedenen Stadien seiner persönlichen Entwicklung und der Entwicklung der Berufsgemeinschaft anhand von klinischen Beispielen illustriert. Die (...) umfangreichste klinische Illustration handelt von der Reaktualisierung traumatischer Erfahrungen, einschließlich transgenerationaler Erfahrungen, durch den Krieg. (shrink)

This article explores theoretical conditions necessary for “quantum immortality” as well as its possible practical implications. It is demonstrated that QI is a particular case of “multiverse immortality”, which is based on two main assumptions: the very large size of the universe ; and a copy-friendly theory of personal identity. It is shown that a popular objection about lowering of the world-share of an observer in the case of QI does not succeed, as the world-share decline could be compensated by (...) merging timelines for the simpler minds, and because some types of personal preferences are not dependent on such changes. Despite large uncertainty about the truth of MI, it has appreciable practical consequences for some important outcomes like suicide and aging. The article demonstrates that MI could be used to significantly increase the expected subjective probability of success of risky life extension technologies, such as cryonics, but that it makes euthanasia impractical because of the risk of eternal suffering. Euthanasia should be replaced with cryothanasia, i.e. cryopreservation after voluntary death. Another possible application of MI is as a last chance to survive a global catastrophe. MI could be considered a Plan D for reaching immortality, where Plan A consists of survival until the development of beneficial Artificial Intelligence capable of fighting aging, Plan B employs cryonics, and Plan C is digital immortality. (shrink)