Online research in philosophy

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)

Abstract I develop the idea that there exists a special dimension of depth, or of scale. The depth dimension is physically real and extends from the bottom micro-level to the ultimate macro-level of the Universe. The depth dimension, or the scales axis, complements the standard three spatial dimensions. I discuss the tentative qualities of the depth dimension and the universal arrangement of matter along this dimension. I suggest that all matter in the Universe, at least in the present cosmological epoch, (...) is in joint downward motion along the depth dimension. The joint downward motion manifests itself in the universal contraction of matter. The opposite direction of motion, upward the dimension, would cause the expansion of matter. The contraction of matter is a primary factor, whereas the shrinking of space in the vicinity of matter is a derivative phenomenon. The observed expansion of the Universe is explained by the fact that celestial bodies become smaller due to matter contraction, while the overall space remains predominantly intact. Thus, relative to the contracting material bodies, the total span of cosmic space appears to be becoming vaster. I attempt to explain how the contraction of matter engenders the effect of universal gravity. I use over thirty animated and graphical color visualizations in the text to make the explanation of the proposed ideas more lucid. Content Type Journal Article Category Original Paper Pages 1-39 DOI 10.1007/s10516-011-9178-4 Authors A. Alyushin, Department of Philosophy, The Higher School of Economics, 20 Myasnitskaya Street, 101000 Moscow, Russia Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (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)

Alexey Losev's concept of 'personality' was developed in his writings from the 1920s, "The Dialectics of Myth" and "The Philosophy of Name". In his later works (e.g. on the aesthetics of the Renaissance and in his book about Vladimir Soloviev) Losev also understood the 'personality' outside of the boundaries of philosophy and theology. For him, the mystical dimension of personality in the end dominates logical and cultural structures of the subject. Losev's concept of 'personality' as a myth, a symbol, (...) rather than an abstract theory was an attack on the European individualism seen as a principle of the self-affirmation of the isolated subject. (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.

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)

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 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.

Largely due to the difficulty of observing behavior, empirical business ethics research relies heavily on the scenario methodology. While not disputing the usefulness of the technique, this paper highlights the importance of a careful assessment of the fit between the context of the situation described in the scenario and the knowledge and experience of the respondents. Based on a study of online auctions, we provide evidence that even respondents who have direct knowledge of the situation portrayed in the scenario may (...) develop significantly different assessments of the level of unethical behavior. Further, those assessments may be conditioned in different ways by the same moderating variables. We conclude that care should be exercised when recruiting respondents to choose only those who can be expected to understand the scenario in its true context and that separate analyses should be conducted for groups of respondents who have different perspectives within that context. (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 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.

The classical space-time structure 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. Such a realization is associated with the process of measuring position of macroscopic particles naturally occurring in the universe. The process of decoherence and collapse induced by the measurement is in return associated with the choice of a "decohered" submanifold M of realization H*. The submanifold M (...) is then identified with the classical space-time. The mathematical formalism is developed which permits to recover the usual Riemannian geometry on space-time in terms of the Hilbert structure on S. The specific functional realizations of S are shown to produce space-times of different geometry and topology. (shrink)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schroedinger 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 continuation of [JOH04, OH07], we prove that existentially closed CSA-groups have the independence property. This is done by showing that there exist words having the independence property relative to the class of torsion-free hyperbolic groups.

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)

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} 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 form of tensor analysis 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. Quantum measurement and collapse are interpreted as isometric functional transformations. Several experiments including the two-slit experiment are analyzed in the new context.

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.

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)

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.

Machine generated contents note: -- Introduction to the OneThe Concept of One: From Philosophy to Politics -Artemy Magun Part I. Metaphysics of the One and the Multiple1. More than One -Jean Luc Nancy 2. Condivision, or Towards a Non- communitarian Concatenation of Singularities -Gerald Raunig 3. Unity and Solitude -Artemy Magun 4. The Fragility of the One -Maria Calvacante 5. The One: Construction or Event? For a Politics of Becoming -Boyan Mancher Part II. 20th-Century Thinkers of Unity and Multiplicity 6. (...) Truth and Infinity in Badiou and Heidegger -Alexey Chernyakov 7. Complicated Presence: The Unity of Being in Parmenides and Heidegger -Jussi Bachman 8. The Universal, the General, the Multiple in the Perspective of a Political Utopia: Deleuze and Badiou on the Event -Keti Chukhrov 9. Humanity, Unity and the One -Nina Power Part III. Unity and Multiplicity in Nature 10. Elemental Nature as the Ultimate Common Ground of the World Community -Susanna Lindberg 11. Vegetative Democracy, or the Post-metaphysics of Plants -Michael Marder Part IV. Unity in Action: Forms of Political Consolidation in the Case of Contemporary Russia12. Collectivity in Post-revolutionary Russia -Igor Tchubarov13. Street University: Production of Collective Time and Public Space -Pavel Arsenyev 14. Fighting Together: the Problem of Solidarity -Carine Cle;ment Part V. E Pluribus Unum: Res Publica and Community 5. How Does One Constitute the One? Theology of the Icon, Theory of Non-representative Art and of Non-representative Politics -Oleg Kharkhodin 12. Drawing Lots in Politics: Unity and Totality -Yves Sintomer. (shrink)

Machine generated contents note: -- Introduction to the OneThe Concept of One: From Philosophy to Politics -Artemy Magun Part I. Metaphysics of the One and the Multiple1. More than One -Jean Luc Nancy 2. Condivision, or Towards a Non- communitarian Concatenation of Singularities -Gerald Raunig 3. Unity and Solitude -Artemy Magun 4. The Fragility of the One -Maria Calvacante 5. The One: Construction or Event? For a Politics of Becoming -Boyan Mancher Part II. 20th-Century Thinkers of Unity and Multiplicity 6. (...) Truth and Infinity in Badiou and Heidegger -Alexey Chernyakov 7. Complicated Presence: The Unity of Being in Parmenides and Heidegger -Jussi Bachman 8. The Universal, the General, the Multiple in the Perspective of a Political Utopia: Deleuze and Badiou on the Event -Keti Chukhrov 9. Humanity, Unity and the One -Nina Power Part III. Unity and Multiplicity in Nature 10. Elemental Nature as the Ultimate Common Ground of the World Community -Susanna Lindberg 11. Vegetative Democracy, or the Post-metaphysics of Plants -Michael Marder Part IV. Unity in Action: Forms of Political Consolidation in the Case of Contemporary Russia12. Collectivity in Post-revolutionary Russia -Igor Tchubarov13. Street University: Production of Collective Time and Public Space -Pavel Arsenyev 14. Fighting Together: the Problem of Solidarity -Carine Cle;ment Part V. E Pluribus Unum: Res Publica and Community 5. How Does One Constitute the One? Theology of the Icon, Theory of Non-representative Art and of Non-representative Politics -Oleg Kharkhodin12. Drawing Lots in Politics: Unity and Totality -Yves Sintomer. (shrink)