Vasil Penchev
Bulgarian Academy of Sciences, Institute of Philosophy, Faculty Member
- I am a Bulgarian philosopher, 60 y.o. I am interested first of all in philosophy of quantum information.edit
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
The article is devoted to quantum information (including its subdomains, namely: quantum communication, quantum computer, quantum cryptography), and its philosophical meaning. Paradox EPR, Bell’s inequality, phenomena of teleportation are... more
The article is devoted to quantum information (including its subdomains, namely: quantum communication, quantum computer, quantum cryptography), and its philosophical meaning. Paradox EPR, Bell’s inequality, phenomena of teleportation are discussed of a philosophical point of view. Quantum mechanical nonlocal correlations are interpreted as topological inseparabilities. Information is considered both as a fundamental physical quantity and as a philosophical category
Research Interests:
Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex... more
Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus funda...
Research Interests:
Research Interests:
The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to become mathematical regardless of being a descriptive humanitarian science with investigating unique events... more
The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to become mathematical regardless of being a descriptive humanitarian science with investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or “complementary” to its model. Particularly, a fundamental law of mathematical history, the law of least choice of the real historical pathway is deducible from the same approach. Its counterpart in physics is the well-known and confirmed law of least action as far as the quantity of action corresponds equivocally to the quantity of information or that of number elementary historical choices.
Research Interests:
The paper investigates the understanding of quantum indistinguishability after quantum information in comparison with the “classical” quantum mechanics based on the separable complex Hilbert space. The two oppositions, correspondingly... more
The paper investigates the understanding of quantum indistinguishability after quantum information in comparison with the “classical” quantum mechanics based on the separable complex Hilbert space. The two oppositions, correspondingly “distinguishability / indistinguishability” and “classical / quantum”, available implicitly in the concept of quantum indistinguishability can be interpreted as two “missing” bits of classical information, which are to be added after teleportation of quantum information to be restored the initial state unambiguously. That new understanding of quantum indistinguishability is linked to the distinction of classical (Maxwell-Boltzmann) versus quantum (either Fermi-Dirac or Bose-Einstein) statistics. The latter can be generalized to classes of wave functions (“empty” qubits) and represented exhaustively in Hilbert arithmetic therefore connectible to the foundations of mathematics, more precisely, to the interrelations of propositional logic and set theory s...
Research Interests:
One can construct a mapping between Hilbert space and the class of all logics if the latter is defined as the set of all well-orderings of some relevant set (or class). That mapping can be further interpreted as a mapping of all states of... more
One can construct a mapping between Hilbert space and the class of all logics if the latter is defined as the set of all well-orderings of some relevant set (or class). That mapping can be further interpreted as a mapping of all states of all quantum systems, on the one hand, and all logics, on the other hand. The collection of all states of all quantum systems is equivalent to the world (the universe) as a whole. Thus that mapping establishes a fundamentally philosophical correspondence between the physical world and universal logic by the meditation of a special and fundamental structure, that of Hilbert space, and therefore, between quantum mechanics and logic by mathematics. Furthermore, Hilbert space can be interpreted as the free variable of "quantum information" and any point in it, as a value of the same variable as "bound" already axiom of choice.
Research Interests:
Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the... more
Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement.A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to a well-ordered set after measurement and thus requires the axiom of choice.Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant opera...
Research Interests:
Both transition and transformation link the ideal and material into a whole. Future is what “causes” the present, and the latter in turn is what “causes” the past. That kind of “reverse causality” needs free choice and free will in the... more
Both transition and transformation link the ideal and material into a whole. Future is what “causes” the present, and the latter in turn is what “causes” the past. That kind of “reverse causality” needs free choice and free will in the present in order to be able to be realized unlike classical causality. A few properties feature the concept of “quantum occasionalism” as follows. Some hypothetical entity generates successively a series of well-ordered states. That hypothetical entity is called “coherent state” in quantum mechanics and defined as a superposition of all possible states of the quantum system. The already generated well-ordered series can be interpreted as a causal sequence. Thus the generating cause remains hidden behind the visible well-ordering of the series and hides itself behind the perfect visible order created by it. That visible order only seems to cause itself by itself.
Research Interests:
The way, in which quantum information can unify quantum mechanics (and therefore the Standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the... more
The way, in which quantum information can unify quantum mechanics (and therefore the Standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coheren...
Research Interests:
Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum... more
Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This paper investigates both conditions and philosophical background necessary for that modification. The main conclusion is that the concept of infinity as underlying contemporary mathematics cannot be reduced to a single Peano arithmetic, but to at least two ones independent of each other. Intuitionism, quantum mechanics, and Gentzen’s approaches to completeness an even Hilbert’s finitism can be unified from that viewpoint. Math...
Research Interests:
Research Interests:
Research Interests:
The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the... more
The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coheren...
Research Interests:
Husserl remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence. Husserl’s tradition can be tracked as an idea for philosophy... more
Husserl remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence. Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathematized. The paper offers a pattern borrowed from the theory of information and quantum information to formalize logically a few key concepts of Husserl’s phenomenology such as “epoché” “eidetic, phenomenological, and transcendental reductions” as well as the identification of “phenomenological, transcendental, and psychological reductions” in a way allowing for that identification to be continued to “eidetic reduction” (and thus to mathematics). A basic conclusion states for the unification of philosophy, mathematics, and physics in their foundations and fundamentals to be the Husserl tradition both tracked to its origin and embodied in the development of human cognition in the third mill...
Research Interests:
Research Interests:
The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: weather it is an axiom rather than a theorem inferable from the axioms of... more
The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: weather it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic. The main argument consists in the contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. Thus, the pair of arithmetic and set are similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate: correspondingly, by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. The axiom of choice transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. The Gödel incompleteness statement relies on the contradiction of the axioma of induction and infinity.
Research Interests:
Математическата величина на вероятността се определя стандартно като положително реално число в затворения интервал от нула до единица, еднозначно опредимо в съотвествие с няколко аксиоми, напр. тези на Колмпгоров. Нейната философска... more
Математическата величина на вероятността се определя стандартно като положително реално число в затворения интервал от нула до единица, еднозначно опредимо в съотвествие с няколко аксиоми, напр. тези на Колмпгоров. Нейната философска интерпретация е на мярка за част от цяло. В теорията на квантовата информация, изследваща явленията на сдвояване [entanglement] в квантовата механика, се въвеждат отрицателни и комплексни вероятности. Статията обсъжда проблема какво би следвало да бъде тяхното релевантно философско тълкувание
Research Interests:
Research Interests:
Тhе question which animates Heidegger's paper (''Die onto-theo-logische Verfassung der Metaphysik:) is: "How are God coming in phi1osophy?"; and it is only а sharpening of "th.e question of the onto-theologic... more
Тhе question which animates Heidegger's paper (''Die onto-theo-logische Verfassung der Metaphysik:) is: "How are God coming in phi1osophy?"; and it is only а sharpening of "th.e question of the onto-theologic character of philosophy". Hegel and Heidegger are bothunited and opposed as identity and difference. Both being and existing descend from difference. Equilibrium (Aпstrag) arranges the unit of being and existing
Research Interests:
Research Interests:
The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete... more
The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be seen as informational in a generalized sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a wholeВ данной статье представлены философские выводы...
Research Interests:
“The Square of Opposition”, 5th World Congress Rapanui (Easter Island), Chile, 10-15, November 2016 http://www.square-of-opposition.org/Rapanui2016.html
Research Interests:
Information as the way of the past to be availble in the present
Research Interests:
The success of cinematograph hides an ontological basis still in its fundamental principle for representation of motion by a linear (and thus well-ordered) series of static frames That representation of motion by static frames is absolute... more
The success of cinematograph hides an ontological basis still in its fundamental principle for representation of motion by a linear (and thus well-ordered) series of static frames That representation of motion by static frames is absolute for it rests on the ontological equivalence of discreteness and smoothnessThe equivalence of discrete and smooth (continuous) motion underlies quantum mechanics as the principle of wave-particle duality offered by Louis de Broglie (1924) Henry Bergson (1907) suggested the "cinematographic method of thought" for distinguishing "durée" (time by itself) from the transcendental limitation for it to be represented in human knowledge and cognition<br>
Research Interests:
<p>The transition from the result of a usual computer to the ultimate result of a quantum computer is a leap comparable with human understanding and interpretation to restore the true reality on the base of a finite set of sensual... more
<p>The transition from the result of a usual computer to the ultimate result of a quantum computer is a leap comparable with human understanding and interpretation to restore the true reality on the base of a finite set of sensual or experimental data</p> <p>One can rise the question whether that comparison is only a metaphor or it reveals a deeper link between quantum computation and the human understanding and interpretation of reality</p
Research Interests:
The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both, and especially the latter, seem to be rather philosophical, nonetheless they are postulated... more
The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both, and especially the latter, seem to be rather philosophical, nonetheless they are postulated axiomatically and interpreted physically, and the corresponding philosophical transcendentalism serves heuristically. The exposition of the article means to outline the “forest for the trees”, however, in an absolutely rigorous mathematical way, which to be explicated in detail in a future paper. The “two deductions” are two successive stage of a single conclusion mentioned above. The concept of “transcendental invariance” meaning ontologically and physically interpreting the mathematical equivalence of the axiom of choice and the well-ordering “theorem” is utilized again. Then, time arrow is a corollary from that transcendental invariance, and in turn, it implies quantum information conservation as the Noether correlate of the linear “increase of time” ...
Research Interests:
The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both, and especially the latter, seem to be rather philosophical, nonetheless they are postulated... more
The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both, and especially the latter, seem to be rather philosophical, nonetheless they are postulated axiomatically and interpreted physically, and the corresponding philosophical transcendentalism serves heuristically. The exposition of the article means to outline the “forest for the trees”, however, in an absolutely rigorous mathematical way, which to be explicated in detail in a future paper. The “two deductions” are two successive stage of a single conclusion mentioned above. The concept of “transcendental invariance” meaning ontologically and physically interpreting the mathematical equivalence of the axiom of choice and the well-ordering “theorem” is utilized again. Then, time arrow is a corollary from that transcendental invariance, and in turn, it implies quantum information conservation as the Noether correlate of the linear “increase of time” ...
Research Interests:
A possible interpretation of the equivalence of the Schrödinger equation and the Einstein field equation
Research Interests:
“Aristotle in Phenomelogy”, Fort Wayne, IN, USA April 23-24, 2016 Heidegger called Aristotle’s Physics “the secret, never sufficiently rethought base book of Western Philosophy”. This can explain the choice of Heidegger to comment namely it
Research Interests:
(T1) Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at... more
(T1) Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity That is nothing else than right a new reading at issue and comparative interpretation of Gödel’s papers meant here (T2) Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity The most utilized example of those generalizations is the separable complex Hilbert space: it is able to equate the possibility of pure existence to the probability of statistical ensemble (T3) Any generalization of Peano arithmetic consistent to infinity, e.g. the separable complex Hilbert space, can serve as a foundation for mathematics to found itself and by itself
Research Interests: Set Theory and Logic
The presentation for the paper and talk of the same title at: Nordic Network for Philosophy of sciences, Pärnu, Eesti
April 22-23, 2016
(NNPS2016)
April 22-23, 2016
(NNPS2016)
Research Interests:
“Aristotle in Phenomelogy”, Fort Wayne, IN, USA April 23-24, 2016 Heidegger called Aristotle’s Physics “the secret, never sufficiently rethought base book of Western Philosophy”. This can explain the choice of Heidegger to comment namely... more
“Aristotle in Phenomelogy”, Fort Wayne, IN, USA
April 23-24, 2016
Heidegger called Aristotle’s Physics “the secret, never sufficiently rethought base book of Western Philosophy”.
This can explain the choice of Heidegger to comment namely it
April 23-24, 2016
Heidegger called Aristotle’s Physics “the secret, never sufficiently rethought base book of Western Philosophy”.
This can explain the choice of Heidegger to comment namely it
Research Interests:
Moscow, VII International Congress "Modes of Thinking, Ways of Speaking“ The School of Philosophy of the Faculty of Humanities (National Research University Higher School of Economics) 30 April 2016 The “improper interpretation” of an... more
Moscow, VII International Congress "Modes of Thinking, Ways of Speaking“
The School of Philosophy of the Faculty of Humanities (National Research University Higher School of Economics)
30 April 2016
The “improper interpretation” of an infinite set-theory structure founds the “proper interpretation” and thus that structure self-founds itself as the one interpretation of it can found the other
The School of Philosophy of the Faculty of Humanities (National Research University Higher School of Economics)
30 April 2016
The “improper interpretation” of an infinite set-theory structure founds the “proper interpretation” and thus that structure self-founds itself as the one interpretation of it can found the other
Research Interests:
The CMI Millennium "P vs NP Problem" can be resolved e.g. if one shows at least one counterexample to the conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the... more
The CMI Millennium "P vs NP Problem" can be resolved e.g. if one shows at least one counterexample to the conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the hypothesis for any conditions satisfying the formulation of the problem. Thus, the solution "P is differnt from NP" of the problem in general is proved. The class of counterexamples can be interpreted as any quantum superposition of any finite set of quantum states. The Kochen-Specker theorem is involved. Any fundamentally random choice among a finite set of alternatives belong to "NP' but not to "P". The conjecture that the set complement of "P" to "NP" can be described by that kind of choice exhaustively is formulated
https://arxiv.org/abs/2005.01412?fbclid=IwAR2tLJPQ-lmfhX3mkPQlV7_SLmHVTSmtA4dTFxDD9OMwNRbkAKtS61fd8KU
https://arxiv.org/abs/2005.01412?fbclid=IwAR2tLJPQ-lmfhX3mkPQlV7_SLmHVTSmtA4dTFxDD9OMwNRbkAKtS61fd8KU
Research Interests:
A proof of Fermat's last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity,... more
A proof of Fermat's last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat's last theorem in the case of í µí±í µí± = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat's approach of infinite descent. The infinite descent is linked to induction starting from í µí±í µí± = 3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat's last theorem. As far as Fermat had been proved the theorem for í µí±í µí± = 4, one can suggest that the proof for í µí±í µí± ≥ 4 was accessible to him.
Research Interests:
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein's famous "E=mc^2". Energy conservation is implied by the principle of least... more
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein's famous "E=mc^2". Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether's theorems (1918): any chemical change in a conservative (i.e. "closed") system can be accomplished only in the way conserving its total energy. Bohr's innovation to found Mendeleev's periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (according to Feynman's interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change. The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem). The problem : If any quantum change is accomplished in all possible "variations (i.e. "violations) of energy conservation" (by different probabilities), what (if any) is conserved? An answer : quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether's theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.
Research Interests:
The physical interpretation of the conjecture is meant.
Research Interests:
A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In... more
A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term " theory " includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical means. Husserl's phenomenology is what is used, and then the conception of " bracketing reality " is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being (rather than reality for reality is external only to Gödel mathematics) is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem.
Research Interests:
Поредицата от 7 книги, посветени на философията на квантовата информация, започва с възникването на дисциплината в тясна близост с квантовата механика и дебата около нейните основи. Предпочита се нова мета-математическа интерпретация и се... more
Поредицата от 7 книги, посветени на философията на квантовата информация, започва с възникването на дисциплината в тясна близост с квантовата механика и дебата около нейните основи. Предпочита се нова мета-математическа интерпретация и се обсъждат wзаимоотношенията със съществуващите. Философска и онтологическа проекция е предлаганото видоизменено, а именно „дуалистично питагорейство”. Като символ е
използван „Принстънският дух” и приятелството между Айнщайн и Гьодел. Набедената непълнота на квантовата механика и доказаната непълнота на аритметиката са преплетени и „сдвоени”, така че взаимни отблясъци осветяват аритметиката и математиката с
онтологичен пламък, но и квантовата механика и информация – с философска фундаменталност и способност да обосновава.
Неразрешими твърдения ли са самите т. нар. теореми на Гьодел за непълнотата, ако те се отнесат към самите себе си? Може ли парадоксът на Скулем да се използва за обобщаване на Айнщайновия „принцип на относителността” (1918) от дифеоморфизми и за
дискретни морфизми? Как следва да се тълкуват явленията на сдвояване (entanglement), квантовият компютър и квантовата информация аритметически и логически?
Книгата е предназначена за научни работници в областта на физиката, математиката и философията, за докторанти и студенти, за всеки, който се интересува от този съвсем нов отрасъл на знанието.
използван „Принстънският дух” и приятелството между Айнщайн и Гьодел. Набедената непълнота на квантовата механика и доказаната непълнота на аритметиката са преплетени и „сдвоени”, така че взаимни отблясъци осветяват аритметиката и математиката с
онтологичен пламък, но и квантовата механика и информация – с философска фундаменталност и способност да обосновава.
Неразрешими твърдения ли са самите т. нар. теореми на Гьодел за непълнотата, ако те се отнесат към самите себе си? Може ли парадоксът на Скулем да се използва за обобщаване на Айнщайновия „принцип на относителността” (1918) от дифеоморфизми и за
дискретни морфизми? Как следва да се тълкуват явленията на сдвояване (entanglement), квантовият компютър и квантовата информация аритметически и логически?
Книгата е предназначена за научни работници в областта на физиката, математиката и философията, за докторанти и студенти, за всеки, който се интересува от този съвсем нов отрасъл на знанието.
Research Interests:
The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum... more
The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum systems. In other words, an atom of any chemical element and as a quantum system, i.e. as a wave function, should be represented as a non-orthogonal in general (i.e. entangled) subspace of the separable complex Hilbert space relevant to the system to which the atom at issue is related as a true part of it. The paper follows previous publications of mine stating that “dark matter” and “dark energy” are projections of arbitrarily entangled states on the cognitive “screen” of Einstein’s “Mach’s principle” in general relativity postulating that gravitational field can be generated only by mass or energy.
Research Interests:
Background and prehistory: The French mathematician Henri Poincaré offered a statement known as “Poincaré’s conjecture” without a proof. It states that any 4-dimensional ball is equivalent to 3-dimensional Euclidean space topologically: a... more
Background and prehistory:
The French mathematician Henri Poincaré offered a statement known as “Poincaré’s conjecture” without a proof. It states that any 4-dimensional ball is equivalent to 3-dimensional Euclidean space topologically: a continuous mapping exists so that it maps the former ball into the latter space one-to-one.
At first glance, it seems to be too paradoxical for the following mismatches: the former is 4-dimensional and as if “closed” unlike the latter, 3-dimensional and as if “open” according to common sense. So, any mapping seemed to be necessarily discrete to be able to overcome those mismatches, and being discrete impies for the conjecture to be false.
Anyway, nobody managed neither to prove nor to reject rigorously the conjecture about one century. It was included even in the Millennium Prize Problems by the Clay Mathematics Institute.
It was proved by Grigory Perelman in 2003 using the concept of information.
Physical interpretation in terms of special relativity:
One may notice that the 4-ball is almost equivalent topologically to the “imaginary domain” of Minkowski space in the following sense of “almost”: that “half” of Minkowski space is equivalent topologically to the unfolding of a 4-ball. Then, the conjecture means the topological equivalence of the physical 3-space and its model in special relativity. In turn, that topological equivalence means their equivalence as to causality physically. So, Perelman has proved the adequacy of Minkowski space as a model of the physical 3-dimensional space rigorously. Of course, all experiments confirm the same empirically, but not mathematically as he did.
An idea of another proof of the conjecture based on that physical interpretation:
Topologically seen, the problem turns out to be reformulated so: one needs a proof of the topological equivalence of a 4-ball and its unfolding by 3-balls (what the “half” of Minkowski space is, topologically).
If one adds a complementary, second unfolding to link both ends of the first unfolding, the problem would be resolved: 4-ball would be equivalent to two 3-spaces topologically. Two 3-spaces are equivalent to a single one as follows: one divides a 3-space into two parts by a certain plane (that plane does not belong to any of them). Any part is equivalent topologically to a 3-space for any open neighborhood is transformed into an open one by the mapping of each part (excluding the boundary of the plane) into the complete 3-space.
That idea is linked to the original proof of Perelman by the concept of information. It means that any bit of information interpreted physically conserves causality. In other words, the choice of any of both states of a bit (e.g. designated as “0” and “1” recorded in a cell) does not violate causality (the cell, either “0” or “1”, or both “0” and “1” are equivalent to each other topologically and to a 3-space).
The French mathematician Henri Poincaré offered a statement known as “Poincaré’s conjecture” without a proof. It states that any 4-dimensional ball is equivalent to 3-dimensional Euclidean space topologically: a continuous mapping exists so that it maps the former ball into the latter space one-to-one.
At first glance, it seems to be too paradoxical for the following mismatches: the former is 4-dimensional and as if “closed” unlike the latter, 3-dimensional and as if “open” according to common sense. So, any mapping seemed to be necessarily discrete to be able to overcome those mismatches, and being discrete impies for the conjecture to be false.
Anyway, nobody managed neither to prove nor to reject rigorously the conjecture about one century. It was included even in the Millennium Prize Problems by the Clay Mathematics Institute.
It was proved by Grigory Perelman in 2003 using the concept of information.
Physical interpretation in terms of special relativity:
One may notice that the 4-ball is almost equivalent topologically to the “imaginary domain” of Minkowski space in the following sense of “almost”: that “half” of Minkowski space is equivalent topologically to the unfolding of a 4-ball. Then, the conjecture means the topological equivalence of the physical 3-space and its model in special relativity. In turn, that topological equivalence means their equivalence as to causality physically. So, Perelman has proved the adequacy of Minkowski space as a model of the physical 3-dimensional space rigorously. Of course, all experiments confirm the same empirically, but not mathematically as he did.
An idea of another proof of the conjecture based on that physical interpretation:
Topologically seen, the problem turns out to be reformulated so: one needs a proof of the topological equivalence of a 4-ball and its unfolding by 3-balls (what the “half” of Minkowski space is, topologically).
If one adds a complementary, second unfolding to link both ends of the first unfolding, the problem would be resolved: 4-ball would be equivalent to two 3-spaces topologically. Two 3-spaces are equivalent to a single one as follows: one divides a 3-space into two parts by a certain plane (that plane does not belong to any of them). Any part is equivalent topologically to a 3-space for any open neighborhood is transformed into an open one by the mapping of each part (excluding the boundary of the plane) into the complete 3-space.
That idea is linked to the original proof of Perelman by the concept of information. It means that any bit of information interpreted physically conserves causality. In other words, the choice of any of both states of a bit (e.g. designated as “0” and “1” recorded in a cell) does not violate causality (the cell, either “0” or “1”, or both “0” and “1” are equivalent to each other topologically and to a 3-space).
Research Interests:
The power of the square of opposition has been proved during millennia. It supplies logic by the ontological language of infinity for describing anything... 6th WORLD CONGRESS ON THE SQUARE OF OPPOSITION... more
The power of the square of opposition has been proved during millennia. It supplies logic by the ontological language of infinity for describing anything...
6th WORLD CONGRESS ON THE SQUARE OF OPPOSITION
http://www.square-of-opposition.org/square2018.html
6th WORLD CONGRESS ON THE SQUARE OF OPPOSITION
http://www.square-of-opposition.org/square2018.html
Research Interests:
Abstr act. The paper addresses Leon Hen.kin's proposition as a " light house", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information t heory, and quantum mechanics: Two st rategies to infinity are... more
Abstr act. The paper addresses Leon Hen.kin's proposition as a " light house", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information t heory, and quantum mechanics: Two st rategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness t o be unified and t hus reduced as a joint property of infinity and of all infinite sets. However, only Henkin's proposition equivalent to an internal posit ion t o infinity is consistent. This can be retraced back to set theory and its axioms, where that of choice is a key. Quantum mechanics is forced to int roduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonst rate that some essential properties of quantum information, entanglement, and quantum comput er originate direct ly from infinit y once it is involved in quant um mechanics. Thus, these phenomena can be elucidated as both complete and incomplete, after which choice is the border bet ween them. A special kind of invariance to t he axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted ent irely in the same terms only of set theory. Quantum computer can demonstrat e especially clearly t he privilege of t he internal position, or " observer'' , or " user" to infinity implied by Henkin's proposition as the only consistent ones as to infinity. An essential area of cont emporary knowledge may be synt hesized from a single viewpoint. Both completeness and incompleteness are well distinguishable as to finite-ness: Completeness supposes that any operat ions defined over any finite sets do
Research Interests:
The state of nothing passes spontaneously (by itself) into the state of being ❖ This represents the “creation”. The transition of nothing into being is mathematically necessary ❖ The choice (which can be interpreted philosophically as... more
The state of nothing passes spontaneously (by itself)
into the state of being
❖ This represents the “creation”. The transition of nothing into being is mathematically necessary
❖ The choice (which can be interpreted philosophically as “free will”) appears necessary in mathematical reasons
❖ The choice generates asymmetry, which is the beginning of time and thus, of the physical word
❖ Information is the quantity of choices and linked to time intimately
into the state of being
❖ This represents the “creation”. The transition of nothing into being is mathematically necessary
❖ The choice (which can be interpreted philosophically as “free will”) appears necessary in mathematical reasons
❖ The choice generates asymmetry, which is the beginning of time and thus, of the physical word
❖ Information is the quantity of choices and linked to time intimately
Research Interests:
1. Quantum information can be discussed as the counterpart of action. 2. Quantum information is what is conserved, action is what is changed. 3. The gap between mathematical models and physical reality, needing truth as adequacy to be... more
1. Quantum information can be discussed as the counterpart of action.
2. Quantum information is what is conserved, action is what is changed.
3. The gap between mathematical models and physical reality, needing truth as adequacy to be overcome, is substituted by the openness of choice.
4. That openness in turn can be interpreted as the openness of the present as a different concept of truth recollecting Heidegger’s one as “unhiddeness”.
5. Quantum information as what is conserved can be thought philoso[hically as the conservation of that openness.
2. Quantum information is what is conserved, action is what is changed.
3. The gap between mathematical models and physical reality, needing truth as adequacy to be overcome, is substituted by the openness of choice.
4. That openness in turn can be interpreted as the openness of the present as a different concept of truth recollecting Heidegger’s one as “unhiddeness”.
5. Quantum information as what is conserved can be thought philoso[hically as the conservation of that openness.
Research Interests:
What is the form by which the past is represented in the present as far as the proper quality of the past cannot be conserved literally in the present?
Research Interests:
The outlined approach allows a common philosophical viewpoint to the physical world, language and some mathematical structures therefore calling for the universe to be understood as a joint physical, linguistic and mathematical universum,... more
The outlined approach allows a common philosophical viewpoint to the physical world, language and some mathematical structures therefore calling for the universe to be understood as a joint physical, linguistic and mathematical universum, in which physical motion and metaphor are one and the same rather than only similar in a sense.
Research Interests:
Hilbert space underlying quantum mechanics and pseudo-Riemannian space underlying general relativity share a common base of quantum information. Hilbert space can be interpreted as the free variable of quantum information, and any point... more
Hilbert space underlying quantum mechanics and pseudo-Riemannian space underlying general relativity share a common base of quantum information. Hilbert space can be interpreted as the free variable of quantum information, and any point in it, being equivalent to a wave function (and thus, to a state of a quantum system), as a value of that variable of quantum information. In turn, pseudo-Riemannian space can be interpreted as the interaction of two or more quantities of quantum information and thus, as two or more entangled quantum systems. Consequently, one can distinguish local physical interactions describable by a single Hilbert space (or by any factorizable tensor product of such ones) and non-local physical interactions describable only by means by that Hilbert space, which cannot be factorized as any tensor product of the Hilbert spaces, by means of which one can describe the interacting quantum subsystems separately. Any interaction, which can be exhaustedly described in a single Hilbert space, such as the weak, strong, and electromagnetic one, is local in terms of quantum information. Any interaction, which cannot be described thus, is nonlocal in terms of quantum information. Any interaction, which is exhaustedly describable by pseudo-Riemannian space, such as gravity, is nonlocal in this sense. Consequently all known physical interaction can be described by a single geometrical base interpreting it in terms of quantum information.
Research Interests:
The instructions of Feynman’s pathways interpretation of quantum mechanics for philosophy
Research Interests:
The instructions of Feynman’s pathways interpretation of quantum mechanics for philosophy
Research Interests:
Has AI a soul? Can science approach that problem?
Research Interests:
THE SECOND WORLD CONGRESS ON ANALOGY, POZNAŃ, MAY 24-26, 2017
(The Venue: Sala Lubrańskiego (Lubrański’s Hall at the Collegium Minus), Adam Mickiewicz University, Address: ul. Wieniawskiego 1)
The presentation: 24 May, 15:30
(The Venue: Sala Lubrańskiego (Lubrański’s Hall at the Collegium Minus), Adam Mickiewicz University, Address: ul. Wieniawskiego 1)
The presentation: 24 May, 15:30
Research Interests:
“Formal ontology” is introduced first to programing languages in different ways. The most relevant one as to philosophy is as a generalization of “nth-order logic” and “nth-level language” for n=0. Then, the “zero-level language” is a... more
“Formal ontology” is introduced first to programing languages in different ways. The most relevant one as to philosophy is as a generalization of “nth-order logic” and “nth-level language” for n=0. Then, the “zero-level language” is a theoretical reflection on the naïve attitude to the world: the “things and words” coincide by themselves. That approach corresponds directly to the philosophical phenomenology of Husserl or fundamental ontology of Heidegger. Ontology as the 0-level language may be researched as a formal ontology
Research Interests:
A possible interpretation of the equivalence of the Schrödinger equation and the Einstein field equation
Research Interests:
« Le cours de linguistique générale 1916-2016 »
« Arbtrariness of the sign », Suitzerland, Geneva, University of Geneva, 10-12 January 2017: 11 January, 14:40-15:10
« Arbtrariness of the sign », Suitzerland, Geneva, University of Geneva, 10-12 January 2017: 11 January, 14:40-15:10
Research Interests: Semiotics and Linguistics
“The Square of Opposition”, 5th World Congress Rapanui (Easter Island), Chile, 10-15, November 2016
http://www.square-of-opposition.org/Rapanui2016.html
http://www.square-of-opposition.org/Rapanui2016.html
Research Interests:
“The Real of Reality”, An International Conference in Philosophy and Film
Karlsruhe, Germany, 2-6 November 2016
Zentrum für Kunst und Medientechnologie
(ZKM, Kube, 3 Nov, 11:20-12:50)
Karlsruhe, Germany, 2-6 November 2016
Zentrum für Kunst und Medientechnologie
(ZKM, Kube, 3 Nov, 11:20-12:50)
Research Interests:
The world (wide) web generates a new “estate”, to which a huge part of mankind belongs. Unlike the other “estates”, any human being even a child of own free will might joint it or not. That amorphous, “liquid”, non-professional, and... more
The world (wide) web generates a new “estate”, to which a huge part of mankind belongs. Unlike the other “estates”, any human being even a child of own free will might joint it or not. That amorphous, “liquid”, non-professional, and virtual “estate” is the real “power” in the world, the most powerful one. The world web as a power overcomes the classical three powers and also the so-called fourth one, media. The trends in favor of it are even stronger than its real power and influence in the contemporary world.
Research Interests:
My presentation at the conference “The Historical responsibility: from the myths of the past to the strategies of future”
September 22-23, 2016 (22 Sep, 12:20 – 14:00)
Yekaterinburg, Russia (Lenin av. 51,Ural Federal University, Room 314)
September 22-23, 2016 (22 Sep, 12:20 – 14:00)
Yekaterinburg, Russia (Lenin av. 51,Ural Federal University, Room 314)
Research Interests:
A comment of Vasil Penchev at "Issues on the (Im)possible". Bratialava 30-31 August 2016
Research Interests:
2nd PORTUGUESE CONGRESS OF PHILOSOPHY
Porto, Portugal: 8-9 September 2016 (14: 30, 8 Sep, room 201)
University of Porto - Faculdade de Letras
Porto, Portugal: 8-9 September 2016 (14: 30, 8 Sep, room 201)
University of Porto - Faculdade de Letras
Research Interests:
What might mean “more than impossible”? For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act ⦁ Then, the quantity of the equivalent physical force,... more
What might mean “more than impossible”?
For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act ⦁
Then, the quantity of the equivalent physical force, which would cause the same effect, can serve as a measure of the complex probability
Furthermore, the same effect is interpretable as re-ordering and thus as a certain quantity of information ⦁
One can write a very intriguing equation:
𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙 𝐹𝑜𝑟𝑠𝑒=𝑇ℎ𝑒 𝑆𝑎𝑚𝑒 𝐸𝑓𝑓𝑒𝑐𝑡=𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛
For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act ⦁
Then, the quantity of the equivalent physical force, which would cause the same effect, can serve as a measure of the complex probability
Furthermore, the same effect is interpretable as re-ordering and thus as a certain quantity of information ⦁
One can write a very intriguing equation:
𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙 𝐹𝑜𝑟𝑠𝑒=𝑇ℎ𝑒 𝑆𝑎𝑚𝑒 𝐸𝑓𝑓𝑒𝑐𝑡=𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛
Research Interests:
ISPC’20 - 2016
Boca Raton, FL, USA: 1-4 August 2016
International Society for the Philosophy of Chemistry: 20th Annual Conference
Boca Raton, FL, USA: 1-4 August 2016
International Society for the Philosophy of Chemistry: 20th Annual Conference
Research Interests:
Доклад на конференцията “Магическият реализъм”, София, НБКМ “Кирил и Методий”, 21-22 юни 2016 (15:45, 21 юни)] Целта на този научен доклад е, разбира се, магическа: да оповести пред заклети посветени заклинанието, което ще стори... more
Доклад на конференцията “Магическият реализъм”,
София, НБКМ “Кирил и Методий”, 21-22 юни 2016 (15:45, 21 юни)]
Целта на този научен доклад е, разбира се, магическа: да оповести пред заклети посветени заклинанието, което ще стори Радичков на верблюд. Средствата, както науката изисква, са чисто логически: идват от Логоса, думата и нейната способност да общува с човешката душа.
София, НБКМ “Кирил и Методий”, 21-22 юни 2016 (15:45, 21 юни)]
Целта на този научен доклад е, разбира се, магическа: да оповести пред заклети посветени заклинанието, което ще стори Радичков на верблюд. Средствата, както науката изисква, са чисто логически: идват от Логоса, думата и нейната способност да общува с човешката душа.
Research Interests:
(T1) Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at... more
(T1) Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation
Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity
That is nothing else than right a new reading at issue and comparative interpretation of Gödel’s papers meant here
(T2) Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity
The most utilized example of those generalizations is the separable complex Hilbert space: it is able to equate the possibility of pure existence to the probability of statistical ensemble
(T3) Any generalization of Peano arithmetic consistent to infinity, e.g. the separable complex Hilbert space, can serve as a foundation for mathematics to found itself and by itself
Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity
That is nothing else than right a new reading at issue and comparative interpretation of Gödel’s papers meant here
(T2) Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity
The most utilized example of those generalizations is the separable complex Hilbert space: it is able to equate the possibility of pure existence to the probability of statistical ensemble
(T3) Any generalization of Peano arithmetic consistent to infinity, e.g. the separable complex Hilbert space, can serve as a foundation for mathematics to found itself and by itself
Research Interests: Set Theory and Logic
My presentation at:
2nd Annual Conference of The European Network of Japanese Philosophy (ENOJP)
Université libre de Bruxelles 2016, December 7-10
8 December 15:30 (room 3)
2nd Annual Conference of The European Network of Japanese Philosophy (ENOJP)
Université libre de Bruxelles 2016, December 7-10
8 December 15:30 (room 3)