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1Верблюдът Радичков: въображението като реалностIn Пламен Антов (ed.), Магическият реализъм, Институт По Литература - Бан. pp. 69-86. 2019.The text aims to explain Radichkov's special magical capaЬility of creating imaginary worlds. His words do not mean any external reality to which they refer. Тhеу themselves are reality. Radickov's language consists of "ontological quanta". Any ontological quantum means both reality and а certain image of it, indivisiЫe and indistinguishaЫe from each other. Here we сап also involve non-Saussurean semiotics. The signifier and the signified are indivisiЫe and complementary in any sign. The meanin…Read more
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Proceedings of the 41st Annual Convention of the Society for the Study of Artificial Intelligence and the Simulation of Behaviour (edited book)Curran Associates, Inc.. 2015.
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136Hilbert mathematics versus (or rather “without”) Gödel mathematics: V. Ontomathematics!Metaphysics eJournal (Elsevier: SSRN) 17 (10): 1-57. 2024.The paper is the final, fifth part of a series of studies introducing the new conceptions of “Hilbert mathematics” and “ontomathematics”. The specific subject of the present investigation is the proper philosophical sense of both, including philosophy of mathematics and philosophy of physics not less than the traditional “first philosophy” (as far as ontomathematics is a conservative generalization of ontology as well as of Heidegger’s “fundamental ontology” though in a sense) and history of phi…Read more
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149Isaac Asimov’s sci-fi novella “Profession” versus professionalism: Reflections on the (missing) scientific revolutions in the 21th centuryPhilosophy of Science eJournal (Elsevier: SSRN) 17 (42): 1-38. 2024.This is a partly provocative essay edited as a humanitarian study in philosophy of science and social philosophy. The starting point is Isaac Asimov’s famous sci-fi novella “Profession” (1957) to be “back” extrapolated to today’s relation between Thomas Kuhn’s “normal science” and “scientific revolutions” (1962). The latter should be accomplished by Asimov’s main personage George Platen’s ilk (called “feeble minded” in the novella) versus the “burned minded” professionals able only to “normal sc…Read more
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150Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physicsAstrophysics, Cosmology and Gravitation Ejournal 2 (52): 1-82. 2023.Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hi…Read more
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238Hilbert Mathematics Versus Gödel Mathematics. IV. The New Approach of Hilbert Mathematics Easily Resolving the Most Difficult Problems of Gödel MathematicsPhilosophy of Science eJournal (Elsevier: SSRN) 16 (75): 1-52. 2023.The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a …Read more
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78Коментар към МамардашвилиЛИК. 1996.Книгата е есе, посветена на творчеството и живота на световно известния грузински философ Мераб Мамардашвили, живял по времето на СССР.
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280Hilbert Mathematics versus Gödel Mathematics. III. Hilbert Mathematics by Itself, and Gödel Mathematics versus the Physical World within It: both as Its Particular CasesPhilosophy of Science eJournal (Elsevier: SSRN) 16 (47): 1-46. 2023.The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to conc…Read more
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556This Year's Nobel Prize (2022) in Physics for Entanglement and Quantum Information: the New Revolution in Quantum Mechanics and SciencePhilosophy of Science eJournal (Elsevier: SSRN) 18 (33): 1-68. 2023.The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravi…Read more
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231Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930)Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 15 (1): 1-61. 2023.The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for granting the Gödel incompl…Read more
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371Gödel mathematics versus Hilbert mathematics. I. The Gödel incompleteness (1931) statement: axiom or theorem?Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (9): 1-56. 2022.The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity i…Read more
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259Gentzen’s “cut rule” and quantum measurement in terms of Hilbert arithmetic. Metaphor and understanding modeled formallyLogic and Philosophy of Mathematics eJournal 14 (14): 1-37. 2022.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 ju…Read more
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317Fermat’s last theorem proved in Hilbert arithmetic. III. The quantum-information unification of Fermat’s last theorem and Gleason’s theoremLogic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (12): 1-30. 2022.The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace of Hilbert space and especially its uniqueness can b…Read more
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287Fermat’s last theorem proved in Hilbert arithmetic. II. Its proof in Hilbert arithmetic by the Kochen-Specker theorem with or without inductionLogic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (10): 1-52. 2022.The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quan…Read more
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374Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmeticLogic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (7): 1-57. 2021.In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” h…Read more
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240The Homeomorphism of Minkowski Space and the Separable Complex Hilbert Space: The physical, Mathematical and Philosophical InterpretationsLogic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (3): 1-22. 2021.A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically…Read more
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601What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmeticLogic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (22): 1-32. 2021.Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotatio…Read more
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363“Noema” and “Noesis” by Information after Husserl’s Phenomenology Interpreted FormallyMetaphysics eJournal, SSRN 14 (22): 1-19. 2021.Along with “epoché” or his “reductions”, Husserl’s “noema” and “noesis”, being neologisms invented by him, are main concepts in phenomenology able to represent its originality. Following the trace of a recent paper (Penchev 2021 July 23), its formal and philosophical approach is extended to both correlative notions, in the present article. They are able to reveal the genesis of the world from consciousness in a transcendental method relevant to Husserl, but furthermore described formally as a pr…Read more
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232Hilbert arithmetic as a Pythagorean arithmetic: arithmetic as transcendentalPhilosophy of Science eJournal (Elsevier: SSRN) 14 (54): 1-24. 2021.The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, …Read more
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279Quantum phenomenology as a “rigorous science”: the triad of epoché and the symmetries of informationPhilosophy of Science eJournal (Elsevier: SSRN) 14 (48): 1-18. 2021.Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the …Read more
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206Quantity in Quantum Mechanics and the Quantity of Quantum InformationPhilosophy of Science eJournal (Elsevier: SSRN) 14 (47): 1-10. 2021.The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be r…Read more
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210“Two bits less” after quantum-information conservation and their interpretation as “distinguishability / indistinguishability” and “classical / quantum”Philosophy of Science eJournal (Elsevier: SSRN) 14 (46): 1-7. 2021.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 inform…Read more
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153Светът в езика и във физикатаPhilosophical Alternatives 7 (5-6): 3-14. 1998.Статията изследва и сравнява от филосософска гледна точка естествената представа в света, заложена в езила и шлифована от хилядолетен опит в употребата му, и тази в една модерна наука, каквато е физиката. The article examines and compares from a philosophical point of view the natural idea of the world, embedded in the language and polished by thousands of years of experience in its use, and that in a modern science such as physics.
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321The 'Noncausal Causality' of Quantum InformationPhilosophy of Science eJournal (Elsevier: SSRN) 14 (45): 1-7. 2021.The paper is concentrated on the special changes of the conception of causality from quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical de…Read more
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117Радичковият "Верблюд" - поетика на значениятаБългарски Език И Литература 38 (5-6): 69-76. 1997.Ктратката форма "Верблюд" (която условно меже да се нарече "разказ") от класика на българската литература Йордан Радичков е предмет на анализ. по-скоро философски. екзистенциален и металитературен. Какво е "верблюд" по Радичков? Нещо толкова неопределено, че може да бъде открито навсякъде ... подобно на една философска категория или философски дискурс, релевантен към всичко ...
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195Both Classical & Quantum Information; Both Bit & Qubit: Both Physical & Transcendental TimePhilosophy of Science eJournal (Elsevier: SSRN) 14 (22): 1-24. 2021.Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relat…Read more
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227The Symmetries of Quantum and Classical Information. The Ressurrected “Ether" of Quantum InformationPhilosophy of Science eJournal (Elsevier: SSRN) 14 (41): 1-36. 2021.The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. …Read more
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167"Ние, духовата музика": Ние, философитеPhilosophical Alternatives 8 (3-4): 117-131. 1999.Едноименната творба от класика на българскта литература Йордан Радичков е ситуирана в шеговита аналогия със "занаята на философа", премеждията на философската традиция с прогреса, кризата в институцията на философията, особено в контекста на прехода през 90-те години на миналя век в Бтлгария..
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142Физическият и философски проблем "Какво е сега?"Philosophical Alternatives 8 (1): 26-34. 1999.Сред времевите модуси "Сега" заема особено място между винаги добре нареденото минало и напълно неопределено и неподредено бъдеще. Така същността на настоящия момент може да се определи като избор и така нуждаещ се от свободна воля, способен да превръща неподреденото в подредено: едно свойство постулирано в теорията на множствата като аксиома за избора, а нейната еквивалентност с т. нар. теорема за добрата наредба може да бъде доказана елементарно. Физическата същност на "Сега" може да се предст…Read more
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131За любовта и езика - Радичковата новела "Козел"Philosophical Alternatives 9 (5-6): 131-138. 2000.Новелата "Козел" от класика на българската литература Йордан Рдичков (1929-2004) се обсъжда от гледна точка на философските идеи, заложени в нея. Любовта и езикът, два най-общи философски екзистенциала, се оказват свързани. Сякаш не само човекът овчар се грижи за стадото, но и козелът, водач на стадото, - за човека.
Sofia, Bulgaria
Areas of Specialization
Metaphysics and Epistemology |
Science, Logic, and Mathematics |