Results for 'epoché, Hilbert arithmetic, Husserl reductions, information and quantum information, qubit Hulbert space'

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  1.  45
    Quantum Phenomenology as a “Rigorous Science”: The Triad of Epoché and the Symmetries of Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (48):1-18.
    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 final analysis. The paper offers a pattern borrowed (...)
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  2.  47
    Hilbert Arithmetic as a Pythagorean Arithmetic: Arithmetic as Transcendental.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (54):1-24.
    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, Hilbert arithmetic identifies by itself information (...)
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  3.  48
    Fermat’s Last Theorem Proved in Hilbert Arithmetic. I. From the Proof by Induction to the Viewpoint of Hilbert Arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (7):1-57.
    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 (...)
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  4.  42
    Both Classical & Quantum Information; Both Bit & Qubit: Both Physical & Transcendental Time.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (22):1-24.
    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 relativity of the finite and infinite, of the (...)
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  5. Choice, Infinity, and Negation: Both Set-Theory and Quantum-Information Viewpoints to Negation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (14):1-3.
    The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds (...)
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  6.  36
    The Symmetries of Quantum and Classical Information. The Ressurrected “Ether" of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (41):1-36.
    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 (...)
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  7. What Is Quantum Information? Information Symmetry and Mechanical Motion.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (20):1-7.
    The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information (...)
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  8.  87
    The 'Noncausal Causality' of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (45):1-7.
    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 (...)
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  9.  39
    “Two Bits Less” After Quantum-Information Conservation and Their Interpretation as “Distinguishability / Indistinguishability” and “Classical / Quantum”.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (46):1-7.
    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 (...)
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  10.  40
    Fermat’s Last Theorem Proved in Hilbert Arithmetic. II. Its Proof in Hilbert Arithmetic by the Kochen-Specker Theorem with or Without Induction.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (10):1-52.
    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 (...) contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)
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  11.  50
    Skolem’s “Paradox” as Logic of Ground: The Mutual Foundation of Both Proper and Improper Interpretations.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (19):1-16.
    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 (...)
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  12. Universal Logic in Terms of Quantum Information.Vasil Penchev - 2020 - Metaphilosophy eJournal (Elsevier: SSRN) 12 (9):1-5.
    Any logic is represented as a certain collection of well-orderings admitting or not some algebraic structure such as a generalized lattice. Then universal logic should refer to the class of all subclasses of all well-orderings. One can construct a mapping between Hilbert space and the class of all logics. Thus there exists a correspondence between universal logic and the world if the latter is considered a collection of wave functions, as which the points in Hilbert space (...)
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  13.  39
    Quantity in Quantum Mechanics and the Quantity of Quantum Information.Vasil Penchev - 2021 - Philosophy of Science eJournal (Elsevier: SSRN) 14 (47):1-10.
    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 represented as (...)
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  14. Negative and Complex Probability in Quantum Information.Vasil Penchev - 2012 - Philosophical Alternatives (1):63-77.
    “Negative probability” in practice. Quantum Communication: Very small phase space regions turn out to be thermodynamically analogical to those of superconductors. Macro-bodies or signals might exist in coherent or entangled state. Such physical objects having unusual properties could be the basis of quantum communication channels or even normal physical ones … Questions and a few answers about negative probability: Why does it appear in quantum mechanics? It appears in phase-space formulated quantum mechanics; next, in (...)
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  15. The Identity of Logic and the World in Terms of Quantum Information.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (21):1-4.
    One can construct a mapping between Hilbert space and the class of all logic 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 logic, on the other hand. The collection of all states of all quantum systems is equivalent to the world (the universe) as a whole. (...)
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  16.  6
    Husserl and His Alter Ego Kant.Judson Webb - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    Husserl’s lifelong interest in Kant eventually becomes a preoccupation in his later years when he finds his phenomenology in competition with Neokantianism for the title of transcendental philosophy. Some issues that Husserl is concerned with in Kant are bound up with the works of Lambert. Kant believed that the role played by principles of sensibility in metaphysics should be determined by a “general phenomenology” on which Lambert had written. Kant initially believed that man is capable only of symbolic (...)
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  17.  48
    Quantum Information as the Information of Infinite Collections or Series.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (14):1-8.
    The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into (...)
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  18.  69
    What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (22):1-32.
    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 connotations clear up links due to the shared formal structure with (...)
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  19.  57
    Is Mass at Rest One and the Same? A Philosophical Comment: On the Quantum Information Theory of Mass in General Relativity and the Standard Model.Vasil Penchev - 2014 - Journal of SibFU. Humanities and Social Sciences 7 (4):704-720.
    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 (...)
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  20.  46
    The Homeomorphism of Minkowski Space and the Separable Complex Hilbert Space: The Physical, Mathematical and Philosophical Interpretations.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (3):1-22.
    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 (...)
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  21. The Relationship of Arithmetic As Two Twin Peano Arithmetic(s) and Set Theory: A New Glance From the Theory of Information.Vasil Penchev - 2020 - Metaphilosophy eJournal (Elseviers: SSRN) 12 (10):1-33.
    The paper introduces and utilizes a few new concepts: “nonstandard Peano arithmetic”, “complementary Peano arithmetic”, “Hilbert arithmetic”. They identify the foundations of both mathematics and physics demonstrating the equivalence of the newly introduced Hilbert arithmetic and the separable complex Hilbert space of quantum mechanics in turn underlying physics and all the world. That new both mathematical and physical ground can be recognized as information complemented and generalized by quantum information. A few fundamental (...)
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  22. The Isomorphism of Minkowski Space and the Separable Complex Hilbert Space and its Physical Interpretation.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier:SSRN) 13 (31):1-3.
    An isomorphism 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 isomorphism can be interpreted physically as the invariance between 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 another way for proving it, more concise and meaningful (...)
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  23.  72
    Problem of the Direct Quantum-Information Transformation of Chemical Substance.Vasil Penchev - 2020 - Computational and Theoretical Chemistry eJournal (Elsevier: SSRN) 3 (26):1-15.
    Arthur Clark and Michael Kube–McDowell (“The Triger”, 2000) suggested the sci-fi idea about the direct transformation from a chemical substance to another by the action of a newly physical, “Trigger” field. Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”; according to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the (...)
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  24.  76
    The Kochen - Specker Theorem in Quantum Mechanics: A Philosophical Comment (Part 1).Vasil Penchev - 2013 - Philosophical Alternatives 22 (1):67-77.
    Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum (...)
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  25.  45
    A New Reading and Comparative Interpretation of Gödel’s Completeness (1930) and Incompleteness (1931) Theorems.Vasil Penchev - 2016 - Логико-Философские Штудии 13 (2):187-188.
    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 a new reading at issue and comparative interpretation of Gödel’s papers (1930; 1931) meant here. Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity. The most (...)
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  26. The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
    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 (...)
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  27. Representation and Reality by Language: How to Make a Home Quantum Computer?Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (34):1-14.
    A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored. The problem of completeness of mathematics is linked to its counterpart in quantum mechanics. That model includes two Peano arithmetics or Turing machines independent of each other. The complex Hilbert space underlying quantum mechanics as the base of its mathematical formalism is interpreted as a generalization of Peano arithmetic: It is a doubled infinite set of doubled Peano (...)
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  28.  19
    Quantum Information Theoretic Approach to the Mind–Brain Problem.Danko D. Georgiev - 2020 - Progress in Biophysics and Molecular Biology 158:16-32.
    The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind-brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the (...)
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  29. The Case of Quantum Mechanics Mathematizing Reality: The “Superposition” of Mathematically Modelled and Mathematical Reality: Is There Any Room for Gravity?Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (24):1-15.
    A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted (...)
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  30.  96
    Classical and Quantum Mechanics on Information Spaces with Applications to Cognitive, Psychological, Social, and Anomalous Phenomena.Andrei Khrennivov - 1999 - Foundations of Physics 29 (7):1065-1098.
    We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so-called transformers of information, basic processes are information processes and statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that classical and quantum mechanical models on p-adic information spaces can be applied for the investigation of (...)
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  31.  3
    Is the Life-World Reduction Sufficient in Quantum Physics?Michel Bitbol - 2020 - Continental Philosophy Review 54 (4):563-580.
    According to Husserl, the epochè must be left incomplete. It is to be performed step by step, thus defining various layers of “reduction.” In phenomenology at least two such layers can be distinguished: the life-world reduction, and the transcendental reduction. Quantum physics was born from a particular variety of the life-world reduction: reduction to observables according to Heisenberg, and reduction to classical-like properties of experimental devices according to Bohr. But QBism has challenged this limited version of the phenomenological (...)
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  32. Quantum-Information Conservation. The Problem About “Hidden Variables”, or the “Conservation of Energy Conservation” in Quantum Mechanics: A Historical Lesson for Future Discoveries.Vasil Penchev - 2020 - Energy Engineering (Energy) eJournal (Elsevier: SSRN) 3 (78):1-27.
    The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary (...)
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  33.  12
    Is the Life-World Reduction Sufficient in Quantum Physics?Michel Bitbol - 2021 - Continental Philosophy Review (4):1-18.
    According to Husserl, the epochè must be left incomplete. It is to be performed step by step, thus defining various layers of “reduction.” In phenomenology at least two such layers can be distinguished: the life-world reduction, and the transcendental reduction. Quantum physics was born from a particular variety of the life-world reduction: reduction to observables according to Heisenberg, and reduction to classical-like properties of experimental devices according to Bohr. But QBism has challenged this limited version of the phenomenological (...)
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  34.  4
    Paradox, Harmony, and Crisis in Phenomenology.Judson Webb - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    Husserl’s first work formulated what proved to be an algorithmically complete arithmetic, lending mathematical clarity to Kronecker’s reduction of analysis to finite calculations with integers. Husserl’s critique of his nominalism led him to seek a philosophical justification of successful applications of symbolic arithmetic to nature, providing insight into the “wonderful affinity” between our mathematical thoughts and things without invoking a pre-established harmony. For this, Husserl develops a purely descriptive phenomenology for which he found inspiration in Mach’s proposal (...)
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  35.  55
    Quantum Information Theoretic Approach to the Mind–Brain Problem.Danko D. Georgiev - 2020 - Progress in Biophysics and Molecular Biology 158:16-32.
    The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind–brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the (...)
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  36. Two Strategies to Infinity: Completeness and Incompleteness. The Completeness of Quantum Mechanics.Vasil Penchev - 2020 - High Performance Computing eJournal 12 (11):1-8.
    Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which (...)
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  37. Cognition According to Quantum Information: Three Epistemological Puzzles Solved.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (20):1-15.
    The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. 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 (...)
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  38. Main Concepts in Philosophy of Quantum Information.Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (31):1-4.
    Quantum mechanics involves a generalized form of information, that of quantum information. It is the transfinite generalization of information and re-presentable by transfinite ordinals. The physical world being in the current of time shares the quality of “choice”. Thus quantum information can be seen as the universal substance of the world serving to describe uniformly future, past, and thus the present as the frontier of time. Future is represented as a coherent whole, present (...)
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  39.  26
    Derivation of the Rules of Quantum Mechanics From Information-Theoretic Axioms.Daniel I. Fivel - 2012 - Foundations of Physics 42 (2):291-318.
    Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing experimentally observable properties of probability distributions for the outcome of measurements. Axioms I, II, III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by von Neumann (in Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955) and independently by Turing (Teuscher and Hofstadter, Alan Turing: Life and Legacy of (...)
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  40.  41
    Quaternionic Quantum Dynamics on Complex Hilbert Spaces.Matthew A. Graydon - 2013 - Foundations of Physics 43 (5):656-664.
    We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum measurements with positive operator valued measures on complex Hilbert spaces. Furthermore, we prove that quaternionic quantum channels can be simulated by completely positive trace preserving maps on complex matrices. These novel results map all quaternionic quantum processes to (...)
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  41. A Mathematical Model of Quantum Computer by Both Arithmetic and Set Theory.Vasil Penchev - 2020 - Information Theory and Research eJournal 1 (15):1-13.
    A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section I. (...)
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  42.  32
    Quantum Theory Without Hilbert Spaces.C. Anastopoulos - 2001 - Foundations of Physics 31 (11):1545-1580.
    Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient (...)
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  43.  34
    All Science as Rigorous Science: The Principle of Constructive Mathematizability of Any Theory.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal 12 (12):1-15.
    A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of 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 (...)
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  44.  27
    Husserl, the mathematization of nature, and the informational reconstruction of quantum theory.Philipp Berghofer, Philip Goyal & Harald A. Wiltsche - 2021 - Continental Philosophy Review 54 (4):413-436.
    As is well known, the late Husserl warned against the dangers of reifying and objectifying the mathematical models that operate at the heart of our physical theories. Although Husserl’s worries were mainly directed at Galilean physics, the first aim of our paper is to show that many of his critical arguments are no less relevant today. By addressing the formalism and current interpretations of quantum theory, we illustrate how topics surrounding the mathematization of nature come to the (...)
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  45.  36
    Many-Hilbert-Spaces Theory of Quantum Measurements.Mikio Namiki - 1988 - Foundations of Physics 18 (1):29-55.
    The many-Hilbert-spaces theory of quantum measurements, which was originally proposed by S. Machida and the present author, is reviewed and developed. Dividing a typical quantum measurement in two successive steps, the first being responsible for spectral decomposition and the second for detection, we point out that the wave packet reduction by measurement takes place at the latter step, through interaction of an object system with one of the local systems of detectors. First we discuss the physics of (...)
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  46. The Frontier of Time: The Concept of Quantum Information.Vasil Penchev - 2020 - Cosmology and Large-Scale Structure eJournal (Elsevier: SSRN) 2 (17):1-5.
    The concept of formal transcendentalism is utilized. The fundamental and definitive property of the totality suggests for “the totality to be all”, thus, its externality (unlike any other entity) is contained within it. This generates a fundamental (or philosophical) “doubling” of anything being referred to the totality, i.e. considered philosophically. Thus, that doubling as well as transcendentalism underlying it can be interpreted formally as an elementary choice such as a bit of information and a quantity corresponding to the number (...)
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  47.  48
    The Completeness: From Henkin's Proposition to Quantum Computer.Vasil Penchev - 2018 - Логико-Философские Штудии 16 (1-2):134-135.
    The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies 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 to be unified and thus reduced as a joint property of infinity and of all (...)
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  48.  1
    An Introduction to Hilbert Space and Quantum Logic.David W. Cohen & David William Cohen - 1989 - Springer.
    Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and (...)
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  49.  40
    After Derrida Before Husserl : The Spacing Between Phenomenology and Deconstruction.Louis N. Sandowsky - unknown
    This Ph.D. thesis is, in large part, a deepening of my M. A. dissertation, entitled: "Différance Beyond Phenomenological Reduction (Epoché)?" - an edited version of which was published in The Warwick Journal of Philosophy, Vol. 2, Issue 2, 1989. The M. A. dissertation explores the development of the various phases of the movement of epoché in Edmund Husserl's phenomenology and its relevance for Jacques Derrida's project of deconstruction. The analyses not only attend to the need for an effective propaedeutic (...)
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  50.  26
    Quantum Physics, Topology, Formal Languages, Computation: A Categorical View as Homage to David Hilbert.Chiara Marletto & Mario Rasetti - 2014 - Perspectives on Science 22 (1):98-114.
    The role and presence of David Hilbert in Physics are most probably as relevant as they are in Mathematics. His fundamental contributions to functional analysis, in particular the introduction of the notion of infinite-dimensional space (now universally referred to as Hilbert space) became crucial in quantum mechanics as well as in several areas of classical physics; and his discovery of the action of the field equations, in parallel to and independently from Einstein's, had a tremendous (...)
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