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Miklós Rédei [62]M. Redei [11]
  1. Yuichiro Kitajima & Miklós Rédei, Characterizing Common Cause Closedness of Quantum Probability Theories.
    We prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a non-commutative von Neumann algebra together with a countably additive probability measure on the lattice. Common cause closedness is the feature that for every correlation between a pair of commuting projections there exists in the lattice a third projection commuting with both of the correlated projections and which is a Reichenbachian common cause of the correlation. The (...)
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  2. Miklós Rédei (2014). A Categorial Approach to Relativistic Locality. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48:137-146.
    Relativistic locality is interpreted in this paper as a web of conditions expressing the compatibility of a physical theory with the underlying causal structure of spacetime. Four components of this web are distinguished: spatiotemporal locality, along with three distinct notions of causal locality, dubbed CL-Independence, CL-Dependence, and CL-Dynamic. These four conditions can be regimented using concepts from the categorical approach to quantum field theory initiated by Brunetti, Fredenhagen, and Verch . A covariant functor representing a general quantum field theory is (...)
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  3.  16
    Zalán Gyenis, Gabor Hofer-Szabo & Miklós Rédei, Conditioning Using Conditional Expectations: The Borel-Kolmogorov Paradox.
    The Borel-Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. The conditional probabilities (...)
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  4.  13
    Miklós Rédei & Zalán Gyenis, Measure Theoretic Analysis of Consistency of the Principal Principle.
    Weak and strong consistency of thePrincipal Principle are defined in terms of classical probability measure spaces. It is proved that thePrincipal Principle is both weakly and strongly consistent. The Abstract Principal Principle is strengthened by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined. It is shown that the Stable Abstract Principal Principle is weakly consistent. Strong consistency of the Stable Abstract Principal principle remains an open question.
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  5.  29
    Z. Gyenis, G. Hofer-Szabó & M. Rédei (forthcoming). Conditioning Using Conditional Expectations: The Borel–Kolmogorov Paradox. Synthese:1-36.
    The Borel–Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. The conditional probabilities (...)
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  6.  94
    Gábor Hofer-Szabó & Miklós Rédei (2006). Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist. Foundations of Physics 36 (5):745-756.
    A partition $\{C_i\}_{i\in I}$ of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite (...)
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  7. Gábor Hofer-Szabó, Miklós Rédei & László E. Szabó (2002). Common-Causes Are Not Common Common-Causes. Philosophy of Science 69 (4):623-636.
    A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition (...)
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  8.  86
    John Earman & Miklós Rédei (1996). Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics. British Journal for the Philosophy of Science 47 (1):63-78.
    We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the behaviour must ensure that (...)
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  9.  15
    Miklos Redei & Stephen J. Summers (2002). Local Primitive Causality and the Common Cause Principle in Quantum Field Theory. Foundations of Physics 32 (3):335-355.
    If $\mathcal{A}$ (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈ $\mathcal{A}$ (V 1 ), B∈ $\mathcal{A}$ (V 2 ) correlated in the normal state φ there exists a projection C (...)
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  10.  69
    Miklós Rédei (2010). Operational Independence and Operational Separability in Algebraic Quantum Mechanics. Foundations of Physics 40 (9-10):1439-1449.
    Recently, new types of independence of a pair of C *- or W *-subalgebras (1,2) of a C *- or W *-algebra have been introduced: operational C *- and W *-independence (Rédei and Summers, http://arxiv.org/abs/0810.5294, 2008) and operational C *- and W *-separability (Rédei and Valente, How local are local operations in local quantum field theory? 2009). In this paper it is shown that operational C *-independence is equivalent to operational C *-separability and that operational W *-independence is equivalent to (...)
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  11.  49
    Miklós Rédei & Giovanni Valente (2010). How Local Are Local Operations in Local Quantum Field Theory? Studies in History and Philosophy of Science Part B 41 (4):346-353.
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  12.  43
    Miklós Rédei & Stephen Jeffrey Summers (2007). Quantum Probability Theory. Studies in History and Philosophy of Science Part B 38 (2):390-417.
  13.  42
    Zalán Gyenis & Miklós Rédei (2013). Atomicity and Causal Completeness. Erkenntnis 79 (S3):1-15.
    The role of measure theoretic atomicity in common cause closedness of general probability theories with non-distributive event structures is raised and investigated. It is shown that if a general probability space is non-atomic then it is common cause closed. Conditions are found that entail that a general probability space containing two atoms is not common cause closed but it is common cause closed if it contains only one atom. The results are discussed from the perspective of the Common Cause Principle.
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  14.  16
    Miklós Rédei & Zalán Gyenis, General Properties of General Bayesian Learning.
    We investigate the general properties of general Bayesian learning, where ``general Bayesian learning'' means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...)
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  15.  8
    Miklós Rédei, Assessing the Status of the Common Cause Principle.
    The Common Cause Principle, stating that correlations are either consequences of a direct causal link between the correlated events or are due to a common cause, is assessed from the perspective of its viability and it is argued that at present we do not have strictly empirical evidence that could be interpreted as disconfirming the principle. In particular it is not known whether spacelike correlations predicted by quantum field theory can be explained by properly localized common causes, and EPR correlations (...)
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  16.  43
    Miklós Rédei (2010). Einstein's Dissatisfaction with Nonrelativistic Quantum Mechanics and Relativistic Quantum Field Theory. Philosophy of Science 77 (5):1042-1057.
    It is argued that in his critique of standard nonrelativistic quantum mechanics Einstein formulated three requirements as necessary for a physical theory to be compatible with the field-theorectical paradigm, and it is shown that local, relativistic, algebraic quantum field theory typically satisfies those criteria-although, there are still open questions concerning the status of operational separability of quantum systems localized in space like separated space-time regions. It is concluded that local algebraic quantum field theory can be viewed as a research program (...)
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  17.  68
    Miklos Rédei (1996). Why John von Neumann Did Not Like the Hilbert Space Formalism of Quantum Mechanics (and What He Liked Instead). Studies in History and Philosophy of Science Part B 27 (4):493-510.
  18.  28
    Miklós Rédei (1997). Reichenbach's Common Cause Principle and Quantum Field Theory. Foundations of Physics 27 (10):1309-1321.
  19.  23
    Gabor Hofer-Szabo & Miklos Redei, Reichenbachian Common Cause Systems.
    A partition $\{C_i\}_{i\in I}$ of a Boolean algebra $\cS$ in a probability measure space $(\cS,p)$ is called a Reichenbachian common cause system for the correlated pair $A,B$ of events in $\cS$ if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set $I$ is called the size of the common cause system. It is shown that given any correlation in $(\cS,p)$, and given any finite size $n>2$, the probability space (...)
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  20.  24
    G. Hofer-Szabó, M. Rédei & and LE Szabó (1999). On Reichenbach's Common Cause Principle and Reichenbach's Notion of Common Cause. British Journal for the Philosophy of Science 50 (3):377 - 399.
    It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it (...)
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  21.  38
    Zalán Gyenis & Miklós Rédei (2011). Characterizing Common Cause Closed Probability Spaces. Philosophy of Science 78 (3):393-409.
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  22.  17
    Z. Gyenis & Miklós Rédei, Why Bertrand's Paradox is Not Paradoxical but is Felt So.
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  23.  39
    Zalán Gyenis & Miklós Rédei (2015). Defusing Bertrand’s Paradox. British Journal for the Philosophy of Science 66 (2):349-373.
    The classical interpretation of probability together with the principle of indifference is formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called labelling invariance is defined in the category of Haar probability spaces; it is shown that labelling invariance is violated, and Bertrand’s paradox is interpreted as the proof of violation of labelling invariance. It is shown that Bangu’s attempt to block the emergence of Bertrand’s paradox by requiring the re-labelling (...)
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  24.  3
    Miklós Rédei & Iñaki Pedro (2012). Distinguishing Causality Principles. Studies in History and Philosophy of Science Part B 43 (2):84-89.
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  25.  4
    Miklós Rédei (2001). Von Neumann’s Concept of Quantum Logic and Quantum Probability. Vienna Circle Institute Yearbook 8:153-172.
    The idea of quantum logic first appears explicitly in the short Section 5 of Chapter III. in von Neumann’s 1932 book on the mathematical foundations of quantum mechanics [31]; however, the real birthplace of quantum logic is commonly identified with the 1936 seminal paper co-authored by G. Birkhoff and J. von Neumann [5]. The aim of this review is to recall the main idea of the Birkhoff-von Neumann concept1 of quantum logic as this was put forward in the 1936 paper. (...)
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  26.  11
    Miklós Rédei (2014). Hilbert's 6th Problem and Axiomatic Quantum Field Theory. Perspectives on Science 22 (1):80-97.
    This paper has two parts, a historical and a systematic. In the historical part it is argued that the two major axiomatic approaches to relativistic quantum field theory, the Wightman and Haag-Kastler axiomatizations, are realizations of the program of axiomatization of physical theories announced by Hilbert in his 6th of the 23 problems discussed in his famous 1900 Paris lecture on open problems in mathematics, if axiomatizing physical theories is interpreted in a soft and opportunistic sense suggested in 1927 by (...)
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  27.  35
    Miklós Rédei & Iñaki San Pedro (2012). Distinguishing Causality Principles. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (2):84-89.
    We distinguish two sub-types of each of the two causality principles formulated in connection with the Common Cause Principle in Henson and raise and investigate the problem of logical relations among the resulting four causality principles. Based in part on the analysis of the status of these four principles in algebraic quantum field theory we will argue that the four causal principles are non- equivalent.
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  28.  83
    Balazs Gyenis & Miklos Redei (2004). When Can Statistical Theories Be Causally Closed? Foundations of Physics 34 (9):1285-1303.
    The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be (...)
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  29.  55
    Miklos Redei (1995). Logical Independence in Quantum Logic. Foundations of Physics 25 (3):411-422.
    The projection latticesP(ℳ1),P(ℳ2) of two von Neumann subalgebras ℳ1, ℳ2 of the von Neumann algebra ℳ are defined to be logically independent if A ∧ B≠0 for any 0≠AεP(ℳ1), 0≠BP(ℳ2). After motivating this notion in independence, it is shown thatP(ℳ1),P(ℳ2) are logically independent if ℳ1 is a subfactor in a finite factor ℳ andP(ℳ1),P(ℳ2 commute. Also, logical independence is related to the statistical independence conditions called C*-independence W*-independence, and strict locality. Logical independence ofP(ℳ1,P(ℳ2 turns out to be equivalent to the (...)
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  30.  11
    Gabor Hofer-Szabo, Miklos Redei & Laszlo E. Szabo (2002). Common-Causes Are Not Common Common-Causes. Philosophy of Science 69 (4):623-636.
    A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition (...)
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  31.  19
    Miklós Rédei (2007). The Birth of Quantum Logic. History and Philosophy of Logic 28 (2):107-122.
    By quoting extensively from unpublished letters written by John von Neumann to Garret Birkhoff during the preparatory phase (in 1935) of their ground-breaking 1936 paper that established quantum logic, the main steps in the thought process leading to the 1936 Birkhoff?von Neumann paper are reconstructed. The reconstruction makes it clear why Birkhoff and von Neumann rejected the notion of quantum logic as the projection lattice of an infinite dimensional complex Hilbert space and why they postulated in their 1936 paper that (...)
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  32.  28
    Miklós Rédei (1986). Nonexistence of Hidden Variables in the Algebraic Approach. Foundations of Physics 16 (8):807-815.
    Given two unital C*-algebrasA, ℬ and their state spacesE A , Eℬ respectively, (A,E A ) is said to have (ℬ, Eℬ) as a hidden theory via a linear, positive, unit-preserving map L: ℬ →A if, for all ϕ εE A , L*ϕ can be decomposed in Eℬ into states with pointwise strictly less dispersion than that of ϕ. Conditions onA and L are found that exclude (A,E A ) from having a hidden theory via L. It is shown in (...)
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  33.  63
    John Earman & Miklos Redei, Center for Philosophy of Science.
    the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behavior for the finite set of observables that matter, but the behavior must ensure that the approach to equilibrium for these obsersvables is on the appropriate..
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  34.  2
    Miklós Rédei, Michael Stöltzner, Walter Thirring, Ulrich Majer & Jeffrey Bub (2001). John von Neumann and the Foundations of Quantum Physics. Springer Netherlands.
    ... of Quantum Physics Book Editors Miklós Rédei1 Michael Stöltzner2 Eötvös University, Budapest, Hungary Institute Vienna Circle, Vienna, University of Salzburg, Vienna, Austria ISSN 09296328 ISBN 9789048156511 ISBN 9789401720120 ...
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  35.  9
    Miklós Rédei & Zalán Gyenis, Can Bayesian Agents Always Be Rational? A Principled Analysis of Consistency of an Abstract Principal Principle.
    The paper takes thePrincipal Principle to be a norm demanding that subjective degrees of belief of a Bayesian agent be equal to the objective probabilities once the agent has conditionalized his subjective degrees of beliefs on the values of the objective probabilities, where the objective probabilities can be not only chances but any other quantities determined objectively. Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract (...)
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  36.  51
    Miklos Redei (1991). Bell's Inequalities, Relativistic Quantum Field Theory and the Problem of Hidden Variables. Philosophy of Science 58 (4):628-638.
    Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a-c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this (...)
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  37.  4
    Miklós Rédei (2002). Reichenbach's Common Cause Principle and Quantum Correlations. In T. Placek & J. Butterfield (eds.), Non-Locality and Modality. Kluwer 259--270.
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  38.  48
    Miklos Redei, Founded on Classical Mechanics and Interpretation of Classical Staistical Mechanical Probabilities.
    The problem of relation between statistical mechanics (SM) and classical mechanics (CM), especially the question whether SM can be founded on CM, has been a subject of controversies since the rise of classical statistical mechanics (CSM) at the end of 19th century. The first views rejecting explicitly the possibility of laying the foundations of CSM in CM were triggered by the "Wiederkehr-" and "Umkehreinwand" arguments. These arguments played an important role in the debate about Boltzmann's original H-theorem and led to (...)
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  39. M. Rédei (2010). Operational Separability and Operational Independence in Algebraic Quantum Mechanics. Foundations of Physics 40:1439-1449.
  40.  7
    Miklos Redei & Charlotte Werndl, On the History of the Isomorphism Problem of Dynamical Systems with Special Regard to von Neumann's Contribution.
    This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory. In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to Ulam is the very first proof that (...)
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  41. MiklÓs RÉdei (2010). Kolmogorovian Censorship Hypothesis For General Quantum Probability Theories. Manuscrito 33 (1):365-380.
    It is shown that the Kolmogorovian Censorship Hypothesis, according to which quantum probabilities are interpretable as conditional probabilities in a classical probability measure space, holds not only for Hilbert space quantum mechanics but for general quantum probability theories based on the theory of von Neumann algebras.
     
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  42.  32
    Miklos Redei (1993). Are Prohibitions of Superluminal Causation by Stochastic Einstein Locality and by Absence of Lewisian Probabilistic Counterfactual Causality Equivalent? Philosophy of Science 60 (4):608-618.
    Butterfield's (1992a,b,c) claim of the equivalence of absence of Lewisian probabilistic counterfactual causality (LC) to Hellman's stochastic Einstein locality (SEL) is questioned. Butterfield's assumption on which the proof of his claim is based would suffice to prove that SEL implies absence of LC also for appropriately given versions of these notions in algebraic quantum field theory, but the assumption is not an admissible one. The conclusion must be that the relation of SEL and absence of LC is open, and that (...)
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  43.  18
    Miklos Redei (1999). 'Unsolved Problems of Mathematics' J von Neumann's Address to the International Congress of Mathematicians, Amsterdam, September 2-9, 1954. The Mathematical Intelligencer 21:7-12.
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  44.  29
    Miklós Rédei (1985). Note on an Argument of W. Ochs Against the Ignorance Interpretation of State in Quantum Mechanics. Erkenntnis 23 (2):143 - 148.
  45. Miklos Redei & Balazs Gyenis (2011). Causal Completeness of Probability Theories-Results and Open Problems. In Phyllis McKay Illari, Federica Russo & Jon Williamson (eds.), Causality in the Sciences. OUP Oxford
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  46.  32
    Miklós Rédei (1987). Reformulation of the Hidden Variable Problem Using Entropic Measure of Uncertainty. Synthese 73 (2):371 - 379.
    Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states E(A) the composite state ° L E() can be obtained as an (...)
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  47.  4
    Miklós Rédei & Michael Stöltzner (2001). Introduction. Vienna Circle Institute Yearbook 8:1-4.
    John von Neumann was, undoubtedly, one of the true scientific geniuses of the 20th century. The main fields to which he contributed include different disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science and computer design. Von Neumann was also actively involved in politics, science management, served on a number of commissions and advisory committees and had a major impact on U.S. government decisions during, and especially after, the Second World War.
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  48.  4
    Miklós Rédei (2002). Mathematical Physics and Philosophy of Physics. Vienna Circle Institute Yearbook 9:239-243.
    The main claim of this talk is that mathematical physics and philosophy of physics are not different. This claim, so formulated, is obviously false because it is overstated; however, since no non-tautological statement is likely to be completely true, it is a meaningful question whether the overstated claim expresses some truth. I hope it does, or so I’ll argue. The argument consists of two parts: First I’ll recall some characteristic features of von Neumann’s work on mathematical foundations of quantum mechanics (...)
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  49.  23
    Miklós Rédei (2001). Facets of Quantum Logic. Studies in History and Philosophy of Science Part B 32 (1):101-111.
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  50.  6
    Miklós Rédei & Michael Stöltzner (2006). Soft Axiomatisation: John von Neumann on Method and von Neumann's Method in the Physical Sciences. In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer 235--249.
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