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Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
Contexts in quantum, classical and partition logic
 In Handbook of Quantum Logic
, 2006
"... Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud ..."
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Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud
Quantum logic. A brief outline
, 2005
"... A more complete introduction of the author can be found in the book ..."
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A more complete introduction of the author can be found in the book
Conventions in Relativity Theory and Quantum Mechanics
, 2002
"... ons. They lie at the very foundations of our world conceptions. Conventions serve as a sort of "scaffolding" from which we construct our scientific worldview. Yet, they are so simple and almost selfevident that they are hardly mentioned and go unreflected. To the author, this unreflecte ..."
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ons. They lie at the very foundations of our world conceptions. Conventions serve as a sort of "scaffolding" from which we construct our scientific worldview. Yet, they are so simple and almost selfevident that they are hardly mentioned and go unreflected. To the author, this unreflectedness and unawareness of conventionality appears to be the biggest problem related to conventions, especially if they are mistakenly considered as physical "facts" which are empirically testable. This confusion between assumption and observational, operational fact seems to be one of the biggest impediments for progressive research programs, in particular if they suggest postulates which are based on conventions different from the existing ones. In what follows we shall mainly review and discuss conventions in the two dominating theories of the 20th century: quantum mechanics and relativity theory. 2. CONVENTIONALITY OF THE CONSTANCY OF THE CHARACTERISTIC SPEED Sup
Quantum logic. A brief outline
, 2005
"... Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quant ..."
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Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quantum logic, and some of its algebraic properties, such as nondistributivity, whereby emphasis is given to concrete experimental setups related to quantum logical entities. A probability theory based on quantum logic is fundamentally and sometimes even spectacularly different from probabilities based on classical Boolean logic. We give a brief outline of its nonclassical aspects; in particular violations of BooleBell type consistency constraints on joint probabilities, as well as the KochenSpecker theorem, demonstrating in a constructive, finite way the scarcity and even nonexistence of twovalued states interpretable as classical truth assignments. A more complete introduction of the author can be found in the book Quantum Logic (Springer, 1998)
Physics and metaphysics look at computation Contents
"... As far as algorithmic thinking is bound by symbolic paperandpencil operations, the ChurchTuring thesis appears ..."
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As far as algorithmic thinking is bound by symbolic paperandpencil operations, the ChurchTuring thesis appears
Physical unknowables
, 2008
"... Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the nbody problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unk ..."
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Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the nbody problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.