Contexts are maximal collections of co-measurable observables “bundled together ” to form a “quasi-classical mini-universe. ” 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

After a brief review of ontic and epistemic descriptions, and of subjective, logical and statistical interpretations of probability, we summarize the traditional axiomatization of calculus of probability in terms of Boolean algebras and its set-theoretical realization in terms of Kolmogorov probability spaces. Since the axioms of mathematical probability theory say nothing about the conceptual meaning of “randomness ” one considers probability as property of the generating conditions of a process so that one can relate randomness with predictability (or retrodictability). In the measure-theoretical codification of stochastic processes genuine chance processes can be defined rigorously as so-called regular processes which do not allow a long-term prediction. We stress that stochastic processes are equivalence classes of individual point functions so that they do not refer to individual processes but only to an ensemble of statistically equivalent individual processes. Less popular but conceptually more important than statistical descriptions are individual descriptions which refer to individual chaotic processes. First, we review the individual description based on the generalized harmonic analysis by Norbert Wiener. It allows the definition of individual purely chaotic processes which can be interpreted as trajectories of regular statistical stochastic processes.

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A framework for the mind-matter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive non-Boolean description of a world without an apriorigiven mind-matter distinction. Such a description in terms of a locally Boolean but globally non-Boolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely non-Boolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a non-Boolean structure and can be encompassed into a single non-Boolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.

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observations on quantum correlations exceeding

observations concerning the plasticity of nonlocal

PACS. 03.65.Ud – Entanglement and quantum nonlocality. Abstract. – The theorem of Bell is a variant of Boole’s legendary consistency “conditions of possible experience. ” Such an interpretation appears to be immune to arguments involving time dependencies put forward recently by Hess and Philipp [Europhysics Letters 57(6), 775-781, 2002], although experiments need not be. Boole’s “conditions of possible experience ” and Pitowsky correlation polytopes. – In the middle of the 19th century the English mathematician George Boole formulated a theory of “conditions of possible experience ” (COPE) [1–5]. These conditions subsume the consistency requirements satisfied by relative frequencies or probabilities of classical events. They are expressed by certain equations or inequalities. Here, the term “classical ” refers to the fact that events can be joined and united by the usual rules of Boolean algebra. More recently, similar equations for a particular setup relevant in the quantum mechanical context have been discussed by Bell, Clauser&Horne and others [6–9]. Pitowsky has given a geometrical interpretation of COPE in terms of correlation polytopes [4,5,10,11]. Thereby, the rows of the truth tables of events and their joints are interpreted as vectors in a real linear

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 n-body 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.