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  1. Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya & Ichiro Yamato (2013). Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law. Foundations of Physics 43 (7):895-911.
    There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological (...)
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  2. Ellery Eells & James H. Fetzer (eds.) (2010). The Place of Probability in Science. Springer.
    To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...
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  3. Artur Ekert, Complex and Unpredictable Cardano.
    At a purely instrumental level, quantum theory is all about multiplication, addition and taking mod squares of complex numbers called probability amplitudes. The rules for combining amplitudes are deceptively simple. When two or more events are independent you multiply their respective probability amplitudes and when they are mutually exclusive you add them. Whenever you want to calculate probabilities you take mod squares of respective amplitudes. That’s it. If you are prepared to ignore the explanatory power of the theory (which you (...)
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  4. Ian G. Fuss & Daniel J. Navarro (2013). Open Parallel Cooperative and Competitive Decision Processes: A Potential Provenance for Quantum Probability Decision Models. Topics in Cognitive Science 5 (4):818-843.
    In recent years quantum probability models have been used to explain many aspects of human decision making, and as such quantum models have been considered a viable alternative to Bayesian models based on classical probability. One criticism that is often leveled at both kinds of models is that they lack a clear interpretation in terms of psychological mechanisms. In this paper we discuss the mechanistic underpinnings of a quantum walk model of human decision making and response time. The quantum walk (...)
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  5. Shan Gao, The Basis of Indeterminism.
    We show that the motion of particles may be essentially discontinuous and random.
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  6. Amihud Gilead (forthcoming). Pure Possibilities and Some Striking Scientific Discoveries. Foundations of Chemistry:1-15.
    Regardless or independent of any actuality or actualization and exempt from spatiotemporal and causal conditions, each individual possibility is pure. Actualism excludes the existence of individual pure possibilities, altogether or at least as existing independently of actual reality. In this paper, I demonstrate, on the grounds of my possibilist metaphysics—panenmentalism—how some of the most fascinating scientific discoveries in chemistry could not have been accomplished without relying on pure possibilities and the ways in which they relate to each other (for instance, (...)
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  7. Amihud Gilead (2013). Shechtman's Three Question Marks: Possibility, Impossibility, and Quasicrystals. [REVIEW] Foundations of Chemistry 15 (2):209-224.
    The revolutionary discovery of actual quasicrystals, thanks to Dan Shechtman’s stamina, is a golden opportunity to analyze once again the role that pure (“theoretical”) possibilities and saving them plays in scientific progress. Some theoreticians, primarily Alan Mackay, contributed to saving pure possibilities of quasicrystalline structures and to opening materials science for them. My analysis rests upon an original modal metaphysics—panenmentalism—which I introduced and have been developing since 1999, quite independently of any familiarity with modern crystallography, and which deals with saving (...)
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  8. Sheldon Goldstein (2012). Typicality and Notions of Probability in Physics. In. In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. 59--71.
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  9. Ravi V. Gomatam, Popper's Propensity Interpretation and Heisenberg's Potentia Interpretation.
    In other words, classically, probabilities add; quantum mechanically, the probability amplitudes add, leading to the presence of the extra product terms in the quantum case. What this means is that in quantum theory, even though always only one of the various outcomes is obtained in any given observation, some aspect of the non -occurring events, represented by the corresponding complex-valued quantum amplitudes, plays a role in determining the overall probabilities. Indeed, the observed quantum interference effects are correctly captured by the (...)
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  10. James Hawthorne & Michael Silberstein (1995). For Whom the Bell Arguments Toll. Synthese 102 (1):99-138.
    We will formulate two Bell arguments. Together they show that if the probabilities given by quantum mechanics are approximately correct, then the properties exhibited by certain physical systems must be nontrivially dependent on thetypes of measurements performedand eithernonlocally connected orholistically related to distant events. Although a number of related arguments have appeared since John Bell's original paper (1964), they tend to be either highly technical or to lack full generality. The following arguments depend on the weakest of premises, and the (...)
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  11. Edwin T. Jaynes (1973). The Well-Posed Problem. Foundations of Physics 3 (4):477-493.
    Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency definition of probability; yet they may appear wellposed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a definite frequency correspondence; the distribution obtained by invariance under a transformation group is by far the most likely to be observed experimentally, in the (...)
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  12. Andrei Khrennikov (2005). The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics. Foundations of Physics 35 (10):1655-1693.
  13. Jennifer S. Trueblood & Jerome R. Busemeyer (2011). A Quantum Probability Account of Order Effects in Inference. Cognitive Science 35 (8):1518-1552.
    Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a (...)
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  14. Sylvia Wenmackers & Danny E. P. Vanpoucke (2012). Models and Simulations in Material Science: Two Cases Without Error Bars. Statistica Neerlandica 66 (3):339–355.
    We discuss two research projects in material science in which the results cannot be stated with an estimation of the error: a spectroscopic ellipsometry study aimed at determining the orientation of DNA molecules on diamond and a scanning tunneling microscopy study of platinum-induced nanowires on germanium. To investigate the reliability of the results, we apply ideas from the philosophy of models in science. Even if the studies had reported an error value, the trustworthiness of the result would not depend on (...)
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Probability in the Physical Sciences, Misc
  1. Antony Eagle (forthcoming). Is the Past a Matter of Chance? In Alastair Wilson (ed.), Chance and Temporal Asymmetry. Oxford University Press.
  2. Iñaki San Pedro & Mauricio Suárez (2009). The Principle of Common Cause and Indeterminism: A Review. In José Luis González Recio (ed.), Philosophical Essays on Physics and Biology. Georg Olms Verlag.
    We offer a review of some of the most influential views on the status of Reichenbach’s Principle of the Common Cause (RPCC) for genuinely indeterministic systems. We first argue that the RPCC is properly a conjunction of two distinct claims, one metaphysical and another methodological. Both claims can and have been contested in the literature, but here we simply assume that the metaphysical claim is correct, in order to focus our analysis on the status of the methodological claim. We briefly (...)
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