Axiomatic foundations of quantum mechanics revisited: the case for systems

We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.Comment: submitted to International Journal of Theoretical Physics, uses Latex, no figure

Bunge’s Mathematical Structuralism Is Not a Fiction

In this paper, I explore Bunge’s fictionism in philosophy of mathematics. After an overview of Bunge’s views, in particular his mathematical structuralism, I argue that the comparison between mathematical objects and fictions ultimately fails. I then sketch a different ontology for mathematics, based on Thomasson’s metaphysical work. I conclude that mathematics deserves its own ontology, and that, in the end, much work remains to be done to clarify the various forms of dependence that are involved in mathematical knowledge, in particular its dependence on mental/brain states and material objects

New remarks on the Cosmological Argument

We present a formal analysis of the Cosmological Argument in its two main forms: that due to Aquinas, and the revised version of the Kalam Cosmological Argument more recently advocated by William Lane Craig. We formulate these two arguments in such a way that each conclusion follows in first-order logic from the corresponding assumptions. Our analysis shows that the conclusion which follows for Aquinas is considerably weaker than what his aims demand. With formalizations that are logically valid in hand, we reinterpret the natural language versions of the premises and conclusions in terms of concepts of causality consistent with (and used in) recent work in cosmology done by physicists. In brief: the Kalam argument commits the fallacy of equivocation in a way that seems beyond repair; two of the premises adopted by Aquinas seem dubious when the terms `cause' and `causality' are interpreted in the context of contemporary empirical science. Thus, while there are no problems with whether the conclusions follow logically from their assumptions, the Kalam argument is not viable, and the Aquinas argument does not imply a caused origination of the universe. The assumptions of the latter are at best less than obvious relative to recent work in the sciences. We conclude with mention of a new argument that makes some positive modifications to an alternative variation on Aquinas by Le Poidevin, which nonetheless seems rather weak.Comment: 12 pages, accepted for publication in International Journal for Philosophy of Religio

Causality re-established

Causality never gained the status of a "law" or "principle" in physics. Some recent literature even popularized the false idea that causality is a notion that should be banned from theory. Such misconception relies on an alleged universality of reversibility of laws of physics, based either on determinism of classical theory, or on the multiverse interpretation of quantum theory, in both cases motivated by mere interpretational requirements for realism of the theory. Here, I will show that a properly defined unambiguous notion of causality is a theorem of quantum theory, which is also a falsifiable proposition of the theory. Such causality notion appeared in the literature within the framework of operational probabilistic theories. It is a genuinely theoretical notion, corresponding to establish a definite partial order among events, in the same way as we do by using the future causal cone on Minkowski space. The causality notion is logically completely independent of the misidentified concept of "determinism", and, being a consequence of quantum theory, is ubiquitous in physics. In addition, as classical theory can be regarded as a restriction of quantum theory, causality holds also in the classical case, although the determinism of the theory trivializes it. I then conclude arguing that causality naturally establishes an arrow of time. This implies that the scenario of the "Block Universe" and the connected "Past Hypothesis" are incompatible with causality, and thus with quantum theory: they both are doomed to remain mere interpretations and, as such, not falsifiable, similar to the hypothesis of "super-determinism". This article is part of a discussion meeting issue "Foundations of quantum mechanics and their impact on contemporary society".Comment: Presented at the Royal Society of London, on 11/12/ 2017, at the conference "Foundations of quantum mechanics and their impact on contemporary society". To appear on Philosophical Transactions of the Royal Society

Four simplified gradient elasticity models for the simulation of dispersive wave propagation

Gradient elasticity theories can be used to simulate dispersive wave propagation as it occurs in heterogeneous materials. Compared to the second-order partial differential equations of classical elasticity, in its most general format gradient elasticity also contains fourth-order spatial, temporal as well as mixed spatial temporal derivatives. The inclusion of the various higher-order terms has been motivated through arguments of causality and asymptotic accuracy, but for numerical implementations it is also important that standard discretization tools can be used for the interpolation in space and the integration in time. In this paper, we will formulate four different simplifications of the general gradient elasticity theory. We will study the dispersive properties of the models, their causality according to Einstein and their behavior in simple initial/boundary value problems

Parameterized optimized effective potential for the ground state of the atoms He through Xe

Parameterized orbitals expressed in Slater-type basis obtained within the optimized effective potential framework as well as the parameterization of the potential are reported for the ground state of the atoms He through Xe. The total, kinetic, exchange and single particle energies are given for each atom.Comment: 47 pages, 1 figur

Parmenides reloaded

I argue for a four dimensional, non-dynamical view of space-time, where becoming is not an intrinsic property of reality. This view has many features in common with the Parmenidean conception of the universe. I discuss some recent objections to this position and I offer a comparison of the Parmenidean space-time with an interpretation of Heraclitus' thought that presents no major antagonism.Comment: 11 pages, accepted for publication in Foundations of Scienc

Neural circuitry underlying rule use in humans and nonhuman primates

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