In the proposed non-Aristotelian finitary logic (NAFL), truths for formal propositions can exist only with respect to axiomatic theories, essentially as temporary axiomatic declarations in the human mind. An undecidable proposition P in a consistent NAFL theory T is true/false with respect to T if and only if it has been axiomatically declared as true/false by virtue of its provability/refutability in an interpretation T* of T. In the absence of any such axiomatic declarations, P is in a superposed state of 'neither true nor false' and the consistency of T requires the existence of a non-classical model for T in which P&¬P is the case. Here T* is an axiomatic NAFL theory that, like T, resides in the human mind and acts as the 'truth-maker' for (a model of) T. Quantum superposition is justified by identifying 'axiomatic declarations' for the truth/falsity of P (by virtue of its provability/refutability in T*) with 'measurement' in the real world. NAFL also explains and de-mystifies the phenomenon of entanglement. NAFL severely restricts classical infinitary reasoning, but possibly provides sufficient machinery for a consistent axiomatization of quantum mechanics.
The Copernican revolution of the 1500s and 1600s was in large part due to new theories and discoveries, which indicated that the general view of the universe – the more or less Aristotelian, teleological view – was no longer viable. This revolution eventually resulted in a substantially different view on the sort of universe we inhabit. New discoveries in recent years, involving Bell’s theorem, quantum theory, and the outcome of carefully designed and replicated experiments, strongly suggest that the general view of the universe we have had since the Copernican revolution is no longer viable. The main goals of this paper are (i) to present Bell’s theorem and the results of these recent experiments in a way accessible to a non-technical audience, and (ii) to explore the question of whether these new discoveries place us in a similar situation to that of our predecessors in the early years of the 1600s, or roughly, whether we are in the beginning stages of a modern Copernican revolution.
Theories of decoherence come in two flavors---Platonic and Aristotelian. Platonists grant ontological primacy to the concepts and mathematical symbols by which we describe or comprehend the physical world. Aristotelians grant it to the physical world. The significance one attaches to the phenomenon of decoherence depends on the school to which one belongs. The debate about the significance of quantum states has for the most part been carried on between Platonists and Kantians, who advocate an epistemic interpretation, with Aristotelians caught in the crossfire. For the latter, quantum states are neither states of Nature nor states of knowledge. The real issue is not the kind of reality that we should attribute to quantum states but the reality of the spatial and temporal distinctions that we make. Once this is recognized, the necessity of attributing ontological primacy to facts becomes obvious, the Platonic stance becomes inconsistent, and the Kantian point of view becomes unnecessarily restrictive and unilluminating.