4,633 research outputs found

    Good lives: prolegomena

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    Quantum Holism: Reconciling Extended Simples with Supersubstantivalism

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    I argue that the extended simples picture (ESP) is compatible with supersubstantivalism under the quantum holism model, and that reevaluating our limits on the ways an object may be located by fusing the two ontologies can benefit our understanding of modern physics. I first illustrate the explanatory utility of extended simples, using examples of superposition and entanglement. Second, I advocate the use of supersubstantivalism as a way to understand the interface between objects and spacetime, and argue that the ESP suitably fits into a supersubstantivalist interpretation of quantum field theory. In the last section, I propose quantum holism as a framework to reconcile supersubstantivalism with extended simples, and conclude that the causal relationship that interweaves material objects and spacetime render the two ontologies compatible. I will demonstrate that a combined ontology is useful for its parsimony, and for our understanding of quantum field theory

    The Complexity of Reasoning about Spatial Congruence

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    In the recent literature of Artificial Intelligence, an intensive research effort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the computational complexity of reasoning problems for subsets of algebras. The main purpose of these researches is to describe a restricted set of maximal tractable subalgebras, ideally in an exhaustive fashion with respect to the hosting algebras. In this paper we introduce a novel algebra for reasoning about Spatial Congruence, show that the satisfiability problem in the spatial algebra MC-4 is NP-complete, and present a complete classification of tractability in the algebra, based on the individuation of three maximal tractable subclasses, one containing the basic relations. The three algebras are formed by 14, 10 and 9 relations out of 16 which form the full algebra

    Space, points and mereology. On foundations of point-free Euclidean geometry

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    This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means of mereology (resp. Boolean algebras) and Whitehead-like connection structures. We list and briefly analyze axioms for mereological structures, as well as those for connection structures. We argue that mereology is a good tool to model so called spatial relations. We also try to justify our choice of axioms for connection relation. Finally, we briefly discuss two theories: Grzegorczyk’s point-free topology and Tarski’s geometry of solids

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