10,529 research outputs found

    Everything, and then some

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    On its intended interpretation, logical, mathematical and metaphysical discourse sometimes seems to involve absolutely unrestricted quantification. Yet our standard semantic theories do not allow for interpretations of a language as expressing absolute generality. A prominent strategy for defending absolute generality, influentially proposed by Timothy Williamson in his paper ‘Everything’ (2003), avails itself of a hierarchy of quantifiers of ever increasing orders to develop non-standard semantic theories that do provide for such interpretations. However, as emphasized by Øystein Linnebo and Agustín Rayo (2012), there is pressure on this view to extend the quantificational hierarchy beyond the finite level, and, relatedly, to allow for a cumulative conception of the hierarchy. In his recent book, Modal Logic as Metaphysics (2013), Williamson yields to that pressure. I show that the emerging cumulative higher-orderist theory has implications of a strongly generality-relativist flavour, and consequently undermines much of the spirit of generality absolutism that Williamson set out to defend

    Against the iterative conception of set

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    According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the empty set and raises serious epistemological concerns; but the leading realist interpretations---ontological and modal interpretations of priority---are deeply problematic as well. I conclude that the purported explanatory virtues of the iterative conception are, at present, unfounded

    Damage identification in a concrete beam using curvature difference ratio

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    Previous studies utilising changes in mode shape or curvature to locate damage rely on the fact that the greatest change occurs around the defect. However, in concrete beams this fact is undermined due to the nature of the defect as distributed multi-site cracks. In addition, differences in mode shape and curvature as ways to locate the damage is unstable because of occurrence of modal nodes and inflection points. In this paper, one interesting solution to this problem is being tested by establishing a new non-dimensional expression designated the 'Curvature Difference Ratio (CDR)'. This parameter exploits the ratio of differences in curvature of a specific mode shape for a damaged stage and another reference stage. The expression CDR is reasonably used to locate the damage and estimate the dynamic bending stiffness in a successively loaded 6m concrete beam. Results obtained by the proposed technique are tested and validated with a case study results done by Ren and De Roeck [1] also by Maeck and De Roeck [2]. Another contribution of this work is that relating changes in vibration properties to the design bending moment at beam sections as defined in Eurocode 2 specifications [3]. Linking between a beam section condition and the change in vibration data will help to give a better comprehension on the beam condition than the applied load

    Optimal transient growth in an incompressible flow past a backward-slanted step

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    With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 degrees of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin-Helmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic forcing is tackled by means of variational formulation, adjoint method, penalization scheme and orthogonalization algorithm. Dealing with the transient growth of spanwise-periodic perturbations and inspired by the need of physically-realizable disturbances, we finally provide a procedure attaining a kinetic-energy maximal gain of the order of one million with respect to the power introduced by the external forcing.Comment: 17 figure
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