In this paper, we argue for a novel three dimensionalist (3D'ist) solution to the problem of persistence, i.e., cross-temporal identity. We restrict the discussion of persistence to simple substances, which do not have other substances as their parts. The account of simple substances employed in the paper is a trope-nominalist Strong Nuclear Theory (SNT), which develops Peter Simons' trope nominalism. Regarding the distinction between three dimensionalism (3D) and four dimensionalism (4D), we follow Michael Della Rocca's formulation, in which 3D explains persistence in virtue of same entities and 4D in virtue of distinct entities (temporal parts). SNT is a 3D'ist position because it accounts for the persistence of simple substances in virtue of diachronically identical 'nuclear' tropes. The nuclear tropes of a simple substance are necessary for it and mutually rigidly dependent but distinct. SNT explains qualitative change by tropes that are contingent to a simple substance. We show that it avoids the standard problems of 3D: temporal relativization of ontic predication, Bradley's regress, and coincidence, fission and fusion cases. The temporal relativization is avoided because of the analysis of temporary parts that SNT gives in terms of temporal sub-location, which is atemporal part-whole relation.
This paper is the first trope-theoretical reply to E.J. Lowe's serious dilemma against trope nominalism in print. The first horn of this dilemma is that if tropes are identity dependent on substances, a vicious circularity threatens trope theories because they must admit that substances are identity dependent on their constituent tropes.According to the second horn, if the trope theorist claims that tropes are identity independent, she faces two insurmountable difficulties. (1) It is hard to understand the ontological dependence of tropes on substances. (2) The identity-conditions of tropes cannot be determinate, which threatens the determination of the identityconditions of substances. Our reply to the first horn of Lowe's dilemma is to deny the identity dependence of tropes. Yet we can avoid the second horn because our theory
Abstract:The ready to use set of functions to facilitate solving a generalized eigenvalue problem for symmetric matrices in order to efficiently calculate eigenvalues and eigenvectors, using Compute Unified Device Architecture (CUDA) technology from NVIDIA, is provided. An integral part of the CUDA is the high level programming environment enabling tracking both code executed on Central Processing Unit and on Graphics Processing Unit. The presented matrix structures allow for the analysis of the advantages of using graphics processors in such calculations.
According to standard trope nominalism, there are simple tropes that do not have parts or multiply distinct aspects. Douglas Ehring's reductio ad absurdum against this standard view concludes that there are no simple tropes. In this paper, we provide a response to Ehring defending the standard view. Ehring's argument may be refuted by (1) distinguishing the ontological form of tropes from their contribution to the ontological content of the world, and (2) construing tropes as having primitive identity. At the same time, standard trope nominalism is elaborated on by distinguishing between ontological form and content, for which there are also independent reasons.
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