W. V. Quine describes himself as a "robust realist" about physical objects in the external world. This realism about objects is due to Quine's naturalism. On the other hand, Quine's naturalistic epistemology involves a conception of objects as posits that we introduce in our theories about the world. This conception of objects can be seen as anti-realist rather than realist. In this article, I discuss the questions whether there is a tension between Quine's realism and his epistemological conception of objects, and how Quine's conception of objects should be understood if he is also to be regarded as a realist. I also address the question whether Quine should be placed on the realist or the anti-realist side of the current realism debate. I argue that Quine's conception of objects as posits is a general account of the nature of objects, and that this account does not conflict with Quine's realism as long as this realism is properly understood. I also argue that Quine cannot be placed on either side of the contemporary realism debate, since his realism is not metaphysical realism and his conception of objects is not an anti-realist doctrine according to which objects would be less than real.
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.
In this article, we propose a new trope nominalist conception of determinate and determinable kinds of quantitative tropes. The conception is developed as follows. First, we formulate a new account of tropes falling under the same determinates and determinables in terms of internal relations of proportion and order. Our account is a considerable improvement on the current standard account because it does not rely on primitive internal relations of exact similarity or quantitative distance. The internal relations of proportion and order hold because the related tropes exist; no kinds of tropes need to be assumed here. Second, we argue that there are only pluralities of tropes in relations of proportion and order. The tropes mutually connected by the relations of proportion and order form a special type of plurality, tropes belonging to the same kind. Unlike the recent nominalist accounts, we do not identify kinds of tropes with any additional entities (e.g. sets) or abstractions from entities (e.g. pluralities of similar tropes).
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