Taking Skepticism Seriously: How the Zhuang-Zi Can Inform Contemporary Epistemology

This paper explores a few of the ways that the Zhuang-Zi can inform contemporary analytic epistemology. I begin, in section 1, by briefly outlining and summarizing the case for my fictionalist interpretation of the text. In section 2, I discuss how the Zhuang-Zi can be brought into productive dialogue with the question of how we should respond to skeptical arguments. Specifically, I argue that the Zhuang-Zi can be reasonably interpreted as exemplifying an approach that is different from dominant contemporary responses to skeptical arguments in three ways: (i) it is fictionalist; (ii) it motivates a skeptical perspective rather than a claim; and (iii) it accomplishes its aims in an atypical, but nonetheless contextually appropriate, way. However, the Zhuang-Zi is relevant to contemporary debates about skeptical arguments because it can be used: (i) to respond to the same sorts of skeptical arguments that occupy contemporary commentators; (ii) to address a number of questions that arise in connection with such arguments; and (iii) to suggest important new questions for epistemologists to pursue

An Efficient Approach for Computing Optimal Low-Rank Regularized Inverse Matrices

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available. In this paper, we develop a new framework that uses training data, as a substitute for knowledge of the forward model, to compute an optimal low-rank regularized inverse matrix directly, allowing for very fast computation of a regularized solution. We consider a statistical framework based on Bayes and empirical Bayes risk minimization to analyze theoretical properties of the problem. We propose an efficient rank update approach for computing an optimal low-rank regularized inverse matrix for various error measures. Numerical experiments demonstrate the benefits and potential applications of our approach to problems in signal and image processing.Comment: 24 pages, 11 figure