Least-squares approximation of an improper correlation matrix by a proper one

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and sufficient condition is given for a solution to yield the unique global minimum of the least-squares function. Empirical verification of the condition indicates that the occurrence of non-optimal solutions with the proposed algorithm is very unlikely. A possible drawback of the optimal solution is that it is a singular matrix of necessity. In cases where singularity is undesirable, one may impose the additional nonsingularity constraint that the smallest eigenvalue of the solution be , where is an arbitrary small positive constant. Finally, it may be desirable to weight the squared errors of estimation differentially. A generalized solution is derived which satisfies the additional nonsingularity constraint and also allows for weighting. The generalized solution can readily be obtained from the standard unweighted singular solution by transforming the observed improper correlation matrix in a suitable way.     

Descartes and More on the infinity of the world

ABSTRACT

In this paper, I address the controversy between Henry More and René Descartes on the indefinite extension of the world. I provide a new reading of Descartes’ famous final answer of 15 April 1649. I read the entire debate in the terms of a disagreement concerning the epistemological status of the necessity of our judgement about the extension of the universe. Accordingly, the disagreement on the infinity of the world constitutes a case of a more general disagreement on the nature of the necessity of the theorems of Cartesian Physics. In particular, as concerns Descartes’ last reply, I argue that his assertion that a finite world is contradictory should be interpreted as a reply to More’s claim that the thesis of the infinity of the world, in so far as it cannot be grounded on the identity between matter and extension, does not express a logical necessity. Descartes’ assertion of the logical impossibility of a finite world, far from being, as it has always been read, a concession he made under the pressure of More’s objections, expresses the more radical element of the entire debate about the extension of the universe.     

类别型状态不确定独立否定句的加工机制：来自眼动实验的证据

探讨类别型状态不确定独立否定句(如“裙子不是蓝色的”)的动态表征过程。实验1和实验2分别仅给被试提供“与事件备择选项一致的图片” (红色裙子)和“含有否定标签的与事件否定状态一致的图片” (含有否定标签的蓝色裙子); 实验3同时提供以上两种选项。结果发现：3个实验中被试在早期均对“与事件否定状态一致的图片”注视概率更高, 在晚期阶段, 实验1仅对“与事件备择选项一致的图片” 注视概率更高, 实验2和实验3均仅对“含有否定标签的与事件否定状态一致的图片”注视概率更高, 并且选择为事件的最终状态; 实验4的评定结果表明, 当被试有充裕时间完成任务时, 37名评定者中有30名选择“与事件备择选项一致的图片”为事件的最终状态。4个实验的结果为锚激活与限制满足模型和抑制假设提供了进一步证据。     

美国贝克斯特测谎系统在我国法庭科学中的应用

该文简介了美国贝克斯特测谎系统的基本原理及其在我国法院的首次应用情况。在我国这一系统不仅被用于刑事案件,也被用于民事案件,实践证明,测谎技术起到了其他手段所起不到的作用,成为法院办案过程有力的辅助工具和支持系统。为使本系统具有更高的效力和适合中国的国情,需要对贝克斯特测谎系统进行修订,该文也介绍了有关修订和检验的情况。     

Panpsychism,The Combination Problem,and Plural Collective Properties

Panpsychism claims that each fundamental entity is conscious, but then faces the problem of how such entities combine to make up our ordinary consciousness. In this paper, I show how panpsychism can avoid this so-called combination problem by taking seriously plural collective properties at the fundamental level.     

Rumfitt on the logic of set theory

According to a famous argument by Dummett, the concept of set is indefinitely extensible, and the logic appropriate for reasoning about the instances of any such concept is intuitionistic, not classical. But Dummett's argument is widely regarded as obscure. This note explains how the final chapter of Rumfitt's important new book advances our understanding of Dummett's argument, but it also points out some problems and unanswered questions. Finally, Rumfitt's reconstruction of Dummett's argument is contrasted with my own preferred alternative.