Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics.     

Can Constructive Mathematics be Applied in Physics?

The nature of modern constructive mathematics, and its applications, actual and potential, to classical and quantum physics, are discussed.     

Principal component analysis with external information on both subjects and variables

A method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis. In this method, the original data are first decomposed into several components according to external information. The components are then subjected to principal component analysis to explore structures within the components. It is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices. The numerical method based on the QR decomposition is described, which simplifies the computation considerably. The proposed method includes a number of interesting special cases, whose relations to existing methods are discussed. Examples are given to demonstrate practical uses of the method.The work reported in this paper was supported by grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the first author. Thanks are due to Jim Ramsay, Haruo Yanai, Henk Kiers, and Shizuhiko Nishisato for their insightful comments on earlier versions of this paper. Jim Ramsay, in particular, suggested the use of the QR decomposition, which simplified the presentation of the paper considerably.     

The Impossibility of Local Skepticism

According to global skepticism, we know nothing. According to local skepticism, we know nothing in some particular area or domain of discourse. Unlike their global counterparts, local skeptics think they can contain our invincible ignorance within limited bounds. I argue that they are mistaken. Local skepticism, particularly the kinds that most often get defended, cannot stay local: if there are domains whose truths we cannot know, then there must be claims outside those domains that we cannot know even if they are true. My argument focuses on one popular form of local skepticism, ethical skepticism, but I believe that the argument generalizes to cover other forms as well.

Is Sexism a Gender Issue? A Motivated Social Cognition Perspective on Men's and Women's Sexist Attitudes Toward Own and Other Gender

The present research investigated the antecedents of ambivalent sexism (i.e., hostile and benevolent forms) in both men and women toward own and other gender. In two heterogeneous adult samples (Study 1: N = 179 and Study 2: N = 222), it was revealed that gender itself was only a minor predictor of sexist attitudes compared with the substantial impact of individual differences in general motivated cognition (i.e., need for closure). Analyses further showed that the relationship between need for closure and sexism was mediated by social attitudes (i.e., right‐wing authoritarianism and social dominance orientation), which were differently related to benevolent and hostile forms of sexism. In the discussion, it is argued that sexism primarily stems from individual differences in motivated cognitive style, which relates to peoples' perspective on the social world, rather than from group differences between men and women. Copyright © 2011 John Wiley & Sons, Ltd.     

不确定感与从众：决断性与结构需求的中介作用

不确定感伴随从众的现象普遍存在,然而其内在加工过程及个体差异仍不明确。对804名大学生被试进行问卷调查,结果显示：（1）不确定感与从众正相关;（2）决断性与结构需求完全中介不确定感与从众的关系,且存在性别差异;二者关系上,女性更大程度上受决断性的中介,其次为结构需求;男性受决断性和结构需求的平行中介。结果支持不确定−认同理论和认知闭合两阶段模型观点,为不确定状态下不同性别人群从众行为的管理提供了理论依据。     

What is “Intervention”?

I begin by noting that several theologians and others object to special divine action (divine intervention and action beyond conservation and creation) on the grounds that it is incompatible with science. These theologians are thinking of classical Newtonian science; I argue that in fact classical science is in no way incompatible with special divine action, including miracle. What is incompatible with special divine action is the Laplacean picture, which involves the causal closure of the universe. I then note that contemporary, quantum mechanical science doesn't even initially appear to be incompatible with special divine action. Nevertheless, many who are well aware of the quantum mechanical revolution (including some members of the Special Divine Action Project) still find a problem with special divine action, hoping to find an understanding of it that doesn't involve divine intervention. I argue that their objections to intervention are not sound. Furthermore, it isn't even possible to say what intervention is, given the quantum mechanical framework. I conclude by offering an account of special divine action that isn't open to their objections to intervention.     

概率大小、损益结果和认知闭合需要对模糊规避的影响

模糊规避是指在相同奖赏的情况下,决策者会力图规避从主观上判断具有模糊概率的事件而偏好具有相同精确概率的事件。本研究探讨了概率大小、损益结果和认知闭合需要对模糊规避的影响。研究发现,在小概率受益的情况下,个体倾向于模糊寻求;在中概率受益的情况下,个体倾向于模糊规避;在高概率受益的情况下,个体倾向于模糊规避;在小概率损失的情况下,个体倾向于模糊规避;在中概率损失的情况下,个体倾向于模糊规避;在高概率损失的情况下,个体倾向于模糊寻求。但是,研究并未发现认知闭合需要对模糊规避有预测作用。