Hobson’s Conception of Definable Numbers

In this paper, I explore an intriguing view of definable numbers proposed by a Cambridge mathematician Ernest Hobson, and his solution to the paradoxes of definability. Reflecting on König’s paradox and Richard’s paradox, Hobson argues that an unacceptable consequence of the paradoxes of definability is that there are numbers that are inherently incapable of finite definition. Contrast to other interpreters, Hobson analyses the problem of the paradoxes of definability lies in a dichotomy between finitely definable numbers and not finitely definable numbers. To bypass this predicament, Hobson proposes a language dependent analysis of definable numbers, where the diagonal argument is employed as a means to generate more and more definable numbers. This paper examines Hobson’s work in its historical context, and articulates his argument in detail. It concludes with a remark on Hobson’s analysis of definability and Alan Turing’s analysis of computability.     

参照依赖和损失规避对个体收入分配公平判断的影响

收入分配公平判断是人们对自己收入所得公平与否的主观评价。通过对参照点和收入金额的控制,探讨参照依赖和损失规避对收入分配公平判断的共同影响。结果发现,(1)民众的收入公平判断受参照点的影响,在有参照点的情景下比无参照点情景下更感觉不公平;(2)不同工资水平下,民众的公平判断具有显著差异,而且民众对低于平均工资的“受损”比高于平均工资同等金额的“受益”赋予的公平感的权重更大,即存在得失感受的不对称;(3)不同的工资参照点、多得和少得的分配结果共同影响民众的公平判断,即损失规避在参照依赖对公平判断的影响中起调节作用。     

Assertive Ads for Want or Should? It Depends on Consumers’ Power

Advertisements using assertive language are commonly seen in marketing communications, yet assertive language has often been shown to be ineffective in communication and even decrease compliance. Recent research began to examine factors that influence the effectiveness of assertive advertising messages, but little research has studied the potential moderating role of consumer‐related factors. The current research fills this gap by investigating the moderating role of consumers’ power. Across five studies, the authors find that for high‐power consumers, assertive ads are effective in promoting want products but ineffective in promoting should products. For low‐power consumers, however, assertive ads are effective in promoting should products but ineffective in promoting want products. Moreover, the authors show that this pattern of results is driven (mediated) by consumers’ perception of the fit between the advertising message and the advertised product. Theoretical and practical implications of the findings are discussed.     

Mapping differential responses to cognitive training using machine learning

We used two simple unsupervised machine learning techniques to identify differential trajectories of change in children who undergo intensive working memory (WM) training. We used self‐organizing maps (SOMs)—a type of simple artificial neural network—to represent multivariate cognitive training data, and then tested whether the way tasks are represented changed as a result of training. The patterns of change we observed in the SOM weight matrices implied that the processes drawn upon to perform WM tasks changed following training. This was then combined with K‐means clustering to identify distinct groups of children who respond to the training in different ways. Firstly, the K‐means clustering was applied to an independent large sample (N = 616, M_age = 9.16 years, range = 5.16–17.91 years) to identify subgroups. We then allocated children who had been through cognitive training (N = 179, M_age = 9.00 years, range = 7.08–11.50 years) to these same four subgroups, both before and after their training. In doing so, we were able to map their improvement trajectories. Scores on a separate measure of fluid intelligence were predictive of a child's improvement trajectory. This paper provides an alternative approach to analysing cognitive training data that go beyond considering changes in individual tasks. This proof‐of‐principle demonstrates a potentially powerful way of distinguishing task‐specific from domain‐general changes following training and of establishing different profiles of response to training.     

Nonmonetary and nonreciprocal freecycling: Motivations for participating in online alternative giving communities

This research examines consumers' participation in a nonmonetary, nonreciprocal form of online consumer exchange wherein consumers may decide to give only, receive only, or both give and receive. Given the lack of financial incentives or relational norms that would traditionally drive participation in this societally beneficial consumption activity for which we advance the term alternative giving, this research examines consumers' participation motivations. Are consumers, as prior research suggests, motivated to participate in alternative giving activities on the basis of prosocial motives or for other reasons? Through a content analysis of the online Freecycle Network, we found that participation is driven primarily by fundamental consumer needs and wants, though other prosocial, less materialistic factors are also drivers. Our findings also identify an inconsistency in product categories between what givers offer and what receivers seek, suggesting that supply–demand imbalances can emerge within alternative giving communities.     

What do you think I think you think?: Strategic reasoning in matrix games

In reasoning about strategic interpersonal situations, such as in playing games, an individual's representation of the situation often includes not only information about the goals and rules of the game, but also a mental model of other minds. Often such mental models involve a hierarchy of reflexive reasoning commonly employed in social situations ("What do you think I think you think..."), and may be related to the developmental notion of 'theory of mind'. In two experiments, the authors formally investigate such interpersonal recursive reasoning in college-age adults within the context of matrix games. Participants are asked to predict the moves of another player (experimenter's confederate) in a two-choice, sequential-move game that may terminate at various stages with different payoffs for each player. Participants are also asked to decide optimally on their own moves based on the prediction made. Errors concerning the prediction, or translation of those predictions into decisions about one's action, were recorded. Results demonstrate the existence of a "default" mental model about the other player in the game context that is dynamically modified as new evidence is accumulated. Predictions about this other player's behavior are, in general, used consistently in decision-making, though the opponent tends to be modeled, by default, to behave in a myopic fashion not anticipating the participant's own action.     

Measuring Chinese psychological well-being with Western developed instruments

We explored the possibility of applying 4 psychological scales developed and commonly used in the West to Chinese culture. The participants, 273 Chinese and 302 Americans, completed measures of self-esteem (Self-Esteem Scale; Rosenberg, 1965), depression (Center for Epidemiologic Studies-Depression Scale; Radloff, 1977), social support (Multidimensional Scale of Perceived Social Support; Zimet, Dahlem, Zimet, & Farley, 1988), and suicidal ideation (Scale for Suicide Ideation; Beck, Kovacs, & Weissman, 1979). All scales were found to be reliable and valid cross culturally. Comparative analyses suggest that gender differences on all 4 scales are smaller among the Chinese than the Americans. Americans were more likely to score higher on the socially desirable scales (self-esteem and social support) and lower on the socially undesirable scale (suicidal ideation). However, no cultural differences were found in this study on the measure of depression. Results suggest that, with a few considerations or potential modifications, the current measures could be used in Chinese culture.     

The ties that bind what is known to the recall of what is new

Cued recall success varies with what people know and with what they do during an episode. This paper focuses on prior knowledge and disentangles the relative effects of 10 features of words and their relationships on cued recall. Results are reported for correlational and multiple regression analyses of data obtained from free association norms and from 29 experiments. The 10 features were only weakly correlated with each other in the norms and, with notable exceptions, in the experiments. The regression analysis indicated that forward cue-to-target strength explained the most variance, followed by backward target-to-cue strength. Target connectivity and set size explained the next most variance, along with mediated cue-to-target strength. Finally, frequency, concreteness, shared associate strength, and cue set size also contributed significantly to recall. Taken together, indices of prior word knowledge explain 49% of the recall variance. Theoretically driven equations that use free association to predict cued recall were also evaluated. Each equation was designed to condense multiple indices of word interconnectivity into a single predictor.     

多层线性模型在纵向研究中的运用

纵向研究中传统统计技术主要是重复测量的方差分析和多元回归分析，但是这两种技术存在一些局限性，不能合理而充分地解释纵向研究资料。近年来出现的多层线性模型能够更有效地利用纵向数据。为促进多层线性模型在纵向研究中的运用，简要论述了传统统计技术的局限，介绍了多层线性模型的原理及其在纵向研究中的作用，以一组模拟数据为例对多层线性模型中各种参数在纵向研究中的含义进行了详细讨论，对于纵向研究中运用多层线性模型时须注意的问题提出了建议。