Another Paradox In Naive Set-Theory

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox. Presented by Robert Goldblatt     

The Buss–Perry Aggression Questionnaire: Some unfinished business

This article gauges the extent to which items and sum scores of the Buss–Perry Aggression Questionnaire (BPAQ) are contaminated with social desirability response set (SDR), and the extent to which that contamination results in biased findings. Special validity coefficients are introduced for that purpose. Although the SDR confound was quite substantial across all items (with one exception), it is argued on the basis of the size of the introduced validity coefficients and other, logical considerations that paradoxically the confound had minimally distorting effects in estimating the BPAQ models selected for probing the extent of bias.     

数量化维度特征搜索的影响因素探索

有关数量化维度特征搜索的研究表明 ,目标搜索斜率 (反应时间对呈现项目数量函数的斜率 )是由目标与干扰子之间的差异决定的 ,然而以往研究中其差异的值取决于具体的实验条件。根据韦伯定律 ,笔者推测 ,目标搜索斜率应由目标与干扰子之间的相对差异 (C)决定 ,C为目标值 (T)与干扰子值 (D)的差值与该干扰子值的比值。当C值对应相等时 ,不同几何形状刺激的目标搜索斜率应无差异。为此笔者分别采用圆 (实验一 )和三角形 (实验二 )进行实验研究。实验结果支持了上述假设 ,并发现目标大于干扰子时的目标搜索斜率对C值的函数是单调递减函数     

Internal approach to external sets and universes

In this article we show how the universe of HST, Hrbaek set theory (a nonstandard set theory of external type, which includes, in particular, the ZFC Replacement and Separation schemata for all formulas in the language containing the membership and standardness predicates, and Saturation for standard size families of internal sets, but does not include the Power set axiom) admits a system of subuniverses which keep the Replacement, model Power set and Choice (in fact all of ZFC, with the exception of the Regularity axiom, which indeed is replaced by the Regularity over the internal subuniverse), and also keep as much of Saturation as it is necessary.This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.Partially supported by AMS grants in 1993 – 1995 and DFG grants in 1994 – 1995. Robert Goldblatt     

Conditional discrimination in mentally retarded adults: the development of generalized skills.

The development of generalized conditional discrimination skills was examined in adults with retardation. Two subjects with histories of failure to acquire arbitrary matching under trial-and-error procedures were successful under procedures that trained one or more prerequisite skills. The successive discrimination between the sample stimuli was established by training the subjects to name the stimuli. The simultaneous discrimination between the comparison stimuli was established using either (a) standard simple discrimination training with reversals or (b) a procedure in which each of the two sample-comparison relations in the conditional discrimination was presented in blocks of trials, with the size of the blocks decreasing gradually until sample presentation was randomized. The amount of prerequisite training required varied across subjects and across successive conditional discriminations. After acquiring either two or three conditional discriminations with component training, both subjects learned new conditional discriminations under trial-and-error procedures. In general, each successive conditional discrimination was acquired more rapidly. Tests showed that conditional responding had become a generalized skill. Symmetry was shown for almost all trained relations. Symmetry trial samples were ultimately named the same as the stimuli to which they were related in training.     

Some properties of two measures of multivariate association

Two kinds of measures of multivariate association, based on Wilks' and the Bartlett-Nanda-Pillai trace criterionV, respectively, are compared in terms of properties of the univariateR ² which they generalize. A unified set of derivations of the properties is provided which are self-contained and not restricted to decompositions in canonical variates. One conclusion is that asymmetric index based on allows generalization of the multiplicative decomposition ofR ² in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for anasymmetric index based onV.We are indebted to Jos M. F. ten Berge for some fruitful discussions.     

THE NATURE OF PHYSICAL REALITY

Abstract. This account of the dynamical theory of chaos leads to a metaphysical picture of a world with an open future, in which the laws of physics are emergent-downward approximations to a more subtle and supple reality and in which there is downward causation through information input as well as upward causation through energy input. Such a metaphysical picture can accommodate both human and divine agency.     

A Set Theory with Support for Partial Functions

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, proper classes, and partial functions represented as classes of ordered pairs. The underlying logic of the system is a partial first-order logic, so class-valued terms may be nondenoting. Functions can be specified using lambda-notation, and reasoning about the application of functions to arguments is facilitated using sorts similar to those employed in the logic of the IMPS Interactive Mathematical Proof System. The set theory is intended to serve as a foundation for mechanized mathematics systems.