Essai de représentation par des nombres réels d'une analyse infinite des notions individuelles dans une infinité de mondes possibles

The aim of this study is to try to make use of real numbers for representing an infinite analysis of individual notions in an infinity of possible worlds.As an introduction to the subject, the author shows, firstly, the possibility of representing Boole's lattice of universal notions by an associate Boole's lattice of rational numbers.But, in opposition to the universal notions, definable by a finite number of predicates, an individual notion, cannot (as Leibniz pointed out) admits this sort of definition, because each state of an individual subject is characterized by the values (present or absent, applicable or inapplicable) taken by an infinite number of predicates, each of whom may appear or disappear in the next state.The notion of degree of identification of an individual notion is then introduced and arithmetized by a rational number.As an individual notion can be defined by a convergent succession of degrees of identification, the real characteristic number of such an individual notion can be defined by the corresponding convergent succession of rational numbers, satisfying Cauchy's conditions for the convergence of successions.

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Essai de représentation par des nombres réels d'une analyse infinite des notions individuelles dans une infinité de mondes possibles

     

Joint consistency of nonparametric item characteristic curve and ability estimation

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.     

约束大医院无限扩张的冲动——建立和谐医患关系的重中之重

医患关系紧张的原因首先是来自看病贵,而看病贵则主要源于大医院的无限急速扩张。约束大医院的无限扩张冲动,是建立和谐医患关系的重中之重。     

序成六虚上下,数生太极乾坤--今本《周易》卦序排列数学规律三探

今本<周易>序卦是一件完美的数学作品.序卦的分布规律体现于一系列的数列之中,但是,假如这些排列规律彼此间缺乏关联性,显得孤立、分散,便难以真正体现序卦排列的数学规律性.经过更深入的研究,笔者发现这些排列规律并非彼此分散、互不相干的,而是互有关联,整合成一个完美的统一体.序卦排列数学规律其鲜明的特点有四:其一是连续性,其二是周期性,其三是对称性,其四是关联性.连续性、周期性体现其简易性,对称性、关联性体现其统一性.简易性、统一性体现其完美性.     

Infants’ auditory enumeration: Evidence for analog magnitudes in the small number range

Vigorous debate surrounds the issue of whether infants use different representational mechanisms to discriminate small and large numbers. We report evidence for ratio-dependent performance in infants’ discrimination of small numbers of auditory events, suggesting that infants can use analog magnitudes to represent small values, at least in the auditory domain. Seven-month-old infants in the present study reliably discriminated two from four tones (a 1:2 ratio) in Experiment 1, when melodic and continuous temporal properties of the sequences were controlled, but failed to discriminate two from three tones (a 2:3 ratio) under the same conditions in Experiment 2. A third experiment ruled out the possibility that infants in Experiment 1 were responding to greater melodic variety in the four-tone sequences. The discrimination function obtained here is the same as that found for infants’ discrimination of large numbers of visual and auditory items at a similar age, as well as for that obtained for similar-aged infants’ duration discriminations, and thus adds to a growing body of evidence suggesting that human infants may share with adults and nonhuman animals a mechanism for representing quantities as “noisy” mental magnitudes.     

THERE'S MORE TO TIME THAN TICKING AWAY

Time is an element that each of us experiences in the core of our being. Yet it also is one of the great mysteries in our conceptual grasp of reality. The notion of time has therefore been reflected upon and explored by thinkers and scientists since ancient times. In this essay I relate the multiple ways in which Antje's Jackelén's scholarly and stimulating work Time and Eternity analyzes the historical, philosophical, theological, and scientific perspectives on the notion of time lived and its relation to the conceptual endless time that we call eternity, and offer some of my own contextual reflections on the topic.     

Empirically Corrected Rescaled Statistics for SEM with Small N and Large p

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. With typical nonnormally distributed data in practice, a rescaled statistic T_rml proposed by Satorra and Bentler was recommended in the literature of SEM. However, T_rml has been shown to be problematic when the sample size N is small and/or the number of variables p is large. There does not exist a reliable test statistic for SEM with small N or large p, especially with nonnormally distributed data. Following the principle of Bartlett correction, this article develops empirical corrections to T_rml so that the mean of the empirically corrected statistics approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics control type I errors reasonably well even when N is smaller than 2p, where T_rml may reject the correct model 100% even for normally distributed data. The application of the empirically corrected statistics is illustrated via a real data example.     

Negotiating multiple perspectives: a discussion of instructors’ practice within an English-language service course

At the University of the West Indies, large courses often require the involvement of multiple persons in their delivery. Within the English Language Foundation Unit, several of the courses offered cater to over 500 students in any given semester. The large number of students necessitates multiple practitioners providing instructions as part of the same course offering. While stylistics may vary, there is the need for course instruction and content to depict uniformity. Practitioners’ conceptualization of a specific topic will inform the instruction received by students. In instances where practitioners do not conceptualize content in a like manner, students within the same course may receive varied instruction, thus affecting student output and overall evaluation. The paper looks specifically at a service course offered at the University of the West Indies and the practices of the multiple persons involved in the teaching of the course. It provides an overview of practitioners’ discussion of their conceptualization of content areas within the courses and assesses the extent to which there are variations and/or similarities. It also discusses how these impact teaching and learning. The research seeks to derive an actionable direction for collaboration and further discussions within large service courses with the aim of improving teaching and learning.     

数字表征的表象赋义效应:来自数字线估计任务的证据

已有研究中数字线估计任务几乎都使用纯数字。本研究以二到六年级儿童为被试,采用纯数字任务和赋义数字任务来探索赋义表象对数字表征形式的影响。结果表明,对0~1000的数字赋义后,对数模型的解释力上升,而线性模型的解释力下降;表象大小对于赋义数字的估计影响显著,大表象赋义提高了对数模型解释力而降低了数字估计的准确性,小表象的影响比较微弱。     

Taurek, Numbers and Probabilities

In his paper, “Should the Numbers Count?" John Taurek imagines that we are in a position such that we can either save a group of five people, or we can save one individual, David. We cannot save David and the five. This is because they each require a life-saving drug. However, David needs all of the drug if he is to survive, while the other five need only a fifth each. Typically, people have argued as if there was a choice to be made: either numbers matter, in which case we should save the greater number, or numbers don't matter, but rather there is moral value in giving each person an equal chance of survival, and therefore we should toss a coin. My claim is that we do not have to make a choice in this way. Rather, numbers do matter, but it doesn't follow that we should always save the greater number. And likewise, there is moral value in giving each person an equal chance of survival, but it doesn't follow that we should always toss a coin. In addition, I argue that a similar approach can be applied to situations in which we can save one person or another, but the chances of success are different.