如何培养演绎推理能力

结合演绎推理研究的成果,提出了在学校教育中培养演绎推理能力的途径:根据儿童的年龄特点培养儿童演绎推理的能力;创设有利的教学条件,提高学生演绎推理能力;完善教学内容,促进学生演绎推理能力的发展.     

试论替换中项法——对三段论方法的反思与重建

词项逻辑特别是其中的核心部分直言三段论教学内容和方法的革新势在必行。现有的三段论方法本身都存在问题,应该重新探索能克服现有三段论方法的缺陷、能够解决三段论所有问题的简易方法,以利于逻辑学通识教育。研究表明,替换中项法正是我们发现的这种方法。     

What to Do About Zero Frequency Cells When Estimating Polychoric Correlations

Categorical structural equation modeling (SEM) methods that fit the model to estimated polychoric correlations have become popular in the social sciences. When population thresholds are high in absolute value, contingency tables in small samples are likely to contain zero frequency cells. Such cells make the estimation of the polychoric correlations more difficult. Some SEM programs use solutions such as adding .5 to the zero frequency cells. However, the adequacy of this solution has never been systematically explored in the literature. In this article, the frequency with which contingency tables with zero cells occur in small samples is explored. Second, it is explored whether or not adding .5 is in any way preferable to leaving the cell value as zero. Binary and 3-category data and a variety of threshold values and correlation values are considered. The findings suggest that the two methods of dealing with zero frequency cells have quite different properties. With binary data, the method of adding .5 is recommended, unless thresholds are opposite-signed and the underlying correlation is suspected to be large. No adjustment is recommended for greater numbers of categories.     

基于量词语义与性质的扩展三段论

在广义量词理论中,如果一个表达两个集合外延关系的二元量词具有单调性等性质,那么该量词及其外否定、内否定和对偶否定在单调性方面存在相互制约关系,从而构成单调方阵。基于二元量词的语义和单调性等性质,可以简洁明了地进行包括传统三段论在内的扩展三段论推理,从而极大地提高了三段论的表达能力和对日常思维的规范能力。     

Going beyond the book: towards critical reading in statistics teaching

We consider three examples from our own teaching in which much was learned by critically examining examples from books. Even influential and well‐regarded books can have examples where more can be learned with a small amount of additional effort.     

Analysis of group performance with categorical data when agents are heterogeneous: The evaluation of scholastic performance in the OECD through PISA

This paper analyzes the evaluation of the relative performance of a set of groups when their outcomes are defined in terms of categorical data and the groups’ members are heterogeneous. This type of problem has been dealt with in Herrero and Villar (2013) for the case of a homogeneous population. Here we expand their model controlling for heterogeneity by means of inverse probability weighting techniques. We apply this extended model to the analysis of the scholastic performance of fifteen-year-old students in the OECD countries, using the data in the PISA. We evaluate the relative performance of the different countries out of the distribution of the students’ achievements across the different levels of competence, controlling by the students’ characteristics (explanatory variables regarding schooling and family environment). We find that differences in mathematical and reading abilities across OECD countries would lower by between 40% and 50% if the students’ characteristics would be those for the OECD average.     

含负词项的三段论研究

基于词项逻辑的逻辑常项即词项联结词A、E、I、O的逻辑性质如对称性、周延性(范围和方向),可以建立三段论的新方法———替换中项法,来同时解决三段论的判定问题、直接的推理或者直接的证明问题,最后形成包括24个经典有效式的非经典三段论体系。经典三段论的规则立足于直言命题的四个组成要素:主项,谓项,量项和联项来判定三段论的有效性是不恰当的。     

替换中项法研究——补充省略三段论的前提和结论的能行方法

在三段论前提中,通过系词"是"或者其否定"不是",中项与大、小项直接联系起来;同时,中项又把大、小项间隔开来.如何"消灭"、"扬弃"中项,把小项和大项也用系词"是"或者其否定"不是"直接联系起来,以得出所需要的结论?这是三段论的本质问题.解决此问题的方法是替换中项法.替换中项法是补充省略三段论的结论和前提的能行方法.     

《墨子·经上》和《经说上》的逻辑

《墨经》是天下奇书,其表达形式简练出奇、其表达内容长于逻辑科学,是中国传统文化的一大奇迹。《经上》和《经说上》的科学概念、逻辑学、范畴论、方法论和止式论证等理论是中国传统文化和国学中的精华,值得继承弘扬。