个体近似数量系统与其数学能力之间的关系：发展研究的证据

近似数量系统在个体数学能力的发展中起着重要的作用, 二者之间的关系受到年龄因素的影响。主要表现为, 随着年龄的增长, 相关程度逐渐减弱, 二者之间关系的作用机制可能由基数知识中介转变为多种中介变量的共同作用。未来可采用更严格的实验设计和多种研究方法考察各年龄段儿童近似数量系统与不同数学能力之间关系的发展趋势、因果方向、关键转折点和潜在机制, 以更好地理解近似数量系统在个体数学能力发展中所起的作用。     

Number Use at Home by Children and Their Parents and Its Relationship to Early Mathematical Performance

The purpose of this research was to measure the frequency and variety of number activities occurring in the homes of pre-school and kindergarten children and to determine if there was a relationship between those activities and the children's mathematical performance. In two studies, parents were interviewed over the telephone and asked how often their child or they and their child had engaged in each of 33 number-related activities over the last week. Both studies found considerable variability in the frequency and type of number activities that children participated in at home. There was a positive correlation between the frequency of number activities that parents reported for their children and parental participation in the same activities. In addition, in study 2, parental reports of children's number activities at home were predictive of children's performance on a standardized test of early mathematical ability.     

On the Existence of Continua of Logics Between Some Intermediate Predicate Logics

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.     

Incentive theory: IV. Magnitude of reward

Incentive theory is successfully applied to data from experiments in which the amount of food reward is varied. This is accomplished by assuming that incentive value is a negatively accelerated function of reward duration. The interaction of the magnitude of a reward with its delay is confirmed, and the causes and implications of this interaction are discussed.     

《易经》:人类科学思维和审美思维方式的精典阐释

一本诞生于五千年前的中国古书《易经》,已经包含着深刻的现代科学数理逻辑原理,且与美学的审美逻辑原理互为支持、互为表里,使这两大类本来被认为水火不相容的领域及其独具的思维方式得到了高度完善统一的阐释。从这样的角度来看《易经》,也许会有助于目前心理学界对思维方式及逻辑问题的研究,拓开一条崭新的思路。     

Philosophical virtues

It has been suggested that philosophers should adopt a methodology largely inspired by mathematics and that the “mathematical” virtues of rigor, clarity, and precision are also fundamental philosophical virtues. In reply, this paper argues that some excellent philosophy lacks these virtues and that too much emphasis on the mathematical virtues excludes potentially valuable forms of philosophical discourse and makes the profession less diverse than it should be. Unduly restrictive conceptions of philosophical argumentation should be avoided. On a contributory conception, philosophy should try to make a positive contribution to human emancipation where possible. The paper argues that it is possible and desirable for epistemology to contribute in this way and that the mathematical virtues are less significant in this context than the emancipatory virtues of what one might call “liberation philosophy.” These include irony, reflectiveness, imagination, contrarianism, and worldliness.     

以《易》取名的数理统计与文化透视

古人喜取<周易>命名,这一现象一些学者曾加以注意,但未作深入研究.本文对<中国文学家大辞典>采用穷尽式的数理统计,探求出<坤>、<乾>等16卦为常用卦,其卦彖辞、二五爻辞及<文言>等为常用爻,进而推索卦爻取舍背后所隐藏的价值取向与哲理内涵,提出并考察援<易>取名之宋前少宋后多这一现象.     

Mathematical Spandrels

The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on the property that cicada period lengths are expressible as the sum of two perfect squares. I argue that mathematical spandrels pose a particular problem for nominalism because of the way in which they are entangled with scientific explanations.     

学前儿童抑制控制的发展趋势及其对言语理解和数学认知的预测作用

以长春市某幼儿园的122名3~6岁幼儿为被试,采用2(测试任务:无嵌套规则白天黑夜任务,有嵌套规则的白天黑夜任务)×2(测试时间:间隔9个月的第一次测试和第二次测试)×4(年龄分组:3.00~3.75岁组,3.76~4.50岁组,4.51~5.25岁组,5.26~6.00岁组)的三因素混合设计,来分析不同复杂程度的抑制控制在学前阶段的发展趋势,并在控制幼儿年龄和工作记忆水平后,分析不同复杂程度抑制控制对言语理解和数学认知的独立预测作用。结果发现:(1)对3~6岁儿童来说,有嵌套规则的白天黑夜任务的难度水平要显著高于无嵌套规则的白天黑夜任务;(2)较简单的抑制控制(无嵌套规则的白天黑夜任务)在学前阶段的发展速度先快后慢,但较复杂的抑制控制(有嵌套规则的白天黑夜任务)在3~6岁期间持续快速发展;(3)独立于年龄和工作记忆,较复杂的抑制控制能够显著预测幼儿的数学认知和言语理解,但较简单的抑制控制对言语理解和数学认知的预测作用不显著。根据上述结果,在描述学前儿童抑制控制发展趋势时要注意任务难度的设定,而且难度适当的抑制控制任务成绩更能预测幼儿的言语理解和数学认知。