范畴论数学基础的理论根基

探究范畴论数学基础的理论根基,首先要领会数学结构的解释说明,从而认识数学的结构本质;其次要解析范畴论对数学结构的阐释,借由范畴的形式化表征,理解范畴的结构特性,表明范畴论是描述数学结构的理论;最后通过内核与框架阐析范畴论数学基础的本质特征。     

罗比·凯斯的儿童思维发展阶段论

以发生认识论者自称的皮亚杰不仅把人类认识的发展过程推向了一个新水平,而且给心理学的发展引进了一场范式的革命。皮亚杰认知发展心理学理论的最大优势在于:它能为个体心理发展的共性本质提供一个简洁而一致的解释,而且,以此理论为基础而设计的许多实验得到了大量有关数据,其中大部分支持皮亚杰的理论假设。然而,皮亚杰以结构建构论为基础的能力阶段模式本身,也是发展心理学建构发展过程中的一部分,它本身也是处于不断的同化和顺应、不断的平衡化过程之中的。     

寂寞身后事,蓄势待来年——让·皮亚杰(J.Piaget)逝世30周年祭

皮亚杰逝世已30年,但皮亚杰所创立的发生认识论研究不应走向历史。皮亚杰的理论遭到许多人的误解。遗传论和生物学化是两项最为不恰当的帽子。皮亚杰不是传统意义上的心理学家,心理学只是其研究康德意义上的"先验范畴"之个体发生发展的"方法论插曲"。发生认识论具有鲜明的跨学科性质,应该进行"发生认识论"与当代"认知科学"的比较研究。应正确认识理论生物学、结构主义方法论、代数工具和逻辑学在发生认识论研究中的作用和地位,尤其应注重晚年皮亚杰运用新的意义逻辑(logic of meaning)和态射(morphisms)、范畴(categories)等新的代数概念作为形式化认知结构之工具的价值和意义。要深入研究发生认识论对以"具身化"和"回归大脑"为特色的第二代认知科学的启示,探讨它们之间的联系。至少在两个方面可以明显看到这种联系:一是发生认识论中的"动作协调"及对由协调而产生的逻辑—数学经验的"反省抽象"这两个概念,表明了皮亚杰对心智具身性的卓越洞见;二是在皮亚杰所主张的"表型复制"(phynocopy)观点中体现的衍生论(epigenesis)和建构论(constructionism)思想,它们与第二代认知科学的动力系统理论之基本思想——所涉因素或变量之间的关系是一种互为因果、相互塑造的对偶(coupling)关系而不是线性的单向因果关系——两者是完全一致的。皮亚杰及其发生认识论定会随着认知科学的未来发展而被"再发现"。     

熠熠生辉的"皮亚杰新形式化理论"——评李其维策划《皮亚杰发生认识论精华译丛》

皮亚杰新形式化理论涉及的是如何把思维机制加以形式化--心理逻辑学--这一特殊问题.本译丛向读者表达了皮亚杰新理论的两大学术贡献:(1)从群-格概念转向"态射-范畴论";(2)从外延取向的外延逻辑转向注重意义蕴涵的内涵逻辑.     

皮亚杰晚年的“新理论”及其思考

皮亚杰的经典认知发展理论堪称典范,但也并非尽如人意,以致20世纪60、70年代其理论经常遭受抨击。文章以对皮亚杰经典理论的批评和质疑为起点,重点介绍皮亚杰在生命的最后阶段所进行的理论建设,并试图对皮亚杰的新理论做出初步评价。作者认为,皮亚杰晚年的新理论建立在对应性、态射、范畴、转换等新的概念体系之上,并将发展视为从心理内态射到心理间态射,再到超态射的演变过程。由此,新理论强调了“水平”概念和“意义逻辑”,弱化了早期的“阶段”概念和“命题逻辑”。     

皮亚杰发生认识论研究

近年来,国内学术界对皮亚杰的发生认识论表现出越来越浓厚的兴趣,对皮亚杰的儿童心理学和发生认识论的研究,已从一般性介绍进入较具体、较细致和较深入的探讨,兹将探讨情况,概述于后。一、关于皮亚杰发生认识论中的“活动”范畴“活动”(或“动作”)是皮亚杰发生认识论的逻辑起点和核心范畴,有关主体和客体的关系、认知的本质、主体认识与客体结构的一致性等问题的思考,都是建立在对活动范畴     

皮亚杰儿童智慧发展结构论概论

杰出的瑞士学者让·皮亚杰(Jean Piaget),一生致力于儿童智慧发展的研究。他所创立的发生认识论体系深受国际学术界的推崇,已成为当代儿童智慧发展理论中的主要学派。本文试对皮亚杰的结构论思想作一概略的评述。一、结构论是一种研究方法皮亚杰的发生认识论从一般方法论的角度分析,乃是一种发展的结构论。儿童智慧(思维)的发展是通过儿童主体的认知结构(从低级的不完善的行动格式到高级完善的形式运算结构)与从物理环境和社会环境的经验之间的同化和顺化的相互作用而实现的。因此,皮亚     

评发生认识论的"反省抽象"范畴

论文分析了皮亚杰发生认识论中“反省抽象”范畴的发展脉络、主要内涵及其与某些相关概念(如概括化、平衡化、矛盾与否定的构造、意识化与觉知等)的联系。作者认为：反省抽象不仅体现皮亚杰的独创性．而且也是发生认识沦中最为核心和最为重要的概念。它合理地解释了知识创新的源泉,使发生认识论的逻辑一数学范畴研究及认知发展一般规律的研究奠基于科学认识论之上。作者主张应准确继承皮亚杰的学术遗产,深化对认知发展机制的探索。     

论皮亚杰的方法论及其当代意义

皮亚杰从生物学的适应性和平衡化概念出发, 论证了有机体和外部环境之间的双向互动关系, 进一步通过认知过程与生物学过程的“同构”, 建立了一种结构论的发生认识论。发生认识论的主要论题包括:主客体相互作用论、认知结构的建构论, 以及心理逻辑论等。皮亚杰的理论建构方法有两个重要特征:第一, 皮亚杰强调功能相对于结构的逻辑先在意义。功能是有机体对环境的适应与平衡化。因此, 皮亚杰的方法论是一种功能论。第二, 皮亚杰方法论的思想基础是辩证法。皮亚杰的发生认识论一方面批判唯理论, 另一方面批判经验论, 最终形成了一套独特的认识论体系。皮亚杰的发生认识论对当今心理学和心灵哲学研究中诸多“难问题”, 诸如“他心问题”、“归纳问题”等, 可能提供了元理论层面和方法层面的引领和启发。     

对研究形式运算的“组合系统”和INRC群的方法论探讨

根据皮亚杰的认知发展阶段论,形式思维作为一种不同于具体运算的思维方式,在青少年和成人中是普遍存在的。皮亚杰认为,“形式思维的一般特征—它超出与经验事实直接有关的转换的框架之上,并且从属于一个假设-演绎运算,即关于可能的运算的系统”。实质上,这个系统是由形式运算构成的一种机能性的运转结构。它的运转是动态     

Studying Children’s Religious Knowledge: Contributions of Ethnography and the Clinical-Critical Method

We analyze different methodological and conceptual contributions of anthropology and psychogenetic theory to the research of children’s religious knowledge. We argue that for the study of children’s points of view it is possible to build an approach that links aspects studied by both disciplinary fields. With this aim, we revise some of their basic theoretical assumptions and recent reviews as well as their methodological proposals. Then we review the core characteristics of ethnography and the clinical–critical method—proposed by Piaget’s psychogenetic theory—with the goal of stressing their potentialities as well as their limitations in research. We argue that within an ethnographic approach, we must establish certain restrictions on the clinical–critical method following basic premises of social anthropology. This approach lets us demonstrate the importance of understanding children’s constructions by placing them within social relations that children produce and update in everyday interactions.     

Experimental Studies of Children's Learning

This article compares John Dewey's theory of inquiry with Jean Piaget's analysis of the mechanisms implied in the increase of knowledge. The sources for this paper are Dewey's studies on logic and the theory of inquiry and Piaget's historical-critical and psychogenetic investigations. Three major conclusions result from the comparison: first, there are significant convergences between the two theories; second, Piaget's developmental analysis makes explicit what is programmatic in Dewey's investigations; and, finally, Piaget is incorrect in characterizing Dewey's pragmatism as a method that does not meet the criteria of intelligent activity.     

Piagetian Studies of Cognitive Development in India

The paper presents a review of studies on cognitive development of children in India inspired by Piaget’s theory of cognitive development. Piaget’s theory is briefly introduced before examining its cross-cultural applications. Early studies of cognitive development, which focus on age-related changes in cognition, are described. These are followed by the studies of the last decades in which developmental contexts, such as those provided by ecology, culture, schooling, and various forms of training, are implicated. Studies of spatial cognition are discussed in some detail and points of convergence between findings of Indian studies and those reported by Piaget are critically examined. The issue of “performance” vs. “competence” is addressed and research evidence that considers performance difference as a matter of cognitive style is presented. Possible reasons for decline of research interest in Piagetian studies in recent years is examined and suggestion for future studies in this field are offered.     

关于弗洛伊德与皮亚杰心理发展观的比较分析

弗洛伊德和皮亚杰都是心理学的大师,他们关于心理发展的阶段、过程、结构等方面的思想既有关联,也存在不同。揭示两位大师心理观的关联和异同不仅有助于认清心理学思想的发展逻辑,而且对心理学理论的建构和研究也有裨益。     

From qualitative differences to a continuum of development: commentary on Leslie Smith's epistemological principles for developmental psychology

In his article Epistemological principles for developmental psychology Leslie Smith helps to re-open some of the key issues Piaget explored through his genetic epistemology. Smith shows the important parallels between logician Gottlieb Frege's understanding of rational thought, and the way in which Piaget developed such notions in his own theory. But while Frege's theory helps set the parameters for whether thought can be judged as rational, or if it even should be judged as rational, it also shows the logicians' disdain for exploring anything resembling development of rationality. Thus Frege might have an important, but necessarily mediated impact on the field of human development. Piaget's carefully crafted theory of epistemological development potentially serves as such a mediating device. It can be argued that Piaget crafted together arguments of logicians such as Frege, and epistemologists such as Lévy-Bruhl, to develop his extraordinary achievement of a genetic epistemology that leads to an understanding of the human condition. One of Piaget's accomplishments was to develop a continuum out of the logicians' dichotomy between non-logical and logical in which the non-rational flows into the rational.     

Children's appraisals of antisocial acts: A Piagetian perspective

This study examines developmental aspects of children's appraisals of antisocial acts by integrating the two micromodels Piaget used at different points in his research programme to describe and explain the child's transition from pre‐operational to operational thought. One model guided by game theory involves a cost‐gain evaluation, and is mainly a functional model (Piaget, 1957); the other, based on equilibration theory, appeals to the initial priority of affirmations over negations, and is mainly a structural model (Piaget, 1975). The integration of these two models leads to the prediction that while younger children tend to perceive antisocial acts in terms of gain‐perception and affirmation, older children tend to think of them in terms of cost‐construction and negation. The participants were 96 children from three age levels (32 5–6‐year‐olds, 32 7–8‐year‐olds, and 32 10–11‐year‐olds). They were first confronted with four hypothetical antisocial scenarios and were then asked to engage in a task measuring gain‐perception/cost‐construction for each one. Children's responses showed that they are more likely with age to consider prototypical antisocial acts (e.g. stealing, pushing) in terms of cost‐construction and negation than gain‐perception and affirmation. In addition to supporting the hypothesized prediction, this finding may turn out to be of value in the design of further research and provide a better understanding of some developmental aspects reported in the literature on children's antisocial behaviour.     

Piaget and Levy-Bruhl

Levy-Bruhl exerted a powerful influence, seldom considered, on Piaget. The Levy-Bruhlian thesis of a "pre-logical mentality" characterized by "mystical participation" is outlined, together with its initial reception. The first evidence of Piaget's interest in it dates from 1920, and when he began his studies of children's thinking he compared it with that of 'primitives," also adopting Levy-Bruhl's concept of "participation." By 1928 Piaget had elaborated a theory of the social foundations of different types of thought, which he regarded as also explaining the alleged similarity between the thinking of primitives and children. Both are subject to constraint, primitives by elders and children by parents and teachers. Logical as opposed to pre-logical thought was said to depend on cooperation in free social interaction. Piaget continued to maintain essentially the same views long after Levy-Bruhl himself had renounced the notion of pre-logicality.     

Implicit cognitive development in cultural tools and children: lessons from Maya Mexico

Zinacantec Maya weaving tools and apprenticeship practices contain an implicit theory of cognitive development that corresponds to Piaget and Inhelder’s explicit theory of cognitive development [The Child’s Conception of Space, London, Routledge and Kegan Paul, 1956]. A set of preoperational and concrete operational spatial problems from the weaving domain provided empirical support for the ethnotheory of cognitive development implicit in Zinacantec weaving tools and their developmental sequencing. A structurally similar set of preoperational and concrete operational spatial problems were adapted from Piaget and Inhelder’s Swiss research. Both sets of problems were presented to children aged 4–13 in Nabenchauk, a Zinacantec hamlet in Chiapas, Mexico, and in Los Angeles, CA, USA. While the sequence of operational development was the same across both domains and both cultures, Zinacantec children were more precocious with the weaving problems, whereas U.S. children were more precocious with the spatial problems adapted from Piaget and Inhelder. After a brief instructional procedure, children in both Nabenchauk and Los Angeles improved on the weaving problems only, within the maturational constraints typical of concrete operational development. Nonetheless, the brief learning experience could not reverse the advantage of long-term cultural familiarity with backstrap-loom weaving. Our conclusions are threefold: (1) An implicit ethnotheory of cognitive development, built into the sequencing of cultural tools, can be as developmentally valid as an explicit formal theory. (2) Culture-general Piagetian stages are harnessed in culture-specific situations. (3) Maturational readiness interacts with both long-term cultural experience and short-term learning experience to actualize concrete operations in a specific context. Cross-context generalization of Piagetian stages is far from automatic; it requires cultural learning.     

From Piaget's Epistemic Subject to Pascual-Leone's Metasubject: Epistemic Transition in the Constructivist—Rationalist Theory of Cognitive Development

The explanation of the transition from one epistemic theory to another is an important part of Piaget's genetic epistemology. It is argued that this epistemic transition leads to a retrodictable orthogenetic tendency toward optimizing equilibration. The objective of this paper is to establish a relationship between Piaget's epistemic subject and Pascual-Leone's metasubject and to demonstrate that the postulation of the latter can be considered as an epistemic transition between two constructivist—rationalist theories, which leads to the development of a theory with greater explanatory power. Epistemic transition in this paper refers to a progressive problemshift (cf. Lakatos, 1970), between the theories of Piaget and Pascual-Leone. Piaget builds a “general model” by neglecting individual differences, that is, studies the epistemic subject, whereas Pascual-Leone by incorporating a framework for individual difference variables, studies the metasubject—the psychological organization of the epistemic subject. Empirical evidence is presented to demonstrate that Pascual-Leone's theory of constructive operators is a model of the psychological organism (the metasubject), which is at work inside Piaget's epistemic subject. Finally, it is concluded that the greater explanatory power of Pascual-Leone's theory can be interpreted as an epistemic transition between Piaget's epistemic subject and Pascual-Leone's metasubject.