The Role of Diagrams in Mathematical Arguments

Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs.     

On the Persuasiveness of Visual Arguments in Mathematics

Two experiments are reported which investigate the factors that influence how persuaded mathematicians are by visual arguments. We demonstrate that if a visual argument is accompanied by a passage of text which describes the image, both research-active mathematicians and successful undergraduate mathematics students perceive it to be significantly more persuasive than if no text is given. We suggest that mathematicians’ epistemological concerns about supporting a claim using visual images are less prominent when the image is described in words. Finally we suggest that empirical studies can make a useful contribution to our understanding of mathematical practice.     

Misrepresentation in “Misrepresentation in Context” in Context

I argue that in aiming to integrate the notions of representation and resemblance in the arts, philosophy of sciences and cognitive sciences one needs to focus on those processes of reasoning and creative inquiry that (i) exploit our faculties of imagination and mental imagery, (ii) create novel and useful metaphors based on iconic types of meaning, and (iii) may result in discovery through the interactive practices of artists and scientists. To address these matters within the confines of Goodmanian conventionalist and symbolic theories of logic, thought and language is unlikely to deliver these points. A comprehensive philosophy of signs, however, might do the job.     

对维特根斯坦反私人语言论证的一种解读

维特根斯坦反私人语言的论证过程由环环相扣的三个分论证构成。首先,维特根斯坦提出不为别人所知道的私人感觉是一种语法虚构;其次阐明即使有所谓私人感觉存在,在私人感觉的基础上也不可能建立起私人语言;最后指出,即使有所谓私人语言,这种语言也毫无意义。他承认个体感觉的存在,但这种感觉可以为别人知道。感觉不是语言意义的终极来源,恰恰相反,感觉总在一定的语言游戏中获得意义。与个人感觉相联系的语言总是公共语言,总在一定的语言游戏中充当一定的角色。维特根斯坦的反私人语言论证在心理哲学的层面进一步批驳了建立在实指定义基础上的意义理论,对观念论哲学的根基提出了严峻的挑战。     

《数学汇编》中的数学问题在中国——兼与古希腊数学思想比较

帕普斯的《数学汇编》是世界数学史中一部承前启后的重要数学著作,它对希腊经典数学问题的研究为后来的数学指出了方向,拓展和预见了许多数学新领域。本文分析了明末至清末近300年间传入的《数学汇编》中的典型问题,探讨了中算家对古希腊传统问题的理解、接受情况。通过比较发现其在中国和在希腊发展的差异,西方由此导致了数学的进化,而中国延续了中算以算为主和重视实用的传统,发展了不严谨的证明方法,在西学的引导下触及到了数学发展的一些理论问题,所有这些为中国进一步接受近代数学奠定了基础。     

Misrepresentation in Context

We can witness the recent surge of interest in the interaction between cognitive science, philosophy of science, and aesthetics on the problem of representation. This naturally leads us to rethinking the achievements of Goodman’s monumental book Languages of Art. For, there is no doubt that no one else contributed more than Goodman to throw a light on the cognitive function of art. Ironically, it could be also Goodman who has been the stumbling block for a unified theory of representation. In this paper, I shall contrast the ways how differently misrepresentation has been treated in cognitive science, aesthetics, and philosophy of science. And I shall show that it is Goodman’s unnecessary separation of resemblance and representation in art that made such a difference. As a conclusion, I will indicate some of the most promising projects toward the unified theory of representation the revolt against Goodman’s rejection of resemblance theories might promise to us.     

创新中的社会关系:围绕青蒿素的几个争论

本文利用文献检索和访谈调研方法,全面论述了20年来围绕青蒿素展开的几个重要纷争,包括专利权、发明权、中西药和单复方之争.揭示了这些争论的关键要点,分析了这些争论背后的主导原因.     

社会语境中的科学

科学是社会的产物,其发生和发展只能在社会背景中才能得到说明。科学本身又是一种社会现象,也只能在社会历史中得到解释。本文运用语境分析方法,将科学当作一种文本放到产生它的社会大背景中去考察,提出“社会语境”和“科学语境”的概念,探讨了它们的结构,进一步揭示了语境作用于科学的机制和科学语境产生科学知识的机制。     

道教外丹术性质三论

道教外丹术颇受学界关注,有关外丹术特性之探究却少有.外丹炼制的年轮昭示着技术的历史积淀;外丹术有明显的实用性考虑;其中也体现了炼丹者的宗教信仰本色.对道教外丹术这些特性进行深入考察,有助于发掘道门技术活动的规律,也可以鲜明展现道教教义教理.     

关于科学的文化学构想与论证

文章提出当前对于科学文化的现象研究的深入应当具有文化学的规范和支撑,并初步分析了科学文化学的概念、特征、学科体系,及在此框架内业已展开的问题,从而论证了科学文化学的建立不仅为理论上所需要,而且在现实上也是可能的.     

当代语境下的科学传播研究

科学技术与人类社会的关涉深刻又多元,科学技术的传播活动是连接二者的桥梁。回溯历史,科学技术的传播活动的理论发展与时代背景、社会需求密不可分,经历了科学普及、公众理解科学和科学传播三个阶段。当前,科学传播面临着全新的局面:警惕科学思想分离了知识进展与实践行动;城市化进程分离了人类与自然;个体差异造成价值观念的不一致并因此造成信任危机。当代语境下的科学传播应着力建构科学共同体和公众双方参与、互相理解的"参与科学模型",增加科学传播的历史维度,并推动建立科学传播的标准体系。探索科学传播的理论与实践,是推进科学技术与人类社会良性发展与互动的必要途径。     

Building Context in Everyday Life

Social context is generally thought toinfluence how humans act. Here we argue thathumans rarely accept the context as it isgiven, but rather undertake conscious actionsto make it favourable. The example chosen isfrom northern Cameroon, where nomad herdsmeninduce the sedentary farmers to trust them, bydifferent means: creation of interpersonallinks, exhibition of good behaviours byrespecting certain norms. Trust is consideredas an element of the context, necessary forthem to perform acts that present a certainrisk. An attempt was made to translate one ofthe traditional behaviours into a model,implemented in an artificial society:autonomous agents would make gifts in order tocreate an image of themselves in a group. Inthe simulations, a form of reputationstratification appears in time. One notes thatan agent can build the image it wants only ifthe part of the population that wants to beinvolved in the same dynamic is big enough. Asa conclusion, we suggest that althoughindividuals try to create consciously a contextfor their living, this is not just anindividual choice, but needs a commonbackground of rules, a context enabling contextcreation.     

论科学解释语境与语境分析法

本文分析了科学解释语境的基本结构，揭示了科学解释语境的六种基本功能，在此基础上，阐述了语境分析法的本质和运用语境分析法应该坚持的六条基本原则。     

德绍尔技术思想的结构性逻辑与争论

德绍尔独特的技术思想使其在技术哲学史上极具影响力。追溯其思想渊源,它的结构性逻辑极为明晰:以苏格拉底的"techne"为基础构建思想基石;以柏拉图式的"理念"和宗教神学的创世学说为基础阐释技术发明成为可能的先验前提,构建思想内核;阐明康德先验哲学中"物自体"发生必然联系的"中介",构建思想支点;发展康德的三大王国,构建系统的"第四王国"技术思想,到达形而上学的顶峰。这不仅填补了关于他对思想渊源缺乏详细分析的"空白",而且阐明了其思想的四维结构,明确了其思想中引发争论的焦点问题。     

对医疗领域中的认知不公正论证的反思

卡瑞尔和基德认为弗里克提出的"认知不公正"概念在医疗领域中也存在,她们论证了这一领域的证言不正义和阐释不正义.然而本文认为,医疗领域与认知不公正问题的典型领域存在显著差异,其差异主要在于专业知识的不对称,病人证言依赖于知识语境和医生能力.因而用认知不公正的概念来表述这些问题会一定程度掩盖其中更为深层的两类知识之间的交互...     

科学的"计划"与"自由"发展:争论及其影响

20世纪以来，围绕科学的“计划”与“自由”发展这一主题，科学家、政治家、人文学者与社会民众展开了三次热烈的争论。在争论中，人们逐步达成一致的观点：政府应主导和组织科学发展，科学发展最终要体现国家目标。这些观点对知识经济时代的国家科学政策产生了深刻影响。     

对称性理论的逻辑起点及其推论

内容提要对称性及对称破缺是非常重要的概念，数学家、物理学家对其有深入的研究。本文旨在探讨对称性理论的逻辑起点及其推论，我们认为，时空点及其自然维数应是对称性及对称破缺理论的最原始的概念。     

Objects and Processes in Mathematical Practice

In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics.     

逻辑学语境下的科学实用主义

作为实用主义的鼻祖,皮尔士首先和主要是一位逻辑学家.他的实用主义从根本上讲是一种逻辑学说,要求从逻辑学理论上对其进行解读.审视科学实用主义同逻辑学的内在的、历史的联系及其形而上的蕴含,可以更清晰地认识实用主义理论的本真意义.