Mathematical Arguments in Context

Except in very poor mathematical contexts, mathematical arguments do not stand in isolation of other mathematical arguments. Rather, they form trains of formal and informal arguments, adding up to interconnected theorems, theories and eventually entire fields. This paper critically comments on some common views on the relation between formal and informal mathematical arguments, most particularly applications of Toulmin’s argumentation model, and launches a number of alternative ideas of presentation inviting the contextualization of pieces of mathematical reasoning within encompassing bodies of explicit and implicit, formal and informal background knowledge.     

《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。     

周易式逻辑图解

用欧拉图和文恩图表示一些逻辑内容是逻辑教学及研究中的有益手段,但两种图形在刻画逻辑内容的范围上却是很狭小的,如在表示概念之间的关系时,两种方法都不能表示多于三个概念之间的某些逻辑关系。如四个概念的外延相交叉而区分出的...     

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。     

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.     

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。     

工具与文化之间的数学品格——模式观的数学本体论下对数学意义的探索

数学是通过逻辑建构模式并以模式为对象进行研究的科学.这种数学模式观扬弃了数学本体论中的实在论与反实在论的极端主义哲学理解,充分肯定了数学的抽象性与客观性.在模式观的数学本体论视野下,数学兼具工具与文化两种品格.数学无形地渗透在科学的每个分支里,为其提供必要的工具;数学是理性精神的化身,深刻地影响着人们的观念、精神以及思维方式的养成.     

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.     

The Role of Symmetry in Mathematics

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of mathematics and the relationship of mathematics to physics.     

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.     

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.     

晚清中算家的数学观

晚清是中西数学深入对话的关键时期,对当时中算家数学观的考察可以加深对晚清数学发展的理解。通过研读晚清的数学著作,梳理了此时中算家对数学重要性,数学的理、法、用,数学最精之诣以及古今、中西数学关系的看法,并总结出了晚清中算家数学观的特点,即在统一的基调上又存在着差异。     

中日数学哲学比较研究

本文认为，中日数学哲学之共同点在于双方都十分重视马克思，因格斯有关著作与数学思想方法的研究，而异同点主要表现为：经典著作认识上的哲学价值观与科学史观，研究成的理论性与实用性，开展活动上的计划性与灵活多样性，如果双方能互为借鉴，取长补短，则各自必有更大发展。     

The Role of Conscious Attention in Perception

Impressions, energy radiated by phenomena in the momentary environmental scene, enter sensory neurons, creating in afferent nerves a data stream. Following Kant, by our inner sense the mind perceives its own thoughts as it ties together sense data into an internalized scene. The mind, residing in the brain, logically a Language Machine, processes and stores items as coded grammatical entities. Kantian synthetic unity in the linguistic brain is able to deliver our experience of the scene as we appear to see it. Uniquely, the brain records its own history, synthesizing a Movie-in-the-Brain, called the Noumenal Cosmos. Attempting thereby to represent the actual Universe, this makes for a sovereign brain that governs itself. The brain is domicile of an Ego, with its selfhood at stake at all times. Yet, it can know itself only by its actions, in which it appears as an actor in its own movie. Phenomena enter garbled, as confused apparitions, and must be put in good form using top–down feedback control by Ego, so that each movie frame makes rational sense within the overall context of the Noumenal Cosmos. A stack of frames is processed typically in 40 Hz rhythm with 300 ms process time each, for about 12 in the stack at any time. Successive neural centers are processing the stack in the brain assembly line, based on data from increasingly global receptive fields. Ego stitches together the movie frames, but only the top frame is in consciousness for 25 ms. The top frame contains the whole scene where the Ego makes an appearance as the actor that imposes Kantian synthetic unity on the scene, merely an assembly of grammatical texts, in a system-internal coded process language, fitting the scene into the Noumenal Cosmos. But Ego observes Ego only to the extent permitted by the objectivity rule, only what it does and thinks, not its true face. From the Noumenal Cosmos, the Ego receives grammatical messages in the internal sense code. They are integrated into a whole in the reaction of the Ego to the momentary scene. The voluntary nature of Ego’s decisions is explained, based on its ability to code in advance its own actions sequentially in time, as it sees fit with a view to an orderly Noumenal Cosmos, records of code being arranged spatially in neural structures.     

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...     

ETCS数学基础的语境分析意义

基于范畴论的语境特性,探索语境分析方法在数学基础研究中的实质功能。在对ETCS公理系统进行语境分析的过程中实现对ETCS的整体解读,把握ETCS公理系统的内在蕴涵,理解ETCS在当前数学哲学中的基础定位,进而揭示ETCS数学基础的语境分析意义。     

试论刘徽的数学思想方法

本文从三个方面论述了刘徽的数学思想方法:(1)刘徽的极限思想及其关于研究刘徽极限思想方法中的值得商榷的问题;(2)刘徽的数学方法——定义方法和证明方法及其特点和意义;(3)刘徽在数学研究中体现出来的科学精神。     

数学证明严格性之相对意义与综合评判标准

数学命题的证明在结构上必然存在某种预设性,在其论证过程中必然存在逻辑空隙。数学推理在所采用的逻辑工具和方法上并非无懈可击,加之数学形式体系的非完整性与非封闭性,这些都充分表明数学知识无论是在其原初形式上、形成过程中和构成方式三个维度上都无法获得完全意义上的可靠性。即使在元层面的证明论诉求亦复如此。数学证明的标准是一个综合评判的动态体系。     

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。