Model-Based and Manipulative Abduction in Science

What I call theoretical abduction (sentential and model-based)certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good (preferred) explanations of data, but fails to account for many cases of explanation occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action in many interesting situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. Many external things, usually inert from the epistemological point of view, can be transformed into what I callepistemic mediators, which are illustrated in the last part of the paper, together with an analysis of the related notions of ``perceptual and inceptual rehearsal' and of ``external representation'.     

数学视野中的中国古代历法--评曲安京著《中国历法与数学》

曲安京所著《中国历法与数学》一书，探讨中国古代历法中天文常数与算法的构造机理及其数学思想，对上元积年、渐近分数、内插法、历法中的公式化计算等历法中的重要数学问题进行了原创性的研究，提出了很有说服力的观点与论据。该书把数学史与天文史结合在一起的研究思路也是富有启发性的，是一部成果颇丰的交叉学科性学术著作。     

穿过离散与连续之间的无穷小逻辑距离——基于物理学统一的数学统一性

目前试图结合广义相对论与量子力学的量子引力论强调了最小普朗克距离。这种离散化的要求是否意味着以无穷小距离、连续和微积分为基础的近代数学的终结?如果从离散与连续的角度重新分析已有物理学统一理论所需要的数学理论,就会发现,它们都不同程度地处理了离散、连续以及离散与连续之间的统一问题;而当前的量子引力论仍旧需要处理离散与连续之间的统一问题,并且,其相应的量子几何学有可能全面实现离散与连续之间的统一。     

论19世纪的逻辑学——在数学与哲学之间

19世纪的逻辑学处于数学与哲学之间:一方面,数学家在对传统逻辑的改革过程中形成了逻辑代数和数理逻辑;另一方面,哲学探讨热衷于逻辑学的性质、地位、基础等问题,由此形成了心理主义和反心理主义之争。这种状况从各个方面影响了20世纪的逻辑学、心理学和哲学的发展。     

Abduction as a Logic and Methodology of Discovery: the Importance of Strategies

There are various ``classical' argumentsagainst abduction as a logic of discovery,especially that (1) abduction is too weak amode of inference to be of any use, and (2) inbasic formulation of abduction the hypothesisis already presupposed to be known, so it isnot the way hypotheses are discovered in thefirst place. In this paper I argue, bybringing forth the idea of strategies,that these counter-arguments are weaker thanmay appear. The concept of strategiessuggests, inter alia, that many inferentialmoves are taken into account at the same time.This is especially important in abductivereasoning, which is basically a very weak modeof inference. The importance of strategicthinking can already be seen in Charles S.Peirce's early treatments of the topic, and N.R.Hanson's later writings on abductionalthough they did not use the concept of``strategies.' On the whole, I am arguing thatthe focus should be more on methodologicalprocesses, and not only on validityconsiderations, which have dominated thediscussion about abduction.     

中国数学史研究状况与趋势——基于2001—2010年数学史文献的计量分析

通过对2001—2010年数学史主流期刊文献的统计和分析,呈现出我国数学史研究在主题和内容、研究队伍及其区域分布、基金资助三个方面的情况,以揭示我国数学史研究的趋势和特征。     

论中国逻辑与中国传统数学

中国传统数学受到了中国逻辑尤其是墨家逻辑的影响,形成了自己的推理方法体系--以"以类合类"为方法论基础,以"类"和"分类"为推理的核心成分,以"推类"为主导推理范式.这一方法体系,在相当长的时期内使中国传统数学处于世界的领先地位,因此,可以下这样的结论:中国逻辑不是阻碍中国传统数学进一步发展的因素,中国传统数学自身逻辑思路也不是制约中国传统数学发展的原因.     

"哥白尼革命"的另一种解读--从数学哲学的角度看

哥白尼革命和数学有着不可分割的联系.评介了库恩对哥白尼革命根源和性质的"纯数学解释".由于纯数学是由数学哲学思想决定和规划,所以,理解哥白尼革命有必要开启数学哲学的视野.在伯特思想的启发下,从数学哲学的角度分析了哥白尼革命的根源以及性质,提出了与库恩有本质不同的观点,为理解近代科学的数学性提供了一个有益的视角.     

"数学常青"——从第22届国际科学史大会看数学史研究的特点与走向

通过对第22届国际科学史大会上数学史的特邀报告、主题讨论会和论文报告的全面分析，我们看到传统内史型的数学史研究依然具有重要的生命力，但新的“热点”更应值得关注，比如，“多元文化之间数学知识的交流与传播”就已成为新的主流。为了应对“全球化和文化多样性”带来的挑战，这次国际科学史大会上展现出的新思想、新视角和新进路，对于中国数学史是十分重要的。     

抛弃中心还是成为中心——现代性与无限空间观

在古代和中世纪,人被视为有局限的存在,身体的局限决定了人只能待在有限的宇宙的中心。现代人不再认为身体能够束缚心灵,于是摧毁了宇宙的边界,放弃了人类身体在空间意义上的宇宙中心位置,这实际上意味着人类心灵超越了空间,成为宇宙万物的真正中心。     

Analogical Reasoning and Modeling in the Sciences

This paper aims at integrating the work onanalogical reasoning in Cognitive Science into thelong trend of philosophical interest, in this century,in analogical reasoning as a basis for scientificmodeling. In the first part of the paper, threesimulations of analogical reasoning, proposed incognitive science, are presented: Gentner's StructureMatching Engine, Mitchel's and Hofstadter's COPYCATand the Analogical Constraint Mapping Engine, proposedby Holyoak and Thagard. The differences andcontroversial points in these simulations arehighlighted in order to make explicit theirpresuppositions concerning the nature of analogicalreasoning. In the last part, this debate in cognitivescience is applied to some traditional philosophicalaccounts of formal and material analogies as a basisfor scientific modeling, like Mary Hesse`s, and tomore recent ones, that already draw from the work inArtificial Intelligence, like that proposed byAronson, Harré and Way.     

先秦数学史研究的新进展--评邹大海著《中国数学的兴起与先秦数学》

20世纪60年代初,中国科学院自然科学史研究室(今自然科学史研究所前身)数学史组在钱宝琮主持下完成<中国数学史>[1]后,开始实施了一个断代专题研究的宏大计划:把中国数学史分几个断代进行更细致而深入的研究,以便将来在更高层次上编写一部中国数学史[2].钱宝琮在世时组织了宋元时期的断代研究并出版了一部<宋元数学史论文集>[3]."文革"使这个计划中断."文革"后,顺着他的这一思路,自然科学史研究所对于两汉魏晋和明清的断代研究也相继展开,并获得了很大进展,在学术杂志上发表一系列论文,并出版了一部论文集<明清数学史论文集>[2]和专著<〈九章算术〉汇校本>[4]、<古代世界数学泰斗刘徽>[5]等.近年出版的邹大海所著的<中国数学的兴起与先秦数学>(以下简称<先秦数学>)则是一项先秦数学的断代研究.     

世界技术成果时空分布的量化特征及世界技术中心的转移

基于一本美国出版的技术史年表提供的3329条数据,本文通过数理统计方法探讨了世界技术成果时空分布的量化特征及世界技术中心的转移.从时空上看,世界技术中心是在转移的,转移顺序大体上是:古埃及、两河流域→古希腊、古罗马→中国→意大利、英国、法国、德国、美国.本文从技术门类层次上揭示了近现代世界技术中心转移规律的内在机制.     

Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model ${\mathcal{S}}$ as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In ${\mathcal{S}}$ , all definable sets of reals are Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace ${-\hskip-9pt\int}$ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy.     

《缀术算经》:东亚数学归纳推理的典范

《缀术算经》是日本和算家建部贤弘最富创造性的一部和算著作,代表了当时日本数学发展的最高成就。文章在前人工作的基础上,从数学传播史和比较数学史的角度,将其置于整个汉字文化圈数学文化背景下,对其数学内容、思想实质与中国传统数学的关系予以深入分析,对其数学成就与建部贤弘的数学方法论予以客观公正的评价。     

休闲教育:个体生命与生活世界的需求

促进个体生命的完善与圆满是休闲教育的根本目的，而生活世界是个体生命生存与生活的现实世界。休闲教育正是在促进日常生活世界和非日常生活世界的相互融合中，不断提升个体生命的质量。     

Mimesis and the Representation of Reality: A Historical World View

The representation of reality is a fundamental concept in the perception of theworld. Its historical consideration leads to an understanding of historical andcontemporary culture. In this paper we specifically investigate theanthropometric stage of cultural development as a historical world view. Wedefine this stage on the basis of René Girard's hypotheses on the origin ofculture, and we isolate its principles. Next, we consider the function of art asthe representation of cultural values. We investigate the three major motivesof artistic representation in the anthropometric stage, i.e. beauty, dramatizationand mimesis. We show how and why these motives play an essential partin the obfuscation and explanation of the origin of culture. Finally, we showhow these developments are dealt with in the aesthetics of Plato and Aristotle.     

技术:人类在世的方式

本文从神话、现实等视角解读技术对人的本质性意蕴，指出人凭藉技术进入存在，假之于技术而得以生存与发展；从事实、考古学、哲学的维度剖析技术在人类社会的普遍性特质；得出人必然是技术性的存在物，技术是人类在世的方式。     

科学与美学联姻的古代形态:美与数理学科的联姻

在西方美学发展的漫长历程中,科学与关学尤其是数学与美学的关系值得关注.早在古希腊时期,揭开了古希腊美学思想发展的序幕的是毕达哥拉斯及其学派.正是他们首先将数学与美学相结合,开始了美与数理学科相联姻的潮流.后来经德谟克利特的发展,到柏拉图与亚里士多德都对数学与美学的关系极为关注.由于古希腊美学是西方美学的重要源头,这就使西方美学不仅与科学紧密相联,而且形成了与中国美学不同的精神风貌.