Human Culture and Science: Equality and Inequality as Foundations of Scientific Thought

We argue that the concepts of `human equality' and `inequality' play an important role in the structure of science and philosophy. When the value of `human inequality' predominates, scientific categories are formed in accordance with the principle of `hierarchical differentiation' and concepts remain closely tied to the objects they are referring to. Following Mirowski we define this as the `anthropometric stage' of human thought and development. Contrary, Mirowski's `syndetic stage' refers to societies where the value of `human equality' prevails. Here concepts appear that are universally applicable. However, because of their conventional nature these concepts cannot be `grasped' any longer by human intuition. Between the `anthropometric' and `syndetic' stages, a `lineamentric stage' appears, a period of transition from `human equality' to `human inequality'. Being both a bridge and gap between the two other stages, the `lineamentric' stage contains many contradictions between an `abstract attitude' and `concrete categories'. In this paper we examine the anthropometric, lineamentric and syndetic stages and discuss several examples taken from philosophy, logic, mathematics and physics.     

Essential Tension: Mathematics - Physics - Philosophy

The author focuses on the tension "realism - idealism" in the philosophy of mathematics, but he does that from the perspective of a theoretical physicist. It is not only that one's standpoint in the philosophy of mathematics determines our understanding of the effectiveness of mathematics in physics, but also the fact that mathematics is so effective in physical sciences tells us something about the nature of mathematics.     

黎曼的几何思想萌芽

在分析黎曼的几何思想和其他学科关系基础上，指出了其几何思想的三个来源：数学、物理和哲学。这其中，19世纪前半叶几何学对黎曼有着直接影响；物理研究也是黎曼的兴趣所在，尤其是他一度试图建立各种作用力的统一理论，促使黎曼用无穷小分析研究流形，并触发了黎曼对空间几何基础的讨论；哲学上，黎曼对空间认识论的思考从赫尔巴特那里得到了灵感，并且在流形概念上可能也借鉴了赫尔巴特的研究。最后指出：研究黎曼几何思想不能把各学科分开考虑，必须全面考虑其间关系。     

伊斯兰精密科学对印度及其邻国的传播和影响

Ⅰ Let me first clarify that science as developed in Islamic cultural areas or societies during the Middle Ages is abbreviated here as Islamic Science. In that context, the Exact Science is confined to astronomy (including mathematical geography) and mathematics only; physics was then a part of natural philosophy, and chemistry a branch of medicine.     

Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which we use work by Haggith on argumentation structures, and identify connections between these structures and Lakatos’s methods.     

科学普适性信念批判的SLK进路研究及其意义

西方学术传统所坚持的科学普适性信念,多年来受到来自数学哲学、物理哲学等多条进路的批判。布鲁尔的SSK思想也是对这种信念的一种批判,作为其SSK组成部分的SLK思想,是这种批判的集中体现。他以逻辑学这门硬科学为例,从逻辑基础和逻辑规则社会性两个方面,提供了对于科学普适性信念更为深入的批判路径,从而导致了科学形象的极大变革。     

试论数学哲学的文化转向及其影响

数学文化研究是数学哲学研究与发展的一个新的方向,开辟了数学哲学研究的全新视角。本文从文化哲学、科学文化哲学以及数学哲学的后现代发展历程中梳理了数学哲学的文化转向,以及所产生的影响。     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

结构实在论评析

曹天予提出的结构实在论知识论版本在科学哲学界有很大影响，并引发了《综合》期刊专刊讨论。他既批评反实在论的观点，也对结构实在论的知识版本与本体版本有所批判。他从结构、本体、建构这三个概念出发，论证了科学理论的客观性体现为建构性、历史性、整体性、修正性、革命性。本文对曹天予的结构实在论进行了系统的梳理与分析。笔者赞同他对“不充分决定”论旨的批评，对他批评“本体论不连续性”持中立态度，但对他的“普遍语法论证”有所存疑。     

现代物理学需要思辨——评吴孟超的《宇宙解的构思》

现代物理学研究的极限问题越来越多。极限问题离直接经验最远。极限问题既有科学解，也有哲学解。极限问题的研究需要哲学与思辩。吴孟超教授的《宇宙解的构思》一书，对一些物理学的极限问题作了有益的探讨，并表明现代物理学需要思辩，物理学应关注哲学，哲学应参与思辩。     

Games as formal tools versus games as explanations in logic and science

This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are critically surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning.     

科学、女性与客观性--兼评女性主义对科学客观性的探索

科学自诞生以来，客观性一直是它引以为豪的根据，而解释科学何以能成为“客观的”也成为科学哲学产生和发展的一个重要的动机和基础。女性主义科学哲学对科学的客观性概念和意义作了一系列独特的有意义的探究，本文对其观点进行了分析、阐释和评价，并提出了一些自己的看法。     

The Heuristic Function of Mathematics in Physics and Astronomy

This paper considers the role of mathematics in the process of acquiring new knowledge in physics and astronomy. The defining of the notions of continuum and discreteness in mathematics and the natural sciences is examined. The basic forms of representing the heuristic function of mathematics at theoretical and empirical levels of knowledge are studied: deducing consequences from the axiomatic system of theory, the method of generating mathematical hypotheses, “pure” proofs for the existence of objects and processes, mathematical modelling, the formation of mathematics on the basis of internal mathematical principles and the mathematical theory of experiment.     

Top-Down and Bottom-Up Philosophy of Mathematics

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach.     

道家哲学与现代物理哲学的契合性考察

与儒家"向内觅理"有别,道家重视外向的"天之道",对自然之源和万物之本多有探讨,形成了独特而深刻的自然哲学思想,诸如"道""朴""无""有""阴阳"等自然哲学概念,在此基础上形成了"道生万物"的宇宙创生观,"负阴抱阳"的自然运行观,"道通为一"的世界统一观等自然哲学思想.这些概念和思想被现代物理科学,特别是量子物理学所...     

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.     

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.     

实践与"运用概念的艺术" --略论恩格斯的自然科学认识论思想

恩格斯的自然科学认识论既不同于近代经验论、唯理论、先验论,也不同于反映论.通过恩格斯对数学概念、物理学概念、形而上学概念的考察可以看出,恩格斯的自然科学认识论属于实践论.     

客观性与科技的价值性

客观性是科学哲学研究的重要问题之一，而从客观性的概念分析来看，客观性是对事物对象本质的普遍性把握。以往把科学仅仅理解为工具性技术，这是时科学技术本质的遮蔽。科技价值的客观本质是对人的存在方式的展示，是人的科学。科学技术是人的存在方式之一种，不是惟一的方式。     

科学客观性:外在性与内在性的交融

本文试图从内在性与外在性两个层面重建科学客观性。一方面,科学对象的客观实在性并非一种外在于人的自在性,而是主体在自身的对象性活动中与客观世界耦合而得到的结果,是一种属人的现实,是在实践中被确立起来的。科学家们借助于直观方法与理性工具把所捉到实体与过程、类型与结构、解释句与理论模型等等,都在某种程度上独立于我们的主观表象,承载着对象的客观性——外在客观性。它们构成了"科学共同体"的"本体论承诺"。另一方面,这种外在的客观性,是在人类主体的内在化过程中实现的。在现代科学中,科学家们自觉地运用对称性工具实现的"内在化"所得到的"变换下的不变性",使得科学具有了公共可理解性与可接受性。这种在人类旨趣、目的和价值引领下对世界实行的主动干预所实现的公共性,就是内在客观性。因此,科学客观性是一曲由外在性与内在性合奏出来的交响曲。