再论数学史与数学哲学的关系

学术界往往从学理上谈论数学史与数学哲学的密切关联,而较少从研究层面论证两者之实际关系。从研究实践看,数学哲学研究大致有自上而下论述并辩护数学哲学理论与自下而上举例分析数学哲学问题两种范式,数学史研究则经历了由辉格史到反辉格史的范式转变。由于研究范式的自然本性,数学哲学问题范式与反辉格数学史具有天然的亲缘关系。数学史与数学哲学的实作转向之后,两者都以数学实作为研究对象,从而关系更为紧密。因此,历史上数学的发展与当时某种哲学思想的关联是原初意义上数学史与数学哲学的关系;19世纪后半叶开展现代数学史与数学哲学研究以来,两者存在着变动的关系——共同研究数学实作则使得两者的关系比以往任何时候都要密切。     

海德格尔与维特根斯坦比较研究述评

本文在概述国外海德格尔与维特根斯坦比较研究的总体情况后,着重对国内海氏与维氏的比较研究做一简明述评。     

现象学的现象与量子现象的相遇

现象学的现象与量子力学的量子现象属于不同的领域,但是,它们之间具有很大的相似性,表现在显现的活动、显现者本身及其演化都属于现象概念。从方法论来看,它们也具有很大的相同性：现象都用“可能性”概念来描述;对现象的全面理解则从基本上相同的自由变更原理和互补原理来展开。     

论科技与道德协调发展的原则

面对现代科技的发展与人类道德的激烈冲突，寻求二者的协调发展是人类必须应对的新课题。科技与道德协调发展应遵循人本原则和生态原则，这两大原则具有内在统一性和不可替代性。在这两大原则的指导下，才能呈现科技与道德的协调发展。     

人和自然关系的历史审视

本文从哲学的角度,探讨了人和自然关系历史演进,提出可持续发展是解决人和自然冲突的必然选择.     

浅谈程序正义基本原则对学术评审制度的构建

程序正义是建设和完善学术评审制度的必要工具.将程序正义原则与相应的程序制度相结合,是构建公平合理的专家评审制度的有效工具.本文对构造科学的评审制度及其运行机制进行了思考,论述了在学术评审领域中引入程序正义原则的适用性及其重要作用,并初步探讨了在学术评审活动中与各程序正义原则相应的程序制度和规则.     

量子测量问题新解

量子测量问题悬而未决已近一个世纪,而目前学界日益倾向于将之归结为两个必须由量子理论回答的问题,即"明确结果问题"和"优先基矢问题"。21世纪初,John H.Conway、Simon Kochen等人提出了"自由意志定理",主张粒子具有自由意志。这意味着粒子具有自主选择与知觉的能力。粒子的知觉能力与自由意志均进一步地与能量这一基本物理量紧密相连,从而形成两条基本原理:"知觉-能量原理"和"意志-能量原理"。凭借这两条基本原理,"明确结果问题"和"优先基矢问题"便可得以解决,一条新颖的量子力学诠释进路也因此而呈现出来。     

对新型量子计算范例的哲学透视

本文围绕着突破经典计算能力的问题，对量子计算范例作全面深入的哲学透视。除了系统介绿这种“自然机制＋算法”的新兴计算范例外，还将量子计算范例同其他现有的主要计算范例进行了比较。结果说明，到目前为止，只有量子计算范例才真正突破经典计算的计算范围，因而其有着深远的科学和哲学意义。     

由量子计算看科学与哲学的层次观

量子计算是建立在量子力学基础上的一种全新的计算,被认为是最有可能突破现有的传统计算设备之计算能力的计算方式。量子计算具有"反直觉"的特点,这使得许多我们日常生活中认为是常识的知识在量子计算中不再成立;同时,我们在一般的认知能力中认为决无可能发生甚至有些"唯心主义"的现象恰恰成为量子计算可能远远超过传统计算的有力证据。量子计算特别是量子计算机近几年的巨大发展启示我们,哲学是科学发展的一个高级阶段,哲学的发展和进步同时也可解释科学并促进科学的发展。科学的发展可能存在着本质的局限性,哲学也许能在更高的层次对这种局限性提出解决方案。     

Quantum Theory and the Nature of Consciousness

Our interest focusses on the idea, that consciousness is a powerful acting entity. Up to now there does not exist a scientific concept for this idea. This is not due to problems within the field of psychology or brain research, but rather in resisting theories of modern physics. That is, why we have to search for a solution in the field of physics. A solution can be found in a new understanding of the basics of physical theory. That could be given by abstract and absolute quantum bits of information (AQI bits). To avoid the popular misunderstanding of “information” as “meaningful” it was necessary to find a new word for the free-of-meaning AQI bits: the AQI bits establish a quantum pre-structure termed “Protyposis” (Greek: “pre-formation”), out of which real objects can be formed, starting from energetical and material elementary particles. The Protyposis AQI bits provide a pre-structure for all entities in natural sciences. They are the basic entities, whereof the physical nature of the brain, on the one hand, and the mental nature of consciousness, on the other hand, were formed during the cosmological and the following biological evolution. A deeper understanding of quantum structures may help to overcome the resistance against quantum theory in the field of brain research and consciousness. The key for an understanding is the concept of Protyposis, which means an abstract quantum information free of any definite meaning. With the AQI bits of the Protyposis, both, massless and massive quantum particles can be constructed. Even quantum information with special meanings, in example grammatically formulated thoughts, eventually could be explained. As long as the fundamental basis of quantum theory is misunderstood as being formed by a manifold of some small objects like atoms, quarks, or strings, the problem of understanding consciousness has no solution. If instead we understand quantum theory as based on truly simple quantum structures, there would be no longer fundamental problems for an understanding of consciousness.     

The Generalised Liar Paradox: A Quantum Model and Interpretation

The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, &; Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth–falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m) ^m -dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous ‘time’ dynamics is possible: typical truth and falsehood value oscillations are described by Schrödinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of ‘truth-value by inference’ projectors, (iv) time invariance of unmeasured state.     

Schwinger and the Ontology of Quantum Field Theory

An epistemological interpretation of quantum mechanics hinges on the claim that the distinctive features of quantum mechanics can be derived from some distinctive features of an observational basis. Old and new variations of this theme are listed. The program has a limited success in non-relativistic quantum mechanics. The crucial issue is how far it can be extended to quantum field theory without introducing significant ontological postulates. A C*-formulation covers algebraic quantum field theory, but not the standard model. Julian Schwinger’s anabatic methodology extended a strict measurement-based formulation of quantum mechanics through field theory. His extension also excluded the quark hypothesis and the standard model. Quarks and local gauge invariance are postulates that go beyond the limits of an epistemological interpretation of quantum mechanics. The ontological significance ascribed to these advances depends on the role accorded ontology.

“内生的科学技术”考察

本讨论了用“内生”一词来表达科学技术与经济的关系的合理性与限度。在方法论意义上,科学技术作为经济模型中的“内生变量”只具有“理想类型”的工具性意义,而不能完全表达经济现实;从科学社会学和经济学意义上,科学技术是“市场内生”的观点并不充分,但技术和部分科学可以被视为市场内生的。“市场内生”的观点关联着对科学的思想、化地位的认识。     

论空间时间的量子观念

本文论述了空间时间量子观念的物理内容，并给出某些哲学反思特别是时空和真空的关系和不同之处。     

物理学的结构与结构实在论辩护——以经典力学为例

以经典力学中拉格朗日力学和哈密顿力学的结构分析为例,文章通过二者数学上同构的建立,揭示数学结构是物理学结构的必要前提和基础。运用范畴结构主义的本体论特征,尝试突破结构实在论的困境,为结构实在论做出辩护。     

法拉第研究电磁旋转现象的过程及相关问题的再探讨

根据法拉第的论著、书信和日记等文献,对他研究电磁旋转现象的过程进行了仔细考察,论述了《电磁历史概要》的写作对其发现电磁旋转现象所产生的重要作用.认为法拉第的这一发现是由一系列关键实验组成,不能仅以单一实验为其标志.阐述了奥斯特、安培和沃拉斯顿等人的相关研究及思想对法拉第研究电磁旋转现象所产生的影响,指出法拉第能够作出这一发现的决定因素还在于其敏锐的观察能力、高超的实验技能和坚忍不拔的探索精神.同时,还对前人相关研究中的一些问题提出了不同的见解.     

Spin and Wind Directions II: A Bell State Quantum Model

In the first half of this two-part article (Aerts et al. in Found Sci. doi: 10.1007/s10699-017-9528-9, 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.     

论“经典模组性”的理论价值

本文主要考查目前关于心理机制模组性的三种方法,即福多的"经典模组性"、科拉索斯的"大规模模组性"以及西格尔的"适度模组性"观点。自福多提出输入系统是模组性、中央系统是非模组性的观点之后,该观点一直处于争议之中。通过分析可以发现,尽管当前对"经典模组性"的观点仍存在争议,但从最简原则出发,它目前仍是对心灵机制的最佳解释理论之一。     

再论中国古代的五星盈缩差算法

五星盈缩差算法是中国古代行星运动理论中的一个关键算法,五星地心真黄经和五星定合、定见、定伏时刻的推算都与这个算法密切相关.由于科学史家通常认为五星盈缩差就是行星中心差,从而在很大程度上影响了他们对中国传统行星理论的客观评价.本文在前人的研究基础上,重新构建了五星盈缩差算法的理论模型,指出五星盈缩差是为修正行星中心差而设计的,但它既不等同于行星中心差,也与太阳中心差无关.通过对《纪元历》盈缩差算法精度的考察,可以较好地解释中国古代行星计算精度.     

Quantum Nonlocality and the Challenge to Scientific Realism

In this essay I examine various aspects of the nearcentury-long debate concerning the conceptualfoundations of quantum mechanics and the problems ithas posed for physicists and philosophers fromEinstein to the present. Most crucial here is theissue of realism and the question whether quantumtheory is compatible with any kind of realist orcausal-explanatory account which goes beyond theempirical-predictive data. This was Einstein's chiefconcern in the famous series of exchanges with NielsBohr when he refused to accept the truth orcompleteness of a doctrine (orthodox QM) which ruledsuch questions to be strictly inadmissible. I discussthe later history of quantum-theoretical debate withparticular reference to the issue of nonlocality,i.e., the phenomenon of superluminal(faster-than-light) interaction betweenwidely-separated particles. Then I show how thestandard `Copenhagen' interpretation of QM hasinfluenced current anti-realist orontological-relativist approaches to philosophy ofscience. Indeed, there are clear signs that somephilosophers have retreated from a realist positionvery largely in response to just these problems. So itis important to ask exactly why – on what scientificor philosophical grounds – any preferred alternative(causal-realist) construal should have been ruled outas a matter of orthodox QM wisdom. Moreconstructively, my paper presents various arguments infavour of one such alternative, the `hidden-variables'theory developed since the early 1950s by David Bohmand consistently marginalised by proponents of theCopenhagen doctrine.