Natural and Formal Infinities

Concepts of infinity usually arise by reflecting on finite experiences and imagining them extended to the infinite. This paper will refer to such personal conception as natural infinities.Research has shown that individuals' natural conceptions of infinity are `labile and self-contradictory' (Fischbein et al.,1979, p. 31). The formal approach to mathematics in the twentieth century attempted to rationalize these inconsistencies by selecting a finite list of specific properties (or axioms) from which the conception of a formal infinity is built by formal deduction. By beginning with different properties of finite numbers, such as counting,ordering or arithmetic,different formal systems may be developed. Counting and ordering lead to cardinal and ordinal number theory and the properties of arithmetic lead to ordered fields that may contain infinite and infinitesimalquantities. Cardinal and ordinal numbers can be added and multiplied but not divided or subtracted. The operations of cardinals are commutative, but the operations of ordinals are not. Meanwhile an ordered field has a full system of arithmetic in which the reciprocals of infinite elements are infinitesimals. Thus, while natural concepts of infinity may contain built-in contradictions, there are several different kinds of formal infinity, each with its own coherent properties, yet each system having properties that differ from the others. The construction of both natural and formal infinities are products of human thought and so may be considered in terms of embodied cognition' (Lakoff and Nunez,2000). The viewpoint forwarded here, however, is that formal deduction focuses as far as possible on formal logic in preference to perceptual imagery, developing a network of formal properties that do not depend on specific embodiments. Indeed, I shall show that formal theory can lead to structure theorems, whose formal properties may then be re-interpreted as a more subtle form of embodied imagery. Not only can natural embodied theory inspire theorems to be proved formally, but formal theory can also feed back into human embodiment, now subtly enhanced by the underlying network of formal relationships. This revised version was published online in July 2006 with corrections to the Cover Date.     

形式合理性与宪政

宪法的形式合理性是宪法本身规范结构与宪政运行程序的合逻辑性、透明度、可操作性判断。形式合理的宪政是通过宪法规范的至上性、宪法适用机构的中立性、宪政运行的程序性与法律技术的规范性等机制来实现的。我国宪法及宪政建设存在形式合理性方面的缺憾,这制约着宪政的实现和发展。     

Formal and Informal Styles

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Formal verification

This is a short tutorial on formal methods which are techniques for specifying and verifying complex software and hardware systems. A few examples of successful industrial use of these are also presented.     

形式逻辑与素质教育

本文主要分析了形式逻辑在素质教育方面的基础性地位和工具性作用 ,指出形式逻辑教育是素质教育本身的重要内容。在江泽民总书记关于素质教育讲话发表三周年之际 ,谨写此文 ,以示纪念     

浅议形式语言学与功能语言学

当代语言学界存在着形式语言学与功能语言学分野的看法,国内学者对形式学派与功能学派也有诸多看法,大多数学者认为形式语言学研究语言形式,功能语言学研究语言的交际意义和语用功能。本文将从理论基础,研究对象,研究方法等方面来探讨形式语言学与功能语言学的区别以及今后的交流趋势。     

形式情绪——新诗的声情

从新诗否定形式要素的现象出发,在提出“声情”这一传统诗论概念的基础上,引入了＂形式情绪＂这一概念从心理学的角度入手分析形式情绪的自我赋形机制.     

形式情绪--新诗的声情

从新诗否定形式要素的现象出发,在提出"声情"这一传统诗论概念的基础上,引入了"形式情绪"这一概念从心理学的角度入手分析形式情绪的自我赋形机制.     

“然诺”辨

然诺,是上古文明积淀下来的一种理念。《史记》把然诺与义相提并论,以"仁"、"义"二字,提炼"然诺"观念以概括游侠特色,其意义在于提倡正直的侠义精神,弘扬天下为公、行仁重义的文化观念。     

形式思维与艺术创造

从根本上来说,艺术最终要归结于一种形式。艺术本来就是人类对客体对象抽象和简化的形式化结果,形式是艺术思维的一个范畴,思维靠形式得以规范和调节。形式化思维能力取决于艺术家的形式感知能力。在艺术创造中,艺术思维与艺术形式建构是统一在一起的,体现在一种一体化的动力过程之中。     

邵阳、临沂方言形式单位概念形式表征的对比研究

该研究以邵阳、临沂方言形式单位为研究对象,对比了两地方言形式单位概念的突显成分;接着,对邵阳、临沂方言形式单位结构式的数量进行了对比、分析,发现两地方言形式单位多见于偏正式,其次为动宾式;再者,该研究发现较临沂方言形式单位而言,邵阳方言形式单位中的直陈式更多,且于二者中,转喻式皆最多;最后,该研究总结出了三点邵阳、临沂方言形式单位概念形式表征的不同之处,并指出了造成上述差异的动因,有利于两地人认知模式和文化模式的研究与认识。     

Formal Analysis in Linguistics

Formalism,represented by the Chomskyan theory,has been dominating the development of linguistics and made great contributions to it since 1960s.In the past few decades,issues on formalism have been heatedly discussed.When it comes to the respect of meaning,quite a few embrace the idea that formalism makes no account of the correlation between the form and meaning.Hence,this paper,besides drawing a general picture for formalism from the angles of its theoretical principles and research subject,will address the correlations between the form and meaning as well from formalist’ s perspective.     

论艺术的形式美及形式美的创造

内容与形式作为一对哲学范畴,它普遍存在于一切事物之中。艺术作品应该是内容美与形式美的有机统一,形式美既受内容的制约和影响,同时又具有相对的独立性和能动作用,有其自身的规律。“黄金律”、“有意味的形式”等,都是形式美规律的体现。形式美的创造则应遵循变化统一与化繁为简的基本法则。     

一个形式公理体系及其应用

给出了一个很有趣味的形式公理体系:一个集合、一种关系、五条公理、若干定理,还找到了该体系的一个应用对象:n维欧氏空间中的邻域系.     

LEACH协议的形式化分析与仿真

基于形式化建模的思想,分别建立簇首节点和簇中成员节点的有限状态机模型,描述LEACH协议的路由行为及算法思想,分析影响LEACH协议性能的可能性因素,利用NS2对LEACH协议进行仿真,仿真结果表明,改进后的LEACH协议在节省了整个网络的能量消耗并很好的均衡了网络内节点的能耗,延长了节点的生存时间,改善了网络的性能.     

形式正义与实质正义间的冲突

法律实践中普遍存在着形式正义与实质正义之间的矛盾。无论是民法还是涉外民事关系法律适用法,法的确定性与灵活性之间的抉择是司法者难以避免的问题,具体体现为法律原则与法律规则之间的矛盾。形式正义在国际私法领域也称为冲突正义,它要求法官严格遵守法律规则办案。在一般情况下,维护形式正义就意味着实质正义的实现,因此,法律规则体系的稳定性、连续性不可随意破坏。然而,当绝对遵守法律规则将在特殊案件中导致实质不正义的结果时,法官应把握法的精神与主旨,合理发挥自由裁量权,灵活运用法律原则,维护实质正义。     

形式逻辑与思维训练

形式逻辑是对思维规则、格式的提炼和总结,并在思维训练方面起着不可替代的作用.形式逻辑对思维的训练是通过训练主体运用思维形式的能力来实现的.     

人的存在形态嬗变与师生关系

传统的认识论以知识为基础来构建师生关系,存在明显的不足。事实上,应以人的存在为师生关系的认识基础,以人的存在状态演变为路径,来考察师生关系从古代到近代、现代的演变过程。指出了现在的生存状态下的师生关系应该具有互动、民主、平等、对话的特点。