马克思如何理解关于上帝存在的本体论证明

在一切有神论的证明中,关于上帝存在的本体论证明是最不寻常的一个,并且该论证有着悠久的历史,马克思对于本体论证明的独特理解可以归结为三个命题:本体论证明是空洞的同义反复;康德对本体论证明的批判毫无意义,他所举的例子反而会加强本体论的证明;本体论证明不外是对人的自我意识存在的证明。马克思的这三个命题都可以得到经验事实和逻辑分析的双重支持。     

论民事诉讼当事人的证明权:以实定法基础为中心的考察

法治社会中,司法公信力在个案中的实现有赖于对当事人程序权的充分保障.在现代民事诉讼中,证明权是当事人程序权的核心,而证明权生成的实定法基础也只存在于近代之后的民事诉讼制度中.历经改革的中国民事诉讼制度与证明权相契合,既具备了证明权生成的实定法基础,也亟待证明权的有效配置以提升民事诉讼结果的正当性.     

论病历资料的法律价值

从法律价值角度,探讨病历资料具有的外在价值、内在价值及法治价值,病历资料作为证据法中的书证,能够证明客观事实的内在品质和其外在的证明作用、法治功能,在司法证明活动和处理医疗纠纷中发挥着重要作用,旨在提高人们对病历资料证据的认识,规范病历资料的书写、归档、保存和利用,促进司法证明和医疗服务质量的提高。     

从上帝存在的本体论证明看思维与存在的同一性问题

作为西方近代哲学核心问题的思维与存在的同一性问题,最初是由古希腊哲学家巴门尼德提出来的,后来在中世纪经院哲学的神学证明中得到进一步讨论和深化,最后在近代哲学中才被自觉地确立为哲学的基本问题。经院哲学对此问题的思考典型地表现在关于上帝存在的本体论证明及其所引起的争论中,这个证明在近代的笛卡尔哲学中再一次得到重申,并且遭到了康德的致命批判。后来,当黑格尔对这一证明以及康德的批判进行再批判时,才揭示出它所包含的思维与存在相同一的深刻内容。一、本体论证明的提出及其思想实质关于上帝存在的本体论证明最初是由安瑟尔…     

显示法证明分析

亚里土多德在建立三段论理论系统的过程中,明确提出了三种证明方法:化归法(换位法)、归谬法和显示法(王路)。其中,化归法和归谬法在三段论证明中的作用已世所公认,但是对显示法证明(proofsby exposition)的作用,长期以来人们一直认识不清,甚至有的逻辑学家认为,显示法证明对于亚里士多德的三段论理论系统没有什么重要性(Lukasiewicz,pp.66-67)。本文通过对亚里士多德模态三段论理论系统的分析,将使人们对显示法证明获得一个新的认识。     

模型论视角下对正规多元模态逻辑的阐述（英文）

本文对正规多元模态逻辑做了模型论视角的整体阐述。正规多元模态逻辑(PML)是对一元模态逻辑系统K,在n元算子上的推广。而多元模态逻辑的研究相对于一元逻辑较为匮乏。文献中的一系列有关PML的结果也被看作是有关K的结论的直接推广,而缺少部分完整证明,且已有证明多为代数证明。PML对于K的推广在某些方面是非平凡的,忽略这一点导致了一些教材及文章中甚至存在各种错误。从证明的角度上讲,对于PML的证明有时也需要不同的方法。基于以上几点考虑,我们认为有必要从模型论视角对PML做一个细致的考察,并给出一些模型论版本的证明,来简化以往的代数证明,从而给研究者提供一个统一的参考。本文从两个模态逻辑常用的模型构造方法(滤子和超滤扩张)出发,以经典教材中的定义为准,补全一些重要定理在多元语言下的模型论方法的详细证明。然后我们对van-Benthem刻画定理的多元版本证明做了一个澄清,考察了多元语言和一元语言下证明的具体区别。最后我们用模型论方法证明了PML具有插值性,而该定理在文献中往往是被当作一些代数事实的推论。     

塔斯基定理的一种推广

当把塔斯基对真概念提出的T-模式拓展到有向图上,塔斯基定理成立与否取决于归谬过程中使用的悖论及有向图的特征。本文证明了在使用说谎者悖论证明塔斯基定理时,在并且仅在有向图中含有奇循环时,说谎者悖论才会导致矛盾;在使用佐丹卡片悖论证明塔斯基定理时,在并且仅在有向图中含有高度不能被4整除的循环时,佐丹卡片悖论才会导致矛盾,这表明当T-模式拓展到有向图时,哥德尔关于"认识论悖论"应用于不完全性证明的思想能够被非平庸地类推于真之不可定义性的证明中。     

科学方法论与民族精神的升华

在中华民族对科学精神的艰辛追索中,对科学方法论的探求曾经是一个十分显著的现象。这是因为,在以儒学为核心的中国传统学术的数千年发展中,虽然具备了论辩、证理等证明方法,但均未能达到现代科学方法论的水平。古人在考察或证明一个理念或者观点时,往往是将现象与事实逐条罗列,进行简单类比的评     

我国海洋环境民事公益诉讼证明制度及其完善路径——证明责任分层与证明标准降格的契合

建设海洋强国和全球海洋中心城市的国家发展战略,要求具备涉海纠纷化解规则的立法支撑。海洋环境民事公益诉讼在立法中虽已确立,但是鉴于涉海侵权时空的特殊性,在涉海纠纷化解最为关键的证明环节,仍然存在证明责任和证明标准难以契合司法适用的难题。因此,有必要从立法适用、侵权性质和规则适用三个维度识别海洋环境民事公益诉讼的特殊性,以海洋环境侵权“二阶性”的时间逻辑来分层适用证明责任,并以层次化的证明责任分配主体来设定比例降格的证明标准,实现证明责任分层与证明标准降格的契合,以完善我国海洋环境民事公益诉讼的证明路径。     

浅议数学归纳法中的第一步

数学归纳法是初等数学中重要的数学方法,它是—种证明与正整数的关的命题的一种重要方法,是一种完全归纳法。大家者知道它的证明过程有二步,总结起来就是“递推基础不可少,归纳假设要用到,结论写明莫忘掉”（n=k＋1,及n∈N＋时）。在证明过程中老师过多的强调第二步中利用归纳假设证明是关键,给学生造成一种错觉,     

Bull's Theorem by the Method of Diagrams

We show how to use diagrams in order to obtain straightforward completeness theorems for extensions of K4.3 and a very simple and constructive proof of Bull's theorem: every normal extension of S4.3 has the finite model property.     

Response to Abrusán,Shaw, and Elbourne

In my book Category Mistakes (OUP 2013), I discuss a range of potential accounts of category mistakes and defend a pragmatic, presuppositional account of the phenomenon. Three commentators discuss the book: Márta Abrusán focuses on a comparison between my book and Asher’s Lexical Meaning in Context, suggesting that Asher’s theory has the advantage of accounting not only for category mistakes, but also for additional phenomena such as so-called ‘coertion’ and ‘co-predication’. I argue that Asher’s account of all three phenomena is deficient, and, moreover, that it is far from clear that the latter two phenomena are related to that of category mistakes. James Shaw challenges two of my arguments against the MBT view. I respond to these challenges. Paul Elbourne provides a novel argument in support of my account of category mistakes, involving multi-sentence discourses and ERP experiments. I show that it is not entirely straightforward for my account to explain this data, but that his argument does ultimately provide support for my view.     

On two problems of Harvey Friedman

The paper considers certain properties of intermediate and moda propositional logics.The first part contains a proof of the theorem stating that each intermediate logic is closed under the Kreisel-Putnam rule xyz/(xy)(xz).The second part includes a proof of the theorem ensuring existence of a greatest structurally complete intermediate logic having the disjunction property. This theorem confirms H. Friedman's conjecture 41 (cf. [2], problem 41).In the third part the reader will find a criterion which allows us to obtain sets satisfying the conditions of Friedman's problem 42, on the basis of intermediate logics satisfying the conditions of problem 41.Finally, the fourth part contains a proof of a criterion which allows us to obtain modal logics endowed with Hallden's property on the basis of structurally complete intermediate logics having the disjunction property.Dedicated to Professor Roman SuszkoThe author would like to thank professors J. Perzanowski and A. Wroski for valuable suggestions.     

Algorithmic logic. Multiple-valued extensions

Extended algorithmic logic (EAL) as introduced in [18] is a modified version of extended ⁺-valued algorithmic logic. Only two-valued predicates and two-valued propositional variables occur in EAL. The role of the ⁺-valued logic is restricted to construct control systems (stacks) of pushdown algorithms whereas their actions are described by means of the two-valued logic. Thus EAL formalizes a programming theory with recursive procedures but without the instruction CASE.The aim of this paper is to discuss EAL and prove the completeness theorem. A complete formalization of EAL was announced in [20] but no proof of the completeness theorem was given.     

What is Radical Behaviorism? A Review of Jay Moore's Conceptual Foundations of Radical Behaviorism

B. F. Skinner founded both radical behaviorism and behavior analysis. His founding innovations included: a versatile preparation for studying behavior; explicating the generic nature of stimulus and response; a pragmatic criterion for defining behavioral units; response rate as a datum; the concept of stimulus control; the concept of verbal behavior; and explicating the explanatory power of contingencies. Besides these achievements, however, Skinner also made some mistakes. Subsequent developments in radical behaviorist thought have attempted to remedy these mistakes. Moore's book presents a “party line” version of radical behaviorism. It focuses narrowly on a few of Skinner's concepts (mostly mentalism and verbal behavior) and contains no criticism of his mistakes. In fact, Moore adds a few mistakes of his own manufacture; for example, he insists that the mental realm does not exist—an unprovable and distracting assertion. The book's portrayal of behavior analysis would have been current around 1960; it mentions almost none of the developments since then. It also includes almost no developments in radical behaviorism since Skinner. Moore's book would give an unwary reader a highly distorted picture of contemporary behavior analysis and radical behaviorism.     

Mathematical Method and Proof

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect.     

Craig's interpolation theorem for the intuitionistic logic and its extensions—A semantical approach

A semantical proof of Craig's interpolation theorem for the intuitionistic predicate logic and some intermediate prepositional logics will be given. Our proof is an extension of Henkin's method developed in [4]. It will clarify the relation between the interpolation theorem and Robinson's consistency theorem for these logics and will enable us to give a uniform way of proving the interpolation theorem for them.The results in this paper were reported at Symposium on Mathematical Logic held at Shizuoka in December 1982.     

On the proof of Solovay's theorem

Solovay's 1976 completeness result for modal provability logic employs the recursion theorem in its proof. It is shown that the uses of the recursion theorem can in this proof be replaced by the diagonalization lemma for arithmetic and that, in effect, the proof neatly fits the framework of another, enriched, system of modal logic (the so-called Rosser logic of Gauspari-Solovay, 1979) so that any arithmetical system for which this logic is sound is strong enough to carry out the proof, in particular I₀+EXP. The method is adapted to obtain a similar completeness result for the Rosser logic.     

Human and Machine Interpretation of Expressions in Formal Systems

This paper uses a proof of Gödels theorem, implemented on a computer, to explore how a person or a computer can examine such a proof, understand it, and evaluate its validity. It is argued that, in order to recognize it (1) as Gödel's theorem, and (2) as a proof that there is an undecidable statement in the language of PM, a person must possess a suitable semantics. As our analysis reveals no differences between the processes required by people and machines to understand Gödel's theorem and manipulate it symbolically, an effective way to characterize this semantics is to model the human cognitive system as a Turing Machine with sensory inputs. La logistique n'est plus stérile: elle engendre la contradicion! – Henri Poincaré ‘Les mathematiques et la logique’     

Reconsidering Reid's Geometry of Visibles

In his Inquiry , Reid claims, against Berkeley, that there is a science of the perspectival shapes of objects ('visible figures'): they are geometrically equivalent to shapes projected onto the surfaces of spheres. This claim should be understood as asserting that for every theorem regarding visible figures there is a corresponding theorem regarding spherical projections; the proof of the theorem regarding spherical projections can be used to construct a proof of the theorem regarding visible figures, and vice versa. I reconstruct Reid's argument for this claim, and expose its mathematical underpinnings: it is successful, and depends on no empirical assumptions to which he was not entitled about the workings of the human eye. I also argue that, although Reid may or may not have been aware of it, the geometry of spherical projections is not the only geometry of visible figure.