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塔斯基与《形式化语言中的真理概念》- 引言

已有 666 次阅读 2021-9-27 12:56 |个人分类:解读哥德尔不完全性定理|系统分类:科研笔记

《形式化语言中的真理概念》(The concept of truth in formalised langages)是波兰数学家、逻辑学家塔斯基(Alfred Tarski, 1902— 1983)于1933年发表的文章,旨在提出关于真理Truth)的语义学定义,对现代逻辑和许多当代语言哲学产生了重要影响。


一,《形式化语言中的真理概念》引言的译文


形式化语言中的真理概念 - 塔斯基


引言 


本文致力于解决一个问题真理的定义,其任务是针对一种给定的语言,为真语句 true sentence )这一术语建立一个实质充分且形式正确的定义。这个问题属于哲学的经典问题,具有相当大的困难,因为尽管真语句一词在口语中的含义似乎相当清晰易懂,但迄今为止,所有试图更精确地定义这一含义的努力都没有结果,许多使用这一术语并从明显的前提开始的研究往往导致了悖论和反例(然而,对于这些,已经找到了或多或少令人满意的解决方案)。在这方面,真理的概念与语义学领域的其他类似概念有着相同的命运。


只有当给出一个术语清单,通过该清单来构建所需的定义时,才能正确提出如何定义某个概念的问题。如果定义要完成其适当的任务,这个清单中的术语的意义就必须不容置疑。因此,问题自然而然地产生了:在构建真理的定义时,我们应该使用哪些术语?在这些研究的过程中,我不会忽略澄清这个问题。在这个构建过程中,如果之前我不能把任何语义学概念还原为其他概念,我就不会使用这些概念。


这里不打算对真理一词在日常生活中的含义进行彻底的分析,每个读者都或多或少地拥有对真理概念的直觉知识,他可以在知识理论的著作中找到对它的详细讨论。我只想说,在这工作中,我只关注把握所谓的经典真理概念(“true—与现实相对应)中所包含的意义,与例如功利主义概念(“true—在某方面有用)形成对比。


要定义的概念的外延在本质上取决于所考虑的特定语言。同样的表达在一种语言中是一个真实的陈述,在另一种语言中却是一个虚假的陈述,或者是一个无意义的表达。这里不存在给这个词下一个单一的一般性定义的问题,我们感兴趣的问题将被分割成一系列独立的问题,每个问题都与一种语言有关。


在第1章中,日常语言是我们调查的对象,结果是完全否定的。对于这种语言,不仅真理的定义似乎是不可能的,甚至连符合逻辑规律的这一概念的通常使用也不可能。


在进一步的讨论中,我将只考虑目前已知的科学构造语言,即演绎科学的形式化语言,它们的特点将在第二章的开头描述。我们会发现,从目前的问题来看,这些语言分为两组,划分的依据是某一语言中的语法形式的多寡。对于较贫乏的语言,真理的定义问题有一个积极的解决方案:在此情况下,有一个统一的方法来构建所需的定义。在第二章和第三章中,我将对一种具体的语言进行全面的构建,并以这种方式促进对上述方法的一般描述,这将在第四章中概述。然而,对于更丰富的语言而言,我们问题的解决将是消极的,这将从第5章的考虑中得到,对于这样的语言,我们永远无法为真理的概念构建一个正确的定义。然而,一切都表明,即使在这些情况下与日常生活中的语言相比也有可能通过将其视为一门特殊科学,即真理理论的原始概念,并通过公理化使其基本属性变得精确,从而引入这一概念的一致和正确使用。


对形式化语言的研究自然需要对现代形式逻辑的原理有所了解,对于真理定义的构建,某些纯数学概念和方法是必要的,尽管要求不高。如果这项工作能够使读者相信,这些方法甚至对于研究纯哲学问题来说是必要的工具,我将很高兴。


二,《形式化语言中的真理概念》引言的原文


The concept of truth in formalised langages


Introduction 


The present article is almost wholly devoted to a single problem - the definition of truth. Its task is to construct - with reference to a given language - a materially adequate and formally correct definition of the term « true sentence ». This problem, which belongs to the classical questions of philosophy, raises considerable difficulties. For although the meaning of the term ‘true sentence’ in colloquial language seems to be quite clear and intelligible, all attempts to define this meaning more precisely have hitherto been fruitless, and many investigations in which this term has used and which started with apparently evident premisses have often led to paradoxes and antinomies (for which, however, a more or less satisfactory solution has been found). The concept of truth share in this respect the fate of other analogous concepts in the domain of the semantics of langage.


The question how a certain concept is to be defined is correctly formulated only if a list is given of the terms by means of which the required definition is to be constructed. If the definition is to fulfil its proper task, the sense of the terms in this list must admit of no doubt. The question thus naturally arises : What terms are we to use in constructing the definition of truth ? In the course of these investigations I shall not neglect to clarify this question. In this construction I shall not make use of any semantical concept if I am not able previous to reduce it to other concepts.



A thorough analysis of the meaning current in everyday life of the term 'true' is not intended here. Every reader possesses in greater or less degree an intuitive knowledge of the concept of truth and he can find detailed discussions on it works on the theory of knowledge. I would only mention that throughout this work I shall be concerned excessively with grasping the intentions which are contained in the so-called classical conception of truth (‘true - corresponding with reality’) in contrast, for example, with the utilitarian conception (‘true - in a certain respect useful’. 


The extension of the concept to be defined depends in an essentiel way on the particular language under consideration. The same expression can, in one langage, be a true statement, in another a false one or a meaningless expression. There will be no question at all here of giving a single general definition of the term. The problem which interests us will be split into a series of separate problems each relating to a single langage.


In chapitre 1 colloquial langage is the object of our investigations. The results are entirely negative. With respect to this language not only does the definition of truth seem to be impossible, but even the constant use of this concept in conformity with the laws of logic.


In the further course of this discussion I shall consider exclusively the scientifically constructed langages known at the present day, i.e., the formalised languages of the deductive sciences. Their characteristically will ne described at the beginning of chapitre 2. It will be found that, from the standpoint of the present problem, these languages fall into two groupes, the division being based on the greater or less stock of grammatical forms in a particular langage. In connexion with the ‘poorer » languages the problem of the definition of truth has a positive solution : there is a uniform method for the construction of the required definition in the case of each of these languages. In chapitre 2 and 3 I shall carry out this construction for a concrete language in full and in this way facilitate the general description of the above method which is sketched in chatter 4. In connexion with the ‘richer’ languages, however, the solution of our problem will be negative, as will follow from the considerations of chapitre 5. For the languages of this groupe we shall never be able to construct a correct definition of the notion of truth. Nevertheless, everything point to the possibility even in these case - in contrast to he language of everyday life - of introducing a consistent and correct use of this concept by considering it as a primitive notion of a special science, namely of the theory of truth, and its fundamental properties are made precise through axiomatisation.


The investigation of formalised languages naturally demands a knowledge of the principes of modern formal logic. For the construction of the definition of truth certain purely mathematical concepts and methods are necessary, although in a modest degree. I should be happy if this work were to convince the reader that these methods already are necessary tools even for the investigation of purely philosophical problems.


参考文献:

http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf




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