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塔斯基与《形式化语言中的真理概念》- 引言

已有 1419 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。


形式化语言中的真理概念 - 塔斯基


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。








The concept of truth in formalised langages


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.





2 杨正瓴 邹晓辉

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