Abstract

In his 1933 monograph on the concept of truth, Alfred Tarski claimed that his definition of truth satisfied “the usual conditions of methodological correctness”, which in a 1935 article he identified as consistency and back-translatability. Following the rules of defining for an axiomatized theory was supposed to ensure satisfaction of the two conditions. But Tarski neither explained the two conditions nor supplied rules of defining for any axiomatized theory. We can make explicit what Tarski understood by consistency and back-translatability, with the help of (1) an account by Ajdukiewicz (1936) of the criteria underlying the practice of articulating rules of defining for axiomatized theories and (2) a critique by Frege (1903) of definitions that conjure an object into existence as that which satisfies a specified condition without first proving that exactly one object does so. I show that satisfaction of the conditions of consistency and back-translatability as thus explained is guaranteed by the rules of defining articulated by Leśniewski (1931) for an axiomatized system of propositional logic. I then construct analogous rules of defining for the theory within which Tarski developed his definition of truth. Tarski’s 32 definitions in this theory occasionally violate these rules, but the violations are easily repaired. I argue that the Leśniewski-Ajdukiewicz theory of formal correctness of definitions within which Tarski worked is superior in some respects to the widely accepted analogous theory articulated by Suppes (1957).

中文翻译：

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塔斯基的定义形式正确性理论

摘要

阿尔弗雷德·塔斯基 (Alfred Tarski) 在其 1933 年关于真理概念的专着中声称，他对真理的定义满足“方法论正确性的通常条件”，他在 1935 年的一篇文章中将其定义为一致性和可回译性。遵循公理化理论的定义规则应该可以确保满足这两个条件。但塔斯基既没有解释这两个条件，也没有提供任何公理化理论的定义规则。我们可以借助（1）Ajdukiewicz（1936）对公理化理论定义规则的实践所依据的标准的说明和（2）弗雷格的批评，明确塔斯基对一致性和可逆翻译性的理解。 （1903）的定义将一个对象想象为满足特定条件的对象，而无需首先证明恰好有一个对象这样做。我证明，如此解释的一致性和可逆可译性条件的满足是由 Leśniewski（1931）为命题逻辑公理化系统阐明的定义规则所保证的。然后，我为塔斯基发展其真理定义的理论构建了类似的定义规则。塔斯基在该理论中的 32 个定义偶尔会违反这些规则，但这种违反很容易修复。我认为塔斯基所运用的 Leśniewski-Ajdukiewicz 定义的形式正确性理论在某些方面优于 Suppes (1957) 阐述的广泛接受的类似理论。