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首页> 外文期刊>History and philosophy of logic >Quine's Substitutional Definition of Logical Truth and the Philosophical Significance of the Lowenheim-Hilbert-Bernays Theorem
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Quine's Substitutional Definition of Logical Truth and the Philosophical Significance of the Lowenheim-Hilbert-Bernays Theorem

机译：奎因的逻辑真理的替代定义以及洛伯伯特 - 伯纳德定理的逻辑事实的哲学意义

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The Lowenheim-Hilbert-Bernays theorem states that, for an arithmetical first-order language L, if S is a satisfiable schema, then substitution of open sentences of L for the predicate letters of S results in true sentences of L. For two reasons, this theorem is relevant to issues relative to Quine's substitutional definition of logical truth. First, it makes it possible for Quine to reply to widespread objections raised against his account (the lexicon-dependence problem and the cardinality-dependence problem). These objections purport to show that Quine's account overgenerates: it would count as logically true sentences which intuitively or model-theoretically are not so. Second, since this theorem is a crucial premise in Quine's proof of the equivalence between his substitutional account and the model-theoretic one, it enables him to show that, from a metamathematical point of view, there is no need to favour the model-theoretic account over one in terms of substitutions. The purpose of that essay is thus to explore the philosophical bearings of the Lowenheim-Hilbert-Bernays theorem on Quine's definition of logical truth. This neglected aspect of Quine's argumentation in favour of a substitutional definition is shown to be part of a struggle against the model-theoretic prejudice in logic. Such an exploration leads to reassess Quine's peculiar position in the history of logic.
机译：洛伯姆-Hilbert-伯尔尼定理指出，对于算术的一阶语言L，如果s是一个满足的架构，则替换L的谓词字母是L的真正句子的谓词的真实句子。本定理与相对于奎文的逻辑真理定义的问题有关。首先，它使奎因能够回复对他的账户提出的广泛反对意见（词典依赖性问题和基数依赖问题）。这些反对意见旨在表明Quine的账户超然：它将算作直观或模型的逻辑上真实的句子，理论上不是这样的。其次，由于这个定理是奎因在他的替代账户和模型 - 理论上的等价之间的重要前提，它使他能够表明，从元素的角度来看，没有必要支持模型 - 理论在替换方面占1。因此，这篇文章的目的是探讨奎恩对逻辑真理的定义的洛根海姆-Hilbert-伯纳斯定理的哲学轴承。这种忽视的尊重方面，有利于替代定义，被证明是对逻辑模型 - 理论偏见的斗争的一部分。这样的探索导致魔法在逻辑历史中的特殊位置。

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