The Löwenheim-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 Löwenheim-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.

中文翻译：

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蒯因对逻辑真理的替代定义和洛文海姆-希尔伯特-伯奈斯定理的哲学意义

Löwenheim-Hilbert-Bernays 定理指出，对于算术一阶语言 L，如果 S 是可满足模式，那么用 L 的开句替换 S 的谓词字母会导致 L 的真句。有两个原因，这个定理与奎因对逻辑真理的替代定义有关的问题有关。首先，它使蒯因有可能回应对他的解释提出的广泛反对（词汇依赖问题和基数依赖问题）。这些反对意见旨在表明奎因的叙述过度生成：它会被视为逻辑上真实的句子，而直觉上或模型理论上并非如此。其次，由于这个定理是奎因证明他的替代解释和模型理论之间的等价性的关键前提，它使他能够证明，从元数学的角度来看，就替代而言，没有必要支持模型理论的解释。因此，这篇文章的目的是探讨 Löwenheim-Hilbert-Bernays 定理对奎因对逻辑真理的定义的哲学意义。奎因支持替代定义的论证中这一被忽视的方面被证明是与逻辑中的模型理论偏见斗争的一部分。这种探索导致重新评估蒯因在逻辑史上的特殊地位。奎因支持替代定义的论证中这一被忽视的方面被证明是与逻辑中的模型理论偏见斗争的一部分。这种探索导致重新评估蒯因在逻辑史上的特殊地位。奎因支持替代定义的论证中被忽视的这一方面被证明是与逻辑中的模型理论偏见斗争的一部分。这种探索导致重新评估蒯因在逻辑史上的特殊地位。