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<p>This paper examines Carnap’s concept of semantic analyticity, as presented in <i>Logical Foundations of Probability</i>, and extends it to Languages I and II in <i>Logical Syntax of Language</i>. The primary objective is to assess whether the semantic and syntactic explications of analyticity are equivalent for these two languages. The results demonstrate that, for the contracted version of Language I—obtained by removing functors—the semantic and syntactic explicata are indeed equivalent. However, for the contracted version of Language II, which is derived by removing functor-expressions, the two explicata diverge and lack logical equivalence. Notably, for the first-order fragment of the extracted II, which excludes unlimited quantifiers, a formula that is semantically analytic in II is also syntactically analytic in II, though the reverse does not necessarily hold. Furthermore, all theorems in II that are syntactically analytic are also semantically analytic in II.</p>

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On Carnap’s Syntactic and Semantic Explications of Analyticity

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Weijun Shi

摘要

This paper examines Carnap’s concept of semantic analyticity, as presented in Logical Foundations of Probability, and extends it to Languages I and II in Logical Syntax of Language. The primary objective is to assess whether the semantic and syntactic explications of analyticity are equivalent for these two languages. The results demonstrate that, for the contracted version of Language I—obtained by removing functors—the semantic and syntactic explicata are indeed equivalent. However, for the contracted version of Language II, which is derived by removing functor-expressions, the two explicata diverge and lack logical equivalence. Notably, for the first-order fragment of the extracted II, which excludes unlimited quantifiers, a formula that is semantically analytic in II is also syntactically analytic in II, though the reverse does not necessarily hold. Furthermore, all theorems in II that are syntactically analytic are also semantically analytic in II.