无意义的虚假：古典阿拉伯语中任意符号的结构不可能性
The No-Meaning Falsity: The Structural Impossibility of the Arbitrary Sign in Classical Arabic
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中文总结 AI 辅助
本文通过构建阿拉伯语非拼接形态的形式数学模型，证明古典阿拉伯语的相对任意性可判定且小于1，与印欧语系存在系统复杂性不对称，探讨了索绪尔任意符号公理与古典阿拉伯语结构的相容性。
中文摘要 AI 辅助
本文研究后现代关于语义无限制不确定性的主张及其奠基性的索绪尔任意符号公理，是否与古典阿拉伯语的结构架构相容。我们构建了阿拉伯语非拼接形态的形式数学模型，其中词汇意义由不变词根与形态句法范式的相互作用决定。在该框架内，我们证明了形态对应定理，即每个词汇项都由词根-范式对唯一生成；还证明了语义定位定理，即词汇意义在表层实现之前的派生层面被确定。为处理索绪尔较弱的相对任意性概念，我们通过条件柯尔莫哥洛夫复杂度将其形式化，将任意性算法定义为无规则属性。我们证明一般相对任意性在形式上不可判定，而阿拉伯语的相对任意性可判定，且其有动因能指（W级和M级）的任意性可证小于1，确立了其与印欧语系语言间严格的系统复杂性不对称性。
英文摘要
This paper investigates whether the postmodern claim of unrestricted semantic indeterminacy, and its foundational Saussurean axiom of the arbitrary sign, are compatible with the structural architecture of Classical Arabic. We develop a formal mathematical model of Arabic non concatenative morphology in which lexical meaning is determined by the interaction between an invariant root and a morphosyntactic pattern. Within this framework, we establish a Morphological Correspondence Theorem, demonstrating that every lexical item is uniquely generated by a root pattern pair, and a Semantic Localization Theorem, proving that lexical meaning is determined at the derivational level prior to surface realization. To address Saussurean weaker notion of relative arbitrariness, we formalize it via conditional Kolmogorov complexity, defining arbitrariness algorithmically as the no rule property. We prove that general relative arbitrariness is formally undecidable, while Arabic relative arbitrariness is decidable and provably less than 1 for its motivated signifiers (Levels W and M), establishing a strict system complexity asymmetry over Indo-European languages.
