证明古典阿拉伯语的词形变化结构排斥任意符号，意义由根与模式唯一确定。
The No-Meaning Falsity: The Structural Impossibility of the Arbitrary Sign in Classical Arabic
- 构建阿拉伯语非连写构词的数学模型，根与模式共同决定词义。
- 证明词义在派生阶段即已确定，且阿拉伯语相对任意性可判定且低于1。
- 揭示阿拉伯语符号系统比印欧语言更少任意性，适合语言学与认知研究者。
本文探讨后现代主张的语义无限不确定性及其索绪尔关于符号任意性的基础公设，是否与古典阿拉伯语的结构架构相容。我们建立了一个阿拉伯语非连写构词形式数学模型，其中词汇意义由不变的词根与形态句法模式的交互决定。在此框架下，提出形态对应定理，证明每个词汇项均由唯一的根-模式对生成；提出语义定位定理，证明词汇意义在表层实现前即已在派生层面确定。为处理索绪尔较弱的相对任意性概念，通过条件柯尔莫哥洛夫复杂度形式化定义，将任意性算法化为无规则性质。证明普遍相对任意性在逻辑上不可判定，而阿拉伯语的相对任意性可判定，且其有动机的符号项（层级W和M）严格小于1，揭示阿拉伯语与印欧语言之间存在显著系统复杂性不对称。
原文摘要 · Abstract (English)
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.
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