The No-Meaning Falsity: The Structural Impossibility of the Arbitrary Sign in Classical Arabic

arXiv cs.CL Papers

Summary

This paper mathematically models Classical Arabic morphology to argue against Saussurean arbitrary sign and postmodern semantic indeterminacy, proving that Arabic lexical meaning is structurally determined via root-pattern pairs and showing a complexity asymmetry over Indo-European languages.

arXiv:2608.07737v1 Announce Type: new Abstract: 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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# The No-Meaning Falsity: The Structural Impossibility of the Arbitrary Sign in Classical Arabic
Source: [https://arxiv.org/abs/2608.07737](https://arxiv.org/abs/2608.07737)
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> Abstract: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\.

## Submission history

From: Elnaser Abdelwahab \[[view email](https://arxiv.org/show-email/d5c0192c/2608.07737)\] **\[v1\]**Fri, 7 Aug 2026 20:01:20 UTC \(38 KB\)

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