arXiv paper proves Classical Arabic's grammar rejects Saussure's arbitrary sign

A new arXiv preprint from researcher Elnaserledinellah Mahmoud Abdelwahab challenges a core tenet of postmodern linguistics: the Saussurean axiom that the sign is arbitrary. The paper, 'The No-Meaning Falsity: The Structural Impossibility of the Arbitrary Sign in Classical Arabic' (arXiv:2608.07737), develops a formal mathematical model of Arabic non-concatenative morphology. In this system, lexical meaning arises from the interaction between an invariant consonantal root and a morphosyntactic pattern. The author proves a Morphological Correspondence Theorem, showing every lexical item is uniquely generated by a root-pattern pair, and a Semantic Localization Theorem, proving meaning is fixed at the derivational level before surface realization.

To rigorously address Saussure's weaker notion of relative arbitrariness, the paper defines it algorithmically using conditional Kolmogorov complexity as a 'no-rule property.' The key result is a sharp asymmetry: general relative arbitrariness is formally undecidable, but Classical Arabic's relative arbitrariness is decidable and provably less than 1 for motivated signifiers (levels W and M). This establishes a structural complexity gap between Arabic and Indo-European languages, suggesting that claims of unrestricted semantic indeterminacy are incompatible with Arabic's architecture. While this is a domain-specific linguistic proof rather than an applied AI system, the methodology—using computational complexity to settle philosophical debates—resonates with current efforts in formal semantics and interpretable NLP.