Semiotic Anarchy and Logical Fractures: The Collapse of Bivalence in Language and Reality

Abstract

This paper interrogates the boundaries of classical logic by examining violations of the Law of Excluded Middle (LEM) and the Principle of Bivalence (PB) across two seemingly disparate domains: semiotic sand formal systems. Drawing from Frege’s sense-reference distinction, Russell’s theory of descriptions, and Wittgenstein’s later pragmatism, we first deconstruct how natural language smuggles surplus meaning through implicature, metaphor, and performative utterances. We then demonstrate how quantum mechanics and mathematics dismantle LEM/PB by revealing ontic indeterminacy. The synthesis of these threads exposes a fundamental tension: while language thrives on ambiguity, classical logic demands binary precision. By bridging Gricean pragmatics with quantum logic, we argue that meaning and truth are emergent phenomena, requiring a pluralistic framework that accommodates gradient truth-values, contextual indeterminacy, and paradoxical utterances.