A Contextual Seven-Valued Logic (\emph{Saptabhangīnaya}) for Quantum Systems

TL;DR

The paper reframes the quantum measurement problem as a context-sensitive issue by proposing a seven-valued paraconsistent logic anchored in the Jaina saptabhaṅgīnaya and inspired by Wittgenstein and Bohr. It offers two complementary formulations: a triplet-valued semantics with explicit context indexing, and a quantificational context logic that encodes experimental arrangements directly in the syntax. Through worked examples (e.g., Double-Slit, incompatible spin bases) and canonical paradoxes (Schrödinger’s Cat, Wigner’s Friend), it shows that context-explicit semantics dissolve cross-context contradictions while preserving descriptive power. The proposed framework yields a flexible semantics for quantum discourse that aligns with Bohr’s complementarity and Wittgensteinian ideas about language use, with potential applicability beyond quantum theory. The combination of algebraic paraconsistency and context-syntactic formulations provides a robust toolkit for context-dependent truth in complex scientific domains.

Abstract

The quantum measurement problem is often presented as a conflict between unitary evolution and non-unitary collapse. Drawing on Wittgenstein's later philosophy of language and Bohr's principle of complementarity, we argue that this conflict is a grammatical illusion arising from cross-context conflations. To address this, we introduce a contextual seven-valued logic modeled on the Jaina doctrine of \emph{saptabhangīnaya} (sevenfold predication). In one formulation, each proposition is assigned a triplet $(t,f,u)$ indicating its status as true, false, or unsayable within a given context, with paraconsistent rules blocking triviality. In another, contexts are explicitly formalized through quantified conditionals, aligning directly with Bohr's view that meaning derives from experimental arrangements. By comparing these two complementary approaches, we show how canonical paradoxes--including Schrödinger's cat and Wigner's friend--dissolve once context is made explicit. The result is a flexible logical framework that reconciles Wittgensteinian conceptual therapy, Bohr's complementarity, and the Jaina pluralistic tradition, offering a coherent semantics for quantum discourse.