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Springer eBooks

Complementarity and Paraconsistency

Newton C. A. da Costa, Décio Krause

Published Mar 13, 2009• 13 citations
Publisher
DOI
10.1007/978-1-4020-2808-3_25

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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)(t,f,u)(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.
We present the new model of paraconsistent Turing machines and revise the models of quantum Turing machines and quantum circuits, stressing the concepts of entangled states and quantum parallelism which are important features for efficient quantum algorithms. We revise a quantum circuit that solves the so-called Deutsch’s problem, and then provide another solution to Deutsch’s problem by means of paraconsistent Turing machines. This raises some stimulating questions, and we close the paper by discussing some relationships between paraconsistent Turing machines and quantum Turing machines.