We discuss the modalities by which we humans should (and in fact, do) compute. That is, we investigate about the logical languages and the computational modes of human reasoning, and the corresponding physical interpretation. In this context, however, the classical world (physical, logical, and computational) does not seem sufficient to give a complete description of the Mind. In fact, the Mind accomplishes different tasks, where it exhibits, alternatively, both classical and quantum features. There are some novelties in two important issues: the long-standing debate on the mind-body relationship, and Turing’s question about a possible identification of the Mind with a computer. The introduction of a quantum metalanguage (QML) for the logic of reasoning is the most important feature to deal with both issues. As far as the first issue is considered, the QML is physically interpreted as a Dissipative Quantum Field Theory (DQFT) of the brain. The corresponding quantum object-language (QOL), which is the logic of reasoning, and is controlled by the QML, is physically interpreted as the Quantum Mechanics of qubits, that is, Quantum Computing (QC). Therefore, the Mind is both language and metalanguage, and the brain is its physical interpretation.We discuss the modalities by which we humans should (and in fact, do) compute. That is, we investigate about the logical languages and the computational modes of human reasoning, and the corresponding physical interpretation. In this context, however, the classical world (physical, logical, and computational) does not seem sufficient to give a complete description of the Mind. In fact, the Mind accomplishes different tasks, where it exhibits, alternatively, both classical and quantum features. There are some novelties in two important issues: the long-standing debate on the mind-body relationship, and Turing’s question about a possible identification of the Mind with a computer. The introduction of a quantum metalanguage (QML) for the logic of reasoning is the most important feature to deal with both issues. As far as the first issue is considered, the QML is physically interpreted as a Dissipative Quantum Field Theory (DQFT) of the brain. The corresponding quantum object-language (QOL), which is the logic of reasoning, and is controlled by the QML, is physically interpreted as the Quantum Mechanics of qubits, that is, Quantum Computing (QC). Therefore, the Mind is both language and metalanguage, and the brain is its physical interpretation.

Journal of consciousness exploration & researchMay 24, 20121 citation

The propositional language of quantum physics

Ernst-Walther Stachow

Jan 1, 19812 citations

ON THE NOTION OF PROPOSITION IN CLASSICAL AND QUANTUM MECHANICS

Claudio Garola, Sandro Sozzo

The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpretation of propositions problematical. The difficulty can be removed by adopting the objective interpretation of QM proposed by one of the authors (semantic realism, or SR, interpretation). In this case, a unified perspective can be adopted for QM and classical mechanics (CM), and a simple first order predicate calculus L(x) with Tarskian semantics can be constructed such that one can associate a physical proposition (i.e., a set of physical states) with every sentence of L(x). The set $P^{f}$ of all physical propositions is partially ordered and contains a subset $P^{f}_{T}$ of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, $P^{f}_{T}$ turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language $L_{TQ}(x)$ , and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpretation of propositions problematical. The difficulty can be removed by adopting the objective interpretation of QM proposed by one of the authors (semantic realism, or SR, interpretation). In this case, a unified perspective can be adopted for QM and classical mechanics (CM), and a simple first order predicate calculus L(x) with Tarskian semantics can be constructed such that one can associate a physical proposition (i.e., a set of physical states) with every sentence of L(x). The set $P^{f}$ of all physical propositions is partially ordered and contains a subset $P^{f}_{T}$ of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, $P^{f}_{T}$ turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language $L_{TQ}(x)$, and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.

arXiv:quant-ph/0603172Conference on the Foundations of Quantum Mechanics: Historical Analysis and Open QuestionsJun 1, 20061 citation

Interpretation of Quantum Physics

Alfred Landé

NatureMar 31, 19623 citations

“When language goes on holiday”

Patrizia Piredda

The new discoveries of QM led to re-assessing, broadening the meanings of many physical concepts, and formulating a new logic that was no longer based on the classical principles of non-contradiction, identity, and causality. Heisenberg considered the classical logic and the conception of language expressed in the Tractatus Logico-Philosophicus inadequate for the understanding of the problems of language with which the physicists of the Copenhagen school had had to deal in order to define the foundations of Quantum Mechanics. On the contrary, he saw in Wittgenstein’s posthumous Philosophical Investigations the key to solving those problems. One may formulate a proportion and state that the use of language described in the Tractatus fits the use of language in Classical Mechanics, as the use of language described in PI fits the use of language in QM. I interpret the reflections of the physicists of the Copenhagen school on the limits of language relative to QM by highlighting how the epistemological revolution of quantum physics shares a conception of language similar to that expressed by late Wittgenstein in PI. I also aim to explain why Heisenberg considered it inappropriate to subsume the propositions and concepts of QM under the rules of the propositional logic of Tractatus. I explain why the philosophy of language expounded in PI, which is based on language games and resemblance families, sheds a light on how and why QM has contributed to renewing existing concepts (such as space, trajectory, observer, etc.) and to formulate a new logic (quantum logic).The new discoveries of QM led to re-assessing, broadening the meanings of many physical concepts, and formulating a new logic that was no longer based on the classical principles of non-contradiction, identity, and causality. Heisenberg considered the classical logic and the conception of language expressed in the Tractatus Logico-Philosophicus inadequate for the understanding of the problems of language with which the physicists of the Copenhagen school had had to deal in order to define the foundations of Quantum Mechanics. On the contrary, he saw in Wittgenstein’s posthumous Philosophical Investigations the key to solving those problems. One may formulate a proportion and state that the use of language described in the Tractatus fits the use of language in Classical Mechanics, as the use of language described in PI fits the use of language in QM. I interpret the reflections of the physicists of the Copenhagen school on the limits of language relative to QM by highlighting how the epistemological revolution of quantum physics shares a conception of language similar to that expressed by late Wittgenstein in PI. I also aim to explain why Heisenberg considered it inappropriate to subsume the propositions and concepts of QM under the rules of the propositional logic of Tractatus. I explain why the philosophy of language expounded in PI, which is based on language games and resemblance families, sheds a light on how and why QM has contributed to renewing existing concepts (such as space, trajectory, observer, etc.) and to formulate a new logic (quantum logic).

PerspectivasApr 6, 20230 citations

Interpretation of Quantum Physics

T. E. Phipps

NatureSep 1, 19621 citation

P^{f}

of all physical propositions is partially ordered and contains a subset

P^{f}_{T}

of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular,

P^{f}_{T}

turns out to be a Boolean lattice in CM, while it can be identified with QL in QM. Hence the propositions of QL can be associated with sentences of L(x), or also with the sentences of a suitable quantum language

L_{TQ}(x)

, and the structure of QL characterizes the notion of testability in QM. One can then show that the notion of quantum truth does not conflict with the classical notion of truth within this perspective. Furthermore, the interpretation of QL propounded here proves to be equivalent to a previous pragmatic interpretation worked out by one of the authors, and can be embodied within a more general perspective which considers states as first order predicates of a broader language with a Kripkean semantics.