The non-algorithmic side of the mind
This addresses foundational questions in philosophy of mind and AI about the limits of computation in human cognition, but it is speculative and incremental in its theoretical approach.
The paper investigates the existence of a non-algorithmic aspect of the mind, proposing that metathought (thinking about ordinary thought) is Turing-non-computable and can be formalized using a quantum metalanguage, with ordinary thought having quantum and classical computational modes.
The existence of a non-algorithmic side of the mind, conjectured by Penrose on the basis of Gödel's first incompleteness theorem, is investigated here in terms of a quantum metalanguage. We suggest that, besides human ordinary thought, which can be formalized in a computable, logical language, there is another important kind of human thought, which is Turing-non-computable. This is methatought, the process of thinking about ordinary thought. Metathought can be formalized as a metalanguage, which speaks about and controls the logical language of ordinary thought. Ordinary thought has two computational modes, the quantum mode and the classical mode, the latter deriving from decoherence of the former. In order to control the logical language of the quantum mode, one needs to introduce a quantum metalanguage, which in turn requires a quantum version of Tarski Convention T.