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Universal G\"odel statements and computability of intelligence

savelyev, Yasha (2020) Universal G\"odel statements and computability of intelligence. [Preprint]

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Abstract

We show that there is a mathematical obstruction to complete Turing computability of intelligence. This obstruction can be circumvented only if human reasoning is fundamentally unsound, with the latter formally interpreted here as certain stable soundness. To this end, we first develop in a specific setting a certain analogue of a G\"odel statement, which has universality with respect to a certain class of Turing machines / formal systems. As a partial consequence of this universality, this G\"odel statement, or G\"odel string $\mathcal{G}$ as we call it in the language of Turing machines, does not require soundness but only stable soundness. Moreover, this $\mathcal{G}$ is constructed explicitly, given the general form of our class of Turing machines.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
savelyev, Yashayasha.savelyev@gmail.com
Keywords: computability of mind, consciousness, Lucas-Penrose argument
Subjects: General Issues > Computer Simulation
General Issues > Determinism/Indeterminism
Depositing User: Dr Yasha Savelyev
Date Deposited: 20 May 2020 23:45
Last Modified: 20 May 2020 23:45
Item ID: 17201
Official URL: http://yashamon.github.io/web2/papers/immitation.p...
Subjects: General Issues > Computer Simulation
General Issues > Determinism/Indeterminism
Date: 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17201

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