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Incompleteness for stably sound Turing machines

savelyev, Yasha (2020) Incompleteness for stably sound Turing machines. [Preprint]

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Abstract

We first partly develop a mathematical notion of stable soundness intended to reflect the actual soundness property of human beings.
Then we show that given an abstract query machine $M$ the following cannot hold simultaneously: $M$ is stably sound, $M$ is computable, $M$ can stably decide the truth of any arithmetic statement. This can be understood as an extension of the G\"odel incompleteness theorem to stably sound setting. This is a non-trivial extension as stably sound Turing machine can decide the halting problem. In practice such an $M$ could be meant to represent a weakly idealized human being so that the above gives an obstruction to computability of intelligence, and this gives a formal extension of a famous disjunction of G\"odel.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
savelyev, Yashayasha.savelyev@gmail.com
Keywords: Stable soundness, extensions of Godel incompleteness theorem, computability of intelligence
Subjects: General Issues > Computer Simulation
General Issues > Determinism/Indeterminism
Depositing User: Dr Yasha Savelyev
Date Deposited: 16 Aug 2020 02:10
Last Modified: 16 Aug 2020 02:10
Item ID: 17988
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/17988

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