savelyev, Yasha (2020) Incompleteness for stably sound Turing machines. [Preprint]
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Text (The previous manuscript is to be split into parts, with this part focusing on mathematically developing stable soundness.)
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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 | ||||||
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| Keywords: | Stable soundness, extensions of Godel incompleteness theorem, computability of intelligence | ||||||
| Subjects: | General Issues > Computer Simulation General Issues > Determinism/Indeterminism |
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| 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 |
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| Date: | 2020 | ||||||
| URI: | http://philsci-archive.pitt.edu/id/eprint/17988 |
Available Versions of this Item
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Universal G\"odel statements and computability of intelligence. (deposited 20 May 2020 23:45)
- Incompleteness for stably sound Turing machines. (deposited 16 Aug 2020 02:10) [Currently Displayed]
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