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Turing analogues of G\"odel statements and computability of intelligence

savelyev, Yasha (2020) Turing analogues of 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. The most compelling original argument for existence of such an obstruction was proposed by Penrose, however G\"odel, Turing and Lucas have also proposed such arguments. We first partially reformulate the argument of Penrose. In this formulation we argue that his argument works up to possibility of construction of a certain G\"odel statement. We then completely re-frame the argument in the language of Turing machines, and by partially defining our subject just enough, we show that a certain analogue of a G\"odel statement, or a G\"odel string as we call it in the language of Turing machines, can be readily constructed directly, without appeal to the G\"odel incompleteness theorem, and thus removing the final objection.


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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: 14 Feb 2020 03:03
Last Modified: 14 Feb 2020 03:03
Item ID: 16904
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/16904

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