Turing analogues of Gödel statements and computability of intelligence
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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 Gödel, 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 Gödel 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 Gödel statement, or a Gödel string as we call it in the language of Turing machines, can be readily constructed directly, without appeal to the Gödel incompleteness theorem, and thus removing the final objection.
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