Universal Gödel statements and computability of intelligence

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. 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 review the main issues with the Penrose argument, as well as outline a partial direct fix. We then completely re-frame the argument in the language of Turing machines, and by 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. This G\"odel string satisfies a certain universality, and as a partial consequence it works in the context of stable soundness and not just soundness, and thus we eliminate the final objections.