Non-computability of human intelligence
This addresses a foundational problem in AI and philosophy of mind regarding the limits of computational models of human cognition, though it appears incremental as it builds on existing arguments like Lucas-Penrose.
The paper tackles the question of whether human intelligence can be fully modeled by a Turing machine, showing that under a weak soundness hypothesis, at least some meaningful thought processes are not Turing computable, with the result being that some physical processes are unexpectedly non-computable.
We revisit the question (most famously) initiated by Turing: can human intelligence be completely modeled by a Turing machine? We show that the answer is \emph{no}, assuming a certain weak soundness hypothesis. More specifically we show that at least some meaningful thought processes of the brain cannot be Turing computable. In particular some physical processes are not Turing computable, which is not entirely expected. There are some similarities of our argument with the well known Lucas-Penrose argument, but we work purely on the level of Turing machines, and do not use Gödel's incompleteness theorem or any direct analogue. Instead we construct directly and use a weak analogue of a Gödel statement for a certain system which involves our human, this allows us to side-step some (possible) meta-logical issues with their argument.