The author’s take on the Turing Test is a common misconception - Turing did not propose that the machine fool a human into believing that it was human, but rather that the machine fool a man into believing that it was a woman.
The author’s reference to Gödel’s Incompleteness Theorem and Turing’s Halting Problem are also misguided: humans are in no way immune from such logical traps (“will your answer to this question be negative?“)