The modal argument for hypercomputing minds (Q1434374)

Stripped of its trappings, the authors' argument boils down to the following three statements. (1)~We know that it is mathematically/logically impossible for any Turing machine to solve the halting problem of a specified universal TM. (2)~On the other hand, since we can imagine a person performing infinitely many steps of an algorithm in a finite amount of time, it is therefore mathematically/logically (if not necessarily physically) possible for a person to solve that halting problem. (3)~By the two previous statements, people's computational ability exceeds that of TMs. It is certainly possible for a person to find this argument less than convincing.