Super-tasks, accelerating Turing machines and uncomputability

Accelerating Turing machines are abstract devices that have the same computational structure as Turing machines, but can perform super-tasks. I argue that performing super-tasks alone does not buy more computational power, and that accelerating Turing machines do not solve the halting problem. To show this, I analyze the reasoning that leads to Thomson's paradox, point out that the paradox rests on a conflation of different perspectives of accelerating processes, and conclude that the same conflation underlies the claim that accelerating Turing machines can solve the halting problem.