  The diagonal method is often used to show that Turing machines cannot solve
their own halting problem. There have been several recent attempts to show that
this method also exposes either contradiction or arbitrariness in other
theoretical models of computation that claim to be able to solve the halting
problem for Turing machines. We show that such arguments are flawed -- a
contradiction only occurs if a type of machine can compute its own diagonal
function. We then demonstrate why such a situation does not occur for the
methods of hypercomputation under attack and why it is unlikely to occur in any
other serious methods.

Logic;Quantum Physics