Title: Getting around the Halting Problem,
Abstract: The Halting Theorem establishes that there is no program (or Turing machine)
H that can decide in all cases if an arbitrary program n halts on input m. The
conjecture of this paper is that nevertheless there exists a sound program H
such that if it halts it answers either yes or no, and can also in a certain
sense identify all the cases it is unable to decide. The Halting Theorem can be
proved by constructing a counterexample, i.e. a program that attempts to assert
that it itself does not halt. The thesis is that there exists a program that
proves about itself that its own attempt to prove, that the counterexample does
not halt, does not halt. This outcome can be interpreted as it is NOT TRUE that
the counterexample does not halt as opposed to it is FALSE that the
counterexample does not halt. This becomes possible when the Recursion Theorem
is reinterpreted as mutual necessitation rather than equivalence.