William R. Buckley wrote:
Turing showed that if it can be computed, it is
computable
on a TM. There is no machine existing, no machine which may
exist, that can compute a computation which is not also
computable on a TM.
I probably was supposed to have learned in my classes, but apparently
have forgotten: what is the definition of "a computation". I'm hoping
that there is a better (more formal) definition than "that which can be
computed on a Turing Machine". Otherwise, the proof that everything that
is computable is computable on a Turing machine is trivial.