Earlier quoted context omitted.
> That's backwards. See Wikipedia entry for Rice theorem subsection proof by reduction from the halting problem. 1. Have intersting property solver (e.g. is input squared) 2. Convert solver to halting problem solver 3. Solver is undecidable So they are in some equatable/convertible.
Being able to turn an interesting property solver into a halting problem solver is not the same thing as being able to turn a halting property solver into an interesting problem solver.
You can solve it to some extent (e.g. does program terminate in X steps).