The halting problem is uncomputable too, but any given Turing machine either halts or never halts (even if we don't have a general procedure for determining whi

The halting problem is uncomputable too, but any given Turing machine either halts or never halts (even if we don't have a general procedure for determining which). There is no third choice. Similarly, there is definitely a shortest program that outputs a certain string and then halts. We can't always make a program to find it, but that shortest program exists nonetheless. There is no other choice! If there is no shortest program to output it, how can there be any other program?