If it is "undecidable" this means there is no counterexample to the Collatz conjecture, since any counterexample would disprove it. But the Collatz conjecture does exactly state that there are no counterexamples. Which means: If it is undecidable, it is true.
Which seems a bit paradoxical. If you can prove that the Collatz conjecture is undecidable, you would also prove that it has no counterexamples, and thus that it is true. Which would make it decidable -- contradiction. So this seems to prove that if the Collatz conjecture is undecidable, this fact is itself also undecidable.
That is the case for something like Goldbach's Conjecture, which says that every even number > 2 is the sum of two primes. If it's false, then there is a counterexample, and it is easy to prove whether or not a given number is a counterexample (just loop over all pairs of smaller primes).
But that is not the case for the Collatz Conjecture. A Collatz counterexample could be a number whose orbit loops back around. That would be a provable counterexample. Another kind of Collatz counterexample would be a number whose orbit never terminates or repeats, it just keeps going forever. If such an infinite sequence existed, it might not be possible to prove that it's infinite. And if it isn't provable, then the conjecture would both undecidable and false.
