Something about decidable

Decidable implies that the problem can be given a precise answer for each instance of this problem. To reach a precise answer for an instance of the problem a known and proven method is required. Close or probably is not a decidable answer.

If you can prove that there exit some instances of the problem that cannot reach a conclusive and precise answer the problem is not decidable.

Knowledge and learning, in my opinion, has a lot to do with problems that need a good enough answer.

Say you just want to know if there is a high risk of infinite loops the halting-problem comes in another light. It is always not decidable though.

Learning means open for added experience in some sort. So there should often be room for more experience that hopefully leads to more exact judgments/answers. More experience can come with a 'training-cost'. By knowing how precise answer is needed this cost can be smaller.