There's that, too. (Well, we don't have to predict anything. We have to show that halting or not is a decidable condition, and we've shown it isn't. Even if we

There's that, too. (Well, we don't have to predict anything. We have to show that halting or not is a decidable condition, and we've shown it isn't. Even if we had shown it was decidable, there still might be programs where we practically can't figure out it halts. So is the beauty of math - it gives us the gestalt of the world without caring about the world :)