Correcting mistakes is the same thing as problem solving.

In simple terms, the way to solve a problem is to come up with a solution. Or in other words, to learn what a solution would be. Or in other words, to create knowledge of a solution.

So some of these different things we've been talking about are closely connected.

By the way, the theory that all problems can be solved by knowledge is called *optimism*, and it's in David Deutsch's book The Beginning of Infinity.