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.