Though truth is not self-revealing (as Cartesians and Baconians thought), though certainty may be unattainable, the human situation with respect to knowledge is far from desperate. On the contrary, it is exhilarating: here we are, with the immensely difficult task before us of getting to know the beautiful world we live in, and ourselves; and fallible though we are we nevertheless find that our powers of understanding, surprisingly, are almost adequate for the task—more so than we ever dreamt in our wildest dreams. We really do learn from our mistakes, by trial and error. And at the same time we learn how little we know—as when, in climbing a mountain; every step upwards opens some new vista into the unknown, and new worlds unfold themselves of whose existence we knew nothing when we began our climb.
Thus we can learn, we can grow in knowledge, even if we can never know, that is, know for certain. Since we can learn, there is no reason for despair of reason; and since we can never know, there are no grounds here for smugness, or for conceit over the growth of our knowledge.
— Karl Popper, The Open Society and Its Enemies
“It's not logic that is powerful. Logic is actually a weak method because it depends on fragile chains of inference.”
— Alan Kay