As we know, there are known knowns;
there are things we know we know.
We also know there are known unknowns;
that is to say we know there are some things we do not know.
But there are also unknown unknowns –
the ones we don't know we don't know.–United States Secretary of Defense Donald H. Rumsfeld at a Department of Defense news briefing on February 12, 2002
Ei mihi, qui nescio saltem quid nesciam!
(Alas for me, that I do not at least know the extent of my own ignorance!)–Aurelius Augustinus, 354–430, “Confessiones” (Book XI, chapter 25)
Rise and Fall of Determinism
In what follows, a variety of physical unknowables will be discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems that are known to be recursively unsolvable. “Chaotic” symbolic dynamical systems are unstable with respect to variations of initial states. Quantum unknowables include the random occurrence of single events, complementarity, and value indefiniteness.
From antiquity onward, various waves of (in)determinism have influenced human thought. Regardless of whether they were shaped by some Zeitgeist, or whether, as Goethe's Faust puts it, “what you the Spirit of the Ages call, is nothing but the spirit of you all, wherein the Ages are reflected,” their proponents have sometimes vigorously defended their stance in irrational, unscientific, and ideologic ways.