Speaking of Duncan, his unintentional slanders of Feynman prompted a search in the library catalog for Character of Physical Law. No luck, but Six Easy Pieces was available. It was instructive about Feynman's alleged notions how "everything" we know may be wrong.
Science according to Feynman like watching a chess game without knowing the rules. Learning the rules is to understand the game. Learning the rules by merely watching of course is the tricky part. Applying the metaphor to nature, the rules are laws. When we know the laws, we understand. Science is not just deductions from the laws, because we don't know them, and because the mathematical deduction from the laws is beyond our mathematics. The principle of science, "definition almost, the test of all knowledge is experiment." Mathemantics, which has no experiments is therefore not natural science. The scientific method to find the rules, the laws, are "observation, reason and experiment..."
In other words, Feyman believes firmly in the intelligibility of nature, that it has rules, laws. So why does he talk about the impossibility of understanding quantum mechanics, for instance?
One reason is that he sneers at consistency. This makes him hard to understand.
For another, he has the magician's love of befuddling his audience. When at Los Alamos during the Manhattan Project, he loved to break into safes. In his memoirs, he reveals that cleverly deducing combinations in the same way modern hackers deduce passwords were a major technique. He enjoyed impressing teachers in competitive questioning in seminars by secretly reading up on the material, although the unwritten code was that the students were supposed to use native intellect. This concern for effect made him an entertaining lecturer. But there's a reason he was not a particularly successful teacher of graduate students.
And a third reason, of course, is that he, as a mathematical whiz (not into proofs, but then, not even all mathematicians are into proofs!) he relied upon his mathematical intuition. A man who humiliated himself into a 4F for mental instability during WWII by talking about how his mental pictures of the integers is not someone who is fastidiously empirical, despite all his talk about experiment.
And last is that much of his metaphysical certitudes are left to the non-science, mathematics. Which according to P.C.W. Davies' introduction, Feyman held to be Platonic metaphysical entities, except that he wouldn't quite, though almost, openly confess to. Davies observes that Feynman was "suspicious of philosophies..." Well, being suspicious is not the same as not having one. Davies' conclusion that "it was formalism he disliked, not content," is surely true.
In other words, Feynman's metaphysical certainties lay in mathematics. When he talked about not being able to understand, he meant physical, commonsense intuitions. When he talked about everything we know being wrong, he did not mean that the notion of natural law was a nonconcept, he meant something like Einstein revising Newton's view of the world might happen again. This has nothing to do with denying the intelligibility of the universe.
It is not really a secret that Feynman did not mean the universe was lawless. QED certainly attempted to lay bare quantum mechanics in the simplest possible terms. Thus is was possible for Paul Quincey, in a Skeptical Inquirer article a couple of years ago (one of the things that gave me the idea of blogging, which time delay shows how important I consider this blog!) to write an article popularizing QED even further, except as a cure for the notion of quantum weirdness!
Quincey does so by the metaphor of Nature using a surveyor's wheel to measure the action of all possible paths. "The" path is the path of minimum action. When the particles are large compared to the surveyor's wheel (which measures increments in Planck's constant,) the path is a classical trajectory. In other cases, the inability of the surveyor's wheel to distinguish multiple of Planck's constant, plus the circularity of the wheel itself, gives the (identical) mathematics of waves. If you add the concept of "spin," properly isospin, then quantum mechanics gives us chemistry via the Pauli principle.
Thus, according to Quincey, the alleged difficulties of QM come to three. First, QM gives probabilities, while the world is discrete fact. A set of coexisting probabilities is dubbed the future. How the future comes to be one particular thing instead of a mixture is not properly the realm of QM. (This seems to covertly borrow the unspeakability of the notion of the reduction of the wave function from Bohr et al. without confessing to it, to be frank.) Second, the interconnectedness of all phenomena seems to violate special relativity except that it doesn't: There is no information that can be sent superluminally. Third, there is no such thing as a determinable trajectory. This is not a problem since QM sets limits on what can be known. If the trajectory cannot be known, it can't be known, therefore failure to know it is not a failure at all. It is merely an unreasonable expectation. (This too seems to hark back to Bohr and his postivist notions of physics as correlates of experimental measurements, which are unquestionable facts, aka epistemic certainties.)
As to point one, since the equations of QM are time reversible, the inability to predict the future means the inability to retrodict the past as well. The second point, the interconnectedness of events, calls therefore into question the ability of QM to describe a unique spacetime. Which seems to me to be the fundamental problem in reconciling QM and general relativity, which can only be time reversible by adding a cosmological constant. Which I suspect is still Einstein's greatest blunder, even if it has become fashionable as a way to say QM as a description of the real universe. The third point about the inability to determine trajectories of course flows from the previous. The real question is what it says about the reality of the particles. If they have no trajectory, what does it mean to say they are real?
Quantum weirdness exists. Feynman used mathematical intuition to navigate in the topsy turvy world of QM. Our view of nature is likely to be as drastically revised as Newton's was by Einstein. How any of this suggests that Nature is inconsistent is a mystery.