I would remark that truth is conserved, but profundity isn't. If you have two meaningful statements - that is, two statements with truth conditions, so that reality can be either like or unlike the statement - and they are opposites, then at most one of them can be true. On the other hand, things that invoke deep-sounding words can often be negated, and sound equally profound at the end of it.

In other words, Bohr's maxim seems so blatantly awful that I am mostly minded to chalk it up as another case of, "I wish famous quantum physicists knew even a little bit about epistemology-with-math".