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Ignorance is bliss in the pedestrian world of everyday academic research:

Over a restaurant dinner (Harris tells us), three professional mathematicians resurrected an issue from the great "crisis of foundations" that racked mathematics in the early 20th century — during roughly the period from Russell’s paradox (1901) to Gödel's theorem (1931). This "crisis of foundations" arose because mathematicians had begun inquiring into the logical and philosophical underpinnings of their subject, trying to find the fundamental axioms underlying all of math, trying to find unshakably firm foundations for the process of mathematical proof, asking questions like: "What is a number, really?"

Well, the three diners all expressed different opinions on the issue in question, which is a very crucial one. ("The ontological status of the continuum" — but you don't need to know this to understand my point.) Harris sought to pursue the discussion down into deeper matters…but found that his colleagues did not have the necessary knowledge, and didn't actually care. These foundational issues, though interesting in their own right, and fine for a few casual conversational exchanges over the dinner-table, do not really matter in the day-to-day work of most mathematicians.

My point is that a field of knowledge can endure a "crisis of foundations," in which the most fundamental issues are opened up for inquiry and deconstruction, without causing any permanent harm to the field. Harris's restaurant colleagues were working mathematicians — number theorists, actually — who knew about the "crisis of foundations" and found it mildly, historically, interesting, yet went on with their daily work as if it had never happened.

-- John Derbyshire