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TimS comments on Rationality Quotes March 2012 - Less Wrong
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The "non-expressible in the new concept-space" thing that you think never actually happens.
Isn't that exactly what happened? The phrase "set of all sets that do not contain themselves" isn't really expressible in Zermelo-Fraenkel set theory, since that has a more limited selection of ways to construct new sets and "the set of everything that satisfies property X" is not one of them.
I don't think it's terribly useful to frame the discussion in terms of concepts that never actually happen :-)
This looks very like trying to define away something that sure felt like a paradigm shift to the people in the field. Remember that "paradigm" is a belief held by people, not a property inherent in the universe.
Perhaps this is a limitation of my understanding of Kuhn, in that I'm misusing his terminology. I am unaware of mathematics abandoning fundamental objects as inherently misguided the way physics abandoned epicycles or impetus. I expect physics will have similar abandonments in the future, but I expect mathematics never will. The difference is a property of the difference between mathematics and empirical facts. This comment makes the argument I'm trying to assert in slightly different form.