Imagine some philosopher answers a question of the form "What is X? ". Then a critic points out that, according to this answer, O is not X, but we clearly consider it to be X. It seems that the philosopher's reply can take one of two directions:

1. "Oh, you're right. My answer is wrong. Back to the desk with me!"
2. "No, you're wrong. My answer is right. It is simply an error to think that O is X."

I'm looking for a term (or terms) for this dichotomy of approaches. Answer 1 takes our commonsense idea of X for granted, while answer 2 challenges it to change. I, therefore, dabbled with words like "conservative" and "progressive", but it's awkward, and I can't imagine that no one before me coined a word for that. I would also be grateful for pointers towards literature discussing this dichotomy.

(A historical example might be parts of the Popper-Kuhn controversy. Popper answered the question "What is science?". Kuhn pointed out that, according to Popper, normal science is not science, but actually, we consider it to be science. Popper opted for answer 2, called normal scientists people "one ought to be sorry for", and stuck with his demarcation criterion. But many philosophers of science went "back to the desk" and tried to accommodate normal science.)