Ben,
Instead of thinking of a tall building with weakened foundation, think of a pyramid with a wide foundations that can support the peak because the foundation is spread out over a lot of shifting sands. Science, from which general semantics is abstracted, has such a large base going back many centuries and widely covering an incredibly large base of observations.

Another analogy is that of a very large cruise ship at sea. The ship occasionally rocks and sways, but it remains afloat, and you have "faith" in the builders that it won't sink. If we need to repair a hull fitting at sea, we build a cofferdam around it temporarily. Then we can cut the fitting out with the protection of the cofferdam, revise it, and re-install it before removing the cofferdam and putting it back in service. What is needed is a balance between doubt and faith. Sometimes it takes a while to get your "sea legs" so as to rock and roll with the changing tides, but once you have them, you can function just fine on a deck that is not rigidly stable.

My entire general semantics site is based, in part, on applying general semantics to itself. It raises questions, and they are not all answered satisfactorily. You have to develop your "see legs" (pun intended) and balance your uncertainty and doubt with faith in the process. See Doubt and Faith for a balancing perspective. (You can skip the mathematical notation section without loss of generality.) Note particularly the last sentence.