What, if any, is the role of unprovable/undecidable statements in physics?

Speculation should not be confused with philosophy, IMO.

Whether speculation is a good thing or bad and whether there is too much speculation in today’s physics are sensible topics for discussion, of course. But that’s not the topic here.

Karl also posted this statement in another thread:

This thread is another stab at finding a way to support that statement. I find the statement unsupportable, even nonsensical. YMMV.