In my experience, that assumption isn't in principle "unprovable" - the parties to the disagreement usually don't realize they're making such assumption in the first place! Switching positions can make the existence of that assumption apparent to all, and if people involved are intellectually honest and discussing in good faith, it's pretty much impossible for their disagreement to remain as strong as it was before.

> Personally, I prefer having convictions and sticking to them.

Good point about competing interests and "reducing to something manageable". I prefer "strong opinions weakly held", but in practice, I embrace the natural inertia of beliefs. I.e. I don't consider me already believing something to be strong evidence the belief is true (i.e. "having convictions") - but the stronger a belief is, or more high-impact changing it would be (e.g. suddenly feeling a moral compulsion to upend my entire life), the more evidence and time I need to change my mind.

This may be also a dumber and less admirable strategy, but it's effectively a low-pass filter on evidence: it saves me from changing my mind every other day, and suffering the costs (including cognitive dissonance if I plain override my beliefs for sake of quality of life).

It is a rather offensive way to portray the world. All the questions, all the puzzles, all the mystery, everything has been answered and further investigation frowned upon. They would have to again defend their chosen "truth", they would have to question everything!