Your Body: Ground Wire for the Unverifiable
The problems with the unverifiable include self-delusion, chicanery, ignorance, blind spots and all that error-prone mental activity humans are so creative with. Look how delusional your consciousness is about its own self, its control of you! You can't just give up on checking yourself when you get into the 'unverifiable (yet)' range.
Understanding your biases, shoring up your information, staying curious, holding hypotheses lightly... this is essential. There is a famous book, 'Your Body Keeps the Score,' but there maybe should be another one: 'Your Body Keeps you Relatively Grounded.' Or, more to the point: your body is one of the tools for letting you go into the unverifiable range with a modicum of common sense.