Karl Popper maintained that empirical sciences should be based on the principle of falsifiability rather than verifiability for no amount of observations can guarantee veracity but a single contradicting observation is enough to falsify.

This emphasis promotes empiricism and fits well empirical sciences.

Assumptions are simply axioms with a different name. They carry a metaphysical burden. They are our building blocks, our groundwork, our operating cost. They are a necessary evil. So we should do well and at least pick acceptable assumptions. Falsifiability seems to be a good starting point (Necessary? Sufficient?)

The question now:

How falsifiable are assumptions based on probability or any other limit when x tends to infinity; how can one make infinite observations? How valuable, acceptable and warranted are non-falsifiable assumptions?

Example Statistical Models in Physics (Medical or Not).

How acceptable and warranted is the assumption of linearity in linear no-threshold model? How could such an assumption be empirically falsified? What would the observation be?