The paradigm I'm currently looking at this is, generally, the accumulation of evidence over long periods. In the year 1800, not even Dalton had published his (wrong) results about the mass of oxygen; there was no particular evidence /to/ believe in the atomic theory.. In 1900, Einstein had yet to publish his work on Brownian motion; there was still a small but reasonable possibility that somebody would come up with a non-atomic theory that made better predictions. In 2000, atomic theory was so settled that few people even bothered calling it a 'theory' anymore. At any given point during those two centuries, a certain amount of evidence would have been collected relating to atomic theory, and it would have been reasonable to have different levels of confidence in it at different times. In the present-day, the possibility that atomic theory is false is about as small a probability as anyone is likely to encounter - so if I can work out ideas that cover probability estimates that small, then it's probably (ahem) safe to assume they'll be able to cover anything with greater probability.

Or maybe I'm wrong. In which case I don't know a better way to find out I /am/ wrong than to work through the same thing, and come across an unresolvable difficulty.