Unlike in maths, the concept of "proof" in a the context of something like geology isn't a clear cut concept, as Popper wrote:
"In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by 'proof' an argument which establishes once and for ever the truth of a theory,"
Which is a convenient argument to make, because it can be applied to the argument itself. But by extension, all we know would be that we don't know anything. Which is a good starting point, but not really satisfactory. The word em-piri-cal is related to ex-peri-ance and ex-peri-ment, so ... the idea is what isn't broken doesn't need fixing. And by a stretch, imperial is related, though the latter is from latin whereas the former is from greek; Both go back to "* per", which still exists on its own and in "perform", e.g. ... so I guess the idea is proof by construction. A program is isomorphic to a proof, according to the Curry Howard Correspondence, this is well known around here.
As a student of Physics and CompSci I had to defend the "pure math" perspective. Anyway, the circular reasoning of the quote is just the way the mind works. Still, the certainty can be quantified with Bayesian reasoning, but there has to be a threshold of what's transmitted.
"In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by 'proof' an argument which establishes once and for ever the truth of a theory,"