It's kinda a pet peeve of mine as well, having to switch between 'proof' meaning a conclusion that logically necessarily follow from premises, to proof meaning "really strong evidence".
But, as harshreality was getting at, if we used 'proof' that strictly, nothing outside of pure math and logic would be a 'proof'.
> But, as harshreality was getting at, if we used 'proof' that strictly, nothing outside of pure math and logic would be a 'proof'.
True that. But isn't that an important part of the scientific method (at least in the karl-popper-scientific-method sense), and part of the point of science, really? Strictly speaking, you can't prove anything using the scientific method; only 'falsify' it (hence Popper's 'falsificationism', 'science as falsification', etc.) To 'kinda-sorta-prove' something in science, you formulate a null hypothesis, and then attempt to falsify it. But strictly speaking, one is not able to 'prove' anything (only provide weak/strong evidence for/against something.)
Well, then, don't use the word "proof" outside pure math and logic. Everyone agrees that "proof" means to render something beyond (reasonable) doubt, so it's not a problem of ambiguous definition, just incorrect usage.
But, as harshreality was getting at, if we used 'proof' that strictly, nothing outside of pure math and logic would be a 'proof'.