You can't prove it's impossible!
A common sophistry which really annoys me is the one that conflates an utterly negligible probability with a non-negligible one. The argument goes:
- There is technically no such thing as certainty.
- Therefore, [argument I don't like] is not absolutely certain.
- Therefore, the uncertainty in [argument I don't like] is non-negligible.
Step 3 is the tricky one. Humans are, in general, really bad at feeling the difference between epsilon uncertainty and sufficient uncertainty to be worth taking notice of — they can't tell a nonzero chance from one that's worth paying attention to ever. (This is why people buy lottery tickets.)
It’s a terrible, terrible argument, and an unfortunately common one. It needs to be bludgeoned to death every time it’s brought up.