If one hangs out long enough on the internet, one will hear it said, “you can’t prove a negative.” This is of course obviously false stated in this level of generality. You can easily prove that the sun didn’t explode ten thousand years ago killing all life on earth and leaving the earth a barren wasteland by simply pointing up in the daytime sky at the intact sun, and noting that you yourself are alive and on the earth while you do it.
But people do not, generally, mean the statement at that level of generality. What they do mean varies with the circumstance but is usually some version of either:
You can’t prove the universal non-existence of a thing which could be anywhere due to the limitations of finite time plus one’s inability to travel to everywhere.
One cannot prove that a thing which would have left no trace did not happen over a time period large enough that there were no witnesses who saw whatever was not doing the action over the entire time.
Both of these are things no sensible person would object to, though occasionally you do see them come up. “You deleted a tweet you made over the last six months!” “How can I possibly prove that I didn’t since Twitter keeps no record of deleted tweets?”
(I think it’s worth noting in passing that the inability to provide physical evidence for things that would leave no physical evidence is precisely why we have witness testimony in the first place.)
These sensible things are not, however, the limits of that to which people will apply “you can’t prove a negative”. While not going so far as to claim that all negatives are strictly unprovable, I have seen this taken to rather ridiculous extremes. The one that comes to mind is a point I made in my recent video about Deconverted Man:
I pointed out that much of what he says rests on the idea that he’s never seen any evidence nor any “logically coherent” arguments for God’s existence, and that furthermore this is rather implausible because all the world is evidence for its creator and there are many sound arguments which demonstrate God’s existence.
The first of those two points is arguable only by trying to creatively redefine “evidence” to mean something like “unambiguous evidence” or “conclusive evidence” or something else which cannot in theory exist because what they really are asking for is something which would force them to believe in God, and that’s not how the human mind works.
The second, though, is curious, because I was told by more than one of Deconverted Man’s fans that it’s impossible to prove a negative so he has nothing to prove. Of course they didn’t think this through and don’t really take it as a principle, but it is amusing to consider what the principle would mean: as long as you phrase it negatively, you can make the most outlandish claim and it’s up to others to prove you wrong. “I’ve never stood on a floor” is a negative claim, as is, “I am not affected by gravity.”
(In case you’re wondering what would happen if I were to try to push that issue, in addition to being told I’m stupid, I’d then encounter the average online atheist’s inability to distinguish between a Straw Man and a Reductio Ad Absurdum.)