You cannot conclusively prove that something does not exist – the best you can do is show that the lack of evidence likely means that the something probably doesn’t exist.
Take, for example, Big Foot. It would be easy enough to prove that he does exist, just either bring him in as proof or get some high quality photos and/or other evidence (e.g. scat, bones, etc) that proves he exists. On the other hand though, the best we can do to prove that big foot does not exist is to use the fact that conclusive evidence showing his existence doesn’t exist but that could be countered using the numerous possible reasons as to why we cannot gather that evidence (e.g. he is good at avoiding human contact and good at not leaving any traces behind).
My favorite example of this is one made by John Oliver.
Indiana Representative Dan Burton famously claimed that there was a link between vaccines and autism. He said something to the effect of “scientists will say there’s no evidence of that, but there’s no evidence that *disproves* it, either!”
To which John Oliver claimed that Dan Burton fucks donkeys. There may be no evidence of it, but there’s no evidence it’s not true, either. Since any evidence of Dan Burton *not actively fucking a donkey* just means he’s not fucking one in the moments you were able to observe.
[Link to John Oliver episode.](https://youtu.be/7VG_s2PCH_c?si=_ziFxXnbekJDQMYg) Dan Burton segment starts around 11:48.
It describes information that is unfalsifiable. Good examples of this would be God, Sasquatch, and ETs. Ultimately, you can’t prove their _non-existence_, because what constitutes evidence something _doesn’t_ exist? As Donald Rumsfeld put, “the absence of evidence is not the evidence of absence.” Coincidentally, we never found evidence of WMDs in Iraq.
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