Here’s a bad idea that needs to die:
You can’t prove a negative!
This claim is, unfortunately, quite often the vice of skeptics and atheists. Most of the time, it’s mistakenly used when trying to explain the concept of the burden of proof, even though the validity of the burden of proof doesn’t rest on this non-principle at all.
The biggest problem with the claim is that it’s simply flat-out self-contradictory! I strongly suspect that the statement originated as a joke, and how it ever started to be taken seriously, I have no idea. Not only can you prove negatives, but the idea of doing so is essential to, among other things, the scientific method, where discarding or invalidating hypotheses is essential to the process.
In fact, negative claims are often easier to prove than positive ones. “All dogs go to heaven” is a statement that would require knowledge of every single dog that had lived or will ever live and whether it ever had, or ever will go to “heaven.” On the other hand, disproving a statement like “No dogs go to heaven” requires a quick search of “heaven:” if there is even a single dog there, the claim is definitively refuted.
For these reasons and more, logicians have been trying to purge this myth from common usage for years and years, and yet despite their efforts it still persists.
And yes: it is true that proving existential negatives in particular (that is “X does not exist, period”), is in practice anywhere from hard to near impossible. This is what people generally mean, but fail to say, when they claim that proving negatives is impossible.
But this still isn’t a particularly important point: the burden of proof makes it simply unnecessary to even bring this issue of difficulty up. It wouldn’t make any difference at all if it was easy to prove an existential negative: it’s still the full responsibility of a person claiming the existence of something to provide reasons for believing this claim. Asserting that something is true simply because it has not been disproven is the fallacy of negative proof, which is not the same thing as anyone being unable to prove a negative.