What do you mean by "the logical fallacy of attempting to prove a negative statement?". I can prove the negative statement "I did not assassinate JFK" by citing the fact that I wasn't born yet.
You're right in that in this particular case, the practical difficulties of quantifying "less cobra-ness" or "cobra void" as you call it is difficult, but there are plenty of cases where quantifying the absence of something is straightforward.
Strictly speaking, you're proving the positive assertion that you were born after the assassination, which is incompatible with your having been the assassin. You can only prove or disprove a positive assertion. "Proving a negative" is done by proving a positive assertion that's contrary to, or incompatible with the thing you're trying to "disprove".
I do not believe in the existence of fire-breathing dragons outside of fiction, but I can't prove they don't exist. See also: UFOs, angels, god(s), and so on. In logic, the onus is on the person making the positive claim (that such things do exist) to furnish the evidence to back it up. The skeptic's lack of knowledge is not proof of non-existence, of course.
I'm talking about mathematical truths for which establishing non-existence follows directly from proving a positive assertion, not that white ravens don't exist.
I understand that, but 'proving a negative' is philosophical shorthand for the latter rather than the former. You are just going to have to put up with the slight vagueness of the term.
I imagine he was thinking of the problem of proving a negative general statement, e.g. "nobody has assassinated anybody". It's trivial to prove the statement is false (if indeed it is false), but it's nigh impossible to prove that it's true.
The more controversial wording of this is that you can't prove there is no god.
What people usually mean when they say this is that it is impossible to prove a global proposition about the real world. I don't know when the irrelevant word "negative" was added (after all, every "positive" statement can be trivially re-written in a "negative" form), but it's become very popular for some reason.
For example: "There are no orange swans" is equivalent to "All swans are either colorless or colored other than orange." Similar techniques can be applied to all statements.
People keep saying "prove a negative" when they mean "prove a universal". As if somehow existence statements were more positive than universal statements...
You're right in that in this particular case, the practical difficulties of quantifying "less cobra-ness" or "cobra void" as you call it is difficult, but there are plenty of cases where quantifying the absence of something is straightforward.