I did some research to find what others say "proving the negative" means. Doing that research showed me that the argument is really about "Burden of Proof." For example, I found a reference to "Russell's Teapot" which says,
Russell's teapot, sometimes called the celestial teapot or cosmic teapot, is an analogy first coined by the philosopher Bertrand Russell (1872–1970) to illustrate that the philosophic burden of proof lies upon a person making scientifically unfalsifiable claims rather than shifting the burden of proof to others, ... Russell wrote that if he claims that a teapot orbits the Sun somewhere in space between the Earth and Mars, it is nonsensical for him to expect others to believe him on the grounds that they cannot prove him wrong.Another source:
The burden of proof is always on the claim that X exists rather than on the claim that X does not exist.Another source that may be easier to understand says:
A negative proof is a logical fallacy which takes the structure of:Another good source says:
X is true because there is no proof that X is false.
The negative proof fallacy is where one assumes something is true if it cannot be proven false. It can also happen when one assumes that something is false if it cannot be proven true.As anyone can see, that kind of argument is not really about proving someone wrong. It has to do with claiming something is true because those who disagree cannot prove it to be false.
An infinite amount of silly statements might be declared and be completely unprovable, hence we cannot assume validity in the face of unprovability. This is what is known as burden of proof.
Here's an example of how one Anthrax Truther might argue:
I know that an American-based supporter of al Qaeda was behind the anthrax attacks because it cannot be proved that there was no al Qaeda supporter behind the anthrax attacks. If you claim that all the evidence proves that Dr. Bruce Ivins was the anthrax mailer, all that means is that Ivins was an al Qaeda supporter, if you cannot prove he wasn't.Here's an example of how another Anthrax Truther might argue:
I know that Dick Cheney was behind the anthrax attacks because no one has proved that he was NOT behind the attacks.The burden on the proof MUST be on the person making the claim, not on the person who disputes the claim.