"A principle of folk logic is that you can’t prove a negative. Skeptics and scientists routinely concede the point in debates about the possible existence of everything from Big Foot and Loch Ness to aliens and even God. In a recent television interview on Comedy Central’s The Colbert Report, for example, Skeptic publisher Michael Shermer admitted as much when Stephen Colbert pressed him on the point when discussing Weapons of Mass Destruction, the comedian adding that once it is admitted that scientists cannot prove the nonexistence of a thing, then belief in anything is possible. [...] There is one big problem with this. Among professional logicians, guess how many think that you can’t prove a negative? That’s right, zero.
So why is it that people insist that you can’t prove a negative? I think it is the result of two things: (1) Disappointment that induction is not bulletproof, airtight, and infallible, and (2) A desperate desire to keep believing whatever one believes, even if all the evidence is against it. [...] Meaning: your argument against aliens is inductive, therefore not incontrovertible. Since I want to believe in aliens, I’m going to dismiss the argument no matter how overwhelming the evidence against aliens, and no matter how vanishingly small the chance of extraterrestrial abduction.
If we’re going to dismiss inductive arguments because they produce conclusions that are probable but not definite, then we are in deep manure. Despite its fallibility, induction is vital in every aspect of our lives, from the mundane to the most sophisticated science. Without induction we know basically nothing about the world apart from our own immediate perceptions. So we’d better keep induction, warts and all, and use it to form negative beliefs as well as positive ones.
You can prove a negative — at least as much as you can prove anything at all.
Steven D. Hales, Skeptic.com, 7. December 2007