It's often said, "You can't prove a negative." Ha! For starters, that statement itself is a negative — so if it's true then it must itself be unproveable. But no such luck ... it's simply false. There are plenty of easily-proved negatives ranging from the quasi-definitional ("There are no odd numbers divisible by 2") to the finite-specific ("This deck of cards has no Queen of Hearts").
When somebody sensible says "You can't prove a negative" what s/he really means, most of the time, is "This is a complicated open-ended problem and you can't claim complete knowledge of all possibilities." That's reasonable. To demonstrate rigorously that "There are no white crows" would require examining every crow in the universe and confirming that not one of them is white. Not an easy task.
Tuesday, April 10, 2001 at 05:52:40 (EDT) = 2001-04-10
(correlates: DippyHeuristics, CertaintyAndDoubt, MetaJoke, ...)