Proving the Negative
There are all sorts of things that people do which annoy me. But what gets on my next-to-last nerve is when someone repeats a cliché that is grossly incompatible with even rudimentary logic. “You can’t prove a negative” is probably the worst offender on the list of such statements.
Every time any statement is disproven, its negation is proven. Negative statements are made and proven constantly – and technically, what constitutes a “negative” isn’t even well-defined. Any statement about any property can be considered a “negative” one from a properly-chosen perspective.
Trying to establish any statement through a process of elimination of its alternatives tends to be tedious and, in practice, unworkable once the space of possible alternatives becomes large enough. Attempting to demonstrate that there is no golden needle in a stack of hay by picking up and examining each and every straw will work. Eventually. It’s hard, certainly, but not impossible. Even if the haystack were infinitely large, the strategy would still work – given infinite time.
When people say “you can’t prove a negative”, it often seems that they’re referring to situations with arbitrarily large haystacks and attempts to rule out a golden needle. Picking through the straws one by one probably isn’t the best available strategy, certainly. But they should just say that instead.