Explain the expression--"you can't prove a negative," and how one would use it in a sentence.

From the study of logic. If I assert that there are no casserole recipes that include vinegar, I have said something I can't prove, because it's always possible that somebody will find one recipe like that and prove me wrong. The principle applies only to certain kinds of negative statements. It doesn't apply to the statement "I don't have a gallon of blue paint in my pants pocket." I can prove that one by turning the pocket inside out.

http://www.phrases.org.uk/bulletin_b...ssages/22.html

Proving a Negative:

I know the myth of "you can't prove a negative" circulates throughout the nontheist community, and it is good to dispel myths whenever we can. As it happens, there really isn't such a thing as a "purely" negative statement, because every negative entails a positive, and vice versa. Thus, "there are no crows in this box" entails "this box contains something other than crows" (in the sense that even "no things" is something, e.g. a vacuum).

http://www.infidels.org/library/mode...er/theory.html

Science progresses by proving negatives. More specifically, it is by constructing possible models of a phenomena (a hypothesis), and then testing them (falsification), that we advance and build on the knowledge that we already have. By doing so, we prove many negatives along the way. We came to the conclusion that oxygen is the necessary gas in burning because we were first able to disprove the existence of phlogiston, which was the reigning scientific position at the time. More exactly, we now say that oxygen is a better explanation of burning than phlogiston, because the first fits all the facts while the second does not.

http://goosetheantithesis.blogspot.c...-negative.html

The rules of logic and science indicate that there must be some kind of basis (either in substance or in thought) for an assertion or else it must be denied. An assertion, without evidence, is not accepted as true. That is the default position, the position that defines what critical thought is. Critical thought means not believing things you are told unless there is evidence to back it up. And without critical thought, logic and science are abandoned, and this is the only kind of productive thought humanity has ever come up with. To reject critical thought is to turn one’s back on thinking and embrace the Dark Ages. That’s the answer to this statement in theory.

http://www.graveyardofthegods.net/ar...enegative.html

http://en.wikipedia.org/wiki/Negative_proof