Oh? Can you prove that?
A lot of folks love to toss that statement around. But simply to look at it is to recognize the claim as a very stupid one. Simple logic will tell you that it's either wrong, or unproveable.
As it happens, as a general statement it is wrong. For example, in math it is quite common to prove negatives (e.g., "non-existence" statements) by, for example, assuming the positive opposite and demonstrating that it leads to a contradiction. Also, it's quite obvious that a negative statement such as "there are no green mammals" can be refuted by the simple expedient of producing a green mammal.
A lot of folks love to toss that statement around. But simply to look at it is to recognize the claim as a very stupid one. Simple logic will tell you that it's either wrong, or unproveable.
What you prove is you don't understand the rules of logic.
What the Fallacy means is that you cannot prove that which does not exist. For example, I can prove the existence of a horse by providing one to your senses. I cannot prove the existence of a Unicorn because there is no such thing to prove it to you as an example of.
This is why science no longer considers the existence of the "ether" as a valid explanation of the propagation of light and energy. There is no evidence for it and that Einstein's Theories hold sway. You have to give some evidence to support your proposition.
As it happens, as a general statement it is wrong. For example, in math it is quite common to prove negatives
This is the Fallacy of Conflation. Math is a theoretical system, not a physical one. The rules are different. It is possible to prove a statement wrong but it is not possible to prove a fact wrong. Volcanoes exist. Rivers exist. Bears exist. Evolution exists.
ID cannot be prove to exist. By definition.
it's quite obvious that a negative statement such as "there are no green mammals" can be refuted by the simple expedient of producing a green mammal
This is known as the "White Crow Fallacy" since it would require examining every crow in the Universe to prove there are no "White Crows." This is why in logic the Burden of Proof is upon whoever is making the Assertion.
For example, the Assertion that Homosexuality is "unnatural" is refuted by examining the lives of Bonobo apes. They are very "perverted." If homosexuality is a moral issue then mere animals couldn't indulge in such behavior. If not, then the Fallacy holds.
One cannot prove one thing true by proving another thing false. Keep studying. You might understand this truth someday.
That's fine, but the claim is "you can't prove a negative," not "you can't refute a negative" - I don't think your example refutes that claim, speaking of refutation.
Anyway, the claim itself tends to be reflective of the difficulties inherent in demonstrating the truth of universal negative propositions. If I say that there are no green unicorns, the only way to demonstrate whether that's true or not would be to undertake a detailed examination of the entire universe, looking at every portion of it simultaneously, lest the little green unicorns hide someplace I've already looked - in essence, to demonstrate to you that this proposition is true requires us both to be more or less omniscient.
Of course, some negative propositions are rather more specific - "there is no butter in my refrigerator" is somewhat easier to verify. Needless to say, all this doesn't exactly make a nice soundbite, so "you can't prove a negative" is what's remembered, despite being a bit simplistic ;)