How to Prove the Nonexistence of Something

by Lenny Esposito

Atheists commonly claim that they bear no burden of proof since one cannot prove a negative. A couple of years ago, I debated Richard Carrier on the question “Does God Exist?” Given this was a question and not a proposition, each party bears an equal burden of proof in asserting his claim; I must provide evidence for why I believe God exists and Carrier must provide evidence for why he believes God does not. Yet, a lot of atheists felt that I should shoulder the burden is such a debate. “How do you prove the non-existence of something? That’s ridiculous” exclaimed one commenter. In fact, proving universal negatives is important, and something we do all the time in other contexts.

The idea that a universal negative is unprovable is what Steven D. Hales calls “a principle of folk logic,” not rigorous thinking. Hale writes:

Among professional logicians, guess how many think that you can’t prove a negative? That’s right: zero. Yes, Virginia, you can prove a negative, and it’s easy, too. For one thing, a real, actual law of logic is a negative, namely the law of non-contradiction. This law states that that a proposition cannot be both true and not true. Nothing is both true and false. Furthermore, you can prove this law. It can be formally derived from the empty set using provably valid rules of inference. (I’ll spare you the boring details). One of the laws of logic is a provable negative. Wait… this means we’ve just proven that it is not the case that one of the laws of logic is that you can’t prove a negative. So we’ve proven yet another negative! In fact, ‘you can’t prove a negative’ is a negative—so if you could prove it true, it wouldn’t be true! Uh-oh.1

Hale goes on to explain that any proposition that is stated as a positive (i.e. “God exists”) can also be…

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