Continue reading ...You Can Prove a Negative
by Steven D. Hales
A principle of folk logic is that you can’t prove a negative. Skeptics and scientists routinely concede the point in debates about the possible existence of everything from Big Foot and Loch Ness to aliens and even God. In a recent television interview on Comedy Central’s The Colbert Report, for example, Skeptic publisher Michael Shermer admitted as much when Stephen Colbert pressed him on the point when discussing Weapons of Mass Destruction, the comedian adding that once it is admitted that scientists cannot prove the nonexistence of a thing, then belief in anything is possible. Even Richard Dawkins writes in The God Delusion that “you cannot prove God’s non-existence is accepted and trivial, if only in the sense that we can never absolutely prove the non-existence of anything.”
There is one big problem with this. 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.
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