Everyone knows this is true. For one, there are several obvious negative statements that pretty much everyone knows are true and can easily prove (“George W. Bush is not the President,” “Red is not the same color as blue,” “Carlos Mencia is not funny,” etc.). On a less mundane level, whether a statement is positive or negative is a matter of how it is constructed—every positive statement (p) can be restated as a negative (~ ~ p).
And yet you will still hear people—smart people—resort to the obvious fallacy that you cannot prove a negative. Most commonly, you hear it in discussions of atheism. I’m sure even I have resorted to such a claim in my defenses of atheism. Even the brilliant Daniel Dennett erroneously invoked it here to explain why he couldn’t disprove God:
“You can’t prove a negative… I think it was Bertrand Russell who once said that he couldn’t prove that there was not a teapot orbiting Mars. So he’s a teapot agnostic. I’m a teapot agnostic with regard to God, too. I can’t prove that God doesn’t exist.”
This may or may not be true, but just because you can’t prove some negatives doesn’t mean that you can’t prove any. It is, of course, much harder to prove negative statements than positive ones, at least in regards to existence. If I want to prove the statement that “Santa Claus exists,” then all I have to do is find Santa Claus—an unlikely but at least conceivable task. If I want to disprove such a statement, though, I have to prove that every single thing in the universe is not Santa Claus. This partially explains why some people resort to asserting that such proofs are impossible—they are often very time-consuming and difficult.
There is, though, another way to prove a negative: Assume the negative is false and derive a contradiction. In other words, if I want to prove ~ p, then I’ll see if any contradictions would arise from p being true. Some killjoy scientists have done this for Santa Claus.
It may be even easier to do this for God. There are few things easier than deriving contradictions from the assumption that the Christian God exists. The problem of evil, free will, omnipotence vs. omniscience, etc., have all been debated for centuries to no obvious solution. And the contradictions that come from a general belief in a deity have been known for multiple millennia now.
Of course, belief persists despite such obvious contradictions. In fact, it is often a point of pride to believe in the face of these contradictions. The way belief stands up to these issues is by making the concept of “God” elusive, malleable, and mysterious. Trying to get a real, concrete definition of God is like trying to nail Jell-O to the wall. And this is why trying to disprove God’s existence by deriving a contradiction is bound to fail. It seems that the idea of God is inherently contradictory. That, indeed, is part of its appeal: God is all-powerful…except when he’s giving us free will. God is forgiving and merciful…except when he is judgmental and vengeful. God is good…except when he is full of wrath and violence. God is everything and nothing. He is, as James Wood said last year, a “bodiless and indescribable entity.”
Theists and atheists alike are constantly charging each other with being unable “prove” their claims, yet each side deflects the charge comfortably. God’s existence can’t be proven, but theists don’t mind, since the issue is a matter of faith. Similarly, God’s nonexistence can’t be proven, but atheists don’t mind, since we cannot prove a negative.
As we have seen, though, this atheist excuse is a lie—plenty of negatives can be proved, just not this one. But, as commenter Douglas pointed out recently, this is a weakness not of the atheist’s argument, but of the theist’s. As it turns out, the theist claim is worse than unprovable—it is unfalsifiable. It’s unfalsifiable not for any limitations of logic, but because the claim itself is inherently irrefutable…and therefore inherently meaningless.