Can You Prove a Negative?

Updated May 15, 2020
Of course, you can't prove negative -- usually. Proof applies to existence, and the nonexistent is nothing, an absence that can leave no trace. Thus the idea of direct proof of nonexistence makes no sense.

However, might we have indirect ways of (in effect) proving that something does not exist. Why not? Someone charged with a murder could prove he did not do it (at least not personally) by demonstrating that he was somewhere else at the time; he had an alibi. He's hasn't directly proved the negative -- I did not kill the victim -- but by proving a relevant positive -- I was somewhere else -- that logically conflicts with the negative, he has indirectly proved he did not commit the murder.

Yet some negatives are disproved all the time -- even by atheists who say you can never prove a negative. When a theist presents, say, the first-cause argument for God, the atheist will most likely reply, "That argument is not good (or bad or specious); that is, it does not prove what you say it proves," and then will set out to demonstrate his seemingly negative proposition. So it appears that some negatives can be proved. While I think there's good sense in the principle that he who proposes has the responsibility to defend, I wouldn't go the barricades over it.

How does any of this relate to God? Here I draw on George H. Smith's book Why Atheism? (Prometheus, 2000), the follow-up to his classic, Atheism: The Case against God (1974). Smith acknowledges, and atheists and many theists would agree, that providing naturalist answers -- such as evolution -- to questions about the world does not in itself prove that God does not exist. You would have to do more than that to rule God out in any particular case. 

Does that mean that God can never be ruled out? (We'll ignore for the sake of this discussion the logical proof that God cannot exist and therefore must be ruled out.) No it doesn't. We have other good grounds to rule out God. How can that be? Doesn't that fly in the face of open-minded skepticism? Not at all.

To show this, Smith switches from God to Santa Claus. Should an adult positively disbelieve in the existence of Santa ("I believe Santa does not exist".) or should the adult take the so-called skeptic's position ("I do not believe Santa exists because I haven't been shown any good evidence that proves he does.")? I vote for the former position and against the latter. What do the skeptical (or evidentialist) atheists say?

The Santa example is effective because it's hard to imagine a skeptical atheist recommending skepticism on the Santa question. If I'm wrong, I'd like to hear about it. 

The follow-up question is obvious: if we are rationally entitled to believe that Santa does not exist, why aren't we rationally entitled to believe that God does not exist? What's the difference (again, leaving the logical case out of it for now).

Santa is imagined to be a natural being. He's simply a man (helped by elves) who is capable of doing amazing things: namely, deliver presents to Christians all over the world in one night. I've never heard it said that God enables him to do this through some miraculous process. A believer in a natural Santa might say that Santa accomplishes his wonders by using highly advanced technology of which the rest of us are not aware. Without invoking the supernatural or anything like biblical miracles, the believer could spin elaborate explanations about how Santa works his wonders. (If the believer mentions "magic" in his explanation, then we're back to the logical refutation of Santa.)

In other words, the Santist, having presented a picture that contains no logical contradiction, would be able to say to the aSantist: Santa is conceivable and possible. The aSantist might say that he's seen no evidence for the existence of Santa. After all, everyone he knows buys Christmas presents and none has ever seen a present mysteriously turn up on Christmas morning. But the Santist could correctly respond that this in itself does not prove that Santa does not exist. Your never having received a present from Santa does not alone prove that no one else has received a present from Santa or that Santa does not exist. And that's true as far as it goes.

So what's wrong with that argument? How far does the claim "It's possible (or it's not impossible) that Santa exists" get you? Not as far as you may think.  

Before one seriously considers any proposition, it must be more than logically possible because all that tells you is that it is not internally contradictory, like square circle. To earn serious consideration, a proposition must be materially possible as well. (Smith attributes this distinction between forms of possibility to the influential 18th-century German philosopher Immanuel Kant: logical possibility refers coherence, material possibility to truth. ) Just because something is imaginable (as square circles are not) doesn't make it materially possible. To earn serious consideration, a proposition ought to be more than coherent. It ought to be plausible and supported -- to some extent -- by evidence. Conceivability is not even a smidgin of evidence. Plausibility can be in the eyes of the beholder, which is why evidence is properly demanded: the more implausible the claim, the heavier the evidentiary burden. 

Another way of putting it is that the arbitrary has no place in serious discourse. If not a scintilla of evidence is offered for a claim, we are entitled to believe that the proposition is false. Might this change in the future? Of course -- after good evidence is produced. Knowledge and certainty are contextual, although truth is objective and independent of us.

So we've reached the point where we can forthrightly deny that Santa exists. The claim of Santa's existence is implausible and evidence absent.

And if we can say this about Santa Claus, why not about God? God is implausible and no good evidence has been produced after quite a long time. So even if God were not impossible on logical grounds -- which God indeed is -- it would be impossible on material grounds.