If I hear that stupid phrase “you can’t prove a negative” one more time, I’ll explode.

First off, “you can’t prove a negative” seems itself to be a negative (though see below). So, if it were true, you wouldn’t be able to prove it. Of course, we believe many things without proving them. But still, you’ve got to wonder someone would believe something that couldn’t be proven.

Perhaps you can’t prove it, you might respond, but you can support it with something less than a full proof (or is that a foolproof?). Maybe. But that leads to my next point. In considering whether you can prove a negative or not, one mustn’t hold negatives to a higher standard of proof than positives. If I offer what might be a proof for a negative and you say “Aha! You can’t be absolutely sure. You might be dreaming, hallucinating…. etc,” then you have to be prepared to reject all proofs of positives which are susceptible in the same way. In short, “you can’t prove a negative” isn’t meant to be true just because you can’t prove (to your favored standard of proof) anything at all. Those who mistakenly believe that you can’t prove a negative are surely supposed to accept that there is some standard of proof such that you can prove positives to that standard but cannot prove negatives to the same standard.

But we haven’t even got to what’s really wrong with “you can’t prove a negative.” There are two things really wrong with it. First, what is a negative? Is it any statement with “not” or “no-one” or “never” in it? Is “Jones is not alive” a negative? But what about “Jones is dead”? Surely these are more or less equivalent. Is one a negative and the other not? What about “the symphony has finished playing”? Surely this ‘positive’ is more or less equivalent to “the symphony is not playing any more”. If being a negative means just having a negative word like “not” in the sentence, then many negatives are more or less equivalent to positives. If it means something else, what does it mean?

Secondly, and most annoyingly, “you can’t prove a negative” is (assuming that the following really are examples of negatives) just plain wrong. I can prove there is not a herd of elephants in my room right now. I can prove there is no integer other than 1 and 17 by which 17 is divisible without remainder. I can prove that I don’t have three hands. And on and on. We (not I by myself, but we as a country) have even – wait for it, yes I think we have – proven that there were no weapons of mass destruction in Iraq. Like a herd of elephants in my room, they would have made their presence known had they been there.

Of course, I (and we) are fallible. We might be wrong about some of these things. Maybe I do have a third hand and I’ve been hypnotized not to notice it. So if that’s your worry over the unprovability of some of these negatives, fair enough. But we are fallible about most ‘positives’ too. We could be wrong about whether the Empire State Building exists. That same hypnotist who has gotten me not to notice my third hand may have got us all to imagine a large building on 5th Ave that isn’t really there. It all goes back to that issue of standards of proof I mentioned above. But it is surely ‘beyond a reasonable doubt’ that I have no third hand, that there are no elephants in my room and that there were no WMDs in Iraq. So to that degree of certainty, these negatives have all been proven.

QED.

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