Yes, Virginia, you CAN prove a negative

Groucho Marx (from Wikipedia)
Thanks for loaning the elephant, Groucho. I’ll try to have the pajamas pressed. (Image from Wikipedia)

Logic class, today! After a week of house hunting, a quick post like this feels like just the thing to cleanse the palate, so please forgive my indulgence.

Though it is often claimed–and tempting to believe, because it can sound sensible–it is completely false that you cannot prove a negative. (That is, for instance, that you cannot prove something doesn’t exist.)

I have heard the claim many times, often by wonderful and sincere people but, to be sure, wonderful and sincere people who don’t know what they are talking about — club of which all of us are members from time to time. For instance, I have heard atheists say “You can’t prove a negative!” in an effort to absolve themselves of the need to justify their belief that God does not exist. On the other side, I have heard Christians say “You can’t prove a negative!” in an effort to show that the atheist position is impossible.

Both are in error. Both seem to miss the fact that we prove negatives all the time and the fact that the same sort of “reasoning” they offer would defend belief in Santa Clause, the Easter Bunny, and flying purple leprechauns named Marty.

This was brought up to me more than once by someone who objected to what I wrote for Tomorrow’s World publications concerning the non-existent 2012 Mayan Apocalypse. I would point out that, based on all the evidence we have, the Mayans said no such thing about the year 2012. All of the hoopla and hype was due to New Age goofiness (drug use included) and sloppy, agenda-driven non-scholarship performed by hobbyists and individuals with something to sell. And this is definitely the record we have of the Maya culture–no modern, credible scholar of Mesoamerican culture disagrees with the assessment that the Maya simply did not believe in a 2012 apocalypse.

However, someone apparently bothered when I pointed that out would sometimes write, saying, “You can’t prove a negative!” His point seemed to be that you can’t say that the Mayans never said that the universe would end in 2012. Of course, if it is true that you can’t prove the Mayans did not say something, then it would also be “logically” unreasonable to believe that the Mayans never said President Obama would be elected in 2008, that the Mayans never said “Rome wasn’t built in a day,” or that the Mayans never said they were the descendants of the undiscovered planet Great Googly Gumdrops and never prophesied the coming of their most dangerous foe, Mork from Ork.

Often (though not always, it should be said), the claim “you can’t prove a negative” is made in reaction to something one does not want to hear, as if it will somehow back their opponent into a logical corner. But that is far from the truth.

In fact, you absolutely can prove a negative.

Now, I should qualify that when I say “prove” I mean the same thing we faulty human beings commonly mean when we talk about “proving” anything — for instance, establishing something as the most reasonable position to take among known alternatives. If “prove” means “prove with mathematical exactness and precision but in real life” then virtually all “proofs” would escape us, meaning we could prove neither negatives nor positives! (Actually, we can thank Gödel for helping us to see that, in a very real way, such “proofs” can’t even be assumed for mathematics, itself.)

But if you mean “prove” as in “I can prove you took the cookie from the cookie jar” — a belief established by the preponderance of the evidence — then, oh yeah, we’re golden. We can prove negative statements to just as high a level of certainty as we are able to prove positive statements. In fact, we draw reasonable, sound conclusions about the truth of negatives all the time.

It seems to me that the question is often related to the old saying, “Absence of evidence is not evidence of absence,” which is usually abused in this context. Because, very simply, sometimes absence of evidence is, indeed, evidence of absence. For instance, if I told you that, right now, there was an elephant in your kitchen wearing your pajamas (hat tip to Groucho), and you went into your tiny kitchen and saw no pajama-wearing elephant, you would be perfectly justified by the lack of evidence in saying, “I have proven there is no elephant in my kitchen wearing my pajamas.” Why? Because were a pajama-wearing elephant actually in your kitchen, you would be justified in expecting evidence to be left. If you don’t even see a table pushed out of the way as the elephant fled in embarrassment upon hearing your approach (elephants have big ears), you have very good cause to say that your position is proved. For someone to say, “Well, you can’t say you’ve proven there is no elephant in your kitchen because you can’t prove a negative!” would say more about their misunderstanding of logic than it would about your argument. Your argument would be absolutely valid and sound.

If evidence is to be expected and no evidence is present, then absence can be logically inferred. So, perhaps the saying should be amended to say, “Absence of evidence is not evidence of absence unless evidence should be expected.”

This is why we can, indeed, reasonably conclude that the ancient Mayan culture did not expect the universe to end in some sort of cataclysm on December of 2012. For all the New Agers’ and misguided hobbyists’ hoopla about what was supposed to be a universe-changing event, the evidence that the Maya thought about it as such a vastly significant date is just simply absent. Despite the vast volumes of cultural artifacts we have including volumes and volumes of information they, themselves, inscribed and wrote down, they say nothing about such a day being the end of the world. I won’t go into all of the details again [you can search the blog on “2012” and probably find more than you ever wanted to know], but the tiny crumbs that are generally offered by ill-informed hobbyists and tainted “researchers” always fail to pass the test. Monument 6 in Tortuguero? Understood in cultural context (as opposed to ignorantly imposing upon it non-Mayan ideas), it says nothing about the end of the world. The Comalcalco tile? Ditto. The much-later, Christianity-corrupted Chilam Balam? Actually evidence against 2012 date-setting theories when you understand it. The Dresden Codex? Not even.

(FYI on that last point: As all the unchristian 2012-addiction died down back then, the last stab I saw at trying to magically turn the Dresden Codex into “evidence” that the Mayans thought 2012 might be the end of the world was claiming that the last page of the codex is depicting the transit of Venus. No one offered proof the last page said anything like this, or even real evidence. Just an assertion that it is so, in the apparent hope that a confident sounding statement will add some credibility to what they are saying. Except that people — people with actual training in astronomy and Mayan works — have said that, no, the Dresden Codex absolutely does not mention the Venus Transit. Anyone who says the transit of Venus is in the Codex has no credibility. In fact, there’s a negative that can be proved: “The Dresden Codex does not mention the Transit of Venus.” — Sorry! So much of that pointless 2012 goofiness is still running around in my noggin that it spills out sometimes… Back to the post!)

For what should have been the one of the most significant events in their culture’s eschatology, the supposed “end of the world” date of December 2012 was remarkably and unreasonably absent from the vast collection of writings we have. Indeed, absence of evidence is, in this case, evidence of absence.

And, frankly, all of that ignores the positive evidence that the Mayans did not believe 2012 was the end of the world: many inscriptions concerning dates further out that 2012, the calendar discovery at Xultún, et al., ad nauseam. But that is an aside unrelated to the point of this lazy post, today. 🙂

In similar manner, you can prove the negative that Santa did not come down your chimney last Christmas. (Of course, he’d better not come to my house!) The absence of evidence that a fat man crawled down your chimney while you were asleep is pretty good evidence for the absence of such a fat man.

We can, indeed, prove negatives, and lack of evidence is sometimes evidence, itself. When an atheist claims that he doesn’t need to justify his belief that God doesn’t exist because you can’t prove a negative, he is not being rational. When a believer claims that the atheist’s position is not logical because you can’t prove a negative, he is also not being rational. No one gets off the hook. (Don’t get me started on the illogical fad among many atheists today to claim that “belief” doesn’t mean “belief” anymore. That would be a whole ‘nuther post…)

If someone ever tries to shut you down by claiming “You can’t prove a negative,” feel free to ask them to prove that such a proof does not exist, since that would require proving a negative, themselves. (Did you see that? I turned it around, didn’t I? Yes, I do think I’m clever, thank you.) Or, you can just ask them if it’s reasonable to strongly believe that Santa Claus does not exist. If they won’t say “Yes” to that, then I suspect they have more problems than their grasp of logic. In that case, you might recommend that they keep an eye out for any pajama-coveting elephants…

I’ve hardly scratched the surface of the topic, but I’ve seen the “you can’t prove a negative” fallacy used enough that I thought it would be something fun to write about. Yes, I have an odd idea of “fun,” but it has succeeded in relaxing me a bit after all of this house hunting! If anyone wants to read more about the mistaken notion that one cannot prove a negative, here is a decent essay by Dr. Steven Hales of Bloomsburg University, appropriately titled “You Can Prove a Negative” — knock yourself out. 🙂

6 thoughts on “Yes, Virginia, you CAN prove a negative

  1. I look forward to reading that essay. Thanks for the appetizer – I suspected something untoward was lurking in that defensive statement.

    One of my rebuttals – sorta kinda – to what I suspect really lies behind that statement (by atheists and such like) is, “Sometimes you can tell what’s invisible by the footprints it leaves behind.” Thoughts?

  2. Thomas

    Speaking of things fun and mathematical here’s a fun math factoid that may even stump your favorite math nerd. April 4 of this year marks the 147th anniversary of the birth of Philippa Garrett Fawcett. One of her claims to fame is that she was the first female Senior Wrangler. What’s that? The person with the highest math score of their year at Cambridge University – at the time considered the highest academic achievement in the British Empire. She achieved this in 1890. She would go on to make contributions to the study of fluid dynamics as well as lecturing in both Britain and South Africa. Needless to say her example helped to pave the way for women to gain access to higher learning. Her enthusiasm for the subject was both enthralling and contagious. Here is a quote from one of her students:

    “What I remember most vividly of Miss Fawcett’s coaching was her concentration, speed, and infectious delight in what she was teaching. She was ruthless towards mistakes and carelessness… My deepest debt to her is a sense of the unity of all truth, from the smallest detail to the highest that we know.”

    Sentiments that I thought might be appreciated here.

  3. Robert Petry

    Ah, logic? I read that logic originally was a parlor game for ancient Greek children. It’s purpose was to prove the other person wrong even if he/she was correct. Then it grew up to become an adult game for “professionals” like the game of baseball. Must be great to be paid to tell people who are correct that they are not correct, and then get paid for doing it. Then the atheists took up the game to prove those who are correct are wrong by a negative being a proof that can’t be proved, or in plain language, if you can’t defeat them confuse them.

  4. Ha! 🙂 Thankfully, that is not the real history of logic or reason, though “pretend logic” would fit in there. True logic and reason is a characteristic of God who lovingly invites us to reason with Him.

  5. Lee Strobel dealt with this in a different way in The Case for Christ. There is logical, mathematical, proof, and then there is legal and historical proof. He then makes the case that not only is the Bible a valid historical document, but he also makes the case that there is extrabiblical evidence for Christ, and those combined would create legal proof that Jesus was a living human being.

What are you thinking?

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s