Steven D. Hales: You Can Prove a Negative.

We’ve all heard the argument that you can’t prove a negative from various True Believers™ in Gods, UFOs, Big Foots (Feets?), etc.. It’s a common bit of folk logic, but is it true? Philosopher Steven D. Hales argues that it is not in a small essay titled You Can Prove a Negative:

It is widely believed that you can’t prove a negative. Some people even think that it is a law of logic—you can’t prove that Santa Claus, unicorns, the Loch Ness Monster, God, pink elephants, WMD in Iraq and Bigfoot don’t exist. This widespread belief is flatly, 100% wrong. In this little essay, I show precisely how one can prove a negative, to the same extent that one can prove anything at all.

The essay itself is a small PDF file and it’s an easy read worthy of a look. My favorite bit is from the summary at the end:

Meaning: your argument against aliens is inductive, therefore not incontrovertible, and since I want to believe in aliens, I’m going to dismiss the argument no matter how overwhelming the evidence against aliens, and no matter how vanishingly small the chance of extraterrestrial abduction.

Yeah, that pretty much sums it all up right there. It’s the “I DO believe in faeries! I DO! I DO!” chant in a different form.


10 thoughts on “Steven D. Hales: You Can Prove a Negative.

  1. Great link!

    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.

    It’s going to be a sad few weeks waiting for someone to tell me I can’t prove a negative, so I can throw that at them.

  2. I get told that all the time when I make any sort of statement that implies that God doesn’t exist, aliens aren’t visiting the Earth, or that there is no such thing as psychics.  Oddly enough I use that same argument; that being able to prove you can’t prove a negative is proving a negative.

    I would amend the statement “You can’t prove a negative” to read “We are generally not equipped to prove a negative.”  The reason Woo’s use the argument “You can’t prove a negative” is because they don’t have any evidence, but they do have their belief and they don’t have to “prove” their belief.  OTOH… if someone shows you an empty box and says there is a rabbit inside, then it is their responsibility to provide evidence that the rabbit exists, not your responsibility to ‘prove’ the box really is empty.  They can believe there is a rabbit in the box all they want, but if they want other people to accept it, they must provide the evidence, not simply “You can’t prove there is no rabbit.”

    Another logical argument to use on Christians is that if I can’t prove that a single god can’t exist, then they can’t prove there isn’t more than one.  The same argument that Christians use to say there is a god denies the idea that God is a unique creature.  In an infinite universe the possibility of there being only one of anything is zero.  So God cannot be omnipotent if there are other’s out there who are his equal.

    Of course by that point, their brains have gone into “Damage Control” mode and they’ve stopped really listening, but it is kind of fun to watch the transition their brain takes.

  3. Thought everyone knew, it’s not a rabbit, it’s a cat in the box.

    The question is not is the cat alive or dead, but is the cat the same cat that was put in the box in the first place.

    Then again in a universe with infinite possibilities maybe the cat started out as a rabbit.

    PS The rabbit is friends with the unicorn.

  4. It’s a cute essay, but it also exemplifies why I don’t have the highest opinion of philosophy.

    The essay starts out with a huge equivocation and/or strawman with regards to the meaning of “proving a negative”. The author opts redefines the term to including “proving a negation”, whereas in actuality the term is very narrowly defined. I have never seen it used to mean anything but the prospect of having to disprove a proposition by an exhaustive search of an infinite or at least impossibly large search space.

    As an example and to stick to the formal realm, consider the proposition that the decimal expansion of π has no upper limit on the length of consecutive runs of 9’s (i.e. for any such run of length n, you’ll find an even longer one).

    There are two ways to tackle the above claim. The first way is the one everybody but the essay’s author associates with “proving a negative”—search the decimal expansion of π for all eternity to see if there is such an upper limit or not and obviously, the answer will never come.

    The other way would be to have a really deep understanding of math and the properties of that particular number to settle the question in finite time. The problem is that π is a transcendental number, i.e. it’s not one of these nice rational numbers or even an algebraic number. For all I know, such a direct proof is disproof is as hard as doing an infinite search…

    For all intents and purposes, proving a negative is always a situation where one is asked to disprove a claim by an impossibly long search or by a direct disproof that’s usually beyond our reach, too. Unless you stick the example most frequently encountered on SEB, the one that involves the omnimax sky daddy. It’s well within the powers of human comprehension to figure out that this class of deity can’t exist as defined by professional scam artists^W^W^Wtheologians.

  5. I have never seen it used to mean anything but the prospect of having to disprove a proposition by an exhaustive search of an infinite or at least impossibly large search space.

    I’ve heard far more people argue that because you can’t prove a negative, you can’t prove God doesn’t exist (or ghosts or aliens) so therefore they will go along believing in them thank you very much.

    The one’s who use it “correctly” if you can call it that… the way you use it, are usually greeted with “Oh, you say God (or whatever) doesn’t exist, then hide behind your self-confessed inability to prove it, therefor since you admit you can’t prove me wrong, I must be right.”  although they usually say it much worse than I just did.

    You just can’t get through to some people.

  6. What elwed said, and the two-percenters put it nicely too: formal proof of anything, positive or negative, can only take place in systems of formal logic, and not always then.  “You can’t prove a negative”, applied to the real world, is simply a matter of practicality: the Universe is a very large place, and it’s simply much easier to “prove” (that is, demonstrate beyond “reasonable” doubt) the existence of a rabbit in my hat than to “disprove” the existence of a unicorn, or a god, somewhere.

    I, too, have an ingrained distrust of philosophy.  As the two-percenters say, “philosophy without practicability is fucking masturbation, and no matter how nice masturbation might be, it’s ultimately fairly meaningless, and after a while it chafes.”  If anyone here is feeling particularly masochistic, and wishes to see a good example of philosophical masturbation presented as a proof for the existence of God by way of frogs, take a look at Plantinga’s proof that evolution disproves naturalism.

  7. “I am NOT a woman” and I can prove it. Next time someone says you can’t prove a negative, tell them 5 does not equal 4, and assert that you can prove it. I agree.

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