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December 5, 2007

Urgent Appeal for Support
to Protect Ayaan Hirsi Ali

Most of you will recall the brutal murder of Theo van Gogh (a descendent of the brother of the famous artist) in Amsterdam in 2004 at the hands of a Muslim thug who was offended by Van Gogh’s film about violence against women in the Muslim world (yes, that’s right, for accusing Muslims of being violent he was violently killed — shot eight times and nearly decapitated). The killer left a note proclaiming that the author of the script upon which the film was based, Ayaan Hirsi Ali, would be next. Since then, and especially since her book Infidel became a bestseller, Ali has lived in fear and under Dutch government security. The Dutch government has now removed its protection, leaving Ali to fend for herself, scrambling to find the means to hire private professional security.

I thank my friend Sam Harris for calling my attention to a new fund recently established in her name to raise money to pay for her security. I believe that this is a great moral cause that skeptics, humanists, and believers in civil liberties and freedom of speech can and should rally behind. Normally we call for general assistance in combatting irrationality in its generic form so pervasive in our world; here is a golden opportunity to give to a very specific cause in which irrationality threatens the life of a courageous free thinker and champion of liberty. I’ve made my donation. I hope you will as well. — Michael Shermer, Executive Director

LEARN more about Ms. Ali

WATCH Ms. Ali lecture

DONATE to Ms. Ali

Richard Dawkins Foundation
Supports Ayaan Hirsi Ali fund

In 2007, the Richard Dawkins Foundation for Reason & Science (RDFRS) convened a two-hour meeting between Christopher Hitchens, Daniel Dennett, Sam Harris and Richard Dawkins (jocularly known as the “Four Horsemen”) in Christopher Hitchens’s apartment in Washington DC. Josh Timonen filmed their conversation using two high definition video cameras. Ayaan Hirsi Ali was originally invited to join them, but at the last minute she had to fly unexpectedly to the Netherlands. The remaining four discussants agreed with RDFRS’s proposal to donate to the Ayaan Hirsi Ali security fund all profits from sales of the DVDs from this remarkable conversation. The price will be $20, available at the end of December 2007. RDFRS also proposes to donate to the same fund the profits from a set of two DVDs, again filmed by Josh Timonen. This set features lectures by Ayaan Hirsi Ali, Daniel Dennett, Christopher Hitchens, Sam Harris, Richard Dawkins, J. Anderson Thomson, Matthew Chapman, Eugenie Scott and Edward Tabash, at the 2007 conference of the Atheist Alliance International, held in Washington DC in 2007. The price of this set of two DVDs is also $20. he price of this 2-DVD set is also $20, and is available now through the online store. All DVDs are NTSC, Region Free. READ more about the DVDs >

ORDER the 2-DVD set

In this week’s feature article Steven D. Hales says “you can prove a negative” and that skeptics need not concede this point in debates. Steven Hales is Professor of Philosophy at Bloomsburg University, where he was the 2006 Outstanding Teacher of the Year. He received his Ph.D. from Brown University and specializes in metaphysics and epistemology. His recent books include Relativism and the Foundations of Philosophy (MIT Press, 2006) and Beer and Philosophy (Blackwell, 2007).

You Can Prove a Negative

by Steven D. Hales

A principle of folk logic is that you can’t prove a negative. Skeptics and scientists routinely concede the point in debates about the possible existence of everything from Big Foot and Loch Ness to aliens and even God. In a recent television interview on Comedy Central’s The Colbert Report, for example, Skeptic publisher Michael Shermer admitted as much when Stephen Colbert pressed him on the point when discussing Weapons of Mass Destruction, the comedian adding that once it is admitted that scientists cannot prove the nonexistence of a thing, then belief in anything is possible. Even Richard Dawkins writes in The God Delusion that “you cannot prove God’s non-existence is accepted and trivial, if only in the sense that we can never absolutely prove the non-existence of anything.”

There is one big problem with this. Among professional logicians, guess how many think that you can’t prove a negative? That’s right, zero. Yes, Virginia, you can prove a negative, and it’s easy, too. For one thing, a real, actual law of logic is a negative, namely the law of non-contradiction. This law states that that a proposition cannot be both true and not true. Nothing is both true and false. Furthermore, you can prove this law. It can be formally derived from the empty set using provably valid rules of inference. (I’ll spare you the boring details). One of the laws of logic is a provable negative. Wait … this means we’ve just proven that it is not the case that one of the laws of logic is that you can’t prove a negative. So we’ve proven yet another negative! 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.

Not only that, but any claim can be expressed as a negative, thanks to the rule of double negation. This rule states that any proposition P is logically equivalent to not-not-P. So pick anything you think you can prove. Think you can prove your own existence? At least to your own satisfaction? Then, using the exact same reasoning, plus the little step of double negation, you can prove that you are not nonexistent. Congratulations, you’ve just proven a negative. The beautiful part is that you can do this trick with absolutely any proposition whatsoever. Prove P is true and you can prove that P is not false.

You can easily construct a valid deductive argument with all true premises that yields the conclusion that there are no unicorns. Here’s one, using the valid inference procedure of modus tollens (Latin for “mode that affirms by denying”):

  1. If unicorns had existed, then there is evidence in the fossil record.
  2. There is no evidence of unicorns in the fossil record.
  3. Therefore, unicorns never existed.

Someone might object that that was a bit too fast — after all, I didn’t prove that the two premises were true. I just asserted that they were true. Well, that’s right. However, it would be a grievous mistake to insist that someone prove all the premises of any argument they might give. Here’s why. The only way to prove, say, that there is no evidence of unicorns in the fossil record, is by giving an argument to that conclusion. Of course one would then have to prove the premises of that argument by giving further arguments, and then prove the premises of those further arguments, ad infinitum. Which premises we should take on credit and which need payment up front is a matter of long and involved debate among epistemologists. But one thing is certain: if proving things requires that an infinite number of premises get proved first, we’re not going to prove much of anything at all, positive or negative.

Maybe people mean that no inductive argument will conclusively, indubitably prove a negative proposition beyond all shadow of a doubt. For example, suppose someone argues that we’ve scoured the world for Bigfoot, found no credible evidence of Bigfoot’s existence, and therefore there is no Bigfoot. This is a classic inductive argument. A Sasquatch defender can always rejoin that Bigfoot is reclusive, and might just be hiding in that next stand of trees. You can’t prove he’s not! (until the search of that tree stand comes up empty too). The problem here isn’t that inductive arguments won’t give us certainty about negative claims (like the nonexistence of Bigfoot), but that inductive arguments won’t give us certainty about anything at all, positive or negative. All observed swans are white, therefore all swans are white looked like a pretty good inductive argument until black swans were discovered in Australia.

The very nature of an inductive argument is to make a conclusion probable, but not certain, given the truth of the premises. That is just what an inductive argument is. We’d better not dismiss induction because we’re not getting certainty out of it, though. Why do you think that the sun will rise tomorrow? Not because of observation (you can’t observe the future!), but because that’s what it has always done in the past. Why do you think that if you turn on the kitchen tap that water will come out instead of chocolate? Why do you think you’ll find your house where you last left it? Again, because that’s the way things have always been in the past. In other words, we use inferences — induction — from past experiences in every aspect of our lives. As Bertrand Russell once pointed out, the chicken who expects to be fed when he sees the farmer approaching, since that is what had always happened in the past, is in for a big surprise when instead of receiving dinner, he becomes dinner. But if the chicken had rejected inductive reasoning altogether, then every appearance of the farmer would be a surprise.

So why is it that people insist that you can’t prove a negative? I think it is the result of two things: (1) Disappointment that induction is not bulletproof, airtight, and infallible, and (2) A desperate desire to keep believing whatever one believes, even if all the evidence is against it. That’s why people keep believing in alien abductions, even when flying saucers always turn out to be weather balloons, stealth jets, comets, or too much alcohol. You can’t prove a negative! You can’t prove that there are no alien abductions! Meaning: your argument against aliens is inductive, therefore not incontrovertible. 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.

If we’re going to dismiss inductive arguments because they produce conclusions that are probable but not definite, then we are in deep manure. Despite its fallibility, induction is vital in every aspect of our lives, from the mundane to the most sophisticated science. Without induction we know basically nothing about the world apart from our own immediate perceptions. So we’d better keep induction, warts and all, and use it to form negative beliefs as well as positive ones.

You can prove a negative — at least as much as you can prove anything at all.

Shermer on The Science of Good & Evil

Shermer on am2 Northwest

Michael Shermer’s tour for his book The Science of Good & Evil, found him here explaining why we are moral, the evolutionary origins of moral sentiments, and how to be good without God.


Dinesh D’Souza and Michael Shermer

lecture reminder … The Great Debate

Dinesh D’Souza v. Michael Shermer

Sunday, December 9th, 2pm
Beckman Auditorium

READ about this lecture >



  1. danny says:

    basically completely right

  2. Mars says:

    Very true, I’ve personally found no faults in this article. Aliens, haha, that’s a good one. People will always believe what is more convenient to them regardless of proof. Sad but true, turning a blind eye dismisses all evidence. Say for example, that unicorn theory. Let’s make God the unicorn…


    1) If God exists, there must be proof.
    2) There is no proof.
    3) God does not exist.

    1) If God doesn’t exist, there must be proof.
    2) There is no proof.
    3) God exists.

    Basically, everyone is the same, trapped in the bubble known as their “reality”, blind to the universe around them… What a nuisance.

    and yes, P = -(-)P

  3. Jerome Rebholz says:

    1) If God doesn’t exist, there must be proof.
    2) There is no proof.
    3) God exists.
    Basically, everyone is the same, trapped in the bubble known as their “reality”, blind to the universe around them… What a nuisance

    The theist argument is not complexly true for the following reasons:
    Although there may not be absolute proof of god’s non-existence, there is certainly overwhelming statistical evidence to indicate far beyond any reasonable doubt that he dose not exist. One only needs to look at any branch of science to support this view. The number of references’ I could cite are almost un-limited!

  4. Zaki Aminu says:

    The theist argument is: “God Exists and His Creation is proof of this.”

    Why don’t atheists simply look in the dictionary to determine what the Word “God” means instead of making up the own meaning for It? Here’s how it is defined by Merriam-Webster’s online dictionary:

    noun \ˈgäd also ˈgȯd\
    Definition of GOD

    1 capitalized : the supreme or ultimate reality: as a : the Being perfect in power, wisdom, and goodness who is worshipped as creator and ruler of the universe

    Perhaps atheists doubt there is an Ultimate Reality since they believe everything is meaningless and that there is no such thing as objetive reality.

    Atheists constantly threaten to present “statistical evidence” for the non-existence of God but they NEVER do. Presumably, because they think no one will call their bluff. They’re only gambling that people wil feel sufficiently intimidated by the mention of “scientific evidence” to concede whatever they assert thereafter.

  5. Macflanahan says:

    In his above example he stated:
    1. If unicorns had existed, then there is evidence in the fossil record.
    2. There is no evidence of unicorns in the fossil record.
    3. Therefore, unicorns never existed.

    The problem is, you’re using absolute statements that are incorrect.
    Let’s take it apart:
    1. If unicorns had existed, then there is evidence in the fossil record.
    Do we know this to be true? Could unicorns have special bones which disintegrate upon their death? Could other unicorns come and hide their bones whenever one dies.
    Statement one cannot be proven to be true.

    2. There is no evidence of unicorns in the fossil record.
    Do we know this to be true? Could scientists/cultists/government/ etc. not have hidden these bones from the public?
    Statement one cannot be proven to be true.

    3. Therefore, unicorns never existed.
    Again, this seems to be the case with other animals, but how do we know this is also true of unicorns? Perhaps unicorns don’t have bones to begin with.

    No, you can never prove a negative.
    There are always alternate explanations.
    One can only provide lack of evidence as evidence and leave the door open for future information.

  6. Bob the Chef says:

    Macflanahan: that’s not really the point. No one is saying the premises are absolutely true (well, some armchair atheists might, but there’s not serious intellectuals, are they).

    The problem is that both theists and especially atheists believe that if something cannot be “proven” (for whatever definition of proven), then we are justified not in not believing it to be the case, but rather, in believing it to not be the case. Similarly, it’s incredibly difficult to prove that a single instance of a hybrid lizard-human existed in the past. You’d have to scour the earth, and ultimately, the evidence might have been destroyed. It also assumes that Earth is the only place it could have existed. More to the point, science can say at best “I don’t know”, but that isn’t good enough for practice. In practice, we assume the existence or non-existence of God. It’s not like the existence or non-existence of a teapot in space. If the Christian God exists, our actions matter because they’ll be judged. If God does not exist, they won’t. Our not believing in him won’t prevent us from being judged either, so end up confronting another practical choice. Do we vehemently deny the possibility, or do we live in such a way that treats the possible existence of God seriously? This is the reason why we have such emotionally charged debates. Admitting or rejecting not just God, but the serious possibility of God, changes the way we live, the course of our lives. And don’t buy the Dawkinsians who try to equate Zeus with Jahweh. The two are completely different. One is a being among many who happens to be endowed with powers, the other being itself.

  7. Randy B says:

    this is flawed bc based on this logic countless things have been could have been deemed non existent in the past and as more information is uncovered now and we learn more that which was once Negative is now a positive. In other words, i would prefer an as far as we know.. or based on the information we have uncovered.. but to completely right something off when any intelligent person is aware we know way less then we don’t know is doing a great diservice to anyone who chooses to listen

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