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Posted by on Aug 23, 2012 in Critical Thinking, secularism, skepticism | 9 comments

Can you prove a negative? Positively

The claim is often made in arguments about god, usually between self-described atheists and agnostics, that you can’t prove a negative claim. The claim in question is God. Is this true for the God claim? Is it true generally? The answer to both, is no. I will address the second question first.

Negativity’s Swan Song
This bit of nonsense has its roots in legitimate philosophy. The frailty of induction has often been noted with this example: All swans that have been observed are white. Therefore, swans are white. The weakness is obvious: maybe you haven’t seen every swan. The negative claim “there is a swan that isn’t white” seems hopeless to disprove, and it is. Yet, science proceeds largely via induction (and abduction, but that is a boring story for another day). How is this resolved?

The swan claim in its strict logical form is irrelevant, and frankly, dull. It is pertinent neither to science, nor to our considerations as individuals. Although scientists might speak in a shorthand that sounds like “all swans are white”, the actual scientific fact would merely be “all swans seem to be white based on existing observations”. The degree of certainty is tied to the preponderance of evidence, but it never gets to 100%. Compare the statements:

Logic: The premise “All swans that exist are definitely white”  is not provable.
Scientific reason: “Swans observed have all been white; all of them might be.”

Logic tells us the upper boundary on how sure we can be about some things, but the boundary is so far away from the space we live and think in, that it is totally irrelevant to our considerations. The second statement gives us useful information: you should make predictions based on the strength of the available evidence and not stronger. The first statement tells us nothing because we don’t care if every swan in the universe is white, we care about what the vast majority are, the number that defines “swan-ness”. Here’s another example.

You visit your doctor. She says she has bad news. There is a chance you have the plague. Specifically, she continues, a one in 53 trillion chance. Now you’re not sure if she’s joking with you, and you sort of want to hit her. She explains that you show no symptoms or signs, but that by mere probability theory, there is a nonzero chance you have every disease ever discovered and even diseases never discovered which she is in fact just making up on the spot. That sounds silly, but again, there is a non-zero chance that they might exist, you can’t prove that they don’t. Angry that your time has been wasted, you storm out, and post the anecdote on Reddit.

If you don’t care about the one in 53 trillion chance that you randomly have the plague (or an illness she made-up on the spot), why would you concern yourself with propositions with much lower (but nonzero) probability of the “there’s a swan that is not white” variety?

Everyday negatives
It’s extraordinary how scientifically illiterate so many people who argue the philosophy of atheism can be. A vast number of scientific papers confirm negative statements. Do cell phones cause cancer? For scientists to evaluate this claim, they take as a null hypothesis “not X” or specifically here “cell phones do not cause cancer”. They then collect data on cell phone users versus people who do not use them. After enough rigorous studies have been conducted, they conclude (and indeed they have) that no, there is no link between cell phones and cancer. Like the plague example above, the likelihood has not dropped to zero, but it has dropped low enough that the possibility is no longer worth our time- it is no longer a reasonable suggestion (The actual data on cell phone use does not yet merit this level of certainty, that will take a decade or more of research, but it is the case for many claims, such as from homeopathy). Is species X older than Y? Do vaccines cause autism? Is there a gene for liking rock music? All of these require the evaluation of negative statements.

Science aside, we can confirm negatives in our day to day lives as well. There’s no milk in the ‘fridge. The car is not in the garage. It isn’t noon right now. These are all easily confirmable negative statements.

You are not special
Some negative claims really are impossible to prove (No tyrannosaur that ever lived had red feet). Some are really hard (there’s no teacup orbiting the sun). Some are easy (there’s no car in the garage). In other words, they’re exactly like positive claims. Some positive claims are impossible to prove (Julius Caesar would have loved World of Warcraft), some are hard (there is dark matter out there somewhere), and some are easy (there is a car in the garage). Note that both of those easy claims rest on the same evidence. This is another way of showing that negative claims are not special: almost all positive claims can be restated as negative ones. There is a car in the garage -> The garage is not absent a car. And vice versa: There is no god -> The universe is a purely natural thing. Which brings us back to god.

God: also not special
The first thing to note, is how many gods have already been disproven. Ancient peoples believed the gods actually lived in inaccessible places on or near Earth: the sky, the bowels, the seas, Mount Olympus. Then people checked. Nope. No gods.  Negative proven beyond all shadow of a doubt. This has happened thousands of times. But agnostics today (and theists who magically turn into agnostics at the debate table) love playing games, so they invent ever smaller, more elusive gods and put them in places they think are inaccessible, just as the ancients put the gods on Mount Olympus. These are not gods any significant number of people believe in, but the games must go on, because surely there’s nothing more important to argue about than infinitely elusive, infinitely irrelevant “gods”.

The gods of the game-playing deists and agnostics are nonexistent based on the available evidence from psychology (god ideas are invented by creative humans, not discovered truths), philosophy (ignosticism, causality, etc..,) and cosmology (run back the clock and the universe gets simpler, not more complex) to name just three. Do we know this absolutely? No, but that is not the standard. It is not the standard used by science, by people who successfully navigate their lives, nor by anyone other than those engaged in purely masturbatory philosophical game-playing. It is simply not what we ever mean by true, correct, or valid. Why apply to god ideas a standard we never apply to anything else?

The gods that people actually believe in, people such as Christians and Buddhists (yes, religious Buddhists believe in gods) are disconfirmed by a wide range of observations from history, biology, and physics.

Although it is important to think clearly about these issues for it’s own sake, the practical take-away from this article is that theists love to pull out this would-be trump card to stymie atheist and agnostic critics: stop letting them.

  • http://alephsquared.wordpress.com aleph squared

    P1: You can’t prove a negative
    P2: “You can’t prove a negate” is a negative statement
    C1: Thus, you can’t prove that “you can’t prove a negative”

    Also, if you can prove a positive, then you can prove a negative. (If you can prove P, then you can prove not-notP)

    I don’t understand why this idea that “you can’t prove a negative” is so prevalent.

  • Copyleft

    In addition, I recall that there are certain types of general negative statements that CAN be proven, even ones that are not about the observable universe. “There are no triangles with four corners” is one example of a provable negative because it entails a logical contradiction.

    Some argumens about gods–such as “He’s all-good, all-powerful, and all-seeing, and he lets evil exist” could fall into that category as well. Saying “no such god could exist” is a provable negative becuase of the logical contradiction.

    • http://alephsquared.wordpress.com aleph squared

      It isn’t just certain types. The fact is that, logically, the question of a statements provability has *nothing at all* to do with whether the statement is negative or positive.

  • http://facebook.com/donsevers donsevers

    >Why apply to god ideas a standard we never apply to anything else?

    Great article and comments. Never thought I’d learn anything further about this topic, but I did. Can’t wait to use this one on an unsuspecting believer:

    “There are no triangles with four corners.”

    Sure, I’m a seeker of truth, but I’m human, too.

  • http://facebook.com/donsevers donsevers

    > they invent ever smaller, more elusive gods and put them in places they think are inaccessible

    Even heavyweights like Plantinga and Craig settle for the mere possibility that some type of god COULD exist. At this point, I feel embarrassed for them. Christianity: not impossible! Even if they succeed, all the heavy lifting of homing in on Yahweh remains.

    I’m a former believer. Even I want more for God than to stand on the starting line with flying pigs and orbiting teapots.

    Believers are uniformly shocked to hear that Yahweh has been ruled out. Religion has controlled the conversation so much, often with our cooperation, that saying this is like saying that George Washington was not the first president. He wasn’t. It was Peyton Randolph.

    When we have a good definition to work with, most gods have been proved no to exist.

    http://en.wikipedia.org/wiki/President_of_the_Continental_Congress

  • http://www.skepticblogs.com/justinvacula Justin Vacula

    If we define gods in particular ways, particularly with omni-terms, it seems possible to ‘prove a negative.’ The evidence of egregious natural suffering in the world seems to show that an all-loving, all-powerful, and all-knowing god created the universe.

    In your post, I think it was important to note that a ’100% certainty’ is unhelpful in discussions. Many want that 100% confidence level, but it is unreasonable.

  • Papalinton

    No black swans? Then they haven’t been to Australia yet. :o)

    • Edward Clint

      There are indeed That’s the punchline that is meant to expose the weakness of induction. If you were studying swans, and you just never visited Australia or New Zealand, you’d get more and more confident all swans are white as you observed more or more white swans. The proposition can never be proven, only disproven.

  • http://lippard.blogspot.com/ Jim Lippard

    I wrote something on this subject a few years ago, which has been updated from time to time to link to some other pieces which make the same or similar points: http://www.discord.org/~lippard/debiak.html

    My most recent find was in Vincent Bugliosi’s _Reclaiming History_, the passage in question is cited and quoted at the above link.

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