Wednesday, January 23, 2008

Proving negatives and burden of proof

The Skeptic's society has a weekly online newsletter called eSkeptic. A month ago, they had a great essay titled "You Can prove a Negative". It includes lots of things that I've tried to explain or was thinking of explaining in the future. All claims can be stated as negative claims. Absence of evidence is evidence of absence under certain circumstances. Inductive arguments do not imply their conclusions with certainty, but they still suffice as evidence. Inductive arguments are required to prove most positive claims as well as negative claims.

But I disagree on one point. Why do people think you can't prove a negative? Hales thinks that it's because of confirmation bias and disappointment in the uncertainty of induction. I think he missed an important reason: because it's true! Or at least partly true.

It's true that there is no fundamental difference between positive and negative claims. If we have a claim P, then there exists a negation of this claim which we might call Q. Q is equivalent to not-P (symbolized as ¬P or ~P) and P is equivalent to not-Q. P and Q are in a symmetrical relationship, and there is nothing in the logic to tell you that one claim is harder to prove than the other.

But in practice, this symmetry is often broken. In practice, one of these claims is what we call the null-hypothesis, and the other is not. The null-hypothesis states that there are no unknown processes at work. When we say "you can't prove a negative", the "negative" refers to the null-hypothesis. In practice, the null-hypothesis is not impossible to prove, but it is usually a little harder to prove.

For example, let's take the hypothesis that bigfoot exists. Let's assume that this hypothesis predicts approximately 1% chance of finding bigfoot behind any given tree. We look behind 300 trees. If the bigfoot hypothesis is true, then we have a 95% chance of finding him. If it's false, than we have a 0% chance of finding him. That means that if we don't find him, it's very unlikely that he exists. But if we do find him then that's some smoking-gun evidence for bigfoot (of course, I am making the spectacularly false assumption that our perceptions cannot be tricked). Either way, the evidence is fairly conclusive. But it would take hundreds of trees to prove the null-hypothesis, and only one to prove bigfoot (provided that we pick the right one). The null-hypothesis simply takes more work to prove.

Now, the reason I'm arguing about this asymmetry between "positive" and "negative" claims is not because I care about bigfoot or anything (seriously, bigfoot is boring). It's because the asymmetry is used as the basis for the concept of "burden of proof." Let's face it--proving stuff takes work. Proving the null-hypothesis takes more work than proving bigfoot. Therefore, the people who should be doing the work should be the bigfoot folks (known as cryptozoologists). They have the burden of proof.

The burden of proof concept is abused fairly often, I think because people detach it from its justifications. If you want to know when it's valid, you have to remember why it's valid!


Anonymous said...

The breadth of your chosen subjects leads me to ask this question. What are your personal goals for 10 years or more from now? Or, if that is too personal a question, whom do you admire most (5 to 10 people) for achieving their goals?

miller said...

Me? I'm still a teen. I'm not sure I'm allowed to think that far into the future!

I intend to continue studying physics on into grad school, and maybe further. I want to be a physicist, but other options are still open. I already have some experience in scientific research, in the area of geophysics, but that probably won't be my specialization. Outside of academics, I don't have any particular long-term goals.

J.L. Hinman said...
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J.L. Hinman said...

you cannot disprove the existence of God based upon the notion that you don't buy the reasons for belief in God.

you are seeking to be granted a level of proof the atheist will never allow the theist. Inductive proof, probability, rational warrant, these are not proof. They offer rationally warranted approach, but they are not proof.

atheists never allow theists that level of acceptance. You are seeking to privilege your views in a way that you are not willing to grant others.

Look it's not as though there no good reasons to believe. everyone who believes in God has deeply held personal reason. There are as many reasons as there are believers. I have 42 arguments for God, everyone one of them has help up in argument against atheists. none of them have ever been beaten. they are not proof, they are rational warrants for belief.

If there was a true absence of rational warrant for God then there would be not be "proof" but there would be good probabilistic reason to ignore the belief of others. Of course such is not the case. In the presence of vast overwhelming rational warrant, incredulity and refusal to grant privilege of acceptance is never going to outweigh personal belief.

Belief in God is rationally warranted.

you are wrong about Bigfoot too.You choose Bigfoot because you think people are predisposed to disbelieve it. there is a vast amount of good evidence that Kratz's primate exists. most skeptics don't know what they are talking about.

miller said...

Hey there!

Just so you know, I wasn't even thinking about God when I wrote this. But I'll bite.

First, I did not claim that I can disprove the existence of God. I think you can argue inductively against it, but that's all.

Furthermore, I do grant the theist the same level of inductive proof. I understand where you're coming from, since some will reject inductive arguments whenever it's convenient, but I'm afraid you're over-generalizing with me.

I did not say there are no good reasons to believe. I would only claim that these reasons are not as good as you think. And then there are reasons not to believe.

You are right on bigfoot. That is, I don't know what I'm talking about. I really wasn't thinking about bigfoot at all, and was only using that example because it was in eSkeptic. Really, bigfoot is boring.

Anyways, if you would like to continue to discuss the existence of God, I have only one request: maintain my interest, because I'm sort of busy and apathetic. You're very articulate, so this shouldn't be a problem.