Sunday, April 27, 2014

Extraordinary Claims and the Principle of Indifference

You've probably heard the saying "Extraordinary claims require extraordinary evidence." It's the starting point for perhaps the most common argument by atheists: "The existence of God is an extraordinary claim that lacks extraordinary evidence." Seems logical, right? The only problem is, how can we determine whether the evidence (or the claim) really is extraordinary?

One common definition of extraordinary is "very unusual". But the claim that God exists isn't unusual. By that definition, "There is no God" would be a more extraordinary claim. But that standard doesn't always make sense. For example, someone could make the very unusual claim that I'm currently wearing three socks, but most people wouldn't require extraordinary evidence to be convinced. Another common meaning of "extraordinary" is "very remarkable or amazing". That one brings us right back to the original problem: How can we determine how remarkable or amazing a claim is? There are other definitions of "extraordinary" but all are similarly problematic.

A much more scientific way to formulate "Extraordinary claims require extraordinary evidence" is via Bayes' theorem. In Bayesian terms, an extraordinary claim is a hypothesis with a very low prior probability (e.g., “a coin flipped 5 times will land on tails every time”, which has a prior probability of around 3%). It follows that very strong evidence is required to move the probability high enough to believe the claim. Thus, it can be shown mathematically that extraordinary claims (defined this way) do in fact require extraordinary evidence. In the above example, that evidence could be a measurement that the coin's weight is very unbalanced or an observation that it has tails on both sides.

Applying that framework to the God claim, the strength of evidence required depends on a priori assumptions about the prior probability that God exists. Theists who start with a relatively high prior probability require less evidence. Atheists who start with a low prior require more evidence. Arguments about the sufficiency of the evidence for God become circular on both sides. Thus, it's imperative that we have a good, objective way to determine the prior probability.

Because we don't have specific, definite probabilistic information about the God question, we must use an uninformative prior. The simplest and probably most common of these is the principle of indifference, which says the prior probabilities of all hypotheses are equal. In the binary case of “Does God exist?”, the prior is 50%. Starting with a 50% probability may seem crazy if the claim seems ridiculous, but it makes good sense mathematically. The evidence (or lack thereof) is probably what makes such claims seem ridiculous in the first place, and the other terms in Bayes' rule account for that. Also, if the claim seems ridiculous to most people, that fact alone is evidence that would reduce the probability.

Using the principle of indifference, presuppositions about the probability of God's existence are eliminated as determining factors. The estimate of the probability that God exists now depends entirely on the evidence. In this case, “Extraordinary claims require extraordinary evidence” is a meaningless argument. It doesn't matter how extraordinary the claim is because the evidence will tell us whether to believe it. We'll still argue about the evidence and how to assign probabilities to it, but that's a lot more useful than debating a theist's circular argument vs. an atheist's circular argument.

There are other ways to determine uninformative priors, including some that let us use the “extraordinary claims” standard. But when applied to the God claim, they generally require arbitrary assumptions that lead to self-fulfilling conclusions. That might be good enough for testing the claim that I'm wearing three socks right now, but whether or not to believe in God is a much more important question – one that I don't think should be decided (either way) by arbitrary assumptions made before examining the evidence.

Saturday, April 12, 2014

Free Will in the Bible: Overfitting + Confirmation Bias

A major theme of this blog is that we shouldn't force data to answer questions it doesn't actually answer. Overfitting and confirmation bias can have an insidious synergy. I believe the debate over free will in the Bible is one such example. Before I discuss it, I need to define it, because there are two types of free will that people often confuse:
  1. Free will in the legal sense: freedom to make voluntary choices without coercion. In other words, freedom to choose what we want to choose.
  2. Free will in the philosophical sense: the ability to make choices that aren't determined by prior causes. In other words, what we want to choose might be influenced by God, genetics, environment, etc. but aren't completely determined by them.
Another important term is "determinism", which is the idea that all events are caused by prior events or conditions.

Despite some caricatures I've heard, practically everyone agrees that we have free will in the legal sense, so when I say "free will" without a qualifier I'm referring to the philosophical sense. There are 4 main philosophical views of free will:

  • Hard Determinism: everything happens as a result of what happened before it. Free will is impossible because what we want to choose is determined by prior events & conditions.
  • Libertarianism: the universe is not deterministic. If it was, we wouldn't have free will. It is possible to make choices that are not determined by prior events & conditions.
  • Compatibilism: the universe is deterministic but we have free will. Free will only makes sense using the legal definition and it's pointless to talk about philosophical free will.
  • Hard Incompatibilism: whether the universe is deterministic or not, we wouldn't have free will either way.

People have debated free will for millennia and Bible-believers are no exception. According to Josephus, first century Jews were divided about it. The Essenes were hard determinists who believed that everything was determined by divine fate. The Sadducees were libertarians who denied divine fate and affirmed free will. The Pharisees' view was most similar to Compatibilism. They believed in divine fate for world events but also affirmed free will, particularly in spiritual matters, and their definition of it was more like the legal sense.

Many Christians today are either compatibilist (i.e., Calvinists) or libertarian (i.e., Arminians). Thanks to confirmation bias, it's not surprising that both believe the Bible clearly teaches their view. As readers of this blog might've guessed, I don't believe the Bible writers tried to settle this philosophical debate, so any such interpretation is overfitting. What the Bible does clearly teach is that at least some events are pre-ordained by God and that we make free choices (i.e., we have free will in the legal sense). Those teachings are consistent with all 4 views. Attempts at Bible interpretation on the topic of philosophical free will quickly abandon the original context and inevitably enter the realm of philosophy.

My biases make Hard Determinism (and Compatibilism, which I think is Hard Determinism but afraid to admit it) very attractive to me. Weather is deterministic, and I like to think everything behaves similarly to weather -- maybe because it makes me feel like I have expertise in areas in which I really don't. I see a lot of beauty in deterministic systems, and Chaos Theory provides an excellent answer for why some things appear random or "free". Hard Determinism also is an attractive solution to the problem of evil. If God causes evil, it means evil has a purpose -- a greater good. God doesn't helplessly watch, wishing things were different. Hard Determinism allows for truly divine miracles that don't violate the fundamental laws of nature, demonstrating harmonious consistency in God's interaction with the world. Biological evolution also fits very nicely. And I can feel good when reading the many Bible passages that clearly imply determinism.

I do believe it's the view that is most consistent with the Bible (sorry, Arminian friends), but I must admit that my view is totally based on philosophy, science, and personal bias, not the Bible (sorry, Calvinist friends). What makes me doubt my view is not Libertarian proof texts in the Bible (I have answers for all of them, though not without confirmation bias). What really gives me doubt is quantum mechanics. The more I learn about it, the more I see Hard Incompatibilism and Libertarianism as interesting possibilities.

It's fun to talk about the free will debate as it relates to the God of the Bible. I think the debate would be a better one if we all could admit that it is in fact a philosophical (and perhaps scientific) debate -- one in which the writers of the Bible were not participating.