There’s been a few posts recently about using probability theory to illuminate questions of biblical historicity. It reminded me of a review I wanted to post on last year, but didn’t get time for.
Atheism is not the default position when it comes to God – as if the burden of proof was on the theist – for a number of reasons, but most interestingly because atheism is not the most likely as a prior probability (that is, the probability before you consider any evidence.) Anthony Kenny has offered one argument as to why: atheists have to deny every definition of God; theists have only to affirm one. So the atheist has to prove more than the theist to ensure their position stands, which suggests atheism is a lower prior probability.
The use of probability to talk informally about the existence of God has a long pedigree, but a rather ignominious one. And indeed folks like Swinbourne, and Tony Kenny have dabbled in making it a little more explicit. But this specific argument, whilst also being methodologically confused (it doesn’t understand what ‘prior probability’ means, technically) is also naive in a very freshman-probability-course way.
What is the probability of you not rolling a 6, on three fair dice? It is 5/6 on the first die, 5/6 on the second, and 5/6 on the third, giving 125/216 of not rolling a 6. So even though the chance of rolling a six is small, with three shots at doing it, the odds of avoiding a 6 come out at not far from 50:50 (if we had a fourth roll, the chance would drop below 50:50).
This is Kenny’s hypothesis – what is the chance of no God existing, of atheists being right. We calculate it in the same way: What is the change of Yahweh not existing? What about the Christian Trinity? Vinshnu? Zeus? Allah? Isis? Each probability might be close to one: each God may be unlikely. But multiply them together and the chance of none of them existing drops way down. For example, if we had one thousand potential Gods, each with only a one-in-a-thousand chance of existing, the likelihood of the atheist being right is only 35%.
Unfortunately this line of argument is crock. It assumes independence.
When you first learn statistics and probability, chances are your instructor would have spent a lot of time telling you that things are independent. Flipping heads 10 times on a coin does not mean the next flip is more likely to be tails*. This is counter-intuitive, so it gets a lot of emphasis.
But unfortunately, things in the real world are very rarely independent. The independence isn’t normally the kind that we intuit (our intuitions really are most often wrong in probability**). But we cannot assume independence in general. And in my experience even graduate students of science find it hard to shake the idea, planted in high school, that every probability is independent.
The non-existence of Gods, for example, is highly dependent. And without independence, the Kenny system is laughably naive (and a good way to flunk undergraduate statistics). Yahweh isn’t a completely new option to Allah, or even Isis. The mythologies are connected, deeply, historically and psychologically.
Taking the probability of each of a thousand broadly similar Gods as being one-in-a-thousand, the final probability of there being any God, would end up being pretty much still one-in-a-thousand. And that is definitely not a good argument for agnosticism.
There are better ways to argue for agnosticism, I think, and in fact in Vernon’s article he goes onto a much better one, that the existence of God reduces the number of explanations, which in general tends to be associated with better explanations. I disagree with that, too, but that’s a topic for another day.
* I’ve said before on this blog, that the correct answer is that, a coin that flips heads ten times in a row is more likely to flip heads on the eleventh. When I said that before, I was disagreed with. But, nevertheless, I was right 😉
**Here’s a famous example: My sister has two children, one of whom is a boy – what is the probability of the other child also being a boy? (assume that there is a roughly 50:50 male/female split among children as a whole). For the answer, drag your mouse over this invisible text to select it and read it: There is roughly a 1/3 chance the other child is a boy – if that matches your intuition (and you haven’t heard the puzzle before), then you’re very, very unusual.