Essay:Blake Giunta and the Butchered Bayesian
In a debate against Matt Dillahunty, apologist Blake Giunta presents a bayesian analysis of the probability that a moral arena would be produced by a godded model of the universe creation compared to the probability that it would be produced by a non-godded model of the universe creation process. Mathematically, his mistake is to neglect the sum over the possible models within each set. For instance, for the ungodded model, you must sum over an uncountable sea of similar models, such as the idea of a multiverse of similar universes with slightly different fundamental constants to get the correct result.
Blake Giunta would likely complain that the weighted sum in each half should add up to the same value, so it is irrelevant: If there are so many ungodded models, there should be so many godded models too. However, this would be to ignore that the godded model is much more specific. When we state that everything was created by a perfectly benevolent, perfectly capable, magically empowered human-plus mind, we have essentially post-selected our godded models very heavily. And this is why he reaches the absurd conclusion that the mere existence of a moral arena provides support for the christian god even though the authors of every known godded creation theory already knew that there was a moral arena. Also, the weighted sum cannot ever be ignored, in this way, because he implicitly writes P(X|naturalistic)P(Y|naturalistic)P(Z|naturalistic), instead of the correcter P(X|naturalistic)P(Y|X, naturalistic)P(Z|X,Y,naturalistic). Even this subtle difference (which is separate from his main mistake of neglecting the sum) is enough to make his conclusions false, since it massively increases the values that a reasonable person would assign to the probabilities later in Blake Giunta's list.
To elaborate on the post-selection problem, Blake Giunta miscompares a (very specific) post-selected godded set of models with a (very general) un-post-selected ungodded set of models.
I would ask that Blake Giunta acknowledge this, and either compare post-selected models, or un-post-selected models.
To compare post-selected models, we could choose the Christian god vs the naturalistic model that there are a great many possible universes, all effectively infinite in size. In this model, the christian god would be reasonably likely to have created our universe with its moral arena, as  states. It would be probable, though, that that god would either keep itself completely hidden, or show itself. It is a very false statement to say that the christian god, without looking at the universe, would very likely reveal himself in the exact way that the bible says, and then stay hidden. It is also unlikely that the universe would appear quite so full of evil. But Blake Giunta's point remains, that that god would be fairly likely to create a moral arena.
One post-selected naturalistic explanation, one of very many that the atheist is not forced to choose between, would entail a multiverse containing universe after universe, one of which is likely to support life. If intelligence is a product of evolution combined with social pressures, which is very likely, then it is indeed very likely that this particular naturalistic model would produce a moral arena. It is also likely that the inhabitants of this universe would consider some things that happen to their community to be 'evil'. (A discussion of boltzmann brains is below).
So, in the post-selected comparison, we get a naturalistic model winning: the problem of evil goes away, the problem of god's hiddenness goes away, and the models are otherwise similar in their explanatory power.
Blake Giunta makes a valid point that the un-post-selected naturalistic world might be very unlikely to produce a world with a moral arena. Anyone who has tried to make computer simulations of simple universes knows that moral arenas don't appear in all of them, or even most of them.
However, the un-post-selected godded model is a bizarre comedy of errors: The honest mathematician would acknowledge that before we saw the universe and its weird books, we would have a very open idea of what a god might look like. The only real starting point is that it would contain one or more minds --- a definition of a godded theory. What does the randomly chosen mind look like? If you put random computing elements together (and give it a soul if you want to, and if your world-view needs it), you get something that doesn't function. So the general godded model predicts that in the void there was a mind, but the mind didn't create jack because it was broken.
What is the probability that the god mind happened to be a functioning mind? Well most minds we are aware of belong to lower creatures: They massively outnumber humans. So the median possible god model (once we get rid of the broken majority) would be "In the void was a mind. The mind had rudimentary thoughts, but was vastly incapable of designing a universe".
So, let's say that this randomly chosen mind was actually human-plus in intelligence, somehow. That's massively unlikely for someone who hasn't seen the universe, by the way. This mind doesn't necessarily have the capability to create anything. A disembodied mind in space doesn't. If I was put in space by myself, I wouldn't be able to create much. Would you?
What is the probability that this mind would have some extra set of creation mechanisms?
Creation mechanisms are complicated. What are the chances that the mind would start off knowing how to use them? There's no a-priori reason to think that the god-mind would just know: Remember that nothing designed it.
What are the chances that the functioning, human-plus, empowered, pre-knowledged mind would try to create a universe with a moral arena in it? Well, that depends on whether this mind was interested in humans, moral agency. That depends on a lot. If you hadn't seen humans, you couldn't a-priori assume that.
And even if it could, would it manage to? I would probably make a mistake when writing down the field equations when creating the universe, and it would probably not work. What are the chances that an un-post-selected god would manage to create a universe?
Our conclusion is that un-post-selected models are impossible to compare: there are too many uncertainties. The resulting probability has an uncertainty that is probably hundreds of orders of magnitude, and the conclusion you would reach would simply depend on your bias. It is certainly not the case that an un-post-selected godded model would have a 1% probability of creating a moral arena.
So this line of reasoning doesn't work.
In conclusion, if you do probability theory honestly, you don't get that god is massively more likely to have created a moral arena at all. I would also suggest that a way for someone to address this problem using bayesian analysis would be to ban any supporting facts that would have been consciously or subconsciously apparent to the authors of the theory. In effect, the more honest question is "What are the chances that the bible version is true, given the set of facts that either contradict the bible or that the authors of the bible could not have known".
This would avoid the probably inadvertant dishonesty that Blake Giunta presents in comparing a heavily post-selected godded model with a deliberately un-post-selected ungodded theory.
(to preempt a boltzmann brain defence: If, as the godded so often claim, the chances of a single bacterium coming into existence naturalistically are vanishingly small, then surely the chances of a mind coming into existence without evolution are vanishingly vanishingly small, so we're more likely to be in a life-supporting place, which has a much higher probability of producing brains, than in empty space created by random fluctuations, which have an infinitesimal (even taking into account the size of empty space) chance of having brains in them)