I think your post is confused.
The problem of evil is ultimately a problem of counterevidence. The reality doesn’t look like what the theory predicts. Therefore, the theory is quite likely wrong. Simple as that.
But this is the entire crux of the debate! The whole question is whether reality (i.e. a reality that appears to contain evil) looks like what the theory (i.e. the world is created by an omnipotent and omnibenevolent God) would predict.
Many theodicies argue that reality does look like what the theory would predict.
Here's how I would frame things in a Bayesian way, using your notation of G for "the world is created by an omnipotent and omnibenevolent being" and E for "the world appears to contain evil".
Suppose we have 1000 different theodicies T₁, ..., T₁₀₀₀. Let T⁺ denote the disjunctive event "some theodicy is correct" and T⁻ denote "no theodicy is correct".
If no theodicy is correct, then evil is strong counterevidence against God:
P(G | E, T⁻) ≈ 0
Now suppose that if any theodicy is correct, the existence of evil provides at most weak evidence against God — say, a likelihood ratio of at most 10:1 against:
P(G | E, T⁺) ≥ P(G) / 10
Then by the law of total probability:
P(G | E) = P(G | E, T⁺) · P(T⁺ | E) + P(G | E, T⁻) · P(T⁻ | E) ≥ P(G)/10 · P(T⁺ | E)
Matthew's claim amounts to: there are 1000 theodicies, the probability that any individual one is correct is non-negligible, and there is sufficient decorrelation between them, so the disjunction P(T⁺ | E) is reasonably large — say, at least 10%.
This gives P(G | E) ≥ P(G)/100, i.e. evil provides at most a 100:1 likelihood ratio against God.
That seems like a lot, but:
- If your prior P(G) is already fairly high, and
- You have independent evidence for God (e.g. fine-tuning arguments, anthropic arguments, etc.)
then P(G | all evidence) could still be substantial.
Your formal argument assumes P(G & E) ≈ 0 as a premise — but that's precisely the conclusion the theodicist is contesting.
But this is the entire crux of the debate! The whole question is whether reality (i.e. a reality that appears to contain evil) looks like what the theory (i.e. the world is created by an omnipotent and omnibenevolent God) would predict.
When the theory really predicts the outcome it's pretty clear, no one needs to write bazillion papers to persuade anyone that it's indeed the case.
On the other hand, such behavior happens, when you try to argue that your theory "totally has predicted the evidence" but only after the evidence was already revealed can you say what exactly it "had predicted".
I grant that some people may be confused about these two cases and maybe I'll even have to dedicate a separate post to it in the future, but at least to Mathew's credit, he has publicly acknowledged that he would expect a world created by omnipotent and omnibenevolent God to be a paradise which our world is not. So whether unconditional P(G&E) ~ 0 is not, in fact, a crux of disagreement.
Explicitly, where your math breaks down, and things shaped like your theodicies are often useful, is that pretty often a naive compute limited estimate of P(G & E) will be zero with high probability unless you importance sample using T. The classic case is trying to work out the probability that a photon will hit a speck of dust in a raytraced scene, where introducing the theodicy that a photon will zing straight from the lightbulb filament to your speck produces the correct probability through an expression just like P(G&E) = P(G&E|T)P(T) + P(G&E| ¬T)P(¬T)
This isn't an attempt to make a claim that Bentham's Bulldog is right in any meaningful way, just that this post probably introduces additional confusion, because detached from what E and G and T are supposed to mean, the math in the post doesn't prove what the text says it does.
pretty often a naive compute limited estimate of P(G & E) will be zero with high probability unless you importance sample using T
I'm having troubles parsing what you said here.
The classic case is trying to work out the probability that a photon will hit a speck of dust in a raytraced scene, where introducing the theodicy that a photon will zing straight from the lightbulb filament to your speck produces the correct probability through an expression just like P(G&E) = P(G&E|T)P(T) + P(G&E| ¬T)P(¬T)
Of course it produces the correct probability. Why would anything I said imply that it doesn't? I'm explicitly appealing to Law of Total Probability, after all.
I'm really interested in figuring out your objections to the post, but for now they seem quite incoherent to me. As if some words were wrongly changed by autocomplete, and, in case with this reply, as if your message was sent before you finished writing it.
Could you try once again and present me a simple and and explicit real world example where my math fails, writing your post not from a phone?
Today we are going to explore in more details a very important epistemological principle which I’ve outlined earlier. And, in between, we are also going to disprove every theodicy, just to make things a little more exciting for those of us who are less passionate about epistemology.
Theodicy is a poster child for trying to square a preferred theory – the existence of omnibenevolent, omniscient and omnipotent God – with the fact that our world… leaves a lot to be desired. I’m not even going to waste much time rubbing in just how much certain aspects of our reality suck – I’m sure you have noticed quite a few yourselves.
There are lots and lots of individual theodicies. I even made one myself when I was a child. All of them are flawed in myriads of ways. But trying to tackle each of them individually is an ungrateful task. This is the classical “unfairness of rationality”. Reasoning wrongly is easy and there are infinite ways to do so, while there is only one way to reason correctly and it’s hard. Some people, like Bentham's Bulldog in his post can exploit this predicament in such a manner:
It may seem that we have no choice but to engage with all of these works, spotting errors in them. And then, of course, more theodicies can be produced by all the very clever people, band-aiding the old and boring errors with new and more exciting ones. Therefore, putting us in a never-ending cycle. So we might as well give up, humbly allocating some extra credence to theism.
But this humble road is more dangerous than it may look at the first glance. If we give up in this particular case, why not in every other case like it? Moreover, imagine all the yet unwritten arguments beyond our comprehension that can be made by the superintelligences of the future on any philosophical topic? At this point we might as well give up on philosophy as a whole.
Ironic, isn’t it? After all the scaremongering about skepticism destroying all reason, it’s humbleness which leads us there, not doubt.
So if we are not yet ready to give up on philosophy, then what? Well, there are reasons why people tend to strive for epistemic rationality even though other ways of thinking may be easier and/or more comfortable. Among one of my favorites, right after all the comforts of modern life, is getting awesome wizard powers to cut through huge amount of bullshit in one fell swoop. And that’s exactly what we are going to do here.
Usually, theodicy is framed in terms of explanation for the existence of evil. The idea is – if evil is explained, then this is not a problem anymore. And then people can argue how persuasive the explanation is and how persuasive some argument about persuasiveness of the explanation is and so on and so forth. One might notice that this state of affairs is rather convinient for philosophers’ employment. But let’s not dwell too much on it for now.
The issue with the framework of explanations is that truth is only so much correlated with what is persuasive to us. Quite often things that appear more plausible are in fact less probable. Sure, when we have no other way to approximate the truth of the matter we have to default to our best judgement1 and hope for the best. But in this case, we actually have a better way.
Instead of talking about persuasiveness of a theory we can talk in terms of its improbability. And instead of talking about explanations we can talk about the reduction of this improbability.
So, let’s do exactly that! We have our quite implausible theory that Omnibenevolent and Omnipotent God coexists with evil:
P(G&E) ~ 0
How can we reduce this improbability? Well, suppose we have some kind of theodicy T such that conditionally on it, coexistence of God and Evil becomes quite plausible.
P(G&E|T) ~ 1
So, job’s done? Well, not exactly. We’ve just added a new element to our theory – our theodicy T. So, our combined improbability is:
P(G&E|T)P(T)
As G&E|T is quite probable, we simply need to demonstrate that theodicy T is also probable. All that is left to do is to find some probable theodicy T. Do that and we’ve successfully solved the problem of evil!
That doesn’t sound so hard, does it? Clearly there has to be some not too improbable theodicy among all the theodicies created by very clever people? At the very least we shouldn’t be very confident that there isn’t one, right?
Nope. In fact, we can formally prove that such theodicy does not exist.
By the Law of Total Probability:
P(G&E) = P(G&E|T)P(T) + P(G&E| ¬T)P(¬T)
Therefore:
P(G&E) > P(G&E|T)P(T)
And as
P(G&E) ~ 0
and
P(G&E|T) ~ 1
Then, inevitably:
P(T) ~ 0
Q.E.D.
The problem of evil is ultimately a problem of counterevidence. The reality doesn’t look like what the theory predicts. Therefore, the theory is quite likely wrong. Simple as that.
Theodicy is an extra epicycle that “explains the counterevidence away”. But it necessarily comes with the compensatory complexity penalty. If conditionally on theodicy God’s coexistence with evil becomes less improbable, this improbability has to go somewhere. And the only place it can go to is the theodicy.
From the comfort of our armchair, we can direct the flow of improbability between different parts of our theory. But the total improbability cannot be reduced. Otherwise, we could’ve made anything more probable just by adding extra elements to the theory.
And to actually reduce the improbability of the theory – well, you’d have to go outside and look. Find new evidence in favor of it. It’s not enough to come up with an awesome story. This story also has to actually be true.