The paper seems to be largely framed as an argument against some sort of dualist naturalist.
But I would argue that reductive materialism has no problem explaining what they're trying to explain. The "correlation" of phenomenal states with physical states is not at all "fortunate", if those physical states are just what phenomenal states are.
The correlation of phenomenal/physical states with one another would be explained by evolution. If a creature has a bunch of neurons just firing randomly with no rhyme or reason, that's probably not going to help them survive. But if some sensory perception causes neurons to fire, and this causes a chain of neurons to fire in a way that ends with sending signals to other body parts to respond appropriately given the perception, that's certainly going to give a survival advantage, and mutations that correspond to this will be selected for. This is evolution 101.
So it would be more strange if we don't see this correlation under physicalism.
The paper does mention evolution, but says that an evolutionary explanation would "presuppose normative harmony", which it doesn't, and arguably reductive materialism is much more consistent with evolution than any other view is (whether that's within atheism or theism).
They address functionalist views
It does spend some time addressing the "functionalist" forms of identity theory (reductive materialism). Actually functionalism is closely related but distinct from reductive materialism, but close enough.
To the credit of the authors, they seem to say that functionalism generally does a good job of explaining this harmony and they don't really offer any direct rebuttal. Instead, they say:
In that case, P(harmony|atheism & functionalism) = 1. But then we can’t infer that P(harmony|atheism) is fairly high, because there’s no reason to think that this highly specific functionalist view should cover a large fraction of the atheist region of our probability space.
What they seem to be missing is that evolution would favour that particular reductivist (what they call functionalist) view, and that makes reductivism the most likely atheist view.
But their fundamental logic here seems to be something like this:
- My car has been stolen.
- Any one of 8 billion people could've stolen my car, or it could've been magic (and we consider P(stolen|person) versus P(stolen|magic)).
- It's unlikely that any of some 7.9 billion people would've stolen the car, on account of not being any near the vicinity at the time.
- Let's consider people living in my city. For one such person, we have video evidence of them breaking into my car and driving away with it. If we suppose they stole it, this does a good job of explaining where my car went...
- But, I have "no reason to think that this highly specific city person should cover a large fraction of the person region of our probability space" (i.e. it's just 1 of billions of people, which is a small probability).
- So I can't infer that P(stolen|person) is high.
- Therefore it was probably magic.
This is clearly absurd. They're arguing that other atheist views are unlikely, and then they're using that to infer that this other atheist view must also be unlikely, even though they literally just argued that it's the one that makes the most sense.
They're not making a positive case
But even if we put that glaring issue aside, another more fundamental problem with the paper is that it doesn't actually make a positive case for what it's trying to argue for.
At best, it seems to be saying "this thing seems unlikely, therefore God". That's not strong evidence. To call it weak evidence would be generous. That's little more than "we don't know why this happens", and then inserting God in the gap in our understanding. It's equally valid as evidence for invisible fairies that give babies consciousness using magic. Now maybe you have reasons to favour the God hypothesis above invisible fairies, but this argument certainly isn't it.
The paper mentions the similarity to fine tuning, and that has been criticised for similar reasons (but fine tuning is a popular apologetic, so this might meet that very low bar).
They do acknowledge this, though:
"For simplicity’s sake, we frame this as an argument for theism, which we can understand as the claim that the universe was created by an all-powerful, all-knowing, and all-good being. But the data to which we appeal may be equally good evidence for other hypotheses.
Some may call it "simpler", others may call it "misleading".
They also say they're arguing against a universe that is "not teleologically ordered toward the realization of any kind of value, whether extrinsically (...) or intrinsically", but one might wonder whether this could be said to exclude evolution (and therefore would be about 160-something years behind the science). Certainly a species derives a sort of "value" from not dying out, even if this isn't value in any sort of objective sense. But maybe I'm just nitpicking a bit.
Their argument from improbability
They (mis)use Bayesian probability in support of their argument from improbability. But unlikely many people who do this, they do at least admit that they may be starting from what I consider a very questionable premise:
Likelihood Comparison is only interesting if the prior probability of theism is not so fantastically low that its posterior probability is negligible even after the evidential boost it receives from psychophysical harmony.
This is always going to be the problem with trying to use Bayesian probability in this way. You can't use Bayesian probability and just handwave the probabilities of dependent states (theism and atheism).