After Free Will
Of course compatibilists (those who say free will is compatible with determinism) will argue that Davies is mistaken about what free will is, and that it has nothing to fear from science. But they will likely agree that what he means by free will might not survive a naturalistic understanding of ourselves. The obvious point being that we can avoid confusion on the free will issue by stating up front what capacity or characteristic of an agent we refer to when we say "X has free will." Or better yet, simply talk about the capacities and characteristics themselves, whether there’s reason to believe they exist, and what their existence or non-existence implies for how we think about ourselves and, for instance, our responsibility practices. Talk about free will, absent clear definitions, is simply a recipe for miscommunication.
Davies himself speculates that even as strictly material creatures, we have robust, neurally based capacities for extracting and creating meaning that will likely see us through the death of free will as he defines it (the death of the contra-causal soul, more or less). He says there’s no evidence yet for such optimism, but I think there’s at least some anecdotal evidence coming in, see here. And as Shaun Nichols pointed out at the end of his Scientific American article (discussed by yours truly here), there’s evidence that determinists don’t give up on moral responsibility. Life, meaning and ethics and will go on after the soul is gone. Not that it’s going quietly, see Creationists declare war over the brain and Steven Novella's good 3 part commentary starting here.
I also take some (friendly) issue with Davies' description of the poor beleaguered self: he says it gets pushed around by internal and external stimuli. But if we agree the self isn’t an immaterial soul, is there anything else we’d call the self that’s separate from neural activity or from the brain and body that could be pushed around? If not, then we might say there is no self, in which case the problem of being pushed around disappears. But we might instead say (and this is my preference) that the self or person is, for instance, an integrated, functionally coherent construction of physical and psychological parts (see here). This stable, identifiable agent is just as real as its causal antecedents and external environment, and therefore we can justifiably assign it causal powers, just as we assign causal powers to the antecedent factors that created it and the environment that impinges on it. So we shouldn’t feel demoralized, disempowered or in any sense disestablished when admitting our complete integration into the causal matrix (see here). After contra-causal free will is gone, we'll still be recognizable as people, moral agents, and the readily identifiable individuals we so reliably are. And again, life will go on with its usual ups and downs, but minus a major incitement to pride, contempt, resentment, shame, guilt, and other not-so-lovely reactive attitudes.