In non-reductive physicalism, what we call the ‘self’ is not reducible to specific epiphenomena or brain states. The self cannot be given an adequately reductive physicalist account. The irreducible bit about the human person is what religious persons refer to as the ‘soul.’
This is not a blanket endorsement of non-reductive physicalism. Several philosophers actually believe that non-reductive physicalism cannot be reasonably held; instead, it leads to physicalism. Others prefer the term “neutral monism.” These formulations are usually attempts to avoid the extremities of a Cartesian-type dualism. Nonetheless, I like the term ‘non-reductive’ physicalism. It emphasizes the importance of the brain, but also maintains that consciousness is not identical with mental states in the brain.
It seems to me that several models within the non-reductive physicalist framework are compatible with Christian theology. The main emphasis within a Christian account of the afterlife is the resurrection of the dead. So long as there remains a bit of conscious-information not reducible to the human body, I see no problem in supposing that God might be able to imbue this irreducible aspect into a newly reconstituted, resurrection body.
Consider also the illustration of cell reproduction I’ve heard before. The information about cell reproduction given to us by biologists states that, over time, every cell in the human body is replaced. Thus, I do not have the same series of cells I possessed when I was seven years old. However, it would seem odd to claim that I have a completely different identity, or I’m a completely different person, than when I was seven. To be sure, I’ve grown, matured, and changed. But my basic personality and self still remains. There is some bit of information about me that remains constant even when all of my cells are replaced. (Of course, most of this due to genetic coding, but the illustration still might have some force to it).
I see this non-reductive identity as a being potentially true for many animals as well. Thus, I think there is an incredible high chance that many animals may also be granted eternal life as well.
I often think of this issue in terms of computers and data. If I have a certain system on my computer, I can delete it. However, I can also remove this system from my computer without completely erasing it by downloading it onto a USB. The system may leave my computer, but the information — what gives the system its identity — is not completely gone. Furthermore, by plugging the USB into my computer, the system can be reloaded.
I think of our ‘selves’ as this information system. It can be removed from the world (the computer) through death, but that does not mean it is completely gone from existence — for God himself (the USB) sustains that bit of information and can re-upload it when the time is right. Not only is this the case for humans, but for animals as well.