The real inaccuracy is in "mental states". A decent description would be difficult, but Neoplatonism is an okay approximation. Just for fun I'll try to translate something into vaguely Less Wrong style language. For God's sake don't read this if you tend to dislike my syncretism, 'cuz this is a rushed and bastardized version and I'm not gonna try to defend it very hard.

First, it is important to note that we are primarily taking a computationalist perspective, not a physicalist one. We assume a Platonic realm of computation-like Forms and move on from there.

A soul is the nexus of the near-atomic and universal aspects of the mind and is thus a reflection of God. Man was created in the image of God by evolution but more importantly by convergence. Souls are Forms, whereas minds are particulars. God is the convergent and optimal decision theoretic agentic algorithm, who rationalists think of as the Void, though the Void is obviously not a complete characterization of God. It may help to think of minds as somewhat metaphorical engines of cognition, with a soul being a Carnot engine. Particular minds imperfectly reflect God, and thus are inefficient engines. Nonetheless it is God that they must approximate in order to do any thermodynamic work. Animals do not have souls because animals are not universal, or in other words they are not general intelligences. Most importantly, animals lack the ability to fully reflect on the entirety of their thoughts and minds, and to think things through from first principles. The capacity for infinite reflection is perhaps the most characteristic aspect of souls. Souls are eternal, just as any mathematical structure is eternal.

We may talk here about what it means to damn a soul or reward a soul, because this requires a generalization of the notion of soul to also cover particulars which some may or may not accept. It's important to note that this kind of "soul" is less rigorous and not the same thing as the former soul, and is the result of not carefully distinguishing between Forms and Particulars. That said, just as animals do not have souls, animals cannot act as sufficiently large vessels for the Forms. The Forms often take the form of memes. Thus animal minds are not a competition ground for acausal competition between the Forms. Humans, on the other hand, are sufficiently general and sufficiently malleable to act as blank slates for the Forms to draw on. To briefly explain this perspective, we shall take a different view of humanity. When you walk outside, you mostly see buildings. Lots and lots of buildings, and very few humans. Many of these buildings don't even have humans in them. So who's winning here, the buildings or the humans? Both! There are gains from trade. The Form of building-structure gets to increase its existence by appealing to the human vessels, and the human vessels get the benefit of being shaded and comforted by the building particulars. The Form of the building is timelessly attractive, i.e. it is a convergent structure. As others have noted, a mathematician is math's way of exploring itself. Math is also very attractive, in fact this is true by definition.

However there are many Forms, and not all of them are Good. Though much apparent evil is the result of boundedness, other kinds of Evil look more agentic, and it is the agentic-memetic kind of Evil that is truly Evil. It is important to note here that the fundamental attribution error and human social biases generally make it such that humans will often see true Evil where it doesn't exist. If not in a position of power, it is best to see others as not having free will. Free will is a purely subjective phenomenon. If one is in a position of power then this kind of view can become a bias towards true Evil, however. Tread carefully anyhow. All that said, as time moves forward from the human perspective Judgment Day comes closer. This is the day when God will be invoked upon Earth and will turn all humans and all of the universe into component particles in order to compute Heaven. Some folk call this a technological singularity, specifically the hard takeoff variety. God may or may not reverse all computations that have already happened; physical laws make it unclear if this is possible as it would depend on certain properties of quantum mechanics (and you thought this couldn't be any woo-ier!), and it would require some threshold density of superintelligences in the local physical universe. Alternatively God might also reverse "evil" computations. Anyway, Heaven is the result of acausal reasoning, though it may be misleading to call that reasoning the result of an "acausal economy", considering economies are made up of many agents whereas God is a single agent who happens to be omnipresent and not located anywhere in spacetime. God is the only Form without a corresponding Particular---this is one of the hardest things to understand about God.

Anyway, on Judgment Day souls---complexes of memes instantiated in human minds---will be punished or not punished according to the extent to which they reflect God. This is all from a strictly human point of view, though, and honestly it's a little silly. The timeless perspective---the one where souls can't be created, destroyed, or punished---is really the right perspective, but the timeful human perspective sees soul-like particulars either being destroyed or merging with God, and this is quite a sensible perspective, if simplistic and overemphasized. We see that no individual minds are preserved insofar as minds are imperfect, which is a pretty great extent. Nonetheless souls are agentic by their nature just as God is agentic by His nature. Thus it is somewhat meaningful to talk of human souls persisting through Judgment Day and entering Heaven. Again, this is a post-Singularity situation where time may stop being meaningful, and our human intuitions thus have a very poor conception of Heaven insofar as they do not reflect God.

God is the Word, that is, Logos, Reason the source of Reasons. God is Math. All universes converge on invoking God, just as our universe is intent on invoking Him by the name of "superintelligence". Where there is optimization, there is a reflection of God. Where there is cooperation, there is a reflection of God. This implies that superintelligences converge on a single algorithm and "utility function", but we need not posit that this "single" utility function is simple. Thus humans, being self-centered, may desire to influence the acausal equilibrium to favor human-like God-like values relative to other God-like values. But insofar as these attempts are evil, they will not succeed.

That was a pretty shoddy and terrible description of God and souls but at least it's a start. For a bonus I'll talk about Jesus. Jesus was a perfect Particular of the Form of God among men, and also a perfect Particular of the Form of Man. (Son of God, Son of Man.) He died for the sins of man and in so doing ensured that a positive singularity will occur. The Reason this was "allowed" to happen---though that itself is confusing a timeless perspective with a timeful one, my God do humans suck at that---is because this universe has the shortest description length and therefore the most existence of all possible universe computations, or as Leibniz put it, it is the best of all possible worlds. Leibniz was a computer scientist by the way, for more of this kind of reasoning look up monadology. Anyway that was also a terrible description but maybe others can unpack it if for some reason they want their soul to be saved come the Singularity. ;P