I came up with this idea first in response to Rob_the_Bob http://www.gamesas.com/topic/1504463-aldmeri-resentment-of-man-the-dragonfires/?p=23709780, when he asked why some people like Archmage Shalidor are able to retain their selfhood, if most souls go back to the Dreamsleeve where they're washed clean of their selves. In response I came up with this, and then realised that I think it ties in really nicely with /u/MareloRyan's http://www.reddit.com/r/GodheadModel/comments/24e1qd/a_model_of_the_godhead_and_its_contents_part_i/ on Reddit. I posted this to /r/teslore a couple of days ago and now I'm finally getting around to posting it here too.
I'm sure there are holes to fill, and it's possible that I've not explained some things in the best way possible and might need to clarify. In particular, if you haven't read the Godhead Model I suggest you do so first, because it's fascinatingly good and also I use a lot of its technical language here.
u/MareloRyan's theory about souls is summarised in http://www.reddit.com/r/teslore/comments/1viqa9/why_are_briar_hearts_souls_black_while_hagravens/cesttbz. It goes that souls are made of (at least) two parts, the AE-- the self-- and magicka. This is why white souls being used in enchanting is not considered necromancy. The AE has departed and you're only using the magicka. Black souls are much more tightly bound to their magicka, so black soulgems capture both parts of the soul.
My theory goes into why black souls' AE and magicka are so tightly bound to each other, and what that might mean, given that the Aurbis is a story that is a song that is software that is a dream.
I've split it into three parts which continue on from one another.
1. Awareness and Subgradience
2. Stories, Themes, and Data
3. Black soul = AE + magicka = Aim + Action = Story
1. Awareness and Subgradience
Essentially, I have a theory that as subgradience happens, self-awareness rises and falls in a bell curve. If your soul is too big, you have no identity because you have too much Potential. If it's too small, you have no identity because you have too much Limit. There's a sweet spot around the middle where you have enough Potential to be aware, but just enough Limit to recognise that you are a separate and defined entity. This is why neither gods nor mudcrabs can achieve CHIM-- one is too infinite to say I AM, and the other is a mudcrab.
However, I also don't think that subgradience is discrete, in the data sense. There aren't specific tiers of subgradience, it's continuous from Everything to the smallest fragment of soul you can break it down to. So some Black souls are slightly smaller or bigger than others, without ceasing to be Black souls.
Now this ties in with the Aurbis-as-myth model. God-souls are themes, Black souls are stories. Bigger Black souls have more of a story to play out. But I propose that at some point, if their souls are large enough, they start to take on properties of themes without ceasing to be Black souls.
Themes unite disparate stories. You could remove Harry Potter from literature, but you couldn't remove "loss" or "reconciling with death" unless you not just destroyed every book ever written which deals with it, you fundamentally changed humans. Loss and death are part of what make us human.
Or, if you'd rather think of it as music, you could remove La Fille aux Cheveux de Lin from the canon of western music, but you couldn't remove G flat minor without a radical overhaul of our musical system. Every musical key stands relative to every other key. They all need each other to define themselves.
2. Souls, Themes, and Data
If, as in /u/MareloRyan's model, souls are packages of information, then themes are metadata.
I think little forms of supergradience-- not apotheosis specifically-- can be achieved by becoming a larger part of your story-plot in the Mundus.
The Skaal believe that everything has a soul. They're correct, of course; everything is a fragment of Ald-Anu's soul, by which I mean that everything is data.
A soul is a data package. Everything has a soul, including abstract concepts, because stories are reality in the Aurbis. Here is where I get into conjecture again. By becoming more powerful, or more knowledgeable, or even aligning yourself with a theme or idea, you are adding a small amount of data to your soul, shared between you and another source.
So by taking on the aspect of a minor idea or even just, say, becoming a stronger mage you're performing a very tiny sort of soul-stacking. You're adding more data to your soul-package. It's so very tiny that it makes no discernible difference up to a certain point.
But then there's a certain point where if you rise high enough, you become a part of a theme. You have so much of that theme's data in your own data-package that the metadata is no longer separable from your identity.
Shalidor could be said to be a tiny part of the overarching theme of the Mage. Obviously that's a super important theme, because the Mage is the Observer, and the enantiomorph is an echo of Creation itself.
So the Dreamsleeve cannot wash away Shalidor without also removing the theme of the Mage/Observer from the Aurbis, and that is as impossible as removing Death from the human experience.
At this point, I think I can tie this in fairly well with /u/MareloRyan's model of souls, the Godhead and the Dreamsleeve.
3. Black soul = AE + magicka = Aim + Action = Story
If a Black soul is a story, and it is AE tied tightly to its magicka, and magicka is Potential, then magicka holds the means by which the information package of an AE can enact its story. Plots are made by characters. Characters are the story. In order for a story to have a plot, the characters all have to have an aim: a driving force behind what they do.
All is mythopoeia here. The AE is the aim. But in order for an aim to become a story, the character has to act. Without Potential, all is Limit-- maximum entropy, where no further actions are possible. You need magicka to make things possible. Black soul = AE + magicka = Aim + Action = Story.
Or, again, for the musical people: music is nothing until it's played. Black soul = score + instrument = song.