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I feel like I have misunderstood or butchered this tractate, but I do not wish to get hung up on it; here is my best guess for the moment, and I'll have to return to it some other time when my understanding is deeper.
(That's true of every tractate, I suppose. I'm just saying it's extra true of this one.)
V 7: Is There an Ideal Archetype of Particular Beings?
Where does a person's characteristics come from? We hold, of course, that bodies are reflections in matter of souls, so the soul must contain that information—but we also hold that soul contains the entire scope of possibility in the Cosmos, so this isn't much help.
Since an individual doesn't resemble all possible individuals, only some of the characteristics latent in the soul must be active at a time; further, since children resemble their parents, the characteristics active must come, in part, from those parents. This does not imply that the parent's souls exist prior to the child's or that the parents are more archetypal than the child, for if this were the case there would be a degeneration over time and we have already established the eternity of the Cosmos. No, it simply that some amount of communication or deference to their the parent's souls is held by the child's for a time.
But what of twins or the many puppies of a litter—they appear to be the same, so do they have the same soul? No, that cannot be: even if they superficially appear to be the same, they have different bodies and thoughts and actions and so on. We suppose that the Intellect, working out all the unique possibilities in the world, produces a soul unique to each of those possibilities, and those souls are what inhabit the bodies.
That there could be limitless possibilities and therefore unlimited souls should be of no concern to us, as the Intellect is the definition of limit: this would simply imply that the Intellect is unlimited in scope, too.