I like Douglas Hofstadter's concept of the soul as a self referential mechanism. His book: 'I am a strange loop' expands on this, which is a bit more spiritual (for lack of a better word) expansion of his ideas in Gödel, Escher Bach.
It also explains how your own loop incorporates and curates the memories of the people you love and how you're able to live, and see though their 'eyes' after they have died.
So the soul of others finds an explanation in yourself, and allows you to live in in other people's minds, without any super natural constructs.
Always glad to find another student of Hofstadter in the wild. G.E.B. blew my mind wide open when I read it in my early 20s.
I Am a Strange Loop is a far more accessible distillation of some of the same ideas, but I recommend both to anyone who wants a better grasp on how something seemingly infinitely complex like a human mind can emerge from mere atoms dancing around one another.
I'd recommend people to read past the sections with logic and mathematics in them, and just read the textual chapters. So minutes the overly Gödel pieces. It gets across the point very well.