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.