There is a scene in one of my favorite novels, "A Spell For Chameleon," where a monster asks a wizard, "do I have a soul?", and the wizard replies that the fact that the monster asked this question is the proof that it has a soul.
Everyone knows what the soul is according to religious philosophy, such as Platonism or Christianity: a non-physical spirit that occupies and animates a body, a ghost in a machine. But Aristotle and Ayn Rand both wrote much about "the soul," and I suspect they meant something different.
This is a list of my top ten thoughts about how Aristotle and Ayn Rand would define "the soul." Aristotle had some (strange) beliefs about God, but Ayn Rand never conceded the existence of any non-physical aspect of reality, so her conception of the soul is not that it is something that does not physically exist; instead, the soul is an aspect of the moral existence of a human being, which, for Rand, begins with the mind and reason as the fountainhead of morality.
The Soul of a Person is Their:
3. Self-Esteem (In The Fountainhead there are scenes where to destroy someone's self-esteem is stated as their soul being destroyed)
4. Their self-aware Brain
5. Their Mind that Sees
6. Their Mind that Thinks
7. Their Mind that Thinks with Integrity and Acts in a Moral Way (so for a person to compromise their integrity is for them to lose their soul)
8. A Human Body Living a Moral Life - in other words, The Person as a "Person," in the Moral Sense
10. Purpose in Living Their Life and the Meaning for Them of Their Life - this particularly would mean Aristotle's theory of the "Final Cause," which was Aristotle's belief that the end state that something seeks to achieve is literally a cause of its physical existence.