I'm rather torn. Logically, evolutionary etc says that we're all just salty mushy fat encased in a calcium shell, hallucinating we can think.
But then-
About ten years ago I drove to a small local mall. As I was pulling up, I noticed two ambos loading up a stretcher into an ambulance. They were in no hurry, so I wasn't too concerned, and by the time I'd gotten out of my car and walked to the entrance, they were closing the ambulance doors. It's rude to gape at people while they're sick or working, so I did not hang around to watch, and went inside. About two metres in, the air had this profound sense of... emptiness. It felt exactly like something very large and important had just left, leaving a vacuum behind. It wasn't a sense of grief, it was absence, which isn't quite the same. I stumbled a bit but made myself march on. In the centre of the mall, a group of women were discussing the man who'd been taken to the ambulance. On a bench, a woman had her arm around a crying little girl and was very gently telling her what death is. I quickly gathered that the man who had been taken on the ambulance had had a very sudden event that took his life, like a heart attack or a massive aneurysm. That was why the ambos had not been in a hurry; there was no saving someone that had already left.
I'm not sure what a soul is, but I've felt its departure. So there's that.