I'd say don't be thrown off by the colorful language like "souls." All of science has this language problem and philosophers of science are asked to address the meaning of these kind of words all the time.

Having read a lot of Carlo's work along with Hans Reichenbach's who is coming from the same hardline empirical stance, I think what he's trying to say here is that consciousness or a soul (I prefer the term "volition") arises from natural and physical elements that we can observe. In other words, nothing about consciousness, life, etc comes from beyond the empirical. We are already looking at it.

Does that make sense? He really objects to inserting a god or other axiomatic beliefs and the "soul as entity" must go in that box.