This is my first post, and I’m not a theologian, but it appears that you’re not satisfied with the answers you’re getting, so I’d like to offer my thoughts on the matter.
The “soul,” as some of the earlier posters have already said, is the principal of operation for a living being. How I understand that is this: When we say that something is “alive,” what we are really doing is describing how it operates. Living beings have certain ways that they function—for example, they consume resources (i.e. eat), eliminate waste, procreate, respond to their environment, etc.
Every living being, whether plant, animal, or human, has a soul, though not all souls are alike. The human soul also includes functions such as consciousness, intelligence, self-awareness, etc. Moreover, each person, in addition to the functions they have in common with other living beings, have certain ways that they alone function, which means that each person has their own “principal of operation” that makes them distinct from all other people. Therefore, each one has their own soul.
A principal of operation that is performed by an object is distinct from the object that performs it. This is a critical point. The principal can be perceived, understood, and applied, even without the object being present. This is how most of science works. We observe certain objects in certain environments, deduce the principals behind their behavior, then use those principals in the abstract—sometimes to predict how other similar objects will behave, and other times to deduce things about phenomena that bear little, if any, direct relationship to the original objects observed.
In the engineering field (where I work), we normally proceed in the opposite direction. We see what we want to do, establish a function to do it, then build the physical system to perform the function. If I establish a certain function that I need performed, write up a “functional specification” of some sort, and give that specification to two designers, each may end up with a system that looks quite different from the other. One designer may, for example, build a hard-wired electronic circuit, while the other may use a computer and implement most of the logic in software—but both objects will perform the same function. How would this be possible if the function has no meaning or existence distinct from the objects themselves?
In short, the soul operates the body, but it is *not *the body and can exist without the body being present. It is therefore possible that the soul can survive the death of the body, as long as there is someone who can perceive it, understand it, and cause it to be executed some how. We would take this “someone” to be God.
We don’t know exactly how this happens; it may be beyond our capacity to understand, but I think we can see a shadow of how it might happen in our own memories (since we were made in God’s “image and likeness”). My mother, for example, passed away years ago, and I can remember many things about her—how she talked and laughed, how she smiled—but what I can remember is only a tiny fraction of what I saw of her, and what I saw was an even more tiny fraction of what made her who and what was. My finite human mind probably could not even begin to comprehend the totality of her “operating principal.” God, on the other hand is perfectly capable of doing that.
In summary, every living being (obviously) has some principal of operation, and the “soul” is defined as that principal, therefore, every living being (obviously) has a soul. Further, since the soul is distinct from the body, it’s possible that it can exist separate from the body, as long as someone (i.e. God) makes that happen.
As for proof that the human soul does survive death, I don’t think anyone can give you that. There’s no logical principal that I know of which says the human soul *must *survive death. We don’t *have *to exist at all. We exist (and survive death) simply because God wills it. The Church teaches that there are some things we can know about God, and His plans for us, by our reason alone, but other things which we can only know through Divine revelation.
Hope this helps.