A quick thought on the idea of human soul

A lot of hubbub surrounds the concept of the soul. To give the idea legitimacy in the modern world, theists put the soul in the category of "fundamentally unknowable things" by declaring that it cannot be measured or observed in any significant manner. What I think they don't realize is that this is more or less a concession that admits that there is no soul, as it is traditionally thought of. If the soul is not a product of the brain then it is meaningless, because the mind is easily demonstrated to be a product of the brain. Even if the soul is said the be the thing responsible for subjective experience, what good is a soul without a mind? What good is a continued subjective experience left after death if thoughts, feelings, memories, and senses are all absent?

For purpose of illustration, imagine that after the rest of you died, your pinky finger continued (somehow) to live, taking in energy and replacing dead cells, doing all the things it did while you were alive. Few people would consider this to be "eternal life" because the part of them that survives is not an essential part of themselves. Similarly, there's not much "self" left for any theoretical soul to have because the vast majority of the self is confirmed to be part of the body and brain. So even if our "soul" lived on, there would still be no "afterlife" as most people see it.