Without the indefinable and individual soul of photography, I suspect our images would be very standardized, lacking the personal stamp of each photographer.
Take a moment to think about the practicalities of your photography. From the novice digicam owner to those who have graduated from the film darkroom to digital editing, we all perform the same repeated actions. A two-way communication begins from the moment we pick up a camera. The first glance through the viewfinder frames the intended scene or object and that which we observe through the lens becomes an extension of our own vision; the camera merely provides the mechanism for freezing particular moments in time and providing us with images.
At the pc, scanning, editing and post processing allow further individualization of your pictures. You may see an ordinary looking image on your screen, and you have the ability to transform it with a tweak of levels here, a deepening of saturation there; the result will be a combination of the data the camera captured, your skill as a photographer and your prowess with software at the computer. Most of all, your pictures will have soul.
Your camera is your non-judgemental friend, your amenable traveling companion and your invaluable learning resource. It enables you to see your surroundings in a broader, more interesting way. The process of photography can in itself be balm to the soul. I know of few better stress-busters than a planned photo jaunt to put your problems into perspective. Conversely, if you are having a bad day pictorially, nothing will go right, you will come home with an empty CF card and the camera will be summarily banished back to its bag!
The advent of digital photography also provides what could be called the century desire for instant gratification. We no longer have to possess the patience to wait for film to be developed, and this adds to the appeal of the whole process for many photographers.
Over time, you get to know your camera and how it interprets visual information, until it is a familiar and customized accessory to your self (try picking up someone's camera and taking a shot with it, and you will see what I mean). Even two identical camera models will behave slightly differently.
Perhaps I am imbuing my camera with too much personality; after all, it is an inanimate object, but I believe that as soon as I pick up a camera to take a photograph, there is a unique interplay between us. I do not underestimate my own camera's ability to continually surprise me with the images it captures. Although I press the shutter button, there are numerous occasions when I am amazed at the clarity or amount of detail in particular shots, that I did not realize would be "seen" by the camera.
So then, what of the original question, is your camera's soul a computer? I love my cameras dearly for what they represent to me, the opportunity to create and share photographs; to discuss photography and continue to travel along the fascinating learning curve of the associated technology. My answer has to be that my camera's soul represents my own soul, or part of it, and I hope to strike a chord with many others when I say, "My photographs are a little bit of me".