I don't believe in Strong AI. But lots of other people do. If the term's unfamiliar, it goes like this: given the right computer hardware, and some mechanism for copying the programming of one's brain circuitry, one could load a person's consciousness and memories, what I call his soul, into a computer. Likewise, you could copy this programming into another brain, perhaps one in a cloned body. This is the stuff of science fiction and we've seen it in several popular SF stories.
This idea was picked up by mathematician Roger Penrose. But he added a spin to it I hadn't considered. If my "soul" is essentially a program, then it has the same ontological status as any other program. That's where some considerations by Alan Turing come into play. Turing was able to define a "space" where all computer programs that could possibly be written reside. Thus, we end up with a result that most Strong AI proponents would find revolting: a sort of metaphysics that defines a platonic realm where mathematical objects, including turing machines, or these Strong AI souls.
What got me thinking this way was something R.C. Sproul said today on the radio. He spoke of human pre-existance--another idea I do not believe in. And referred to a type of "realism" that teaches that before one is born, he exists "in the mind of God." This is another thing I don't believe, but it makes some sense.
This all fits into a Platonic metaphysic where mathematical objects like the theorem of Pythagoras and more complex things like turing machines, have a "real" existence in the mind of God. This also tends to fit with the theonimist stuff that Herman Dooyeweerd's notion of logos.