According to the Logical Positivists, and the general theory of science, there is nothing left over, and if we knew all the variables involved, we could predict a person's behaviour exactly.
Larc, have you ever considered quantum mechanics. Not that i understand it greatly, its very hard to get your head around. But As i understand it, a mechanistic view of the world is ultimately thrown out the window with quantum physics. We can predict with great accuracy the orbits of the earth and of the planets but when you get down to the sub-atomic level this kind of exact predictive ability gives way to just probabilty. That there is no way of determining exactly how a particle will behave. There is only a certain probability that it will behave a certain way, but no guarentee. Since everything is made of sub-tomic particles, this idea has lead physicists to postulate multiple realities. One reality where i chose to do a certain thing and another where i chose to go the opposite way. I find it hard enough to understand these ideas let alone explain them here, but i've heard this idea of multiple realities come from the likes of Paul Davies etc...not just fringe quacks!