How is the human mind neither a blank slate nor purely pre-determined?
The human brain is an organ, albeit a sophisticated one. Humans are animals, and the brain is pre-programmed with instinctual reactions, the ability to remember and learn, and the capacity for emotion, language, math, higher order thinking and reasoning (plus a whole lot more). So that which is in the brain at birth includes our instincts and emotions, and to some degree our personalities and intelligence.
What we learn, e.g. languages, mathematical processes, as well as not to touch a hot stove are all things we acquire after birth through the process of learning. We are not born with the knowledge, rather we are born with the ability to acquire that knowledge, and some human brains can do so more rapidly and easily than others.