The freedom to choose makes predictions of the future a matter of probability. Quantum Darwinism would overcome the uncertainty principle and seemingly restore microscopic physics to classical physics where particle motion is deterministic as in Laplace's opinion.
But human beings and perhaps lower forms of life are often faced with a number of options to choose from. What choice we make may sometimes be predictable, but very often it is not predictable; and this makes the future only predictable within bounds. I assert that the unpredictability of human choice is an empirical fact that follows from what is called clinical data in medical science.
Take for example a basketball game. You can often predict whether a ball player will shoot. But almost as often, the ball player does something unpredictable. Even the winner final score is largely unpredictable. Not so in a road race. We runners almost need not run as the outcome is very predictable from the start.
So I contend that there is ample evidence for human unpredictability and this makes the future unpredictable. It is humans that play dice. God is just a spectator in the game of life.
That does not mean that the future is random.
Another example I have used before is that on any given planet it is only a matter of time for an intelligent species to discover nuclear energy and make hydrogen bombs and the ability to deliver them anywhere on the planet. This is predictable. It seems that sooner or later every intelligent species will blow themselves up, unless something even more powerful is discovered-something like a god.
As before I think there is religious evidence of the unpredictability of human action in the bible. Revelations makes the most concrete predictions of any other biblical book. Yet there seem to be a range of predictions in that book, from nuclear holocaust to a 1000 years of peace. I think you can understand the contradictions in these prophecies on the basis that human action is unpredictable and the author of that book could only present the range of possibilities.
So the answer to: "This lecture is about whether we can predict the future, or whether it is arbitrary and random.." is neither option. The future is both. We can predict bounds on behavior, but within the bounds, behavior is largely unpredictable.