Free Will, Decision making and religion

[Smaug]

Wait. Are you saying that free will never exists because in fact there is always a trajectory leading to just one outcome? Or are you saying sometimes the choice of possible resolutions for a decision really can be rich in some cases and few in others?

What I've tried in my post is to define the Free Will. When people speak of Free Will they usually have not even a slightest definition of it. Basically my definition means what you've said in the latter part of your question. Yes, Free Will is when you have more than one possible choices. To add to it, the posibilities of these choices must be roughly the same. Strictly speaking in a fully deterministic model there will be no possibilities and no room for anything we may call Free Will. But if we take our Universe (or Solar system) as a deterministic dynamical system, such a system is so complex and full of interconnections that for us it technically does not differ from a truly stochastic one. It's a vague definition but I've not been able to come up with something better for now.

I'm a little confused by this. Is it that there appear to be multiple possible choices but in fact there is only one trajectory rendering all other of those choices void?

In a fully deterministic model there's only one trajectory which theoretically may be computed from 'now' to infinity. The other possible trajectories are to be meant as "alternative histories" which could've taken place if the conditions at some selected moments of time (decision-making moments) were slightly different. This means no Free Will at all. However this never works in real life problems because even if we consider our world to be fully deterministic we never know the exact initial conditions to solve the problem with. Here it's good to remember that complex dynamical systems prone to be sensitive to initial conditions (which means that if two trajectories start from aproximately the same points after a period of time they may end up far apart from each other). There is also such a thing as bifurcations of trajectories. This is a complex topic in a Theory of Dynamical systems and I'm not able to go further right now without having to prepare to discuss it beforhand.

Speaking of a stochastic model, each act decision-making (this may be called bifurcation, but not in the same sence as in deterministic models) involves some probabtilities.

If we consider a more common intuitive definition of Free Will as a possibility "to do whatever you want" then you may arrive at a conclusion that there's no such thing. Both of the models I proposed deny Free Will in this intuitive sence. If we imagine decision-making as passing some points (junctions) on a railroad track then the difference is that in the first case you are potentially able to know the position (left or right) of all the points and in the second case the points flip left and right sporadically and you know only the probabilities. But in both cases it's not you who choose the tracks but the laws of Nature, deterministic or stochastic ones.