Quote (piddywiffle @ Dec 15 2012 06:43pm)
That's a formula, not a deciding factor in a defined term.
that is exactly the point. The future states of a deterministic systems can be predicted with a 'formula' if you know enough data about the system in its current state, and you have evolution laws for the system. That is what it means for a system to be deterministic.
Even without the evolution laws, you can still tell if a system is not deterministic by the following:
If you start a deterministic system in state A, and let it evolve for n seconds, and you find it in state B; then it must always do this if you restart it in state A. If it does not... it is not a deterministic system.
In classical mechanics (where everything was assumed to be deterministic) the problem was to measure state A to infinite precision so you could be sure to restart it exactly in state A. If you couldn't do this, then you couldn't be sure you restarted it in the same state later, so when you reached a different outcome, you couldn't be sure if you had actually correctly started in state A (failure to reach state B would be dismissed by assuming you didn't get state A exactly right).
Now we know that even if you magically had state A perfectly measured, some systems will not evolve to B every time. These systems are not deterministic. And since the world contains at least some of these non-deterministic systems, the world as a whole can never be deterministic. Which means the input into a human being senses is not deterministic, meaning the behavior of a human being can not be deterministic (even if internally the human being was deterministic, which i doubt, but its a moot point).
Now making a statement about freewill based on this is not easy, but it seems like it at least leaves room for freewill.
But forget about determinism, that pig don't fly.