Bringing a quote on "determinism" from as good a source as any on this:
Quote:
Due to its assumption of determinism, Laplace's thought experiment is inherently incompatible with quantum mechanical theories, where chance is an essential part of the world's unfolding. The Heisenberg Uncertainty Principle, for example, forbids exact measurements of positions and velocities simultaneously.
John Polkinghorne argues that nature is cloud-like rather than clock-like and points out that, apart from any other problems, uncertainty about the exact position of an electron on the other side of the universe would be sufficient to invalidate a calculation about the position of an O2 molecule in air after 50 collisions with its neighbours (i.e. in about 0.1 ns), even if they were solely influenced by Newton's laws.[2]
According to chemical engineer Robert Ulanowicz, in his 1986 book Growth and Development, Laplace's demon met its end with early 19th century developments of the concepts of irreversibility, entropy, and the second law of thermodynamics. In other words, Laplace's demon was based on the premise of reversibility and classical mechanics; thermodynamics, i.e. real processes, however, are, under current theory, thought to be irreversible.
In 2008, David Wolpert used Cantor diagonalization to disprove Laplace's demon. He did this by assuming that the demon is a computational device and showing that no two such devices can completely predict each other.[3]
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Some folks used to argue that if you could step up from our 3-d view to a total spacetime view, free will would vanish -- problem is that view doesn't take into account quantum mechanics (i.e. its 'classical'). Every point from the "present" forward exists in a multiply possible set of conditions, so such a viewpoint would be clear and concrete to the past and murkier and cloudier to the future.
So free will *can* exist... BUT -- humans operate far more frequently on "mental automatic pilot" than they themselves often realize. They let their past experience and mental baggage, flaky world-view models, etc. drive their choices without re-examining them. This makes them very predictable. Brains that are always learning and adapting to new information (and hence rewiring itself, dropping connections, adding connections) are harder to predict for future behavior other than they're likely to be more successful in adjusting to new situations. Recent neuroscience studies also show that humans make many kinds of decisions *prior* to the higher function parts of the brain kicking in... in other words, the decision gets made by a much faster lower function area (fight vs flight, muscle memory, etc), then the much slower higher functions *rationalize* why they made that decision.