Free Will and Finite Precision Computation 2

Continuation of Free Will 1:

David Foster Wallace studies the logical argument of the fatalism of Richard Taylor going back to Aristotle stating that we cannot do anything other than what we actually do, in other words that the future is predetermined and free will is only an illusion.

The logic is that a statement of the form "Tomorrow it will rain" is either true or false: If it is true then it will have to rain, and if it is not true then it cannot rain, in both cases showing that what will happen tomorrow is predetermined.

Of course, this is a simple logical trick based on the idea that a statement must be either true or not true. But nothing says that this must apply to the statement "Tomorrow it will rain". It is a statement without definite truth value when (today) it is uttered; only in retrospect knowing the outcome is it possible to assign it a truth value and then the predetermination disappears.

But there are other arguments showing that the future is determined by the present. The best one is that of Laplace's demon:

• We may regard the present state of the universe as the effect of its past and the cause of its future.
• An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom;
• for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

Laplace's demon would thus be able to tell today if it is going to rain tomorrow by simply computing the solution to the equations of motion describing the evolution of particles (atoms, molecules) making up the climate system, and would thus be able to make a necessarily true prediction of a coming event, thus showing that it is predetermined.

But is there a Laplace demon? Human computing power is capable of solving the equations of motion for particle systems of millions or billions of particles (10^6 - 10^9), but not the octillions (10^30) of real systems.

We are all too familiar with the fact that human intellect cannot tell for sure if it is going to rain tomorrow. But is the weather still predetermined?

Is there anything we can do by free will to make it rain or not? Can we make it rain tomorrow by leaving our car windows open? The investigation continues...