Laplace's demon and Godel's Theorem

I think we need to pause for a moment and reflect upon what mechanistic means here. Consider what happens as I discover, at the foot of a mountain, that I am about to be caught in an avalanche. Rocks are falling down, and to avoid being hit, I run. But before I can escape, a large boulder comes crashing down in the direction of my head. It will either hit me or not hit me, depending upon what? Depending on whether it thinks I should suffer a concussion or not? Of course not. It blindly does what the laws of nature say it will do. If we think about how events happened before the advent of life, this is how things happened in the world.  Even though the indeterminism of quantum mechanics complicates things somewhat, it does not really add anything conducive to rationality. Therefore, it is helpful to look at a naturalistic picture of the world from the point of view 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."

The point that has to be stressed here is the information Laplace’s demon has when he knows conditions, say, concerning conditions prior to the formation of planets. The physical information the demon has says nothing about purposes, nothing about a first-person perspective, nothing having to do with what anybody’s thoughts are about, and knows nothing about what his normative in any sense.

            Now consider the mind of Kurt Godel as he proves the incompleteness of arithmetic. The Laplacian demon knows the state of the physical prior to the formation of stars and planets, and therefore knows the positions of the material particles in Godel’s brain when the developed his Incompleteness Theorem. According to the naturalistic view, the positions of the material particles in Godel’s brain determine what mental states he is in, and those brain states are caused by a chain of prior physical states going back to a time when there were no brains, and therefore, according to naturalism, no mental states whatsoever.  So his act of knowing that arithmetic is incomplete can be comprehensively explained by factors that contain reference to no mathematical truths that Godel perceived, and could have occurred whether arithmetic was really complete or really incomplete. When a complete set of causes is adduced, the state of Godel’s brain can be explained without reference to any mathematical truths that Godel knows, at all.