Tuesday, July 11, 2017

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.


unkleE said...

Except couldn't we say that Godel's brain has evolved so that it is able to deterministically arrive at conclusions that are generally mathematically valid? I don't think natural selection on the basis of survival to reproduce could be counted on to produce Godel's brain, but many naturalists think it can. I don't think either of us can prove our viewpoint, so it is an impasse, I think.

grodrigues said...

"Why can't both of those propositions be true?"

I do not see any reason why they both cannot be true. But then again, the second statement has nothing to do with the AfR.

Victor Reppert said...

Well, you have two descriptions of how Godel came to reach his theorem. One makes essential reference to mathematical truths and reasons. The other does not. At the very least the ultimate explanation has to be the one that makes no reference to reasons. The only way both can be true is if you have a workable intertheoretic reduction that goes from the reason-giving theory to the non-reason-giving theory. Such a reduction does not appear to be forthcoming.

Joseph Hinman (Metacrock) said...

my second go round with Bowen in our debate on existence of God

Victor Reppert said...

Jaegwon Kim has argued that in order for there to be a workable account of mental causation, reductionism has to be true. According to his principle of explanatory exclusion:

An event cannot have two separate and complete* explanations.
Take any human behavioral event M (A person decides to change seats, comes to understand a principle of physics,feels sorry for her little sister, etc.) For every M, there can be only one complete explanation. There cannot be two explanations which
a). individually provide a complete explanation of M, and
b). are unconnected to each other.
*An explanation is complete if the events or properties that it specifies are the only ones that need to be mentioned in order to fully explain the occurrence of that event.