Posted: Jun 06, 2010 2:47 am
by Dace
Hello everybody. It's been some time since I last posted to the one-time community, but I was once quite active in the philosophy forums. Anyway, I still have my mind on philosophy and I've recently been trying to put together a blog post in defense of Dawkins' argument in The God Delusion, as I've been consistently disappointed with the interpretations and responses to it in the philosophical literature*.
I take it that Dawkins' argument for the improbability of God is rather simple...

1. God himself would have to be more complex than the highly complex universe.
2. What is complex is improbable, and is improbable to the degree it is complex.
3. God is highly improbable. That is, he almost certainly does not exist.

... but the reasoning behind premise 3 is, I think, best interpreted in the light of information theory. Since this outside my expertise, I'm hoping there's someone here who can provide some constructive criticism of my attempt at supporting 3. Here's a fragment of my draft concerning that...

So it remains for us to see if 3 is justified - what reason do we have to believe that God himself would have to be more complex than the highly complex universe?
For the most part, Dawkins takes 3 to be obvious..

"Any entity capable of intelligently designing something as improbable as a Dutchman's Pipe (or a universe) would have to be even more improbable than a Dutchman's Pipe." (120)

.. citing a logical connection between the complexity of what is designed and the greater complexity of a designer. But to cite this general principle is of little help to us, if we are concerned about the justification of the principle. I suspect what Dawkins has in mind here draws upon information theory. According to the concept of 'Kolmogorov complexity', the complexity of a string of symbols can be measured in terms of the shortest program able to reproduce the string. This definition can be extended to objects, since an adequate description of an object is constituted by a string of symbols, and so we can measure the object's complexity by the complexity of its description. The interesting thing about Kolmogorov complexity is that it provides the necessary bridge between computation, which has become the foundation of cognitive science, and objects themselves. That is, if we take a measure of the complexity of the universe, then this measure is in terms of the shortest possible program able to reproduce the string, and given that the mind works on computational principles, this implies a minimum complexity of the mind which is able to store this information. But this amounts to saying that a mind must be at least as complex as that which it conceives, as we have defined the complexity of the conceived in terms of the complexity of that which conceives it. More formally:

1. The complexity of an object is measured by the shortest program able to reproduce a string of symbols which accurately describe that object. The complexity is inversely proportional to the length of the program.
2. A program exists insofar as it is instantiated in a substrate.
3. A program which is instantiated in a substrate can itself be considered an object, whose complexity is measured by the shortest program able to reproduce a string of symbols which accurately describe that object.
4. If P1 is the shortest program describing an object O1, and P1 is instantiated as an object O2, then P1 is likewise the shortest program which describes O2.
5. So, the complexity of a given object O1 is equivalent to the complexity of an object O2 which instantiates a program describing O1.
6. The mind works on computational principles - that is, the information held by a mind consists in such programs, instantiated in a substrate.
7. Therefore, the complexity of an object as conceived by a mind cannot be more than the complexity of the mind itself, as instantiated in a substrate.

Premise 1 explicates the notion of complexity we're working with. 2 treats a program as an abstraction, a form of sorts, which requires a substance for existence. 3 is obvious, but 4 may not be. Suppose that 4 is false: then P1 is the shortest program describing O1, is instantiated in O2, and P2 describes O2, P2 being shorter than P1. But if that's so, then P2 also describes O1, for by describing the object in which P1 is instantiated, it thereby describes the object P1 describes. Given that both P1 and P2 describe O1, and that P2 is shorter than P1, it follows that P1 is not the shortest program which describes O1, and so we've derived a contradiction. The negation of a contradiction is always true, so premise 4 is true. 5 draws on 4: if P1 is the shortest program describing both O1 and o2, then the complexity of O1 and O2 is equivalent. 6 is a deliverance of cognitive psychology: [quote concerning CogPsy here] . 7 is inferred from 5 and 6. Suppose O1 is an object conceived by a mind: then P1 is the shortest program describing it, and the instantiation of P1 in O2 is of equal complexity to O1. But, of course, O2 is itself part of the mind. So the mind, being at least as complex as O2, is also at least as complex as O1. This gets us so far as saying that a designer of the universe would have to be as complex as the universe. But Dawkins thinks that a God would be even more complex than the universe. How can we support this stronger conclusion? Well, by simply adding to the complexity of the designer's mind by adding to the objects we can consider such a mind to know:

1. A designer is a person, with a conception of some particular object (the designed).
2. Self-conception is a necessary feature of persons.
3. Therefore, a designer conceives of himself/herself as a person, as well as the designed object.
4. The conceived person and the object together are more complex than the object alone.
5. So, a designer is necessarily more complex than the object designed.
6. God is the designer of the universe (assumption).
7. So, God himself would have to be more complex than the highly complex universe.

That's as far as I've got, for now. I'll greatly appreciate some input on the argument, hopefully reassuring me that I'm not abusing the concepts of science. Please note: I'm not asking for someone to tell me whether or not I have Dawkins' argument right, as I've elsewhere done the exegetical work necessary to support my interpretation, but I would like anyone familiar with information theory or cognitive psychology to weigh in on my reasoning in the second and third arguments.

*William Lane-Crag, Alvin Plantinga, Eric Wielenberg, Mark Sharlow and others have had a go. I'll point anyone to these on request.