Hello everybody. It's been some time since I last posted to the one-time RD.net 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...

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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.
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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.

Here is my basic refutation of Dawkins' argument from complexity: evolution.

Basic single celled life forms after billions of years exploded into myriad complex forms about 500 million years ago. So our basic understanding of the history of life on earth tends to refute Dawkins' greater complexity theory if man can evolve from a protozoan it would tend to invalidate Dawkins whole line of reasoning.

Now I'm aware of the argument of the late Stephen Gould that evolution isn't an onward and upward advance of complexity or intelligence; the biomass of ants and people are about equal and there is considerably more blue-green algae, so from a strictly evolutionary standpoint they are at least as "successful" as we are if not far more since they have been around for hundreds of millions or billions of years. Evolution can also work in the opposite direction e.g. pre-cellular prions and viruses, apparently degenerate forms of life. But the mere fact that a higher complexity (as measured in genome size) can be emergent from a lesser complex state refutes Dawkins' point handily and elegantly.

Besides is the universe in fact all that complex? It has been reduced to the basic operation of just three fundamental forces: strong, electroweak, and gravity.

Now onto the theory that the universe is actually a nested simulation with quantum level resolution!

AMR wrote:Here is my basic refutation of Dawkins' argument from complexity: evolution.

Basic single celled life forms after billions of years exploded into myriad complex forms about 500 million years ago. So our basic understanding of the history of life on earth tends to refute Dawkins' greater complexity theory if man can evolve from a protozoan it would tend to invalidate Dawkins whole line of reasoning.

The more complex things evolved from simpler things, so you can give an explanation of how complex things came to exist in terms, eventually, of something simple. You don't have to invoke complex beginnings. That's the whole point of Dawkins' line or argument, so it seems to be completely backwards to say it's a refutation of it.

This was the line of reasoning I was responding to in the originial post:

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.

Assuming this is a correct summation of Dawkins' argument: God's complexity>Universe complexity, & complexity=rare, then it should follow that God is rare or improbable. I just upended his argument that the progenitor of highly complex phenomena must be even more complex, it doesn't.

Dace wrote: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.

Given the necessity of a designer, who designed `GOD'

ymitchell wrote:
Given the necessity of a designer, who designed `GOD'

This question should also be a puzzlement to agnostics or atheists as well since it is ultimately reducible to:

AMR wrote:This was the line of reasoning I was responding to in the originial post:

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.

Assuming this is a correct summation of Dawkins' argument: God's complexity>Universe complexity, & complexity=rare, then it should follow that God is rare or improbable. I just upended his argument that the progenitor of highly complex phenomena must be even more complex, it doesn't.

I don't think he ever said that any progenitor of any complex phenomenon must be even more complex; he was just talking about the particular case of something deliberately created, and contrasting the case where you assume something complex to start with against a satisfying 'bottom up' explanation starting with simple things, like evolution.

AMR wrote:

ymitchell wrote:
Given the necessity of a designer, who designed `GOD'

This question should also be a puzzlement to agnostics or atheists as well since it is ultimately reducible to:

"Why is there something instead of nothing?"

Because "nothing" is unstable.
[youtube]http://www.youtube.com/watch?v=7ImvlS8PLIo[/youtube]

Interesting talk by Krauss, years ago I enjoyed his Physics of Star Trek, thanks for the link.

But of course a cosmos in which "nothing is unstable" presupposes something doesn't it? Namely a cosmos in which nothing is unstable. . . which is, in fact, something. Touché.

Forgive me if I am less than impressed by high-school stoner "philosophy"

Touché

Less than impressed? Less than impressed? Is that another way of saying you have no better argument? If so admit it's so and don't denigrate my witticisms as "high-school philosophy". Stoned or not no high schooler I ever knew could arrive at such a clever riposte.

AMR wrote:Less than impressed? Less than impressed? Is that another way of saying you have no better argument? If so admit it's so and don't denigrate my witticisms as "high-school philosophy". Stoned or not no high schooler I ever knew could arrive at such a clever riposte.

I'm not sure I'd want to say in general that a designer is always more complex than the thing it designs.

Typically when designing a complex system a designer will not have all the details in his head at one time. There will be a hierarchy and when working on one module of the design the other modules will need to be understood only to the extent that they interface with it. Understanding of the system as a whole will be limited to a high level description that skips all the details.

Large designs are usually produced by teams of designers each working on their own part but there is no reason in principle why they can't be carried out over a longer timeframe by a single designer, designing each of these parts sequentially. Of course even a design that took your entire life to complete would still be simpler than a human brain but given long enough there seems no reason that there would be any arbitrary complexity limit to what you could create.

I think the problem for the idea of God the designer of the Universe is that we now assume (post theory of evolution) that the early universe contained no life of any sort and so was probably a much simpler thing than even a human brain (never mind a divine mind!). So it is a case of us explaining something simple by proposing something complicated, because any sentient being is surely more complicated than the inaninate cloud of hot gas that was the early universe.

The reason the idea of a sentient designer still appeals is due to the intuituon that for everything that exists there needs to be an explanation of why it exists. And that even an improbable explanation is better than no explanation at all. But this only works as long as you refuse to ask the further question: why is there a God rather than no God? If there was a God his (uncaused) existence would surely be a bigger mystery than the uncaused existence of a universe (the early universe was tiny and very simple and the laws of physics that describe it can be sumarised in a few pages).

Chrisw, I agree with you in principle that a designer could - possibly - be no more complex than what he designed, and as you say there seems no limit to what could be created given enough time.

However, in context of Dawkins' God Delusion and in context of christian cosmology, that doesn't help the christians any. Because they all suppose that god spoke a word and the universe came into being, fully formed in all its parts. So god must have had the entire plan, all the modules worked out, in mind simultaneously. And that concept of godly creation surely would require a godly mind larger and more complex than the universe it was "containing" at the moment before let-there-be-light.

It's even worse for those christians who believe in theistic evolution, because they have to account for a god who was capable - not only of creating a working universe in one moment - of knowing and arranging all the characteristics of every single bit of matter and energy such that they would inevitably lead to the evolution of us, the pinnacle of creation. I'd say that is god-mind complexity squared.

The problem with the OP and the arguments so far is that Kolmogorov infomation is not the appropriate metric to use when describing the (Christian) universe in terms of information theory.

Why?

Because they propose that the universe and Man were both created perfect and that there was something called a 'Fall' whereby imperfection was introduced. This is directly analogous to Shannon information which considers the effect of noise on the transmission of a message.

If the message is god's plan for the universe then sin and the resulting imperfection is noise. Christians believe that, in the end, god's plan will inevitably come to pass which strongly implies that god designed the system to factor in the effect of noise; either by encoding redundancy in his message or by ensuring that noise did not actually affect any important facet of the message.

In the first instance, god is sending multiple redundant messages through the system with 100% certainty that at least one of them will arrive intact. Mathematically according to Shannon, that means that god is sending an infinite number of messages which, of course, means that god has developed an infinite number of permutations on his message which all reduce the recipients uncertainty by the same amount. While each message contains no more information than each other one, bootstrapping the system up a level shows that god must be able to calculate all states of the system simultaneously in order to be able to formulate his infinite number of messages. Therefore, god is more complex than any single state of the system.

In the second instance, god calculates all possible effects of all possible noise signals on his singular message and encodes the message such that transmission is achieved with 100% fidelity regardless of degradation. Again, god is able to encompass all states of the system at once and is thus more complex than any singular system state.

Conclusion: a hypothetical god must be more complicated than the system he instantiates.

AMR wrote:Here is my basic refutation of Dawkins' argument from complexity: evolution.

the biomass of ants and people are about equal and there is considerably more blue-green algae, so from a strictly evolutionary standpoint they are at least as "successful" as we are if not far more since they have been around for hundreds of millions or billions of years.

Please don't quote incorrect facts. The worldwide biomass of ants is estimated at 10-100 times that of humans.

Regarding ant biomass:

My information on the world population of ants comes from E.O. Wilson's own estimate and the man knows something about ants. He's made the comment several times in published interviews but specifically he writes on page 1 of Journey to the Ants: A Story of Scientific Exploration by Bert Hölldobler, & Edward O. Wilson:

"When combined, all ants in the world taken together weigh about as much as all human beings."

(Hölldobler & Wilson 1994)

Also this informative link http://answers.google.com/answers/threadview?id=536123

Given a sufficient expanse of time even a simple designer (as clichéd monkey's on keyboards) can achieve a remarkable creation. This is the process of evolution. However it's the cosmic substrate, the physical laws themselves which make this operation possible, that should be of real interest here. How could such a delicate interplay between all these extraordinarily precisely finely-tuned constants (e.g. strength ratios of gravity and electrical & nuclear forces, the triple-alpha process, the ratio of our universe's kinetic energy and gravity which allows for precision balance of inflation and homogeneity throughout crucial states in its development, to name but a few) combine to set the stage for a world that not only exists and lives but is aware of itself and contemplates its origins? The so-called anthropic principle just doesn't satisfy. This has led otherwise sober-minded scientists to invoke an evolutionary menagerie of multi-verses without the slightest observational evidence, which is I suppose the ultimate violation of Occam's razor principal entia non sunt multiplicanda praeter necessitatem. How is this in any way superior to a God hypothesis?

To invoke the theological implications of Claude Shannon's information theory and Chaitin-Kolmogorov complexity seems like dressing up a straw man argument in a fancy suit.

Grounding Dawkins 747:
http://www.examiner.com/x-26772-San-Francisco-Apologetics-Examiner~y2010m7d15-Reasons-for-faith-101--The-cosmological-argument-alive-and-well

Umm, welcome to the forum, Ichthus77.

A Jesus Ichthus, I presume ?

Ichthus77 wrote:Grounding Dawkins 747:
http://www.examiner.com/x-26772-San-Francisco-Apologetics-Examiner~y2010m7d15-Reasons-for-faith-101--The-cosmological-argument-alive-and-well

The usual stupidity that god can somehow be "simple" and still have been capable of creating a complex universe out of nothing, all in no time. That god can somehow be the "uncaused cause" that magically is not physical but magically can interact with our physical reality. That god can somehow be the "unmoved mover" just because someone gives it that title.

Just because humans are capable of stringing three letters together - g--o--d - and imagining that string refers to something outside of spacetime, does not render that string magically free of logical constraints.

Whereas Dawkins' argument correctly points out that the only case we know of where something complex has arisen, without being created by an even-more complex entity, is the case of evolution. We know our complex biosphere was built up in little steps evolutionarily from initially simple materials. Similarly, it is at least possible that a complex entity we might entitle "god" could have evolved somewhere, somehow, from simpler stuff, and could have reached a level of competence to create our cosmos. This can't be disproven and would be consistent with the only evidence we have. But of course, that's not the god most christians are thinking of when they think of "Let there be light".