Natural phenomena often seem to be extremely complex. But when a scientific explanation is found, the complexity is invariably seen to originate from some simple fundamental principle. The incredible complexity of the biological world, for example, is beautifully explained by a simple process of random mutations and non-random natural selection [1]. An example from physics of apparent complexity is the proliferation of elementary particles in the early days of particle physics. Once we discovered the theory of the strong interactions, however, the seeming complexity of the "particle zoo" was seen to be a manifestation of a very simple underlying symmetry principle [2].

The notion that complexity should be explainable in terms of some underlying simple principles is itself a basic scientific principle. Indeed, science can be described as the process of discovering the underlying physical principles that give rise to the complex phenomena in the world around us.

The apparent complexity of nature leads many theists to the Argument from Design, which claims that a designer is the best explanation for the observed complexity. An important premise in any Argument from Design is the notion that an extremely complex phenomenon that is also fundamentally complex is extremely improbable. By "fundamental complexity" I mean that the complexity cannot, even in principle, be explained in simpler terms. This premise is needed to justify the claim that only a supernatural explanation will suffice, since non-fundamentally complex phenomena can, at least in principle, be explained in relatively simple natural terms. I think that the premise is correct, but what causes all Arguments from Design to fail is that there is never any demonstration that any observed complex phenomenon is actually fundamentally complex.

One of the latest incarnations of the Argument from Design, is Behe's claim that biochemical processes are "irreducibly complex" and therefore a god must have created that complexity. Behe defines irreducible complexity as follows [3]:

"By irreducible complexity I mean a single system which is composed of several interacting parts that contribute to the basic function, and where the removal of any one of the parts causes the system to effectively cease functioning."

This notion of irreducible complexity is a weaker principle than the notion of fundamental complexity discussed above. It is not enough for Behe to show that a biochemical system is irreducibly complex for his conclusion of a designer to follow; he must show that the system is fundamentally complex and he has not done this. In fact, there are several known examples in evolution that disprove Behe's claim that irreducibly complex systems cannot be obtained by the gradual processes of evolution [4]. Behe's arguments have been criticized by a number of authors for various other reasons as well [5].

Its hard to see how any Argument from Design could ever demonstrate the existence of a supernatural designer, since it is difficult or impossible to prove that any naturally occurring phenomena satisfies the principle of fundamental complexity. It is possible, however, that some abstract concepts could be argued to entail fundamental complexity. A being fitting a very general definition of God, for example, would be fundamentally complex. God is by definition a conscious being. But consciousness is itself an incredibly complex phenomenon, so God must be an incredibly complex being. Furthermore, God is fundamentally complex since God is by definition a fundamental entity; that is, God cannot be described as being evolved from other simpler entities or derived from simpler concepts. (If we found a being that we thought was God and it turned out that this being evolved from other simpler beings, we would conclude that he was not God at all, but an alien life form.) God, if he exists, would be an extremely complex being that is also fundamentally complex, and this implies that the existence of God is extremely improbable.

Formal Statement of the Argument

In evaluating any argument, it is always useful to formally write out the argument, explicitly listing the premises and making sure that the logical structure is valid. The main argument of this essay can be formally stated as follows, with premises indicated by "P" and inferences indicated by "I":

(P1) Extremely complex phenomena that cannot even in principle be explained as arising from simpler, more fundamental principles are extremely improbable.

(P2) God is by definition a being that is a) conscious, and b) fundamental in the sense that he is not evolved or derived from anything more fundamental.

(P3) Conscious beings are necessarily extremely complex.

(I1) From (P2a) and (P3), God is extremely complex.

(I2) God cannot even in principle be explained as arising from simpler, more fundamental principles since, from (P2b), God is defined as being fundamental.

Conclusion: The existence of God is extremely improbable [from (P1), (I1), and (I2)].

By writing the argument out like this, it is clear that the logic is valid and therefore that the conclusion will be correct if the three premises are correct. So now lets see if the premises can be justified:

I have already spent some time above in justifying (P1). To summarize, (P1) is certainly reasonable as it is always the case that when an explanation is found for seemingly complex phenomena, the explanation relies on relatively simple principles. It is also the case that (P1) is widely accepted (and it is not necessary to belabor a premise that everyone already agrees with). (P1) is widely accepted by scientists, for example, since a failure of (P1) would mean the non-improbable existence of complex phenomena that cannot even in principle be explained in simpler terms. The existence of this type of phenomena would mean that science could not proceed. (P1) is also widely accepted by theists who use this premise in an essential way, even if it is not always explicitly stated, in their Argument from Design.

(P2) gives two defining properties of God that most theists, I think, would accept. A person who claims that God does not satisfy (P2a) is abusing the English language by referring to whatever it is that he or she believes in as God. (P2b) is a necessary ingredient to the definition of God, because we would otherwise have to say that God could be a sufficiently advanced alien.

It is (P3) that I think theists would be most likely to attack. They could claim that human consciousness may be complex, but the supernatural, spiritual consciousness of God is not. This type of claim, however, cannot be correct. Consciousness by its very nature is complex; whether we are discussing the consciousness of biological organisms or the consciousness of a hypothetical supernatural being is irrelevant. To see that consciousness itself is complex, consider that consciousness requires the ability to store and access information that is linked together in many intricate ways as well as the ability to process that information and to reason. The web of intricately interconnected data that consciousness requires is extremely complex. One measure of the complexity of a system is the logarithm of the number of states of the system [6]. Applied to a conscious system, this measure of complexity is proportional to the number of pieces of data that the conscious system knows times the degree of interconnectedness in the data. There are three interesting things to note here: 1) this measure of complexity is very large if a large amount of data is accessible; 2) the interconnectedness of data that consciousness requires greatly increases the complexity; and 3) for an omniscient being, this measure of the being's complexity diverges.

So (P2) is true by definition, and although (P1) and (P3) cannot be proven with absolute certainty, I think it is fair to say the I have shown that it is extremely likely that (P1) and (P3) are correct. It then follows that it is extremely probable that the conclusion is correct, i.e., the existence of God is extremely improbable.

Conclusion

The notion of "irreducible complexity" as propounded by Behe is insufficient for both theological and atheological arguments. I have shown that "fundamental complexity" is the requisite concept and that a being fitting a very general definition of God would have to be extremely and fundamentally complex. The existence of such a being is therefore extremely improbable.

References

[1] Richard Dawkins, The Blind Watchmaker (W. W. Norton & Company, 1987).

[2] Kurt Gottfried and Victor F. Weisskopf, Concepts of Particle Physics (Oxford University Press, 1986).

[3] Michael Behe, Darwin's Black Box (The Free Press, 1996).

[4] Don Lindsay, How Can Evolution Cause Irreducibly Complex Systems?

[5] See http://www.infidels.org/library/modern/science/creationism/behe.html.

[6] Kerson Huang, Statistical Mechanics, 2^nd Ed. (John Wiley & Sons, 1987); Thomas M. Cover and Joy A. Thomas, Elements of Information Theory (John Wiley & Sons, 1991).