The following is a philosophical paper which I submitted to the journal Philo. Unfortunately, it was rejected because my reasoning relied on the principle of indifference (PoI), which the editor felt rendered the entire paper wrong because the PoI was, in his words, "provably false." I disagree, and I'd like to explain why. UPDATE: A simpler version of my argument can be found here.
The principle of indifference simply tells us that we should assign all possible outcomes an equal probability if there is no reason to assign any one of them more likelihood. Seems simple enough, and true enough. But in the philosophical literature it has been criticized because it can lead to contradictory probability assignments. I think Ofra Magidor got it right when he characterized the PoI as an action guiding principle and said of it:
"It seems to me perfectly reasonable that an action guiding principle will give me some recommendation as to how to act. It may not suggest a unique course of action, nor does it have to be the only action guiding principle I am using."
I have other criticisms of the paradoxes about the principle of indifference, but I'll save those for another time. I think Magidor's comment is sufficient to prove that the PoI is legitimate, and without further ado I'll post my paper:
“Dawkins’ Dangerous Idea” by Nicholas Covington
ABSTRACT: This paper examines the “central argument” of Richard Dawkins’ The God Delusion. It is concluded that, although Dawkins’ argument is flawed, he has still raised legitimate points which show that the existence of God may have a very low initial probability, and consequently extremely convincing evidence would be needed in order to justify belief in God.
In the 2006 best-seller The God Delusion, Richard Dawkins presents the following argument as his “central argument” against the existence of God:
(1) If God exists, then God has these two properties: (i) He provides an
intelligent-design explanation for all natural, complex phenomena
in the universe and (ii) He has no explanation external to Himself.
(2) Anything that provides an intelligent-design explanation for the
natural, complex phenomena in the universe is at least as complex
as such phenomena.
(3) So, if God exists, then God has these two properties: (i) He is at
least as complex as the natural, complex phenomena in the universe
and (ii) He has no explanation external to Himself. (from 1 and 2)
(4) It is very improbable that there exists something that (i) is at least
as complex as the natural, complex phenomena in the universe and
(ii) has no explanation external to itself.
(5) Therefore, it is very improbable that God exists. (from 3 and 4)[i]
In this paper I will examine three objections to Dawkins’ argument: The Necessary Existence of God, The Simplicity of God, and the legitimacy of his second premise.
The Necessary Existence of God
Probability is only relevant when we are discussing contingent beings. Theists typically define God as a necessary being, and if this is so, then the probability that God exists is 100% and no amount of complexity will show that God is improbable. If this is the case, then it would severely undermine Dawkins’ argument, which depends upon the notion that God is improbable.
I contend that this simple clarification of definition does not solve Dawkins’ challenge, because it raises the question of whether there is a Godlike being (that is, an omnipotent, omnibenevolent, omniscient spiritual being who is like God in every respect but may or may not exist necessarily) who also possesses the attribute of necessary existence. If there is, God exists. If there is not, then God cannot exist.
What reason could be given for thinking that there is some hypothetical Godlike being who also exists necessarily? Theists could appeal to the Ontological argument, or other arguments that attempt to show that God is necessary. Whether such arguments succeed is beyond the scope of the present paper. However, if those arguments do not succeed, then theists are still left with the challenge of showing that some Godlike being possesses the attribute of necessary existence.
Theists could attempt to answer this question by shifting the burden of proof: How do atheists know that there is not a Godlike being who exists necessarily? Perhaps this challenge could be answered in the following way: Logically, either (1) No mind (including the mind of God) exists necessarily, (2) One mind exists necessarily or (3) Two or more minds exist necessarily. Occam’s razor would seem to suggest that the first possibility is most probably correct, since it is ontologically simpler to suppose that no minds exist necessarily than to suppose that one or more mindsexist necessarily. However, let us leave that objection aside momentarily and ponder how we could decide this question without it. Unless some reason were given for supposing that one of these options was more likely than the others, it would seem appropriate to apply the principle of indifference and assign each logical possibility the same probability. We have an infinite number of possibilities here, because it is possible that any positive number of necessary minds exist. Therefore, the possibility that only one necessary mind exists is one in infinity. This has very troubling consequences for most theists (who believe in only one God), because it suggests that polytheism is infinitely more likely than monotheism. In summation: If it cannot be shown that there is only one necessary mind through some argument (such as the Ontological Argument), then both Monotheists and Polytheists must come up with an objection to my application of Occam’s razor here (it is simpler, and therefore more probable, to assume that no Godlike beings are necessary). Monotheists bear the additional burden of showing polytheism is not infinitely more likely than monotheism.
The Simplicity of God
Some theists, such as Richard Swinburne, contend that God is not necessary, but nevertheless God is simple and therefore God would not fall victim to Dawkins’ argument. Dawkins’ seems to object to this on the grounds that God, by definition, is a conscious, knowing, thinking, designing being, and such a being cannot be simple. Of course God is simple in the sense that he does not have any physical parts, but it does not follow that he is not complex in other senses of the word. In order for Dawkins to assert that God is improbable by way of his complexity, he needs to show first that God is complex in some sense, and second that this complexity renders God an improbable being.
Dawkins attempts to clarify his thinking in the following passage:
“A God who is capable of sending intelligible signals to millions of people simultaneously, and of receiving messages from them simultaneously, cannot be, whatever else he might be, simple. Such bandwidth! God may not have a brain made of neurons, or a CPU made of silicone, but if he has the powers attributed to him he must have something far more elaborately and non-randomly constructed than the largest brain or largest computer we know.”[ii]
It seems that Dawkins considers God complex in the sense that he has the powers to receive, store, create, and piece together information in meaningful ways. I believe the following quote from a popular freethought website illuminates what Dawkins means:
“[Theists] 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. 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.”[iii]
So, even a spiritual mind with no physical parts whatsoever would still be constructed in a very complex and non-random way, in the sense that this mind would be, in some sense, structured in the manner and order of steps that it took to process, store, create, and link together information.
Dawkins, to my knowledge, never takes up the burden of showing why this ‘informational complexity’— as we might call it-- is improbable. However, I think his intuition that it is improbable is correct. Consider the number of possible minds. Although I do not know the total number of possible minds, I think we can safely say that it is incredible high, based on the billions of unique human and animal minds that have existed and the possible minds of gods, spirits, and fictional characters that man has conceived of.
Now, if we are considering positing a single spiritual mind as an inexplicable brute fact, what are the odds that this mind would be anything like the mind of God? I suggest that we apply the principle of indifference and assign each possible mind the same likelihood of existing uncaused. When we do this, it seems that the probability of God’s existence would be much less than one in ten billion (after all, there are six billion unique human minds in existence today, plus the minds of chimpanzees, gorillas, other intelligent animals, and fictional characters and invented gods that occupy the space of possible minds).
There is another, more important worry: would this random, uncaused mind even be coherent and intelligent? I am very skeptical of the notion that it would be. I do not believe that coherency and/or intelligence is a feature of most possible minds. After all, the minds we observe around us are a very small subset of the total number of possible minds. Human and animal minds arise from brains that are non-randomly constructed from genetic material which has been fashioned by natural selection, which has surely tended to eliminate lack of intelligence and lack of coherency: the mentally disabled have a very low chance of passing on their genes. If you can imagine a mind that would result from a randomly constructed brain, you can understand my doubts about whether this mind would be coherent and intelligent. Of course, that is not an exact analogy, for a spiritual mind does not arise from a physical brain by definition. However, if you can imagine the mind that would result from a randomly constructed brain, if the mind in question was generated by a material medium like the brain, then my thought experiment should illustrate the same point.
This leads us directly to the conclusion that the existence of God is a priori very improbable if it is admitted that God is a contingent and highly complex being. Of course, just because the God hypothesis has a low a priori probability does not necessarily mean that we could never accept it. It simply means that we need especially good evidence before we may acceptit.
The Questionable Second Premise
Dawkins asserts that any being capable of designing some complicated thing must be at least as complicated as the thing itself. He does not seem justify this assertion. I suppose, if pressed, he would appeal to everyday experience: We do not see human beings creating computers that more complicated than human beings. We do not see beavers building dams that are more complicated than they are. I do not think this justification works on close inspection. For example, human beings have a very limited time frame in which to build things, while an eternally existing mind would not have a time frame. This is relevant for the following reason: Given an infinite amount of time (or at least several billion years), a human being would be capable of tinkering with every possible arrangement of matter, and therefore it might create something more complex than itself (if such things are possible). Of course this is not how theists typically think of God creating, but nevertheless it is a conceptual possibility which defeats Dawkins’ sweeping assertion.
There is another way that a creative being could bring about a creation more complex and more improbable than its creator. Suppose that we accept Dawkins’ assertion that a being must be at least as complex (and therefore, as improbable) as whatever it seeks to explain. At the risk of sounding anthropocentric, let us also suppose that human beings are the most complicated animals in the universe. If a being was complex enough to create a human being, could it not create all of the less-complex animals, plants, and bacteria? It would seem so. This is relevant for the following reason: If we did not have any explanation for the origin of the complexity of life other than sheer chance, it could still very well be the case that an intelligent designer might act in reducing the improbability we faced, therefore acting as a good explanation. By Dawkins’ own criteria the designer only needs to be as complex as the most complex things that he designs. Therefore he is no more improbable than the most improbable thing he designs. It follows from that that in the example above the designer would only have to be as improbable as human beings originating by sheer chance. This would be more probable than all plants, animals, and bacteria originating independently by sheer chance. Thus, what I refer to as the “Transcendental Intelligent Design” hypothesis (TID)[iv] would offer a drastic reduction in improbability, at least in that situation, and perhaps could be preferred on such grounds. Still, Dawkins might object, the TID explanation still has such an incredibly low a priori probability that it should be a last resort of an explanation, after a thorough scientific search has been undertaken and come up with no answers. I would agree with him: it is good practice not to accept incredibly unlikely hypotheses unless we have good reason to suspect that we have no choice in the matter. After all, the search for credible and probable explanations is what drives science. In summation: Dawkins’ assertion that a designer must be at least complex as his designs is not only unjustified, but probably false. It is for this reason that his argument fails to undermine all TID explanations in principle. However, Dawkins’ arguments do show that there is good reason to suppose that TID explanations are incredibly improbable a priori and so there is good reason to demand very strong evidence for them before we accept them and, even then, it may be reasonable to remain agnostic about them until a thorough scientific investigation has been launched and has not provided a better explanation.
The scenario argued above assumes that we could, in principle, calculate the probability of a transcendent designer’s existence, which we would need to do in order to compare its probability to the probability of things the designer was called in to explain. The assumption that we could actually do this is highly questionable: if the designer was not necessary but was considered a ‘brute fact’, we would first need to calculate the total number of possible minds, and then determine what fraction of possible minds resemble the type of designer we wish to postulate. Until such calculations could be made, the odds may be considered low (as I have previously argued) as well as inscrutable. Since a completely unknown probability could never be considered preferable to any other probability, it follows that we could practically forget about ever being justified in postulating a transcendent designer. Only unforeseeable increases in human brain power would allow us the luxury of determining the odds mentioned previously.
Potential Problems With My Reasoning
I have identified two questions about my reasoning in this paper which must be addressed.
First: I mentioned using Occam’s razor to show that it was probable that no Godlike beings existed necessarily. A theist could easily object to this: Occam’s razor states that other things being equal, do not postulate entities beyond necessity. A theist might say that other things are not equal: Perhaps we gain some explanatory scope or power from postulating that God exists. I discuss the possibility of how we might find evidence for God (and how that would affect bear on this issue) in the paragraph below.
Second: When I discussed the contingent existence of God’s mind, I postulated only one mind as a brute fact. Of course, if there were trillions of minds that existed as brute facts, it may be probable that one of them is identical with God’s mind. This option might not be very appealing to traditional monotheists who hold that God created everything (because the other brute-fact-minds could not have been created by God). Even so, the fact that this suggestion conflicts with traditional monotheism does not mean that it is not a possibility. Yet I think this possibility is conclusively ruled out on the following grounds: If we allowed ourselves the luxury of postulating so many brute-fact-minds simply to make God’s existence likely, we would have to have very good reasons for postulating God’s existence in the first place. The reasons we might have for postulating God’s existence fall into two categories: The impossible and the improbable. If we were to find some fact that could not possibly be unless God existed, then of course we would be justified in believing in God, no matter how unlikely he might be. However, if we were to merely try to prove God’s existence by finding facts that were improbable unless God existed, we would almost certainly fail. As we have previously established, the a priori probability that God exists contingently is both very low and inscrutable. It follows from this that any fact(s) we seek to explain with God (which are not strictly impossible on God’s nonexistence) must also be inscrutably low, for why postulate an explanation that may be more improbable than what it seeks to explain? The only exception that I can think of to this rule is the following: if we found two or more facts whose probability (on God’s nonexistence) were inscrutably low, perhaps we would be justified in believing in God because it would reduce the number of inscrutable improbabilities that we had to accept.
I conclude that Dawkins’ Ultimate 747 Gambit, as he formulated it, is flawed and incorrect. However, meditating on Dawkins’ argument has led me to some convictions I discuss in this paper which lead me to believe that unless theists can demonstrate that (A) God’s nonexistence is impossible [either logically or through pointing to some fact in the world that literally could not exist in God’s absence] or (B) Two or more facts are inscrutably improbable on God’s nonexistence, then we have good reasons for disbelieving in God on the grounds that he has an extremely low a priori probability and no a posteriori considerations seem to exist that bring the total probability of God’s existence to an acceptable level.
[i] This formal statement of Dawkins’ argument is quoted from E. Wielenberg, “Dawkins’s Gambit, Hume’s Aroma, and God’s Simplicity,” Philosophia Christi Vol. 11 No. 1, 113-128 (2009).
[ii] Page 154, Richard Dawkins, The God Delusion, Bantam Press, 2006.
[iv] An oft-neglected distinction that must be made is that Dawkins emphatically does not object to all intelligent design hypotheses. For example, he once wrote:
“If incontrovertible evidence for intelligent design were ever discovered, in, say, the organization of the bacterial cell… This could only be evidence of a designer that was itself the product of natural selection or of some other as yet unknown escalatory process… [O]ur minds should immediately start working along the lines of Crick’s directed panspermia, not a supernatural designer.” (Page 106 of “Intelligent Aliens” by Richard Dawkins, published in Intelligent Thought: Science Versus the Intelligent Design Movement, Vintage Books (2006).
The reasoning underlying these statements is that a being like God could only be explained as a very improbable brute fact (God cannot be the result of evolution or the product of design). The alien designer is explicable in principle, and might not turn out to be so improbable, once we take into account natural selection. By Dawkins’ reasoning we should prefer the type of designer who could ultimately be seen as probable, because if we have to live with some gross unexplained improbability, it may as well be the bacterial cell as God. I suppose this reasoning is sound except that the existence of God might be more probable than the chance origin of a bacterial cell (Dawkins supposes that a designer must be at least as improbable as his design(s), I have shown that this reasoning does not stand up to scrutiny), and if it is then we would have good reason for believing that God exists (Namely, it would be a much more probable improbability that we would have to live with). Of course, if we are considering the probability of God’s existence to be equivalent to the probability of a single random possible mind being the mind of God (as I have previously reasoned) then the odds of God’s existence may be considered both tiny and inscrutable (how would we figure out the number of possible minds and the number of possible minds that were identical with what we might call ‘God’?). If the odds are inscrutable, then we will never know how they compare to the odds of anything else, and therefore we would never, even in principle, have a reason to accept the God hypothesis on the basis of Arguments to Design.