Last night, a reader sent me a link to *yet another* wretched attempt to argue for the existence of God using Bayesian probability. I *really* hate that. Over the years, I've learned to dread Bayesian arguments, because *so many* of them are things like this, where someone cobbles together a pile of nonsense, dressing it up with a gloss of mathematics by using Bayesian methods. Of course, it's always based on nonsense data; but even in the face of a lack of data, you can cobble together a Bayesian argument by *pretending* to analyze things in order to come up with estimates.
You know, if you want to believe in God, go ahead. Religion is ultimately a matter of personal faith and spirituality. Arguments about the existence of God *always* ultimately come down to that. Why is there this obsessive need to justify your beliefs? Why must science and mathematics be continually misused in order to prop up your belief?
Anyway... Enough of my whining. Let's get to the article. It's by a guy named Robin Collins, and it's called "[God, Design, and Fine-Tuning][collins]".
Let's start right with the beginning.
>Suppose we went on a mission to Mars, and found a domed structure in which
>everything was set up just right for life to exist. The temperature, for
>example, was set around 70o F and the humidity was at 50%; moreover, there was
>an oxygen recycling system, an energy gathering system, and a whole system for
>the production of food. Put simply, the domed structure appeared to be a fully
>functioning biosphere. What conclusion would we draw from finding this
>structure? Would we draw the conclusion that it just happened to form by
>chance? Certainly not. Instead, we would unanimously conclude that it was
>designed by some intelligent being. Why would we draw this conclusion? Because
>an intelligent designer appears to be the only plausible explanation for the
>existence of the structure. That is, the only alternative explanation we can
>think of--that the structure was formed by some natural process--seems
>extremely unlikely. Of course, it is possible that, for example, through some
>volcanic eruption various metals and other compounds could have formed, and
>then separated out in just the right way to produce the "biosphere," but such a
>scenario strikes us as extraordinarily unlikely, thus making this alternative
>explanation unbelievable.
>
>The universe is analogous to such a "biosphere," according to recent findings
>in physics. Almost everything about the basic structure of the universe--for
>example, the fundamental laws and parameters of physics and the initial
>distribution of matter and energy--is balanced on a razor's edge for life to
>occur. As eminent Princeton physicist Freeman Dyson notes, "There are many . . .
>lucky accidents in physics. Without such accidents, water could not exist as
>liquid, chains of carbon atoms could not form complex organic molecules, and
>hydrogen atoms could not form breakable bridges between molecules" (1979, p.
>251)--in short, life as we know it would be impossible.
Yes, it's the good old ID argument about "It looks designed, so it must be". That's the basic argument all the way through; they just dress it up later. And as usual, it's wrapped up in one incredibly important assumption, which they *cannot* and *do not* address: that *we understand what it would mean to change
the fundamental structure of the universe*.
What would it mean to change, say, the ratio of the strengths of the electromagnetic force and gravity? What would matter look like if we did? Would stars be able to exist? Would matter be able to form itself into the kinds of complex structures necessary for life?
We don't know. In fact, we don't even really have a clue. And not knowing that, we cannot meaningfully make *any* argument about how likely it is for the universe to support life.
They do pretend to address this:
>Various calculations show that the strength of each of the forces of nature
>must fall into a very small life-permitting region for intelligent life to
>exist. As our first example, consider gravity. If we increased the strength of
>gravity on earth a billionfold, for instance, the force of gravity would be so
>great that any land-based organism anywhere near the size of human beings would
>be crushed. (The strength of materials depends on the electromagnetic force via
>the fine-structure constant, which would not be affected by a change in
>gravity.) As astrophysicist Martin Rees notes, "In an imaginary strong gravity
>world, even insects would need thick legs to support them, and no animals could
>get much larger." (Rees, 2000, p. 30). Now, the above argument assumes that the
>size of the planet on which life formed would be an earth-sized planet. Could
>life forms of comparable intelligence to ourselves develop on a much smaller
>planet in such a strong-gravity world? The answer is no. A planet with a
>gravitational pull of a thousand times that of earth -- which would make the
>existence of organisms of our size very improbable-- would have a diameter of
>about 40 feet or 12 meters, once again not large enough to sustain the sort of
>large-scale ecosystem necessary for organisms like us to evolve. Of course, a
>billion-fold increase in the strength of gravity is a lot, but compared to the
>total range of strengths of the forces in nature (which span a range of 1040 as
>we saw above), this still amounts to a fine-tuning of one part in 1031.
>(Indeed,other calculations show that stars with life-times of more than a
>billion years, as compared to our sun's life-time of ten billion years, could
>not exist if gravity were increased by more than a factor of 3000. This would
>have significant intelligent life-inhibiting consequences.) (3)
Does this really address the problem? No. How would matter be different if gravity were a billion times stronger, and EM didn't change? We don't know. For the sake of *this* argument, they pretend that mucking about with those ratios *wouldn't alter the nature of matter at all*. That's what they're going to build their argument on: the universe *must* support life *exactly* like us: it's got to be carbon-based life on a planetary surface that behaves exactly like matter does in our universe. In other words: if you assume that everything has to be exactly as it is in our universe, then only our universe is suitable.
They babble on about this for quite some time; let's skip forwards a bit, to where they actually get to the Bayesian stuff. What they want to do is use the *likelihood principle* to argue for design. (Of course, they need to obfuscate, so they cite it under three different names, and finally use the term "the prime principle of confirmation" - after all, it sounds much more *convincing* than "the likelihood principle"!)
The likelihood principle is a variant of Bayes' theorem, applied to experimental systems. The basic idea of it is to take the Bayesian principle of modifying an event probability based on a prior observation, and to apply it backwards to allow you to reason about the probability of two possible priors given a final observation. In other words, take the usual Bayesian approach of asking: "Given that Y has already occurred, what's the probability of X occurring?"; turn it around, and say "X occurred. For it to have occurred, either Y or Z must have occurred as a prior. Given X, what are the relative probabilities for Y and Z as priors?"
There is some controversy over when the likelihood principle is applicable. But let's ignore that for now.
>To further develop the core version of the fine-tuning argument, we will
>summarize the argument by explicitly listing its two premises and its
>conclusion:
>
>*Premise 1.* The existence of the fine-tuning is not improbable under theism.
>
>*Premise 2.* The existence of the fine-tuning is very improbable under the
>atheistic single-universe hypothesis. (8)
>
>*Conclusion:* From premises (1) and (2) and the prime principle of
>confirmation, it follows that the fine-tuning data provides strong evidence to
>favor of the design hypothesis over the atheistic single-universe hypothesis.
>
>At this point, we should pause to note two features of this argument. First,
>the argument does not say that the fine-tuning evidence proves that the
>universe was designed, or even that it is likely that the universe was
>designed. Indeed, of itself it does not even show that we are epistemically
>warranted in believing in theism over the atheistic single-universe hypothesis.
>In order to justify these sorts of claims, we would have to look at the full
>range of evidence both for and against the design hypothesis, something we are
>not doing in this paper. Rather, the argument merely concludes that the
>fine-tuning strongly supports theism over the atheistic single-universe
>hypothesis.
That's pretty much their entire argument. That's as mathematical as it gets. Doesn't stop them from arguing that they've mathematically demonstrated that theism is a better hypothesis than atheism, but that's really their *whole* argument.
Here's how they argue for their premises:
>Support for Premise (1).
>
>Premise (1) is easy to support and fairly uncontroversial. The argument in
>support of it can be simply stated as follows: *since God is an all good being,
>and it is good for intelligent, conscious beings to exist, it not surprising or
>improbable that God would create a world that could support intelligent life.*
>Thus, the fine-tuning is not improbable under theism, as premise (1) asserts.
Classic creationist gibberish: pretty much the same stunt that Swinburne pulled. They pretend that there are *only* two possibilities. Either (a) there's exactly one God which has exactly the properties that Christianity attributes to it; or (b) there are no gods of any kind.
They've *got* to stick to that - because if they admitted more than two possibilities, they'd have to actually consider why *their* deity is more likely that any of the other possibilities. They can't come up with an argument that Christianity is better than atheism if they acknowledge that there are thousands of possibilities as likely as *theirs*.
>Support for Premise (2).
>
>Upon looking at the data, many people find it very obvious that the fine-tuning
>is highly improbable under the atheistic single-universe hypothesis. And it is
>easy to see why when we think of the fine-tuning in terms of the analogies
>offered earlier. In the dart-board analogy, for example, the initial conditions
>of the universe and the fundamental constants of physics can be thought of as a
>dart- board that fills the whole galaxy, and the conditions necessary for life
>to exist as a small one-foot wide target. Accordingly, from this analogy it
>seems obvious that it would be highly improbable for the fine-tuning to occur
>under the atheistic single-universe hypothesis--that is, for the dart to hit
>the board by chance.
Yeah, that's pretty much it. The whole argument for why fine-tuning is less probably in a universe without a deity than in a universe with one. Because "many people find it obvious", and because they've got a clever dartboard analogy.
They make a sort of token effort to address the obvious problems with this, but they're really all nothing but more empty hand-waving. I'll just quote one of them as an example; you can follow the link to the article to see the others if you feel like giving yourself a headache.
>Another objection people commonly raise against the fine-tuning argument is
>that as far as we know, other forms of life could exist even if the constants
>of physics were different. So, it is claimed, the fine-tuning argument ends up
>presupposing that all forms of intelligent life must be like us. One answer to
>this objection is that many cases of fine-tuning do not make this
>presupposition. Consider, for instance, the cosmological constant. If the
>cosmological constant were much larger than it is, matter would disperse so
>rapidly that no planets, and indeed no stars could exist. Without stars,
>however, there would exist no stable energy sources for complex material
>systems of any sort to evolve. So, all the fine-tuning argument presupposes in
>this case is that the evolution of life forms of comparable intelligence to
>ourselves requires some stable energy source. This is certainly a very
>reasonable assumption.
>
>Of course, if the laws and constants of nature were changed enough, other forms
>of embodied intelligent life might be able to exist of which we cannot even
>conceive. But this is irrelevant to the fine-tuning argument since the
>judgement of improbability of fine-tuning under the atheistic single-universe
>hypothesis only requires that, given our current laws of nature, the
>life-permitting range for the values of the constants of physics (such as
>gravity) is small compared to the surrounding range of non-life-permitting
>values.
Like I said at the beginning: the argument comes down to a hand-wave that if the universe didn't turn out exactly like ours, it must be no good. Why does a lack of hydrogen fusion stars like we have in our universe imply that there can be no other stable energy source? Why is it reasonable to constrain the life-permitting properties of the universe to be narrow based on the observed properties of the laws of nature as observed in *our* universe?
Their argument? Just *because*.
[collins]: http://home.messiah.edu/%7Ercollins/finetune/anth.htm.htm
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And as usual, it's wrapped up in one incredibly important assumption, which they cannot and do not address: that we understand what it would mean to change the fundamental structure of the universe.
Thank you! That's, IMO, one of the biggest problems with this kind of "everything has to be just right" argument, if not the biggest, and one that very seldom seems to get brought up. Most people try to debate these arguments on the basis of multiple universes, or the anthropic principle, or that sort of thing. It's good to know I'm not the only one who sees a problem with the whole assumption that life couldn't exist if things were different in the first place.
I'm surprised the fine-tuning people rarely see fit to address an obvious application of the weak anthropic principle: apparent fine-tuning is pretty much what we'd expect to see if life has evolved within the fundamental constraints of our universe.
A lovely post! And I mean that for several different values of "lovely"!!
It's always struck me a pointless and silly argument, and this is the best exposition of the situation that I've seen.
Thank you ...
They also suffer from the misunderstanding of unlikely events. Events with extremely low probability happen all the time. Consider lottery winners. The odds against winning some lotteries are hundreds of millions to one, and yet someone wins the lottery. I suppose they take that as evidence that the christian god intervened to allow that person to win? If you looked at a piece of quartz somewhere in the mountains of Oregon, could you calculate the odds that a little piece of that rock would end up as a particular grain of sand in a particular location on a beach near San Diego? And yet it happened.
Here's the problem with the Marsian "bio-sphere" comparison. Their argument is built on the fact the the conditions within this "bio-sphere" are so different from the conditions outside. And that's fine, but it can only be made from outside the sphere. We, on the other hand, are stuck inside our universe and the analogy does not work. That's precisely where the anthropic principle kicks in.
Using appropriate analogies is sort of like using correct controls. If they are a bit off, there is no way of knowing what kind of results you are going to get.
As you have pointed out, we have no idea what matter could be like if the rules were different. Furthermore, we don't actually know if and how they could be different. Physicists nowadays are very keen to reduce the number of variables in their thoeries.
The martian biosphere thing also ticks off another bugbear as well. We do not conclude that the biosphere is designed just because the alternative hypothesis is unlikely - we conclude it because we have a set of criteria defined showing features for which we determine things as being designed by a human like designer. But with ID, which studiously avoids saying anything about the designer, we simply lack this reference frame.
IMO, the most important problem with the fine-tuning argument is *not* that we don't know what would happen if the universal constants were different, but rather that we have no idea what range of values for the constants is possible. We can't put a probability (density) on the values, so there's no way to tell whether there is any room for "tuning". Moreover, the number and nature of the constants is a function of our current model of the universe. In a few decades there's probably an entirely different favorite model with different fundamental constants.
"But why should testability be epistemically relevant?"
I have other beefs with these arguments.
First: They mix science, philosophy, religion and atheism with the same weight. But finetuning are a matter within science, so it has first priority. The probability discussion is based on assuming philosophy. ("Epistemic probability".)
Second: Obviously the author is no scientist as evidenced above, or in his various mistakes. (Mixing Newton gravity and inflation, for example.) But it is nevertheless a very basic mistake to call secular cosmologies "atheistic", or rather a typical creationistic one.
BTW on physics, the author goes off rail about multiverses. There are more types than he describes, QM's manyworlds interpretation is one of them. And he describes inflation as if questioning its mechanism is essential. What is essential is that it is confirmed. (Latest WMAP.)
What remains is his objection that there must be variation of physics. (Not a mechanism - what mechanism?) Whether or not string theory becomes confirmed its results on old physics is enough to think that its description of the landscape of possible physics is correct. It is actually a constraint since it is finite - if we don't even know that, anything could be possible as Mark says. To have only one physics in a multiverse one must have a mechanism to pin it *with*.
It is interesting, though, that they feel compelled to *use science and mathematics* -- and that suggests, at least to me, that already these attempts at "creation science" are different, theologically, from their precursors. What I'm wondering is if, once you introduce these types of concepts into the debate, the very nature of the debate and the meaning of its terms isn't fundamentally changed?
OK, say the cosmological parameters of the Universe were "fine-tuned". Then, the argument goes, there had to be a Fine Tuner. But the Fine Tuner does not --- indeed, cannot --- live within the Universe we know. Ergo, intelligence can exist in a realm which is not at all like our Universe. Yet the whole argument was based on the idea that all the peculiarities of our Universe are essential for intelligent life!
All fall down.
I always think, when I hear this argument, "Well, of course it fits us: we're here." I mean, if it were different, we'd be different. It's silly to think the arctic is better than a temperate rain forest, because one has caribou and polar bears and the other only deer and black bears. It is, if you're a caribou. It's not if you're a deer.
But now I have something hard and all sciency to come back with.
Thank you!
The fine tuning argument always puts me in mind of Douglas Adams' puddle:
You also have the problem that God, being omnipotent and all, isn't actually constrained as to the values of the "fine-tuned" constants he uses. If you're omnipotent, you can make a universe full of intelligent life with a fine-structure constant of ten, or negative fifty million, or a value that varies over time in a nice sinusoidal pattern. So even bringing God into the picture explains nothing about why our universe has the properties it does.
Let's examine the support for Premise 1. Either the definition of "good" is "whatever God wants", in which case, "it is good for intelligent, conscious beings to exist" presupposes the existence of God, and is circular; or, there is some standard of good outside the existence of God, and God just happens to be an all-good being -- itself an assertion open to debate, but we'll let it go -- in which case the assertion that "it is good for intelligent, conscious beings to exist" itself lacks any support, since they haven't bothered to define "good" and demonstrate why the existence of intelligent, conscious beings qualifies.
Tangential pedantic whinge follows:
Your sketch of the likelihood principle is actually more descriptive of the so-called "law of likelihood". The likelihood principle is simply the assertion that all of the information in a data set is contained in the likelihood function. The likelihood principle is a trivial consequence of Bayes' Theorem, as Bayesians use it. The law of likelihood, on the other hand, neglects prior information, and thus can be extremely misleading. For example, under the law of likelihood, on the evidence of a single coin toss coming up heads, the most likely explanation is that the coin is double-headed. To avoid this conclusion, one must factor in prior information about the relative scarcity of double-headed coins and the trustworthiness of the coin flipper.
I usually find, at least when debating "god provers" (of the Jewish variety), that the following technique actually works.
Ask them to assume the theoretical existence of a proof of the non-existance of god (we are sticking to formal mathematical like proofs, since only there can you prove a negative). Then ask them if they would still believe in god.
The two most common answers are either the honest "yes" or the assertion that such a proof can never be possible, since there is a god. The first variety usually admits that this means that there is no use in trying to prove the existence of god, and the second variety just annoys you by arguing a contradiction until you or they go away.
"Ask them to assume the theoretical existence of a proof of the non-existance of god (we are sticking to formal mathematical like proofs, since only there can you prove a negative)."
Nitpick: Universal negatives are proved in science all the time, with or without formal theories.
For example, continuing discussing physical laws, we know that no massive object will ever fall against a gravitational field. That is a consequence of a theory that is verified by a finite set of observations, and a prediction that is verifiable in the same manner.
To verify to the standard of beyond reasonable doubt suffice a finite number of observations (obviously, or it would be useless). Perhaps raising unreasonable doubt somehow feels doable compared to arguing against a correct mathematical proof (though it shouldn't really). OTOH a correct theory is guaranteed to be applicable within its range of applicability. :-)
(Come to think of it, the last line is the uncertain point. Often, such as for relativity replacing classical mechanics, the range of applicability of the old theory is clarified by a new. Nevertheless, predictions are verifiable, so can be tested to be within the range of applicability.)
People only say that because they have a personal stake in the matter. That's the REAL origin of their pro-conscious life bias.
This argument has always seemed to me to be an exercise in question begging. Of course the suite of chemical reactions we call "life" are compatable with the properties of the universe. After all, life evolved in the universe. Call me when you can show that life is incompatible with properties of the universe. Take a guitar and fiddle with the tuning pegs at random...that guitar is still "fine tuned" as far as whatever sound it makes.
Like all "proofs" everything depends upon the assumptions you make. Euclidean Geometry is the way it is because of the assumptions made. You change one assumption, and the geometry changes.
The problem with these proofs is that they assume "the Christian God exists". You can only do hand waving if your assumption begins and ends with that. They can only pretend that they did not start with this assumption. Circular.
As we know, given the right assumptions you can prove anything. (You just need an non-consistant framework). So, let us assume that 1+1=2 AND 1+1=3. Therefore, God exists. (Of course, the statement "God does not exist" is also true for this system...)
Blake:
Very nice; basically taking their argument, and going Gödelesque on them. I really like that one.
It seems that this argument falls apart at the very beginning. Assuming we observed such a domed biosphere on Mars, to the extent that it would seem to imply an "intelligent designer" it certainly does not imply that said designer is God or any sort of supernatural being. We could even apply this reasoning to archaeology - since we do not have precise knowledge of how the Egyptians constructed the Pyramids of Giza (which are "obviously" designed), they must have been constructed by God or, as the Stargate franchise would have us believe, aliens.
Yes, this is a Heads I win, tails you lose argument.
1) If life exists (and it does) and the universe is apparently unsuitable for the natural development of life, then God must have done it. This is the biological Intelligent Design argument.
2) If life exists (and it does), and the universe is apparently suitable for the natural development of life, then God must have fine-tuned that universe. This is the cosmological fine-tuning argument.
Oddly, you can find people (Salvador T. Cordova comes immediately to mind) who use both arguments, and don't seem to care that they are playing both sides of the coin.
The other major problem with these sorts of arguments is the question "where did the intelligent designer come from?"
A supernatural being capable of creating the universe doesn't strike me as any more likely than a universe existing that is capable of supporting life. In fact, somewhat less likely, since we evidently have a universe that is capable of sustaining life, while we don't evidently have a god that is capable of creating a universe (that's why the arguers are trying to argue for the existance of God from the existance of the university).
If the imagined domed structure on Mars implies the existance of a intelligent designer, and the structure of our universe, which contains intelligent designers, implies an intelligent designer, then surely the existance of an intelligent designer who can design the universe requires an intelligent designer to design the designer? Ad infinitum.
So, just to be clear on this:
If we do eventually discover a variant of ongoing life outside our personal planet, say on Jupiter, then what will this mean for the idea of God creating the universe just for us?
"If we increased the strength of gravity on earth a billionfold, for instance, the force of gravity would be so great that any land-based organism anywhere near the size of human beings would be crushed."
Heck, it doesn't have to be a "billionfold" for humans to get squished: we're pretty delicate creatures, really. Just put us at the botom of the sea, and that would do it. Perhaps the life on Jupiter would be floating in the atmosphere because that was where the ecological niche was.
My point to this incredibly tired ID argument: what would happen to life on Earth if humans ceased to exist? Here's a hint: the same thing that happens in places where humans aren't now. Look at an abandoned ruin some time and try telling me that humans are the be-all and end-all of existence!
We all realize, of course, that almost nobody is going to be convinced by the logic of the other side, and switch sides. This must be because one side is correct and knows it, and the other side WANTS to believe so badly in their conclusion that they will rationalize it to no end. Now lets step back and look at who has the most motivation to keep their beliefs, atheists or religious people. Hmmmmm...
ParanoidMarvin, I like your approach! I think I will use it, and end the 'debate' since it is almost always emotional (therefore useless) and not rational.
well, that's imprecisely qualified and so indeterminate. if the object had a net positive charge of sufficient strength and the other object generating the large reference gravitational field as well did, then depending upon charge field intensity, the massive object might well be repelled by the other.
in any case, i was drawn to this topic by its possible bearing upon the Bayesian vs classical flames and religious war, e.g., as documented in http://www.law.qub.ac.uk/ice/papers/essay2.html and further in http://vanderwolk.typepad.com/greenpass/2004/08/why_yes_i_iami_.html
"Soon you will be one of us", say i, Bayesian through and through.
so, what is the Bayesian estimate of another Hurricane Katrina this year?
i've resurrected the fight with all but the purest, best intentions over at The Intersection. there's a second comment, too.
i don't know what you mean by "religious Bayesians". do you mean religious people who are misapplying Bayesian stuff to push their agenda? or do you mean disciples of Jaynes?
anyway, i think there's serious stuff to talk about here. maybe everyone wants to wait for me to write my blog entry. maybe not.
but the very fact that there are Big Brains who have lined up on either side of The Question without resolving it sounds to be like It's Of Interest: it doesn't have a And They Lived Happily Ever After ending. clearly there are good results to be had using either formulation.
Why Don't They Have A Consensus?
then again, there's dark energy.
Let's assume that we have proved that GOD exists because things look like they have been intelligently designed. Now, GOD himself looks itself to be a product of intelligent design. Or are we to assume that GOD somehow was a product of some random natural process? Which intelligent supercreator created this GOD? And then who created this intelligent supercreator? And so on.
If on the other hand we assume that GOD always existed and need not be created, then why worry about who created the universe. Universe could have been there always. If GOD did not create the universe, it is hard to believe that he had the power to interfere in an independently created universe to create life.
Re: The Mission to Mars ... isn't Paley's story about finding a "watch on the heath" so much better?
> Let's assume that we have proved that GOD exists because
> things look like they have been intelligently designed. Now,
> GOD himself looks itself to be a product of intelligent
> design.
LOL. Hofstadter's "God := God Over Djinn".
The way I see it, there are two possibilities. 1) Due to some form of symmetry we don't yet understand, there is actually no other possible configurations of forces such as gravity or the cosmological constant. The recent solving of E8 lends credibility to this theory since many subatomic particles seem to exhibit properties in accordance with individual facets of E8.
2) There is a dazzling array of universes with different properties and starting conditions, probably in a meta-universe itself one of many with different initial conditions. So, by the anthropic principle, we are exactly where we are because if we weren't here then we wouldn't be here to talk about it. As is the case with the vast majority of the other universes with initial conditions unsuitable for our variety of life. However I am willing to bet that some form of self-replicating material pattern will appear in any universe, with any initial conditions conceivable.
And so they get it all wrong. First you have to start with a probability P that the design hypothesis is true. Then you can adjust that probability with bayesian argument.
Now, if you assume that P is 50%, or something equally silly, then sure - the fact that the universe looks designed is pretty compelling evidence that it is.
If you think that the likelihood that there is an invisible old man in the sky (I could go on ...) is remote, then it's less compelling.
And if you think it's impossible, or "not even wrong" - that the idea of a God is incoherent - then no amount of bayesian adjustment of P will change it to a nonzero value. That follows straight on from the theorem.
And of course, there's all the Baysian argument going the other way: the existence of nonbelief and evil, the evidence for evolution (indicating that God would be stupid and/or lazy), different religions ... again, I could go on.
Bleh. It all hinges on that initial value of P, and Bayes alone does not provide a way of pinning a reasonable value on it. It always comes down to faith.
Neither the nonexistence nor the existence of God can be proved. It will always be a matter of faith.
Anonymous,
That's true, but we must continue having this argument while they are trying to push this into our biology/science curricula.
Did OJ do it? Nobody knows, but most would put their money on it.
Calling someone stupid for guessing differently than you is stupid. You're both guessing.