The probability of a god existing

[Fire Fly]

I was watching a new Richard Dawkins interview (link) and it really got me into thinking, what is the probability of there actually being a god? So, I wrote a little essay laying out my basic assumptions and then tried to calculate that possibility. I would like others to provide comments or criticisms. Thank you.

The probability of a god existing

Homo sapiens have existed for some 200,000 years. The earliest known existence of what would appear to be a religion appeared some 70,000 years ago. The earliest known human civilization existed some 10,000 years ago in Mesopotamia and the rise of Western atheism appeared only 2,500 years ago in ancient Greece, with modern atheism only existing for a few decades or centuries. It is therefore reasonable to say that, for the vast majority of human history and for the vast majority of the human population, it has been assumed there is a supernatural creator.

The best current estimate of the demography of religion suggests that of the 6.5 billion people, 33% of them are Christians, 21% of them are Islamic, 14% are Hindus, 6% are animistic and 0.22% are Jewish. What these religions all have in common is that they assume there exists a supernatural creator and that their creator is the only true creator.

But a closer analysis reveals greater uncertainty than that which these religions have assumed. For the purpose of demonstration, let us make a few simple and reasonable assumptions.

Assumption 1. Let us say that in the entirety of human history, there has been a total of 50 religions, each religion which assumes that there exists one primary creator, with respect to their religion. This is not an unreasonable assumption given the dozens of animistic religions, the dozens of pagan religions and the handful of monotheistic religions, all having detailed creation stories that have given credit of creation to a specific entity.

Assumption 2. Let us say that the success of a religion is independent of the legitimacy of a religion, that is, the success of a religion does not equate to that religion being more legitimate than another religion. Again, this is not an unreasonable assumption. As an analogy, let us look at the business world. Company A makes product a and Company B makes product b. Both product a and product b have the same function, serve the same purpose and have similar design. However, what distinguishes product a from product b is that product a is consumed at a higher quantity than product b because Company A is significantly richer and has a more talented marketing team, with respect to Company B. Therefore, if extraneous variables, with respect to the actual products, are removed, product a and product b are, for all intensive purposes, the same. This leads us to our final assumption.

Assumption 3. Let us say that a religion is either correct or incorrect with each religion having the same probability of being correct. Therefore, let us assume that the probably of being correct is P(religion is correct)=0.50; this is not an unreasonable assumption since the purpose of religion is to provide an explanation in the lack of physical evidence. In fact, this assumption is quite generous.

Given these reasonable parameters, let us say that k is the number of religion that is true out of all religions; religion assumes that one particular religion is true while the others are false. So 1 religion (be it Christianity, Islam, Judaism, or Pastafarian) is correct out of the total 50 religions which have existed so far. Thus, we can calculate the probably of one religion being true while 49 religions are false with P(k=1). Therefore, k will follow the binomial distribution with probability mass function:



where k=the religion is true and the others are false (only 1 religion can be true, the others must be false), n=the total number of existed religions in human history (n=50) and p=the probability of a particular religion is true (p=0.50).

Solving P(k=1) = (50!/1!*49!) * (0.50)^1 * (0.50)^49 gives us the probability of one’s particular religion being true out of every single religion which has existed thus far to be approximately 8.8817e-16 or 0.00000000000000088817.

Thus, the probability of one particular faith claiming that their religion and their creator to be true while every single other religion which has existed in human history, which has claimed the exact same thing with the exact same fervor, is false is 0.00000000000000088817 or 0.0000000000000088817%, given the above assumptions.

[Fire Fly]

I should clarify, my original question was, "What is the probability of a god existing?" What I calculated was, "What is the probability of a religion's claim that their god exists is true?" So, the calculation doesn't directly answer the original question but rather, it gives a reference frame from which to extrapolate an answer from.

[DPDarkPrimus]

You need to make it more clear that you are assuming there are only 50 religions, when there are in fact many more that have creator gods.

[Fire Fly]

I rewrote some minor things and added some more. I forgot that it is possible to do a normal approximation to the binomial to determine if there is such a thing as a god at all, assuming there are only 50 religions.

The probability of a god existing

Homo sapiens have existed for some 200,000 years. The earliest known existence of what would appear to be a religion appeared some 70,000 years ago. The earliest known human civilization existed some 10,000 years ago in Mesopotamia and the rise of Western atheism appeared only 2,500 years ago in ancient Greece, with modern atheism only existing for a few decades or centuries. It is therefore reasonable to say that, for the vast majority of human history and for the vast majority of the human population, it has been assumed there is a supernatural creator.

The best current estimate of the demography of religion suggests that of the 6.5 billion people, 33% of them are Christians, 21% of them are Islamic, 14% are Hindus, 6% are animistic and 0.22% are Jewish. What these religions all have in common is that they assume there exists a supernatural creator and that their creator is the only true creator.

But a closer analysis reveals greater uncertainty than that which these religions have assumed. For the purpose of demonstration, let us make a few simple and reasonable assumptions.

Assumption 1. Let us say that in the entirety of human history, there has been a total of 50 religions, each religion which assumes that there exists one primary creator, with respect to their religion. This is not an unreasonable assumption given the dozens of animistic religions, the dozens of pagan religions and the handful of monotheistic religions, all having detailed creation stories that have given credit of creation to a specific entity.

Assumption 2. Let us say that the success of a religion is independent of the legitimacy of a religion, that is, the success of a religion does not equate to that religion being more legitimate than another religion. Again, this is not an unreasonable assumption. As an analogy, let us look at the business world. Company A makes product a and Company B makes product b. Both product a and product b have the same function, serve the same purpose and have similar design. However, what distinguishes product a from product b is that product a is consumed at a higher quantity than product b because Company A is significantly richer and has a more talented marketing team, with respect to Company B. Therefore, if extraneous variables, with respect to the actual products, are removed, product a and product b are, for all intensive purposes, the same. This leads us to our final assumption.

Assumption 3. Let us say that a religion is either correct or incorrect with each religion having the same probability of being correct. Therefore, let us assume that the probably of being correct is P(religion is correct)=0.50; this is not an unreasonable assumption since the purpose of religion is to provide an explanation in the lack of physical evidence. In fact, this assumption is quite generous. The more evidence there is, the probability of being correct will increase rapidly and approach 1 where 1=always true; the less evidence there is, the probability of being correct will decrease rapidly and will approach 0 where 0=always false.

Given these reasonable parameters, let us say that k is the number of religion that is true out of all religions; religion assumes that one particular religion is true while the others are false. So 1 religion (be it Christianity, Islam, Judaism, or Pastafarian) is correct out of the total 50 religions which have existed so far. Thus, we can calculate the probably of one religion being true while 49 religions are false with P(k=1). Therefore, k will follow the binomial distribution with probability mass function:



where k=the religion is true and the others are false (only 1 religion can be true, the others must be false), n=the total number of existed religions in human history (n=50) and p=the probability of a particular religion is true (p=0.50).

Solving P(k=1) = (50!/1!*49!) * (0.50)^1 * (0.50)^49 gives us the probability of one’s particular religion being true out of every single religion which has existed thus far to be approximately 4.441e-14 or 0.00000000000004441.

Thus, the probability of one particular faith claiming that their religion and their creator to be true while every single other religion which has existed in human history (assuming that there has existed a total of 50 religions ever), which has claimed the exact same thing with the exact same fervor, is false is 0.00000000000004441 or 0.000000000004441% (4.441e-12%).

Given this, it should be said that the original question was, "What is the probability of a god existing?" What was calculated here was, "What is the probability of a religion's claim that their god exists is true?" So, the calculation doesn't directly answer the original question but rather, it gives a reference frame from which to extrapolate an answer from.

Now, to answer the question, “What is the probability of a god existing?” we must take the summation of all the religions, assuming there has only ever existed 50, that is, we ask the question, “What is the probability of religion 1 being true + the probability of religion 1 and religion 2 being true + the probability of religion 1 and 2 and 3 being true + ……+ the probability of religion 1 and 2 and 3 and …. 49 and 50 being true?” We can calculate the probability of any god existing, no matter what religion, by performing this calculation with a continuity correction P(k ≥ 1) = P( k ≥ 1 - 0.5) and using a normal approximation to the binomial where k~B(50, 4.441e-14) and where k~N(np, sqrt( np(1-p) ) where np=2.2205e-12 and where sqrt( np(1-p) )=1.49e-6, we find:

P(k ≥ 1) = P( k ≥ 0.5)

P(k ≥ 1) = P( k - 2.2205e-12 / 1.49e-6 ≥ .05 - 2.2205e-12/ 1.49e-6 )

P(k ≥ 1) = P( Z ≥ 335570 )

P(k ≥ 1) = 1 - 1

P(k ≥ 1) = 0

Solving for P(k ≥ 1), a value could not be obtained for 335570. It can only be concluded that such a large value is a statistical impossibility.

Therefore, given the assumption that there have only been 50 religions in human history, that the probability of one of these religions being true to be 4.441e-14, it can be concluded that the existence of a god to be a statistical impossibility, that is, there is no god.

[R. U. Serious]

us assume that the probably of being correct is P(religion is correct)=0.50; this is not an unreasonable assumption since the purpose of religion is to provide an explanation in the lack of physical evidence. In fact, this assumption is quite generous.

It's entirely unreasonable, heck it's totally arbitrary. The only people that may agree on that assumption are all people that are not invested in any religion anyways (or will propose lower number, which as you imply wouldn't weaken your overall argument). You argument will fail to convince anybody of anything, it may only give a warm fuzzy feeling to some people to see their assumptions and convinctions wrapped into numbers that appear "scientifical", while being totally arbitrary.

I am not saying that the basic argument is flawed (i.e., there's so many religions, that - even if there was a correct one - you'll most likely be picking the wrong one), but I am saying that trying to represent it with arbitrary numbers doesn't strengthen the argument one bit.

It reminds of the joke about the spherical cow:
http://en.wikipedia.org/wiki/Spherical_cow

[Hugh]

You argument will fail to convince anybody of anything, it may only give a warm fuzzy feeling to some people to see their assumptions and convinctions wrapped into numbers that appear "scientifical", while being totally arbitrary.

What, atheists need to be constantly reassured that God doesn't exist? I thought only religious people have assurance problems...

[Molyneux]

Look at it this way:

There are a literally infinite number of possible Gods, each with a probability of existence greater than or equal to zero.

Given an infinite number of possible outcomes, the probability of any one specific God existing is zero. It's not just close to zero, it is zero.

Therefore, while the probability of a God existing in general may be greater than zero, the odds against the deity of any particular religion existing are infinite.

[Patrick Degan]

So 1 religion (be it Christianity, Islam, Judaism, or Pastafarian) is correct out of the total 50 religions which have existed so far.

I assume the Pastafarian faith preaches the Divine connection between humanity and Italian cuisine?

[Hugh]

Therefore, while the probability of a God existing in general may be greater than zero, the odds against the deity of any particular religion existing are infinite.

What about the polytheistic religions, which explicitly acknowledge the existence of several gods, including (IIRC) those they don't worship?

[Eleas]

So 1 religion (be it Christianity, Islam, Judaism, or Pastafarian) is correct out of the total 50 religions which have existed so far.

I assume the Pastafarian faith preaches the Divine connection between humanity and Italian cuisine?

What is this? Have you not been touched by His noodly appendage?

Repent and be saved, heathen, for the Flying Spaghetti Monster is the one true God.

[Singular Intellect]

My favorite arguement is the fundies who throw around probability calculations as some type of 'evidence' for god.

I just respond with coin flipping probabilities citing figures opposite of theirs and point out that's proof there is no god.

[Molyneux]

Therefore, while the probability of a God existing in general may be greater than zero, the odds against the deity of any particular religion existing are infinite.

What about the polytheistic religions, which explicitly acknowledge the existence of several gods, including (IIRC) those they don't worship?

Still, as long as there are an infinite number of possible pantheons, the probability of any specific pantheon existing is exactly zero.

[Feil]

I think you're missing the point, Mylyneux: a polytheist who believes in every god, even the ones he doesn't know about yet, will by default have the same chance of being right about at least one god as there is a chance of that god existing.

[Fire Fly]

us assume that the probably of being correct is P(religion is correct)=0.50; this is not an unreasonable assumption since the purpose of religion is to provide an explanation in the lack of physical evidence. In fact, this assumption is quite generous.

It's entirely unreasonable, heck it's totally arbitrary. The only people that may agree on that assumption are all people that are not invested in any religion anyways (or will propose lower number, which as you imply wouldn't weaken your overall argument). You argument will fail to convince anybody of anything, it may only give a warm fuzzy feeling to some people to see their assumptions and convinctions wrapped into numbers that appear "scientifical", while being totally arbitrary.

I am not saying that the basic argument is flawed (i.e., there's so many religions, that - even if there was a correct one - you'll most likely be picking the wrong one), but I am saying that trying to represent it with arbitrary numbers doesn't strengthen the argument one bit.

It reminds of the joke about the spherical cow:
http://en.wikipedia.org/wiki/Spherical_cow

There is absolutely no evidence for the existence of a god (where p would equal to 1) but at the same time, you cannot assume that a god does not exist (where p would equal to 0). Therefore, assuming p=0.50 is the most reasonable way to go, that is, the chance of a god existing is base purely on chance. If you pick p=0.75, you have to demonstrate that there is physical evidence for the existence of a god. If you pick p=0.25, you have to demonstrate that there is evidence against god. Picking a number not of p=0.50 will complicate the matter; that is why I chose a simple number and chose p=0.50.

[Kuroneko]

There is a problem with your methodology even if all three assumptions are granted (ignoring the arbitrariness in some of them for the moment): the binomial distribution is a model for k successes in a sequence of n Bernoulli trials (here, fifty of them). What this means is that you implicitly assume that the truth or falsehood of each religion is independent of the truth or falsehood of all other religions. In fact, since by this assumption it is possible that for all fifty religions to be "true", the probability of atheism being "correct" is f(0;50,.5) < 1E-15.

Now, to answer the question, “What is the probability of a god existing?” we must take the summation of all the religions, assuming there has only ever existed 50, that is, we ask the question, “What is the probability of religion 1 being true + the probability of religion 1 and religion 2 being true + the probability of religion 1 and 2 and 3 being true + ……+ the probability of religion 1 and 2 and 3 and …. 49 and 50 being true?”

If you wanted to calculate all fifty religions being "true", that is just f(50;50,.5) = 1/2^50 < 1E-15. The proper question to ask (if all fifty have a creator-entity) is "what is the probability of the truth of at least one religion?", which is 1-f(0;50,.5) > 1-(1E-15).

[Fire Fly]

There is a problem with your methodology even if all three assumptions are granted (ignoring the arbitrariness in some of them for the moment): the binomial distribution is a model for k successes in a sequence of n Bernoulli trials (here, fifty of them). What this means is that you implicitly assume that the truth or falsehood of each religion is independent of the truth or falsehood of all other religions. In fact, since by this assumption it is possible that for all fifty religions to be "true", the probability of atheism being "correct" is f(0;50,.5) < 1E-15.

Now, to answer the question, “What is the probability of a god existing?” we must take the summation of all the religions, assuming there has only ever existed 50, that is, we ask the question, “What is the probability of religion 1 being true + the probability of religion 1 and religion 2 being true + the probability of religion 1 and 2 and 3 being true + ……+ the probability of religion 1 and 2 and 3 and …. 49 and 50 being true?”

If you wanted to calculate all fifty religions being "true", that is just f(50;50,.5) = 1/2^50 < 1E-15. The proper question to ask (if all fifty have a creator-entity) is "what is the probability of the truth of at least one religion?", which is 1-f(0;50,.5) > 1-(1E-15).

Oh I see what I did wrong. Thanks. And yes, the assumptions are quite arbitrary but I needed something to work from.

[Darth Wong]

Let's face it, when debating religion most people are aiming at one of the monotheistic religions. And there is a pretty good way to estimate the probability of a monotheistic deity existing, by noting the following facts:

Fact #1: Despite many claims to the contrary, supernatural religious beliefs all have precisely the same amount of empirical supporting evidence: zero. Hence the importance of "faith".

Fact #2: Supernatural religious beliefs are justified by pointing out that you cannot absolutely prove them false. However, this justification can be equally applied to an infinite number of possible arbitrary beliefs.

Fact #3: Monotheistic supernatural religious beliefs are unusual in the sense that they are exclusive: not only do they postulate some kind of supernatural phenomenon, but they also require that all other possible supernatural phenomena are false.

Take those three facts together and you will find that the probability of a monotheistic deity is 1/x, where x is the number of possible supernatural phenomena which would all have precisely the same justification as the monotheistic deity does, hence the same probability of being true, yet which all must be false for the monotheistic belief to be true. Since x is infinity, the probability of a monotheistic god approaches zero.

[Starglider]

Take those three facts together and you will find that the probability of a monotheistic deity is 1/x, where x is the number of possible supernatural phenomena which would all have precisely the same justification as the monotheistic deity does, hence the same probability of being true, yet which all must be false for the monotheistic belief to be true. Since x is infinity, the probability of a monotheistic god approaches zero.

One of the fundamental debates in Bayesian AI, particularly reflective Bayesian AGI (which is what I'm specifically working on) is what the universal base prior should be, both in terms of what tends to work and trying to derive it from first principles (which there is also a lot of debate on). The best answers are all some variation of Kolmogorov (essentially Occam's razor defined computationally) but the specifics vary widely.

I have looked at this seriously along with colleagues who've spent rather more time on it, and the arguments presented here, yours and the OP, are ludicrously oversimplified. I don't particularly want to write (another) 100 page essay on application of various candidate base priors to various candidate formalisations of the notion of an intelligent creator, but I will note that in this case the ludicrous oversimplification is a fairly harmless one. The most generous sane (IMHO of course) set of assumptions generates probabilities somewhere south of billions to one, with most models many orders of magnitude below that. That's just for the set of all possible universes where an intelligent creator is the first thing to exist and specified physics as we know it. Tacking on even a small fraction of the specific conditions the typical human religion includes rapidly takes the probability down to infinitesimal under any sane model. As I've noted earlier, the probability for many religions is literally zero, because they're rife with internal inconsistencies.

[Starglider]

P.S. The only useful conclusion of the above analysis; we won't get nBSG cylons in real life unless we truly and very deliberately fuck up the initialisation of an AGI system. Designing an AGI initial state that 'believes' a human dogma and is actually stable would be really, really hard, much harder than the already pretty hard task of just ensuring that it is benevolent, essentially because rational intelligence is the inherent antidote to religion. Though I'd guess most members of this board already had an intuitive perception of that.

[Darth Wong]

Take those three facts together and you will find that the probability of a monotheistic deity is 1/x, where x is the number of possible supernatural phenomena which would all have precisely the same justification as the monotheistic deity does, hence the same probability of being true, yet which all must be false for the monotheistic belief to be true. Since x is infinity, the probability of a monotheistic god approaches zero.

One of the fundamental debates in Bayesian AI, particularly reflective Bayesian AGI (which is what I'm specifically working on) is what the universal base prior should be, both in terms of what tends to work and trying to derive it from first principles (which there is also a lot of debate on). The best answers are all some variation of Kolmogorov (essentially Occam's razor defined computationally) but the specifics vary widely.

I have looked at this seriously along with colleagues who've spent rather more time on it, and the arguments presented here, yours and the OP, are ludicrously oversimplified. I don't particularly want to write (another) 100 page essay on application of various candidate base priors to various candidate formalisations of the notion of an intelligent creator, but I will note that in this case the ludicrous oversimplification is a fairly harmless one. The most generous sane (IMHO of course) set of assumptions generates probabilities somewhere south of billions to one, with most models many orders of magnitude below that. That's just for the set of all possible universes where an intelligent creator is the first thing to exist and specified physics as we know it. Tacking on even a small fraction of the specific conditions the typical human religion includes rapidly takes the probability down to infinitesimal under any sane model. As I've noted earlier, the probability for many religions is literally zero, because they're rife with internal inconsistencies.

All you're doing is trying to create a vague blanket definition in order to capture entire classes of ideas, and then ask about the probability of that entire class of ideas being true. The probability of any particular monotheistic god being real is exactly as I defined it.

[Patrick Degan]

Let's face it, when debating religion most people are aiming at one of the monotheistic religions. And there is a pretty good way to estimate the probability of a monotheistic deity existing, by noting the following facts:

Fact #1: Despite many claims to the contrary, supernatural religious beliefs all have precisely the same amount of empirical supporting evidence: zero. Hence the importance of "faith".

Fact #2: Supernatural religious beliefs are justified by pointing out that you cannot absolutely prove them false. However, this justification can be equally applied to an infinite number of possible arbitrary beliefs.

Fact #3: Monotheistic supernatural religious beliefs are unusual in the sense that they are exclusive: not only do they postulate some kind of supernatural phenomenon, but they also require that all other possible supernatural phenomena are false.

Take those three facts together and you will find that the probability of a monotheistic deity is 1/x, where x is the number of possible supernatural phenomena which would all have precisely the same justification as the monotheistic deity does, hence the same probability of being true, yet which all must be false for the monotheistic belief to be true. Since x is infinity, the probability of a monotheistic god approaches zero.

You should quote that on your Creationism pages.

[Starglider]

All you're doing is trying to create a vague blanket definition in order to capture entire classes of ideas

The whole point of the exercise is to create a definition specific enough that you can apply a computational prior to it. That's a lot less vague than typical human religious babble, but obviously to do this you have to take definitional liberties that a fundie would object to (not that they'd really comprehend why - from personal experience they just spout nonsense about god being unquantifiable and incomprehensible, i.e. admit that they worship ignorance).

and then ask about the probability of that entire class of ideas being true

Anything that isn't completely defined down to specific maths is strictly a class of ideas. Christian sects each believe a different subset of Christianity with their own embellishments, and there's still a lot of wiggle room in the definition (which priests love to use of course for justifying whatever they feel like at the time). For general purposes this is semantic nitpicking, but if you're doing a formal analysis it matters.

The probability of any particular monotheistic god being real is exactly as I defined it.

Kinda. You said 'since x is infinity, the probability of a monotheistic god approaches zero'. You're assuming that the total complexity of the universe is or may be infinite, or specifically that there are an infinite number of possible universes that we may be living in. That's a solid axiom, but it means that when you're comparing the cardinality of different classes of universe that we might be in you're invoking transfinite mathematics. For a finite total complexity, some (usually very small) fraction of possible universes correspond to a particular metaphysical belief (as long as it's internally consistent and doesn't contradict observed evidence). Remove the complexity bound (strictly you're applying a more complex prior to the 'total complexity of the universe' variable - a kind of 'meta-Kolmogorov' issue that's a bitch to solve - the best efforts I've seen try to look at effective system bounds that might emerge in an infinite configuration space) and you have to look at how the cardinality ratio between 'metaphysical belief is true' and 'metaphysical belief is false' changes as the complexity increases. If it stays constant, the probability will be very small but finite. If it declines, the probability is likely to be infinitesimal, depending on your exact universal complexity prior. If it increases, the probability may actually be nontrivial, again depending on the base prior. I've yet to see any kind of religious belief that doesn't have a declining ratio (past a usually relatively modest inflection point) so yes in practice if you formalise this into a Bayesian logic system, the answer is generally 'effectively zero'.

Wildly esoteric compared to the usual logic for these debates, but as I say, it's somewhat relevant to my particular field. This is what happens when you do philosophy with maths instead of nonsense words (not that I specialise in that, but I know people who do).

[Lord Zentei]

This has been attempted previously: linka.

Mike Shermer of Skeptic magazine demolishing an argument from a book that claims the probability of God existing is 67%.

He changes the arbitrary numbers assumed by the author of said book and acheives a rather lower figure.

Of course, the assumptions that went into the formula used are silly, which he unfortunately doesn't point out.

[Fire Fly]

Let's face it, when debating religion most people are aiming at one of the monotheistic religions. And there is a pretty good way to estimate the probability of a monotheistic deity existing, by noting the following facts:

Fact #1: Despite many claims to the contrary, supernatural religious beliefs all have precisely the same amount of empirical supporting evidence: zero. Hence the importance of "faith".

Fact #2: Supernatural religious beliefs are justified by pointing out that you cannot absolutely prove them false. However, this justification can be equally applied to an infinite number of possible arbitrary beliefs.

Fact #3: Monotheistic supernatural religious beliefs are unusual in the sense that they are exclusive: not only do they postulate some kind of supernatural phenomenon, but they also require that all other possible supernatural phenomena are false.

Take those three facts together and you will find that the probability of a monotheistic deity is 1/x, where x is the number of possible supernatural phenomena which would all have precisely the same justification as the monotheistic deity does, hence the same probability of being true, yet which all must be false for the monotheistic belief to be true. Since x is infinity, the probability of a monotheistic god approaches zero.

Your calculus based approach is quite elegant. Using this approach, would you say that it is fair to say that the probability of a monotheistic god existing is P(god)=0 and that the probability that there is no monotheistic god is P(god^C), where god^C is the compliment of god existing (i.e. god does not exist)? Then, solving for P(god^C) is:

P(god^C)=1-P(god)

P(god^C)=1-0

P(god^C)=1

Its really quite amazing how once you learn some introductory/intermediate math, how much you can think for yourself. At the same time though, it really makes you look at the world with sheer amazement at how people can believe in such highly, highly, statistically improbable things and it makes you feel quite alone, being one of few people who know the reality; it really is a delusional world.

[Darth Wong]

The whole point of the exercise is to create a definition specific enough that you can apply a computational prior to it.

So you alter the definition in order to suit the computation, rather than altering the computation in order to suit the definition? There's a word for that: ass-backwards.

Anything that isn't completely defined down to specific maths is strictly a class of ideas. Christian sects each believe a different subset of Christianity with their own embellishments, and there's still a lot of wiggle room in the definition (which priests love to use of course for justifying whatever they feel like at the time). For general purposes this is semantic nitpicking, but if you're doing a formal analysis it matters.

Hardly. As long as you are not talking about an incredibly broad class (eg- "anything supernatural"), the logic still holds and you have failed to identify any flaw with it other than saying that it's oversimplified without bothering to explain how.

Kinda. You said 'since x is infinity, the probability of a monotheistic god approaches zero'. You're assuming that the total complexity of the universe is or may be infinite, or specifically that there are an infinite number of possible universes that we may be living in.

I never made any such assumption. x is infinite as long as there is an infinite number of possible ideas for supernatural deities. You don't need infinite universes in order to say that there are an infinite number of possible ideas for supernatural deities.

That's a solid axiom, but it means that when you're comparing the cardinality of different classes of universe that we might be in you're invoking transfinite mathematics. For a finite total complexity, some (usually very small) fraction of possible universes correspond to a particular metaphysical belief (as long as it's internally consistent and doesn't contradict observed evidence). Remove the complexity bound (strictly you're applying a more complex prior to the 'total complexity of the universe' variable - a kind of 'meta-Kolmogorov' issue that's a bitch to solve - the best efforts I've seen try to look at effective system bounds that might emerge in an infinite configuration space) and you have to look at how the cardinality ratio between 'metaphysical belief is true' and 'metaphysical belief is false' changes as the complexity increases. If it stays constant, the probability will be very small but finite. If it declines, the probability is likely to be infinitesimal, depending on your exact universal complexity prior. If it increases, the probability may actually be nontrivial, again depending on the base prior. I've yet to see any kind of religious belief that doesn't have a declining ratio (past a usually relatively modest inflection point) so yes in practice if you formalise this into a Bayesian logic system, the answer is generally 'effectively zero'.

What the fuck does any of this have to do with the simple premise that there are an infinite number of possible ideas for supernatural deities? Are you suggesting that if you have, say, a billion ideas for supernatural deities, it will become impossible to think of any more variations?

Wildly esoteric compared to the usual logic for these debates, but as I say, it's somewhat relevant to my particular field. This is what happens when you do philosophy with maths instead of nonsense words (not that I specialise in that, but I know people who do).

Math is only as good as the reasoning it's based on, and you are adding a completely unnecessary factor by assuming that the number of possible ideas is tied to the complexity of the universe and/or the number of universes in existence: a non sequitur if I ever saw one.