The Probability of God
January 27th, 2007 by 
drunkentune
I’ve read a bit on Bayesian reasoning, and while searching for some topics people write on, I did the natural thing and Googled some key words, such as ‘Bayesian + hat‘, ‘Bayesian + supernatural‘, and finally, ‘Bayesian + god‘ hoping to find some interesting topics. Don’t ask me why I chose ‘hat’.
Stephen Unwin’s homepage came up as the first link under ‘Bayesian + god’. Looking at his webpage, I recalled that I had read a bit on his book a few months ago. He argues in his book The Probability of God: A Simple Calculation that Proves the Ultimate Truth, that we can compute the probability of God’s existence with the use of Bayesian reasoning. If we assume that with a ‘maximum ignorance’, the existence or nonexistence of God is that of 50/50, then we can attempt to assign probabilities to God’s existence. He throws some numbers in the mixing bowl (we’ll get to them later under the fold), and comes up with the probability of God’s existence. Unwin says, ‘The probability that God exists is…
That’s a confident probability, so while he has a ‘personal’ probability of 95% and says that there is a ‘reasoned certainty’ of ~98% (thus making his ‘faith’ 28%, and coming to this concusing by stating ‘Rather, I am proposing that spiritual truth, in analogy to poetic, musical, and artistic truths, is something other than the brute truth of logic’) that does not reflect any of his own data, this should put atheists in a bind. A 67% chance of God existing? Wow. But how exactly did he come to this magic ‘67%’?
Unwin uses a modified verson of Bayenes’s therom, so instead of:
| p(A|X) = | p(X|A)*p(A) + p(X|~A)*p(~A) |
Unwin says:
| p(after) = | p(before)* D + 100% - p(before) |
The final probability of God’s existence is a function of the probability before times D (as Unwin calls it, the ‘Divine Indicator Scale’). This scale operates on a scale of one to five, so that in the five possible probabilities for an occurrence to be due to an existence of God, if at 0.1 it is a tenth as likely to occur if God exists, if 0.5 it’s likely that God does not exist, 1 is neutral, 2 is twice as likely if God exists, and 10 is ten times as likely to occur if God exists.
Unwin has six pieces of criteria, and assigns numbers to each of them:
(1) recognition of goodness (D = 10),
(2) religious experiences (D = 2),
(3) intranatural miracles (prayers) (D = 2)
(4) extranatural miracles (the resurrection) (D = 1),
(5) existence of moral evil (D = 0.5),
(6) and existence of natural evil, such as hurricanes and earthquakes (D = 0.1).
If one plugs these figures into the above formula, where each subsequent posterior probability as the new prior probability - the p(after) figure is then replaced by each p(before) - until all six have been computed, yes, the probability that God exists is 67%.
Yet, I don’t agree with his numbers. With the thousands of religions humans have created, I don’t think the resurrection deserves a D = 1, but D = 0.1; looking at the state of the world, I don’t think an innate goodness (or the fact that we make value judgements) should be D = 10, but D = 1, and with natural answers to both religious experiences and prayers, both are demoted to a conservative D = 0.5. I also dislike his 50/50 assumption of God’s existence, but I’ll leave it where it is. Unwin restricts his data solely to the Christian god, a case of special pleading, but he dances around this issue by claiming that ‘…the specifics of the person-God’s nature is secondary in my mind to the question of his very existence,’ so I’ll allow it. This data only gives the probability of a god. I suppose the theologians can settle out the rest.
It’s a flawed system, and as Unwin confesses: ‘This number has a subjective element since it reflects my assessment of the evidence. It isn’t as if we have calculated the value of pi for the first time.’ Michael Shermer of Scientific American and Skeptic, plugged in his own probabilities, reflecting slightly lower probabilities than my own, and put the probability of the existence of God at 0.02, or 2%.
So my question is this for both believers and nonbelievers, in two parts: (i) what do you think the values should be, and (ii) why?
Extra credit
>An Intuitive Explanation of Bayesian Reasoning, by Eliezer Yudkowsky
January 27th, 2007 at 9:19 pm
I am so proud. On the extra credit by Yudkowsky, I actually got the correct answer, putting me in the top 15% of doctors who are given the problem.
Simon Greenleaf and the more recent James W. Montgomery who are legal experts would place the probability of the events of miracles in the New Testament as higher than chance. See Science, Theology and the Miraculous. So, I suppose I would go with Unwin but increase his fourth factor to D=2, making my probability greater than 67%.
It is interesting to consider this probability calculation in terms of Pascal’s wager. Did Unwin do so?
Another related factor with probabilities is how important the result is to you personally. For example, my oldest son is studying to be an aerospace engineer. If he designs a space vehicle within certain probabilities and someone whose life or career is at stake looks at his work, they will be very vigilent. On the other hand, a person who has little interest in the project may not even pay any attention to his calculations. I suppose with God, there is the issue of death, ultimate meaning, the hereafter, etc., that gets a lot of people focused on their own probability assessment for his existence or not. Also, those who are young and carefree often act as though God doesn’t exist, but become much more sober in their calculations if threatened with death or disability.
January 27th, 2007 at 10:01 pm
Ed,
I’m glad you liked the ‘extra credit’!
It’s great that you mentioned it, ’cause from what I read, yes, Unwin did attempt to refine Pascal’s Wager: ‘Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.’ (Chapter 8) Yet he sets it up in a way so that it is not about belief, but acting in a way that pleases God, even if God does not exist.
Sadly, even without the extortion of fear, the Wager still remains after almost four hundred years a marriage of a false dichotomy and special pleading. There’s still five very heavy objections to Pascal’s Wager (not counting dozens of smaller ones), and Unwin’s attempt doesn’t answer them.
If you don’t mind me asking, why did you pick the values for the other five?
January 28th, 2007 at 1:37 am
Awesome link to the Yudkowsky essay.
January 28th, 2007 at 3:36 am
Interesting that Unwin sets up the wager as about acting in a way that pleases God. In an earlier thread, soulster and I had a mutual admiration moment when we agreed that God cares far more about what we become/do than believe/profess. In fact, as you so aptly point out, there is no absolutely compelling reason to believe in one kind of God over another or even many Gods. Perhaps this probability/statistical reasoning process can also give us some inkling about the nature of God if he exists. Maybe some theological stances are more probable than others based on such observations if we make them correctly. For example, Unwin weighs the knowledge of goodness highly. Perhaps that would infer that religion is derived primarily from an inpetus to become/do good, rather than specific knowledge or witnessing of specific events or rituals. So, if God exists and has acted toward our species, perhaps we can infer that his main purpose is to make us do and become good (better, improved).
In the practice of medicine, which thankfully is becoming more of an application of science than art, physicians constantly weigh various factors, some of them intangible/unconscious/idiosyncratic and some more quantifiable. So, with regards to decisions I make in my practice, I think I’d have a hard time quantifying factors if asked. In regard to Unwin’s numbers, it does seem as though the recognition of goodness factor, if he is using it as I think he is, is the most ubiquitous human trait that seems to be unique. Even when goodness does not happen, it seems we all recognize its absence. For example, in the last thread the theme of persecution against the diaspora of Jewish people over the centuries is an example of that kind of negative evaluation that still proves the recognition of good. I mean, if we were like the Star Trek race the Borg, what problem would we have with sending a class of drones to the recycling bin? But we are not, and recognize the good. I suppose some people have a distorted view of good, like the Inquisitors who thought that a pure Catholic society would be good. Do you see this as illusory, this concept of good, or correspondingly, of evil?
January 28th, 2007 at 5:39 pm
I prefer my theory.
Probability that Smurfs don’t exist.
(1) recognition of the colour blue(D = 10),
(2) number of TV shows, books, colouring books, videos and merchandise about smurfs(D = 2),
(3) number of prayers to smurfs (D = 2)
(4) ordinary activities which can be attributed to smurf involvement(D = 1),
(5) the existence of the colour pink as opposed to the colour blue(D = 0.5),
(6) and the existence of many animals which do not have smurfs as part of their natural diet(D = 0.1).
January 29th, 2007 at 7:03 pm
Ed,
Ah, but how do we know what is good, other than what the religion tells us to do? Most people today disregard what a religion tells us is permissible or forbidden law-wise, and all of the long-lasting religions all incorporate the Golden Rule.
But as you point out, if, hypothetically, we were the Borg, we wouldn’t have any problem with most things humans would find pure evil. Our concepts of ‘good’ and ‘evil’ (as the Borg) would be alien to humans, just as the human concepts of ‘good’ and ‘evil’ would be alien to the Borg. Yet, the Borg aside, humans can usually agree on what’s wrong:
(1) A little girl is playing in a field of wildflowers, when she finds shade under a nice Oak tree and takes a short nap. Evil?
Of course not.
(2) A little girl is playing in a field of wildflowers, dancing around, when she accidentally steps on a derelict landmine, blowing off both of her legs at the knee. Evil?
Of course.
(3) A little girl is playing in a field of flowers, when she is shot in the head from the back of a white van by a deranged postman. Evil?
Of course.
(4) A little girl is playing in a field of flowers, when she picks a few of them, skips home and puts the flowers between the pages of a book. Evil?
Of course not!
Ah! But to the flowers? Their pain is real.
To the flowers, this is the most evil deed they’ve suffered since the little girl’s father mowed their lawn. To say that to other than humans it a bad deed or is evil or good is a strange concept to me. It’s an alien world that I cannot relate to: I continue to order a bouquet of roses each Valentine’s Day.
January 30th, 2007 at 12:50 am
Is there pure evil? I’m not sure, but there sure are grades of it that seem close. In terms of your examples of the little girl, perhaps the flowers found joy in being preserved in the pages of the book, so that the girl, now a old woman, can recollect the story of that beautiful flowing meadow of a long lost summer to her grandchild. Their fate otherwise would have been to be digested by some moose and forgotten. I am not that familiar with Kant, but I think he’s the fellow that really spelled out the idea of the highest good and how it links to God’s existence. I wish I had time to read up on it, but I kant, I’m too busy studying Taoism at your suggestion, hee hee.
January 30th, 2007 at 1:08 am
Great wordplay, Ed. Name-drop time: Kant’s OK, but I’m a much bigger fan of Hume. If you find the passage from Kant, I’d love to read it. I hope you enjoy reading about Taoism. I find it very different than Western religion - if it can even by classified as one.
I’ve been reading off and on some Popper lately (he’s been very big for the past fourty years - specifically Conjectures and Refutations, his most popular), too, but I’m spending most of my time reading on Bayesian arguments and bias.
January 30th, 2007 at 2:23 am
Taoism is one of the eastern philosophies which has my respect. Not that Taoists would care whether it has my respect or not, but I find it satisfying to read.
January 30th, 2007 at 4:13 pm
The probability of a god is directly correlated to the amount of individual existential angst.
January 30th, 2007 at 7:23 pm
Here’s a quote of Kant’s summary: “In this manner, the moral laws lead through the conception of the summum bonum as the object and final end of pure practical reason to religion, that is, to the recognition of all duties as divine commands, not as sanctions, that is to say, arbitrary ordinances of a foreign and contingent in themselves, but as essential laws of every free will in itself, which, nevertheless, must be regarded as commands of the Supreme Being, because it is only from a morally perfect (holy and good) and at the same time all-powerful will, and
consequently only through harmony with this will, that we can hope to attain the summum bonum which the moral law makes it our duty to take as the object of our endeavours. Here again, then, all remains
disinterested and founded merely on duty; neither fear nor hope being made the fundamental springs, which if taken as principles would destroy the whole moral worth of actions. The moral law commands me to make the highest possible good in a world the ultimate object of all my conduct. But I cannot hope to effect this otherwise than by the harmony of my will with that of a holy and good Author of the world; and although the conception of the summum bonum as a whole, in which the greatest happiness is conceived as combined in the most exact proportion with the highest degree of moral perfection (possible in
creatures), includes my own happiness, yet it is not this that is the determining principle of the will which is enjoined to promote the
summum bonum, but the moral law, which, on the contrary, limits by strict conditions my unbounded desire of happiness.
Here’s a link to a translation of Immanuel Kant’s “Critique of Pure Reason”: http://www.infomotions.com/etexts/philosophy/1700-1799/kant-critique-141.txt
Not being a philosopher by training or inclination (such verbage is troublesome), my read of his argument is that the freedom to act upon the recognition of moral good is an evidence of the existence of God. I believe Kant’s paper was in fact a response against Hume’s rational empiricism which is evidenced by his frequent mention of Mr. Hume. In fact, wikipedia’s article on Mr. Hume gives Kant a great deal of credit in increasing Humes’ popularity which was dying out. Times do change, the postmodernist seems to latch more easily onto Hume and kant enjoy Kant as he ought.
January 30th, 2007 at 9:56 pm
One question: What is the moral law?
January 30th, 2007 at 10:47 pm
As I read Kant (or kant read), the quote about the moral law is as follows: “Lest any one should imagine that he finds an inconsistency here when I call freedom the condition of the moral law, and hereafter maintain in the treatise itself that the moral law is the condition under which we can first become conscious of freedom, I will merely remark that freedom is the ratio essendi of the moral law, while the moral law is the ratio cognoscendi of freedom. For had not the moral law been previously distinctly thought in our reason, we should never consider ourselves justified in assuming such a thing as freedom, although it be not contradictory. But were there no freedom it would be impossible to trace the moral law in ourselves at all.”
So, it appears his concept of the moral law is that it is the basis of freedom (as opposed to causal determinism, the idea brought forth by Hume). So, the discovery of freedom in deciding an action or thought is a discovery that there is a moral law which acts as a sort of valence on such decisions, much as atoms display valences in their chemical natures. So, Kant sees freedom and moral law as concepts that make God and immortality probable from this philosophical stance. So, when Unwin is saying that the recognition of good is a strong factor in the probability of God, I think he’s pointing out that Kant’s view of freedom and moral law is generally borne out by the human experience. That is why I point out that the last thread about persecutions is an example of seeing a negative valence of the moral law. It seems that our freedom to decide what is right from what is wrong is something you demonstrated in that thread. For example, we both agree that GWB’s efforts to curtail civil liberties is a bad valence, so we join the ACLU to act in a manner consistent with a good valence. We do so out of our freedom to act, not out of determinism. Now, GWB and his syncophants might evaluate the valence differently. So, that implies that someone is wrong. That, I believe is in one of the steps Kant next takes toward the concept of God as the reasoned answer to the dilemma of who really knows (or causes) the true valence. Again, I’m not your local philosophy guru, so you may want to consult with such an expert to confirm my interpretation of these views.
January 31st, 2007 at 11:24 pm
Ed,
Sorry I dropped the ball on our conversation. A few crazy things have happened all at once, and I can’t grab a computer long enough to respond. Thanks for the quotes from Kant. I don’t know why it is, but translating his theories into real English takes far more brainpower than the theories themselves.
If I understand Kant correctly, what he’s saying - stop me if I’m wrong - is something like, ‘Freedom is conditional of the moral law, and the moral law comes about - or is the condition - when we become conscious of freedom. Freedom is the virtue of the moral law’s existence (a reason to believe), while the moral law is the virtue of which knowledge of freedom is possible (a reason to believe). We’ve reasoned that a moral law must exist, but we shouldn’t assume that freedom exists. But without freedom, we cannot find the moral law within ourselves.’
And freedom from determined external conjunction comes from God?
February 1st, 2007 at 1:39 am
Maybe if you translated your summary into German… Kant is observing two phenomena: freedom and moral law. He says they are related, with the moral law bestowing a freedom to us. That makes some sense to me, after all, a “moral law” that somehow did not give any freedom would be similar to a computer code being executed somewhere with the entire universe just following along over time and space as the code has determined. That would not make it a moral law as we observe it, but like any of the other laws (gravity, relativity, or mathematical). The way he observes the world to work in his philosophy is that we have freedom to decide on moral issues. Remember my referring to of Kohlberg’s stages of moral development? Morality is something people seem to sense, even if they don’t always do a great job mastering it. Some people I know have a hard time just mastering the law of gravity!
So, as I read Kant, he seems to reach his conclusion of evidence for God (and the hereafter) thus: “Morality per se constitutes a system. But we can form no system of happiness, except in so far as it is dispensed in strict proportion to morality. But this is only possible in the intelligible world, under
a wise author and ruler. Such a ruler, together with life in such a world, which we must look upon as future, reason finds itself compelled to assume; or it must regard the moral laws as idle dreams, since the necessary consequence which this same reason connects with them must, without this hypothesis, fall to the ground. Hence also the moral laws are universally regarded as
commands, which they could not be did they not connect a priori
adequate consequences with their dictates, and thus carry with them
promises and threats. But this, again, they could not do, did they
not reside in a necessary being, as the Supreme Good, which alone can render such a teleological unity possible.”
To Unwin, and to the less philosophically inclined like me, the personal experience of a sense of morality along with reports of such a similar sense from others is one of the stronger reasons to believe in God. I seem to recall my inner struggles to ignore or explain away moral law in my agnostic teenage years. Obviously, the explanation of theism fit the bill and there I’ve gone for all these years.
February 1st, 2007 at 11:29 pm
I’ll bypass Kant’s argument for the existence of freedom, and stick with your argument for a system of morality.
I agree with you: people have a sense of morality - they know what is right and wrong. All sorts of people report having it, but, what does it matter when no two people can come to a consensus? One man rationalizes killing his wife as a moral deed; another finds it appalling as it violates his basic morals of right and wrong. Some drive their SUV’s and others pull their hair out over such immoral activity; others have abortions while protestors – due to their own morals – attempt to stop them. Tree-huggers and loggers? Liberals and Conservatives? Isn’t conflict itself just two people fighting over their morals – of fundamental beliefs in right and wrong - deep-rooted assumptions to how the world is?
I think a big problem with Kant is that, yes, we sense that there is morality, but that is far, far different than the existence of a universal morality, or any morality outside of our heads. That doesn’t mean that a universal morality doesn’t exist; only that Kant’s argument doesn’t work. To claim that individuals ’sense’ there is a moral law, so a moral law exists – it just doesn’t follow from that line of reasoning that there is a moral law. ‘Sensing’ something that is not observable, nor any of its effects observable, while just basic observation shows the division between humanity’s assumptions of good and evil, sounds to me like wishful thinking. A friend of mine ‘sensed’ that she was abducted by aliens (I kid you not!), but that does not mean she was really abducted by aliens. She could have been, but feeling that she was just isn’t enough.
If a moral law existed, I couldn’t even tell what it should be. I look around, and plenty of people claim to know what should be moral, but I’m still stuck with questions:
Even if this moral law did exist, how would we attempt to uncover it?
Is it likely or unlikely that the moral law is in fact a way to attain an individual’s desires?
Would the moral law be agreed upon by a majority vote, and if so, would the majority vote be done by city block, town, country, or the whole world?
Is the moral law timeless, or does it change according to culture – and is really just a form of culture, and how can we tell culture and the moral law apart?
Do you believe that this ’sense’ that people have of right and wrong can be explained only by resorting to a supernatural answer?
February 2nd, 2007 at 1:38 am
Be careful not to get too close to that friend, those aliens could have been Borg… Actually, it seems as though our conversation is heading toward the line of reasoning in the Euthyphro dilemma thread. Instead of repeating those posts, let me introduce related musings. One of the things i’ve said that really annoyed you related to the belief that Christianity is more probable to be divinely inspired because it is unlikely. The only way around the Euthyphro dilemma is to conceive of God as outside of time. How likely are a few fishermen and carpenters to introduce that idea to the human race? Or to introduce moral law in a way that people all along Kohlberg’s stages could conceive of it together by listening to a simple, yet profound story?
A photon of light is created. From its frame of reference, no time passes. It has entered eternity. Yet all who conceivably could measure its speed, despite their relative velocities, would all find it to be c.
A pure moral thought is created. From its frame of reference, it is in harmony with the universal moral law. All those around it, who know how to measure morality, despite their different cultures and biases, would find it to be equally pure. It has entered eternity.
I think you are right, it is wishful (hopeful) thinking, but it is not unreasonable thinking. Even Kant described this move from freedom and moral law to God and immortality as a hypothesis that fit, rather than a proof. But that is all Unwin is trying to point out, there is a rational means to measure the probability that God exists, but each of us must make our own assessment.
Personally, I am very pleased to hear your assessment was non-zero. I worry about people whose assessment of the probability of God is either 0% or 100%. They show no doubt, and they have closed their minds. Their search for truth is over. They are the kind that might assess my freedom to think and act as unworthy of their agenda, and try to persecute me (and you). And that would be absolutely immoral.
February 5th, 2007 at 11:18 pm
Come on drunken and soulster. Don’t keep us “in suspenders” - where’s the next post?
February 6th, 2007 at 12:44 am
I don’t know where soulster is. It feels odd to continue to post without his voice heard in the halls of the ol’ Philaletheia (the last few posts have been mine), so I’ve been spending my time (other than work) writing on a few topics that interest me, such as philosophical naturalism and ‘intelligent design’.
February 6th, 2007 at 4:18 am
Somebody get him on “the blower” (phone, email) and tell him his presence is politely requested.
February 7th, 2007 at 9:57 am
In the absence of another philaletheia post, here’s what may be a helpful metaphor.
February 8th, 2007 at 6:51 pm
I hope I didn’t turn soulster into an atheist. He seems far too nice a person to be an atheist. lol
February 14th, 2007 at 11:19 pm
Alas, I is not because I have converted that I have been absent. It has more to do with life which has times of busyness, and times of extremely insane busyness. So far this year has been the latter for me. Thanks for hanging in there. You are all so kind in your desire for my virtual presence here.