On The Probability God Exists


In the beginning, there was nothing. Then God said, “Let there be light”. And there was still nothing but you could see it.
In order not to make the reader sick with jealously, I will not tell him that I sit on the porch on a bright summer morning mere steps away from Lake Michigan—where Yours Truly frolics in the pristine waters daily—and where the blast of the Emerald Isle is shortly expected to announce its daily run to Beaver Island and where there is no other sound save water and waves.

No, that wouldn’t be nice; though the beauty of the scene should be all the proof of God’s existence required. Instead we examine in lazy fashion comments made by our friend Fran at his Alea Deum, in the post “On the certainty that God exists and why Bayesians should go π“. (I am a Bayesian and coincidentally I did go to pie last night; a local blueberry-raspberry creation which was heavenly.)

Fran begins with the excellent question “What is the probability that God exists?” The proposition of interest is “God exists”, and it is obvious he means the classic omnipotent, omniscient, etc. definition. From there our author sallies into his first error, a common one.

I should reply with “50%” or “p=1/2”. This is so because when Bayesians (The Objective Kind) have no information on a problem they use a plethora of principles in a Groucho style fashion to figure out a prior distribution to kick off Bayes’ Theorem machinery.

This is false in two separate ways; actually three. The proposition “Either God exists or not” is just like the proposition “Either X exists or not”. Both are tautologies, statements which are always true no matter what. Adding a tautology to any logical argument changes it not a whit; thus tautologies add no information and can’t be used to infer probabilities. Think of a die throw (we’d rather not; but let’s do it anyway). We could say, “A 6 will show or it won’t” but that is equivalent to “A 6 or a 2 will show or they won’t” and so forth; the partitioning is of no consequence, though it might seem it was.

Falsity two: if there is truly “no information on a problem” then no probability can be deduced. What is the probability the following proposition is true? “A rumfrom is a plorsteen.” You have no information. The tautology “A rumfrom is a plorsteen or it isn’t” adds nothing. Therefore no probability whatsoever can be deduced. It is in cases like these we should heed Wittgenstein and keep our traps shut.

Falsity troix: Groucho would have been funnier.

Fran next tries several attempts at putting “a prior” on the proposition “God exists.” This is unfortunate because the activity makes no sense (all those equations which follow have no life in them), though we graciously admit that thinking they might is forgivable. Subjective and “objective” Bayesians are always running around in the fashion of kids from Brooklyn with fresh cans of spray paint “putting priors” on things. Probabilities aren’t really theirs, they think, until they can be “tagged.”

All probability, like all other logical statements, can only be made conditional on certain fixed evidence, or premises. Textbook Bayesians slap priors on propositions (by whim as often as they do on evidence) because they always enter the problem too late, because they are too used to dealing with “parameters” without thinking about what these creations are and what they mean (here is an explanation). But since there is no parameter in the proposition “God exists”, it’s doubtful a Bayesian would attempt a prior.

A prior here would be some arbitrary (mathematical) probability pulled from the nether region of the mind. It would be based on nothing and take no meaning. It would be like saying the proposition Q is true (or probable) “just because” or “because I said so.” You would start and end with a prior, since if you had other relevant evidence (see below) you would have used it first. Priors float without basis or justification and do not “stick” to the proposition because they are not deduced from evidence relevant to the proposition.

If we’re really interested in the truth of “God exists” (and many aren’t), we should gather propositions which we believe true and which are probative. From these true and believed propositions we could deduce the probability of “God exists”. There would be no priors involved in any way.

Sufficient would be the five sets amassed by St Thomas Aquinas. Here they are done in video (I haven’t watched these; I Googled them as a service to my dear readers). And here is a series in words. And then see this series on the cosmological argument. And there are more besides these (other arguments, I mean).

Actually what we have are a not several arguments, but one grand one, all roads leading to the same inescapable destination. And all traveled without unnecessary mathematical baggage.

And now I won’t tell you that I’ll soon wander over to St Mary’s and from there to the shore (my swimsuit will be concealed cleverly by pants).


41 Comments

  1. Why wouldn’t the probability for “God exists” be 50% without further information? Is there some state between Exists and Not Exists? With the tossed 6-sided framastort, not knowing the resultant state leads to a probability of 1/6 because all that is known is there are six states. I would expect the probability for God’s existence to be 50% sans other information because there are only two possible states.

  2. Briggs,

    No jealousy, as this morning I sat in a gazebo in Victoria Park (Truro, NS) in the shade of a canyon enjoying the cool breeze of a glorious summer day with my faithful dog by my side. My wife was there too. With perfect contentment I gazed on the geological wonder displayed on the canyon wall. A perfect example of deep time – a sedimentary rock formation that in eons past had been heaved on its side to form a 45 degree angle to the horizontal canyon floor.

  3. DAV,

    The prior you get depends on how you ask the question.

    For example, suppose we instead ask “How many Deities are there?” The answer is presumably a non-negative integer, or countable infinity, or possibly an uncountable infinity.

    Even if we exclude the infinities, a uniform (improper) distribution on the non-negative integers would seem to say the probability of any given number (including zero) is zero. Why should any number be any more likely than any other, if we know nothing a priori?

    But perhaps we would argue that there’s no reason to think a uniform distribution is right, either. The choice of prior generally depends on what symmetries we assume. The uniform distribution usually suggests an additive symmetry (adding a fixed number of Gods/Goddesses shouldn’t change the probability) but this sits uncomfortably with the domain being only the positive integers, which is not invariant on translation. Perhaps scale invariance would be better? Twice as many gods is no more nor less likely? But again, whole numbers are not scale invariant, either.

    A more sophisticated argument might pick permutation as the appropriate symmetry transformation – that if you permute all the non-negative integers, the answer shouldn’t change. But besides being an actual symmetry of the non-negative integers, it doesn’t have a lot going for it. It’s not a particularly natural-feeling description of the nature of our ignorance.

    It’s a tricky question. Maybe, therefore, it’s the wrong question.

    Perhaps we should ask what the number of Deities modulo 7 is? (Well, why not?) That’s a bit easier to work with. It makes much more sense to start with a uniform distribution on the 7 possibilities, there are no disturbing infinities to trouble us. (Although we still have a problem if it turns out there are infinitely many Deities.) We can’t exactly answer the question of what the probability of it being zero is, but if the probability of it being 0 mod 7 is 1/7, then we can say for sure the probability of it being 0 cannot be 50%.

    Fran, I think, was making an extended joke about the Bayesian’s problem of induction: the priors are ultimately always arbitrary, and can be adjusted to give whatever answer you want. They’re always guessed, assumed, inserted from outside, taken on faith. So where can true objective knowledge come from in a purely Bayesian framework, where everything is supposed to be founded on observation?

    Fran constructs a prior to support his desired agnostic conclusion, but it is as much an act of faith as any other conclusion. It is at one and the same time an illustration of the ridiculousness of people trying to prove the existence or non-existence of Gods in the absence of any evidence, and of the ridiculousness of those who laugh at them, insisting they draw their conclusions on the basis of observed evidence and not faith. I don’t know if it was intended that way, but I found it amusing, anyway.

    Briggs seems to be taking the joke too seriously. Although it’s hard to tell. Talking about one’s faith can be difficult. If you always turn the other cheek, even your friends will not know when it hurts.

  4. Nullius,

    I didn’t say “prior”. If probability=level of knowledge then P( (a)God | given available knowledge ) = P( (no)God | given available knowledge ) and dividing by the number of possible states comes to 0.5 because my level of knowledge is equally distributed. There is no prior if “prior” means “before”. These knowledge levels may become priors later. Can’t speak for Fran but they are neither based upon faith nor are they arbitrary.

  5. DAV,

    I agree you didn’t say “prior”, you said “without further information” which I interpreted to mean before considering any evidence, without any information besides that there are two states – i.e. the prior.

    I responded that when looked at another way there are actually infinitely many possible states, most of which got lumped together into a single category. How many ‘states’ there are depends on how you ask the question, and it is dangerous to assign equal probability to them without reason to think there’s a related symmetry.

    You’ve probably heard of Bertrand’s paradox – it’s the same sort of thing. There’s no actual problem with assuming a 50:50 spread, so long as you understand the implications of the choice. The output is conditional on the input, and you can use what input you like. But there are other choices, too.

  6. How many ‘states’ there are depends on how you ask the question,

    I emphasized one because the word “God” is singular. Supposing more is adding information — effectively changing the question.

    and it is dangerous to assign equal probability to them without reason to think there’s a related symmetry.

    Again, probability=information level. How is it dangerous to admit having uniformly distributed information and then proceed accordingly?

  7. “I emphasized one because the word “God” is singular.”

    And the word “Gods” is plural. So?

    “Supposing more is adding information — effectively changing the question.”

    I wasn’t supposing more. Zero and one are still both included. But yes, I was changing the question. If you ask one question, one uniform distribution is ‘obvious’, but if you ask a different question, a different and *incompatible* uniform distribution becomes ‘obvious’.

    I start by asking how many Gods there are, and then – having established the probabilities uniformly – modify that to ask whether the number is greater than zero. I assign equal probabilities to all possible numbers, and then I lump infinitely many of those possibilities together, and compare the one with the infinity. The answer is obvious. There are almost certainly an infinite number of Gods.

    One starting point only considers the possibilities 0 and 1 and excludes everything else. The other starting point considers 0, 1, 2, 3, … and all the others, but it doesn’t exclude 0 and 1. The former has constraints while the latter does not. The former adds/asserts infinite information compared to the latter. *Minus* the logarithm of the number of possibilities, remember?

  8. And the word “Gods” is plural. So?

    The question: “What is the probability that God exists?”

    Yes, if you change the question the distribution of available information changes. As you say: “So?”

    There are almost certainly an infinite number of Gods.

    The only certainty is that the answer in constrained within the interval [0,Inf] of integers.

  9. Mr. Briggs,

    You might have misunderstood Fran. Let G = God’s existence, NG= God’s nonexistence and E = evidence. The posterior probability P(G|E) can be written as

    (1) P(G|E) = P(E|G)P(G) / P(E).

    The tautological statement that “either God exists or not” is relevant in applying the law of total probability to correctly replace the denominator P(E) in (1) by

    P(E )=P(E|G)*P(G) + P(E|NG)*P(NG).

    See Bayes theorem.

    In the Bayes framework, P(G) is the prior probability of G before evidence (E). Fran assigns P(G)=0.5 due to the principle of indifference (POI)/ignorance. (BTW, NIV has pointed out the flaw in POI, see also here, page 28. Click on the link, and you won’t regret it.)

    One can also treat P(G) as a parameter, say θ, (think of binomial probability) and then assign a prior probability distribution to the parameter θ, be it an non-informative/objective prior or not. Just slightly more sophisticated. Of course, the value of P(G|E) will depend heavily on the evidence.

    Can anyone really objectively find the probability of god existence? I doubt it.

    [T]he beauty of the scene should be all the proof of God’s existence required.

    So if I read this correctly, “the beauty of the scene” is your evidence (E), and based on the evidence, you conclude that P( G |E) = 1 in this post… assuming that the beauty comes from God. Hmmm… interesting assumption. You don’t assume ALL beauty come from God, do you?

  10. DAV,

    “Yes, if you change the question the distribution of available information changes. As you say: “So?””

    You asked: “Why wouldn’t the probability for “God exists” be 50% without further information?” One possible answer is that you might have asked a different question first – one that provided *less* information.

    “The only certainty is that the answer in constrained within the interval [0,Inf] of integers.”

    Yes. That’s why I used the word “almost”! 🙂

  11. JH,

    Ah, but no. There just is no such thing as “P(G)”. What you call “the prior probability of G before evidence” cannot exist. There is no P(X) where X is any proposition. It is an impossibility.

    But your mistake is also forgivable because it is even more common than Fran trying to put a prior of “P(G).” It is a fatal mistake. So Fran was beating le cheval mort killed by writing “P(G).”

    You cannot have the probability or the truth of any proposition without the argument (this includes the mathematical theorems you know and love and link to). Even axioms are true conditional on our intuition. For example, what is the probability X = “Socrates is mortal”? You cannot say: nobody can. God cannot say. No Bayesian can. No frequentist either. If would do no good, then, to write P(X) and attempt to put a prior on it. It is vapor. You must supply premises to make sense of the proposition.

    As I said in the text, you must supply premises (call it evidence if you like). If we take “All men are mortal & Socrates is a man” then X is true, or it has probability 1. And this is so no matter what “prior” some math-happy Bayesian might have put on “P(X)”, and it is so no matter what some Wikipedia writer might say.

    There just is no such thing as unconditional truth or probability. It is the case that many people reify the notation of such things like “P(G)” and fool themselves into believing there is.

    Again, as I said, if you truly have “no information” then you have no probability. And here’s a link for you, if you care to read it: LOST CAUSES IN STATISTICS II: Noninformative Priors (from Larry Wasserman), the money quote of which is “I like to say that noninformative priors are the perpetual motion machines of statistics. Everyone wants one but they don’t exist.”

    Finally, a challenge to you (you JH) or to anybody who does claim such a things as “P(G)” (or “P(X)”) exists, i.e. the probability of some proposition “before evidence.” Show it to me and I’ll eat my words. Show me how the prior you derive is no evidence.

  12. The word “God” is singular for a reason. The problem lies with undefined terms like “dieties,” which in the present debates lumps together things of unlike natures. Thor is not the same kind of entity as Tengri — or even Zeus!

    It’s like saying “literary character,” which lumps Gore Vidal’s Lincoln in which Agatha Christie’s Miss Marple.

  13. “For example, what is the probability X = “Socrates is mortal”?”

    Socrates is dead.

    “Finally, a challenge to you (you JH) or to anybody who does claim such a things as “P(G)” (or “P(X)”) exists, i.e. the probability of some proposition “before evidence.” Show it to me and I’ll eat my words. Show me how the prior you derive is no evidence.”

    I thought I explained this one previously. Was there something wrong with the argument, or did you miss it?

    There are four different things that “probability” might refer to. There’s the objective reality, there’s our mathematical model of objective reality, there’s our mathematical model of observers making observations, and there’s us real world observers.

    We don’t know how objective reality works. We have no direct, privileged access except via our senses. We can make up theories, but we don’t know.

    Our mathematical model of objective reality is what has the absolute probabilities in it. It’s the thing following the Kolmogorov axioms, or something equivalent. P(G) is an entity in this model. It is *not* a prior.

    Our mathematical model of observers allows us to model their knowledge or beliefs about the modeled absolute probabilities. In the AI literature, this is commonly called “Bayesian Belief” to distinguish it from “Bayesian Probability”. They are entirely different concepts! However, Bayesian Belief is *also* calculated with using the Kolmogorov axioms, and since observers can have no access to absolute probabilities, many people think there’s no harm in conflating the concepts. (Oh, how wrong they are!)

    Real world observers’ observations seem to closely match what the modelled observers ought to see if the Kolmogorov axioms apply. This does *not* mean that the real world works that way! It does mean that we can usefully act as if it does.

    Probabilities like P(G) exist in the mathematical model of reality, but priors are beliefs and only exist in the mathematical model of the observers. The two are distinct. There is also a belief about G, usually written Bel(G), which is the observer’s estimate of P(G). But the latter is the P(G) in the model; it is entirely speculative whether this corresponds to anything in reality. And priors cannot be empirically determined by observation – they’re assumed by means of symmetry arguments, aesthetics guesswork, heuristics, or other non-rational beliefs.

    According to the model, the modeled observers have no way to determine them. What a lot of Bayesians call “probabilities” are actually “beliefs”. The probabilities are objective but inaccessible. The beliefs are accessible but subjective. However, they follow the same axioms, and so for calculational purposes the distinction can be ignored.

  14. YOS,

    “Thor is not the same kind of entity as Tengri — or even Zeus!”

    What’s your distinction?

  15. Zeus was not the god of thunder. He was the thunder. The Greek gods were nature personified. The Norse gods were Viking warriors upped to the nth degree: the übermenschen, so to speak. Tengri was the One God of the Mongols and was an impersonal driving mechanism identified simply with the sky: closer to Aristotle’s prime mover than to either nature gods or supermen.

  16. YOS,

    Well, I’m not sure about that, but never mind.

    Why should we suppose the myths are correct about the nature of the Gods? Why does that mean you can’t count them?

  17. It is possible to estimate the priors. The problem with the estimate is that it zero.

    Let G(i) be the existence clause of God number i. G(i) differs from G(j) for all natural j not equal to i,m i.e P(G(i) AND G(j) ) == 0

    Now, for any natural number N is is clear that P(G(1)) + P(G(2)) + .. + P(G(N) is either equal to 0, or to 1. The sum is zero if the existing God is not mentioned, and the sum is 1 if the existing God is mentioned. We obviously do not know if the existing God is mentioned, because if we did, we would not do the math in the first place.

    First, assume the existing God is indeed not mentioned. Then all priors must be zero. We have no change of finding the existing God among all the non-existing Gods, if the list of Gods doesn’t mention the existing God.

    So, we assume that we list the existing God in the list of all possible Gods. Now, as with the die and the six states example earlier, the best estimate for P(G(i)) is 1/N. But N can be arbitrarily large, hence the priors all tend to zero.

    For the record, G(i) and G(j) can be different interpretations of a single religion. Catholic and Coptic, for instance. If one of them goes to hell and the other one does not, or both of them go to hell but for different reasons, then their Gods are different. Their Gods are the same if both get to Heaven.

  18. I felt a disturbance in The Force. It was…

    Briggs,

    “I should reply with “50%” or “p=1/2″”… This is false in two separate ways; actually three. The proposition “Either God exists or not”… thus tautologies add no information and can’t be used to infer probabilities. Think of a die throw…

    Interestingly you didn’t choose a coin this time. Seems like a coin with its “Either you get heads or not” would fit in your tautologies bag where no probability can be inferred.

    Falsity two: if there is truly “no information on a problem” then no probability can be deduced.

    Careful! You are dangerously close to Frequentists now.

    Falsity troix: Groucho would have been funnier.

    D’accord.

    Fran next tries several attempts at putting “a prior” on the proposition “God exists.” This is unfortunate because the activity makes no sense (all those equations which follow have no life in them),

    Well, I repeatedly stated I was working on a belief system in an attempt to detach the process from anyone’s interpretation of probability.

    In fact, I did the calculations in the scale from 0 to Ï€ to enhance that detachment (though it is true that made calculations simpler) and I even purposely titled the post On the Certainty that God exists… instead “On the Probability” like you did, precisely for the same reasons.

    Measuring the belief one have in God is nothing new, for example, a
    scale has been suggested by Richard Dawkins. It goes from 1 to 7 and he places himself at 6.9… I don’t like it, but I’m making a point that people naturally tend to do so. Not that I like him either; he calls me a coward for being Agnostic.

    A prior here would be some arbitrary (mathematical) probability pulled from the nether region of the mind.

    Well, just like any Objectivist prior, after all in my wandering I found Jeffrey’s prior and it was totally unintended.

    Actually what we have are a not several arguments, but one grand one, all roads leading to the same inescapable destination. And all traveled without unnecessary mathematical baggage.

    This one is very easy to prove is not so. If the destination was so inescapable all the great minds in history would have agreed on it, and they don’t.

    And since you are a Bayesian, you might appreciate the opinion of the creator of Bayes’ Theorem:

    “When Napoleon teasingly remarked to Laplace that God is not mentioned in the Me’chanique ce’leste, Laplace replied, “Sire, I did not need that hypothesis.” When Napoleon later reported this reply to Lagrange, the latter remarked, “Ah, but that is a fine hypothesis. It explains so many things.”

    Thanks for the post though! It was fun 🙂

  19. “When Napoleon teasingly remarked to Laplace that God is not mentioned in the Me’chanique ce’leste, Laplace replied, “Sire, I did not need that hypothesis.”

    Indeed. And Darwin’s theory cannot be found in a manual of auto mechanics, nor the US Constitution in a cookbook. One needn’t invoke theokinetics to describe the mechanics of gravitational motion. Wile it might be useful in explaining why there is gravitational motion in the first place, that gets us into the distinction between a description and an explanation.

  20. Any minute now somebody’s going to prove that black is white and then get killed on a pedestrian crossing…

  21. Fran,

    Come away from the Dark Side.

    Almost a good point with the coin flip, but you have to remember to keep your evidence/premise separate from your conclusion/proposition of interest.

    There is a fundamental distinction in evidence between “Either the earth will tomorrow blow itself into a quadrillion pieces at near the speed of light or it won’t” and “There is a two-sided object, just one side of which is labeled ‘H’, and which when tossed must land on one of its sides”?

    Those are the premises. We still need a conclusion. How about “An ‘H’ shows.” Given the first premise, which is a tautology and true every single day (even after the earth blows up), we truly have no information about the conclusion, thus the probability of the conclusion is unknown. Given the second premise, which is not a truth but an observation, the conclusion has probability 1/2.

  22. Sander van der Wal,

    Dude. I don’t even know where to start. Your “equation” is a complete mess. I’ve already showed that you cannot write anything like “P(G)”, and that includes things like “P(G(i))”. It just doesn’t make any sense.

    Your second point (if I understand it) would be like saying I have two (compound) premises “I have a process which has N states, G(2), G(2), etc., just one of which is chosen (somehow)” and “I have a process which has M states, G(2), G(2), etc., just one of which is chosen (somehow).” The conclusion “G(i) is chosen” has probability 1/N conditional on the first premise and 1/M conditional on the second.

    But who says, and who agrees, that these are the exact right premises for our argument about God’s existence? I don’t. Just as in my advice to Fran, we must keep separate the premises and conclusions.

    All,

    We have to learn to write our probability arguments in the same exact form as ordinary logical arguments. Philosophers have been doing this for thousands of years without difficulty. The problem starts with those darn equations, which are so easy to write, manipulate, and fall in love with. But we must always remember they are not real, that there are mere placeholders for actual propositions. It’s best not to attempt mathematical notation until this is clear.

  23. My Briggs,

    I only want to suggest that you read the book I have referenced above written by a philosopher.

  24. My Briggs,

    I only want to suggest that you read the book I have referenced above. It’s written by a philosopher!

  25. JH,

    Make a deal with you. I’ll read that book if you read any of the many I’ve suggested to you over the years.

    Now I read (admittedly hurriedly) from page 94 through 95. On top of 94 he (eq. 7.5) he writes the evidentiary equation correctly (Bayes’s theorem, which you so helpfully linked for me), conditioning on “background” evidence K. This acknowledges that there is no such thing as conditional probability, though the notation sometimes indicates there is.

    And then on p. 95 he says something very interesting (with regards to eq. 7.4, another instance of Bayes’s):

    This threatens a regress of justification which will be very familiar to philosophers from the theory of knowledge, a regress which must stop somewhere if conditionalisation is to justify any posterior credences at all. Where and how can we stop it, if we must?

    This also accords with what I said. Any “globally” true thing, just like any mathematical theorem, is a chain of evidence which also must be anchored by indubitably true axioms, i.e. propositions which are true without evidence, true conditional only on our faith.

    The author seems to get this, but doesn’t fully grasp his own proof! I think the reason is that people see probability different than ordinary logic and thus forget to apply the same rules.

    Finally, on p. 96 he says

    This is innocuous because, as we noted in chapter 6, since necessary truths, such as those of logic and mathematics, are true in all possible worlds, they can tell us nothing about which world is actual, nor therefore about which contingent propositions are true in it.

    This is still under the subject of conditionalization, where again he agrees (as he must) that conditioning on a truth (like a tautology) does not change an argument.

    Have you read Howson and Urbach yet? Or In Defence of Objective Bayesianism by Jon Williamson? Or all through (as opposed to skimming) Jaynes? Or the book I go on and on and on about, Stove’s Rationality of Induction? Or the many others I’ve touted? (All by philosophers. It will be interesting to see if you answer these questions.)

  26. Briggs

    Nothing wrong with the notation. It is the same one as used in http://wmbriggs.com/blog/?p=6500, Bayesian Probability & Swinburne’s P-Inductive & C-Inductive Arguments (For God’s Existence). And with the same meaning too.

    The only difference is, that I add more premises. A whole bunch of them. With the interesting property that if a single one of them is true, all the others must be false. And with the downsides that you have no guarantee that one of them is true.

    There is a difference with the die. A die always shows a side. And showing one particular side automatically means that all the other sides are not shown.

    But let me adjust my problem a bit more. I will add the premise that God does not exist. And for the sake of argument, I’ll restrict the limit to a thousand possible gods.

    Now, the change that anyone has picked the right religion before examining the evidence is one in a thousand. Apart from the deists. They are happy with any god, so the change they are right is 999/1000.

    Lets lift the limit of a thousand, and allow an infinite, countable number of gods. Clearly, any rational man would be a deist by now.

    Your argument is that such statements must be written as P(G|E). That’s fine, I will write them like that P(G(0) | E) + P(G(1) | E) + … P(G(N) | E) == x <= 1

    Now, the evidence for all religions, and atheism, is exactly the same. It is the world we all live in. That is all the evidence there is. Which means that that sum is some number. But, it is also still the case that if one particular theory is true given the evidence, all the others are false. Hence, nothing changes, with respect to the first version, apart from the priors being smaller is x is less than one.

    So, I am still happy with this description, even though the a priori change I am right about atheism is zero.

  27. Stumbled upon this post, reading various views on probability.

    The Principle of Indifference (aka Maximum Entropy syllogism) stated by a commenter was interesting in this context.

    So i would like to offer my 2 cents of clarification.

    The POI or Maximum entropy is a method to infer/calculate probabilities which is maximally un-biased with respect to missing information or superflous assumptions.

    The commenter’s application of POI seems in-order, however the POI / MaxEnt is applied when the actual problem is well-defined and apt.

    So the actual cases are not
    P(God Exists)=1-P(God does not Exist) because there are NOT 2 outcomes

    There is a third which is : The proposition “God Exists” has no meaning
    (this stems for the fact that to apply POI in the first place the problem/thesis has to be (well-)defined and apt)

    So now we have 3 outcomes but trying to assign 1/3 probability to each is wrong since the the 3rd outcome actually denies this assignment, so it is self-referential and not valid POI reasoning.

    Nikos

  28. Sander van der Wal,

    I will write them like that P(G(0) | E) + P(G(1) | E) + … P(G(N) | E) == x <= 1 …. Now, the evidence for all religions, and atheism, is exactly the same… I am still happy with this description, even though the a priori change I am right about atheism is zero.

    Great example of what happens when you go Bayesian, you always find a prior that makes you happy.

    Nikos M.

    The proposition “God Exists” has no meaning

    If that proposition has no meaning then why should have any meaning to believe in God? Can you elaborate in what do yo mean by “having meaning”?

  29. PS:

    For the case of many Gods same reasoning applies if the following “probability” is used:

    P(Gods exist>=1)=1-P(Gods exist=0)

    3rd case is: The proposition “Gods that exist are 1 or more” has no meaning..

  30. @Fran

    The answer to your question is the exact formulation of the “probability”

    P(foofootos exists)=1-P(foofootos does not exist),

    The proposition “foofotos exists” has no meaning

    Now when onee says “God” one actually implies some qualifications of this concept.

    Without getting into a theological debate, when someone adds these qualifications to the original proposition
    then it is a different proposition and possibly some probability threshold can be calculated

    As stated in the previous comment the POI is applied to (well-)defined problmes/theses

  31. @Nikos M.

    Oh I see, so if I understand you correctly P(Jesus’ heart stopped for three days and then came back to life) would be well defined, right?

  32. The proposition “God Exists” has no meaning

    This assumes that “meaning” exists sans God. cf.: http://wmbriggs.com/blog/?p=8669&cpage=1#comment-99070

    For the case of many Gods…

    As the term is defined, there cannot be many Gods, since God is conceived as completely actual, lacking in potencies. There could, however, be many gods, since these are conceived merely as divine beings, often with contingent rather than necessary existence.

  33. @Fran

    i would not like to get into a theological debate.

    The same reasoning about the proposition applies to similar porpositions
    where statistical reasoning is applied to a set which is not (well-)defined.

    Consider another example of bad application of POI:

    There is a trial and 10 witnesses out of 15 say the accused did the murder.

    What is the probability that the accused being guilty? 10/15

    BUT this result applies only when the witnesses are independent statistically.

    Consider someone who payed these 10 witnesses to produce their witness

    What is the total information conveyed by the witnesses:
    10*Inf(of 1 witness) ?

    NO, it is Inf(of 1 witness) since these 10 witnesses are NOT independent ,

    They only “repeat and transmit” the same information of 1 person (regardless if this information is true or false)

    Hope this is clearer now

  34. In order to give another example of the case in the previous comments
    lets calculate exactly a probability that:

    P(“GOD exists”)=?

    based on the following definition

    Definition: “GOD” is the sum of the Universe.

    Now it is very easy: P(“GOD exists”)=1 (exactly)

    How about that? An age-old problem resolved!

    with a grain of salt..

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