The most logical belief

Alex S.

pH wrote:

Once again ... there's no such thing as a default probability (1/no of outcomes). The only time the you assign a probability of (1/no outcomes) is when you know in advance that all outcomes are equally probable.

Since I don't believe that you genuinely think that you've come up with a massive breakthrough in proving the existance of God, I guess you're trolling at this stage.

Anyway you never took on board hairyheretics point, in your new probability theory what is the probability that there are 2 gods? or 15 gods? or 8293 gods?

Of course there is default probability of 1 / no. of possible outcomes.

w.r.t. hairyheretics point.

The probability of 2 gods, is an entirely different problem. Once again it defaults to the number of possible outcomes. Now what are the number of possible outcomes?
Suppose we know there are five possible outcomes, to that question.
P(No God), P(1 God), P(2 Gods), P(3 Gods), P(4 Gods), but we know nothing else. Each probability starts with 0.2.

Now this can be taken to extremes in which case, we could calculate the probability of an infintie amount of Gods.
Again if all probabilities are mutually exclusive and we know nothing else,
each one including no God, all default to 1 / infinity.

The problem with that approach is we don't know the amount of possible outcomes, so there is no default in this case.

When I write,
P(God), I mean it can be 1 God or >1 God. So it can be 1, 17 or infinity, we actually don't know the amount.
So because there are only two outcomes,
P(God(s)), and P(No Gods), in which case each case:
P(God(s)) = 0.5

I am abbreviating that to
P(God), but will I will write P(God(s)) as I think that clarifies.

Scofflaw

Hmm. P(God(s))=0.5, or "in the absence of information, it's a coin-toss". I'd accept that, although it's fundamentally just a statement of our ignorance - an estimate of the probability rather than the probability itself.

On the other hand, the more tightly you specify God, the lower the probability drops, because the improbabilities multiply. So, the proposition that God is good is, assuming a good/evil binary choice:

P(God(s)) * P(Good) = 0.5 * 0.5 = 0.25

In fact, we can set up as many of these as we like, such as the question of whether God will punish non-believers, whether He/She/It is actually the Creator, etc etc.

So, the possibility of any particular God is vanishingly small. That's God for you - he seems likely, but the minute you focus in, he vanishes away. On that basis, given the high improbability of a god worth worshipping, atheism is perhaps the most logical belief.

cordially,
Scofflaw

Zombrex

Scofflaw wrote:

I'll restrain myself for the moment. I'm waiting to mug Wicknight and his gang of pixies.

Dragons Scofflaw, gang of dragons! ..

Alex S.

Scofflaw wrote:

Hmm. P(God(s))=0.5, or "in the absence of information, it's a coin-toss". I'd accept that, although it's fundamentally just a statement of our ignorance - an estimate of the probability rather than the probability itself.

On the other hand, the more tightly you specify God, the lower the probability drops, because the improbabilities multiply. So, the proposition that God is good is, assuming a good/evil binary choice:

P(God(s)) * P(Good) = 0.5 * 0.5 = 0.25

In fact, we can set up as many of these as we like, such as the question of whether God will punish non-believers, whether He/She/It is actually the Creator, etc etc.

So, the possibility of any particular God is vanishingly small. That's God for you - he seems likely, but the minute you focus in, he vanishes away. On that basis, given the high improbability of a god worth worshipping, atheism is perhaps the most logical belief.

cordially,
Scofflaw

No, because the odds of there being no God never exceed 0.5% atheism is not a logical belief. There's a 50% chance atheism is right, and a 50% chance it is wrong. There is no logical argument to say it is more right than wrong. I agree it has a higher probability of being right than P(God(s) that care about you) which as you say Scofflaw, is 0.25.
But it doesn't have a higher probability of P(God(s)). Atheism, has an equal chance of being right or wrong, therefore it is not a logical belief.

Scofflaw

Wicknight wrote:

Dragons Scofflaw, gang of dragons! ..

Well, they were both equally likely....

cordially,
Scofflaw

robindch

> There's a 50% chance atheism is right, and a 50% chance it is wrong.

You still haven't told me whether or not you think that there's a 50% chance that there's an invisible pink unicorn standing beside me. I await your answer with interest...

Zombrex

Tar.Aldarion wrote:

Please tell me why atheism is more logical than agnosticism, I find that this is not so.

For me the logic that supports atheism is that we (humans) invented the concept of gods, so how can God exist if he/it was just an invention of our collective culture. The likelyhood, the probability, that something we invented actually existing in the universe, is relatively slim as to be quite improbable.

As Scofflaw and others will probably point out I can't know we invented God for certain, or that even if we invented the concept of a god that doesn't mean that we by pure fluke got it absolutely correct and such an entity does actually exist. But then again I can't technically know anything, from a logic position. The only things that are actually true are logical tautologies, which only exist in theoretical logic class rooms.

So while being agnostic in relation to God is technically the most logical position, that position isn't based on the idea that there is a lot of good reasons to think there might be a God, more on the logical reality that you cannot ever know for certain anything. There are in fact, as far as I'm concerned, no good reasons to think there might actually be a God.

Which is why, out here in the real world away from the logic class rooms, I'm an atheists because I believe, based on my understanding of human history and culture, that we invented the concept of gods and as such they can't exist in the real world, any more than the invisable green unicorn sitting beside me (called Bob).

If something "god-like" does actually exists it is something else, some as yet unknown entity, because the clasification "god" is invalid to begin with.

Alex S.

Scofflaw wrote:

Well, they were both equally likely....

cordially,
Scofflaw

Sorry Scofflaw, don't understand your point.

Zombrex

Alex S. wrote:

There's a 50% chance atheism is right, and a 50% chance it is wrong.

As people have been trying to explain to you, in the absence of known probability you don't default to 50/50.

If you don't know the probability you simply say you don't know.

If probability of something defaulted to 50/50 in the absence of known actual probability anyone who failed living cert maths would be winning the Lotto every week.

The probability is constant even if you are not aware of it. Which brings me nicely to point two -

50/50 probability (or 30/70, 10/90, 1/99 etc) only effect unknown outcomes for future events that are effected by external forces.

There being a God or no God doesn't change. There is or there isn't and this fact has always either been true or false, there is no change.

Since atheism is either wrong or correct, and this never changes, the actual probability of it being wrong or correct is either 100% or 0%.

Using an example with cards, if you put a 4 of Spades on a table, walk away and come back an hour later, and nothing has changed the card, the probability that that card will be the 4 of Spades is 100%. The probability that it will be another card is 0%.

The problem with applying this to atheism is you don't know which it is until you actually find out. If atheism is correct the probability it is correct is 100%, if it is wrong the probability is it is correct 0%

UU

It's sorta easier to believe that nature exists. We can't deny that as we're all a part of nature......unless one believes that existence here on Earth is in fact a total illusion and true reality really lies elsewhere. Hmmm......all in all, nature exists pretty much. As for God, etc. well that all boils down to faith and beliefs, eh?

Scofflaw

Alex S. wrote:

Sorry Scofflaw, don't understand your point.

Pixies and dragons...part of an oft-repeated argument that God is as apparently likely as a pixie, or a dragon, or a unicorn. You may have noticed robin urging you towards engaging in this particular discussion...

I'm not sure why people are having such difficulty with the assignment of a probability of 0.5 to God(s). In the absence of information one is entitled to assign any initial probability to outcomes, and 0.5 is the most defensible for binary outcomes.

Obviously, we would hope to improve this assigned probability.

cordially,
Scofflaw

Funsterdelux

I am branded by "society" as an atheist, that is I dont have any beliefs, I'd rather I or "we" are called Humans.

So I dont think there is a "most logical belief"

Alex S.

Wicknight wrote:

As people have been trying to explain to you, in the absence of known probability you don't default to 50/50.

If you don't know the probability you simply say you don't know.

If probability of something defaulted to 50/50 in the absence of known actual probability anyone who failed living cert maths would be winning the Lotto every week.

The probability is constant even if you are not aware of it. Which brings me nicely to point two -

50/50 probability (or 30/70, 10/90, 1/99 etc) only effect unknown outcomes for future events that are effected by external forces.

There being a God or no God doesn't change. There is or there isn't and this fact has always either been true or false, there is no change.

Since atheism is either wrong or correct, and this never changes, the actual probability of it being wrong or correct is either 100% or 0%.

Using an example with cards, if you put a 4 of Spades on a table, walk away and come back an hour later, and nothing has changed the card, the probability that that card will be the 4 of Spades is 100%. The probability that it will be another card is 0%.

The problem with applying this to atheism is you don't know which it is until you actually find out. If atheism is correct the probability it is correct is 100%, if it is wrong the probability is it is correct 0%

Disagree, if you don't know the number of possible outcomes, then you are correct, you don't know the probability. But,
probability analysis begins with the number of outcomes, in this case it is a set of two outcomes. {God(s) exist, God(s) don't exist}.

So both default to 0.5, until you know more. In nearly all binary problems i.e. with two outcomes, you will know more, so you rarely get end where you begin at 0.5.

However, w.r.t. P(God(s)), you know nothing more.
It is an almost unique problem and it remains at 50%, following a probability analysis.

Scofflaw

Alex S. wrote:

However, w.r.t. P(God(s)), you know nothing more.
It is an almost unique problem and it remains at 50%, following a probability analysis.

True only for the general proposition of God(s).

Hmm. If you summed up the probabilities for all the specific Gods that humanity has proposed, would it sum to 0.5, or more, or less?

cordially,
Scofflaw

Zombrex

Alex S. wrote:

So both default to 0.5, until you know more.

They don't, they default to unknown, for any practical purpose.

For a non-practical purpose you can put them at anything you like.

Its like saying "I don't know how many euro I have in pocket, so I'm going to assume I've €10" .. you can assume you have anything you like, but that doesn't mean when you get up to the counter to pay for your Happy Meal you have €10. Practically you don't know how much money you have, so any judgement based on your made up assumptions is meaningless.

Assuming the prob is 50/50 is meaningless, since you don't know it is. You can do it (you can do anything) but any conclusions based on that will be equally meaningless.

You are running into problems when you start using this (meaningless) default as the basis for further exploration. You can't, since the actual prob unknown.

pH

Scofflaw wrote:

I'm not sure why people are having such difficulty with the assignment of a probability of 0.5 to God(s). In the absence of information one is entitled to assign any initial probability to outcomes, and 0.5 is the most defensible for binary outcomes.

I'm not sure where you get the idea that "one is entitled to assign any initial probability" from. I'm sure you can quote the maths text book that comes from, I wouldn't imagine for a minute that you just made that up.

Even if you say "I'll guess the probability as 0.5" it's just a guess and no more defensible than any other random choice.

Alex S. wrote:

Disagree, if you don't know the number of possible outcomes, then you are correct, you don't know the probability. But,
probability analysis begins with the number of outcomes, in this case it is a set of two outcomes. {God(s) exist, God(s) don't exist}.

So both default to 0.5, until you know more. In nearly all binary problems i.e. with two outcomes, you will know more, so you rarely get end where you begin at 0.5.

I'm afraid this is once again total rubbish. So please provide some references


Here's a very simple introduction to probability:

http://davidmlane.com/hyperstat/A109506.html
"In general, the probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. (This assumes the outcomes are all equally likely.)"

http://www-math.bgsu.edu/~albert/m115/probability/equally_likely.html
In general, if there are N possible outcomes in an experiment and the outcomes are equally likely , then you should assign a probability of 1/N to each outcome.

CAUTION: This recipe for assigning probabilities works only when the outcomes are equally likely. It is easy to misuse this. For example, suppose you toss a coin three times and you're interested in the number of heads. The possible numbers of heads (the sample space) are

You and Scoff are obviously not the first people to have difficulty with this, but if you insist you are right, find a reputable maths site to back up your claim:

Provide a link which says,
If you have an event which has N outcomes and have no idea of the individual probabilities of each outcome then the correct thing to do is assign them each a probability of 1/N.

Alex S.

Wicknight wrote:

They don't, they default to unknown, for any practical purpose.

For a non-practical purpose you can put them at anything you like.

Its like saying "I don't know how many euro I have in pocket, so I'm going to assume I've €10" .. you can assume you have anything you like, but that doesn't mean when you get up to the counter to pay for your Happy Meal you have €10. Practically you don't know how much money you have, so any judgement based on your made up assumptions is meaningless.

Assuming the prob is 50/50 is meaningless, since you don't know it is. You can do it (you can do anything) but any conclusions based on that will be equally meaningless.

You are running into problems when you start using this (meaningless) default as the basis for further exploration. You can't, since the actual prob unknown.

Unless you are sure there are only two possible outcomes (which is very unlikely) the 10 euro analogy is inaccurate.

A better analogy is guessing whether a card is red or black, when it can only be red or black, or if I am married or not. In both cases, you are certain there only two possible outcomes.

Zombrex

Alex S. wrote:

Unless you are sure there are only two possible outcomes (which is very unlikely) the 10 euro analogy is inaccurate.

A better analogy is guessing whether a card is red or black, when it can only be red or black, or if I am married or not. In both cases, you are certain there only two possible outcomes.

There are only two possible outcomes, but that does not mean that both outcomes are equally likely, so stating that the probability is 50/50 is meaningless. Unless the cards have been randomised properly, and contain an equal amount of reds and blacks, the chance that you will get a red or black card is not 50/50. If you are unaware of the method used to sort/unsort the cards, or unaware of the number of say red cards, you don't know the probability. They might all be red, in which case the probability of getting a red one is 100% and black 0%

A better example is the Lotto.

There are two outcomes to the Lotto, you win our you don't win. If you were ignorant of the mechanisms of the Lotto, unaware of the number of balls in the drum and the number of numbers picked, you could default to saying that there is a 50/50 probability. But this is meaningless. You could assign any number you like and it would be equally meaningless (unless by chance you actually did hit the correct probability).

So if you conclude from that that you are as likely to win the Lotto as you are to lose the Lotto each time you play (50/50 change), that conclusion is equally meaningless, since your inital values for the probability are meaningless.

Stating that the probability there is a God is 50/50 based on the fact that those are just the defaults you choose is as meaningless as stating the probability of there being a God is anything/anything.

You can't drawn any conclusions from this so you are right back where you started as if you said unknown/unknown

Scofflaw

pH wrote:

I'm not sure where you get the idea that "one is entitled to assign any initial probability" from. I'm sure you can quote the maths text book that comes from, I wouldn't imagine for a minute that you just made that up.

You and Scoff are obviously not the first people to have difficulty with this, but if you insist you are right, find a reputable maths site to back up your claim:

Provide a link which says,
If you have an event which has N outcomes and have no idea of the individual probabilities of each outcome then the correct thing to do is assign them each a probability of 1/N.

Where do I get the idea? Well, doing probability through school and college, I suppose, although only as a supplement to science. I'll kindly ignore your extremely patronising offer of a "good introduction".

Let me reverse your reasoning - if you have an event with N possible outcomes, each mutually exclusive, and you know no more about the system than that, what probability would you assign to each outcome?

If you are going to assign a raised probability to one outcome, in the absence of information, can you justify that?

References: try "probability event n outcomes 1/n" on Google and take your pick.

regards,
Scofflaw

Alex S.

pH wrote:

I'm not sure where you get the idea that "one is entitled to assign any initial probability" from. I'm sure you can quote the maths text book that comes from, I wouldn't imagine for a minute that you just made that up.

Even if you say "I'll guess the probability as 0.5" it's just a guess and no more defensible than any other random choice.



I'm afraid this is once again total rubbish. So please provide some references


Here's a very simple introduction to probability:

http://davidmlane.com/hyperstat/A109506.html
"In general, the probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. (This assumes the outcomes are all equally likely.)"

http://www-math.bgsu.edu/~albert/m115/probability/equally_likely.html
In general, if there are N possible outcomes in an experiment and the outcomes are equally likely , then you should assign a probability of 1/N to each outcome.

CAUTION: This recipe for assigning probabilities works only when the outcomes are equally likely. It is easy to misuse this. For example, suppose you toss a coin three times and you're interested in the number of heads. The possible numbers of heads (the sample space) are

You and Scoff are obviously not the first people to have difficulty with this, but if you insist you are right, find a reputable maths site to back up your claim:

Provide a link which says,
If you have an event which has N outcomes and have no idea of the individual probabilities of each outcome then the correct thing to do is assign them each a probability of 1/N.

I just clicked one of your links (http://www-math.bgsu.edu/~albert/m115/probability/equally_likely.html). In the 2nd sentence of paragraph 1, it states:
"If we have listed all outcomes and it is reasonable to assume that the outcomes are equally likely , then it is easy to assign probabilities."

i.e. if you know nothing more than the number or outcomes i.e. they are equally likely.
I also read the part you referenced:
"CAUTION: This recipe for assigning probabilities works only when the outcomes are equally likely..."

Here, you have four possible outcomes, but the reason why they do not have equal probability is because you know more about the problem. You can deduce all possible permutations and deduce each outcome is not equally likely.

However, w.r.t. P(god(s)), there is absolutely nothing extra you know other than the number of outcomes, which renders all outcomes equally likely.

However, even if you disagree with this and maintain that the probability is unknown and not 50 / 50, you are arguing agnostism as you are arguing the existense of God is unknown and not that the existence of God is false.

Scofflaw

Wicknight wrote:

There are only two possible outcomes, but that does not mean that both outcomes are equally likely, so stating that the probability is 50/50 is meaningless.

Stating that the probability there is a God is 50/50 based on the fact that those are just the defaults you choose is as meaningless as stating the probability of there being a God is anything/anything.

You can't drawn any conclusions from this so you are right back where you started as if you said unknown/unknown

The difference is, as Alex says, that after as much analysis as you like, you still wind up at 0.5 as the likelihood of God(s). It says nothing except that we don't know anything about God, and that agnosticism is a sensible position, which is, I think, what Alex intended to prove.

You are, I think, assuming that an assigned probability has to be meaningful/accurate. It doesn't, although it ought to be.

cordially,
Scofflaw

Zombrex

Scofflaw wrote:

If you are going to assign a raised probability to one outcome, in the absence of information, can you justify that?

You don't assign a raised probability to one outcome, you assign unknown outcome to all outcomes. You don't have to assign any definiate out come to any result if you don't know one. Unknown is a valid probability if you don't know the likelyhood of an outcome.

Zombrex

Scofflaw wrote:

The difference is, as Alex says, that after as much analysis as you like, you still wind up at 0.5 as the likelihood of God(s).

No, you end up with "unknown" as the likelihood of God. There is a mathematical symbol for that, but I forget what it is.

[EDIT]
Actually if I remember correctly I think you do something like this - Probability of God Exists = 1/X where 0 <= X <= 1

Assigning it a "default" value when the likelyhood of outcomes is incorrect. You only assign it a 1/N default probability when all outcomes are equally likely
[/EDIT]

Scofflaw

Wicknight wrote:

You don't assign a raised probability to one outcome, you assign unknown outcome to all outcomes. You don't have to assign any definiate out come to any result if you don't know one. Unknown is a valid probability if you don't know the likelyhood of an outcome.

One assigns an unknown probability where one can work back to find that probability. In this case it's been stated that there are only two possibilities, and that between them they cover all possibilities - that P(God(s))+P(no god(s)) =1, where both P(God(s)) and P(no god(s)) are unknown. In that case, and in the absence of any other useful data, the initially assigned probabilities are 0.5 and 0.5 for the two unknowns.

We do have to assign equal probabilities, because we don't know enough to say that one outcome is likelier than the other. I know you don't like that, but you'll have to work much harder to justify anything else.

As I said, this doesn't do much more than demonstrate our ignorance, and the fact that, after analysis, we still haven't improved on our initial assignments, doesn't do much other than demonstrate our continued ignorance.

Yes, it's the same thing as saying P(God(s))=unknown, but it's much funnier, because you can do pseudo-maths with it to demonstrate the extremely small likelihood of, say, the Bible being inerrant.

cordially,
Scofflaw

pH

Scofflaw wrote:

Where do I get the idea? Well, doing probability through school and college, I suppose, although only as a supplement to science. I'll kindly ignore your extremely patronising offer of a "good introduction".

Let me reverse your reasoning - if you have an event with N possible outcomes, each mutually exclusive, and you know no more about the system than that, what probability would you assign to each outcome?

You can't assign any probability, if they're mutually exclusive all you know is:
P(x1) + P(x2) + ...+ P(xN) = 1

You have no information that allows you assign any probability to each ourcome.

If you are going to assign a raised probability to one outcome, in the absence of information, can you justify that?

Of course not, no meaningful probabilities can be assigned

References: try "probability event n outcomes 1/n" on Google and take your pick.[/QUOTE]
Sorry I couldn't find one, did you?

Alex S. wrote:

I just clicked one of your links . In the 2nd sentence of paragraph 1, it states:
"If we have listed all outcomes and it is reasonable to assume that the outcomes are equally likely , then it is easy to assign probabilities."

i.e. if you know nothing more than the number or outcomes i.e. they are equally likely.

I think you missed the part "If ... it is reasonable to assume that the outcomes are equally likely"

So if you start with the assumption that God existing is equally as likely as God not existing

you can then ...

Prove that god existing is equally as likely as God not existing!

That's not that impressive tbh.

Zombrex

Scofflaw wrote:

the initially assigned probabilities are 0.5 and 0.5 for the two unknowns.

Not sure thats quite true, but anyway, as you said since no conclusions can be drawn from that it means the same as unknown.

Scofflaw wrote:

Yes, it's the same thing as saying P(God(s))=unknown, but it's much funnier, because you can do pseudo-maths with it to demonstrate the extremely small likelihood of, say, the Bible being inerrant.

Maths has a useful function after all

robindch

AlexS is saying "ok, either a god exists or a god doesn't exist, so I'll assume that each outcome is equally likely and therefore I can assign a tentative probability of 50% to each outcome. Therefore, there is a mathematical probability that god exists of 50%". I've bolded two bits of broken logic.

Or, in simpler terms: "I believe there's a 50% chance that a god exists, therefore there is a 50% chance that a god exists". Does that make the problem any easier to see?

...still waiting for an answer on the Unicorn

Scofflaw

pH wrote:

You can't assign any probability, if they're mutually exclusive all you know is:
P(x1) + P(x2) + ...+ P(xN) = 1

You have no information that allows you assign any probability to each ourcome.


Of course not, no meaningful probabilities can be assigned

Scofflaw wrote:

References: try "probability event n outcomes 1/n" on Google and take your pick.

Sorry I couldn't find one, did you?

I think you missed the part "If ... it is reasonable to assume that the outcomes are equally likely"

So if you start with the assumption that God existing is equally as likely as God not existing

you can then ...

Prove that god existing is equally as likely as God not existing!

That's not that impressive tbh.

Er, yes. Like I said, it's a game with numbers. There's no reason to assign probabilities to God's existence in the first place - one can equally sensibly say that all the probabilities involved are unknown (which supports the agnostic position) as say it's 50/50 and can't be resolved further (which supports the agnostic position).

In other words, if we have to assign probabilities to the system, we should assign equal probabilities, but we don't have to assign probabilities.

Now, all of those who don't want to assign probabilities can get off the train, in the full knowledge that their position is entirely valid, if dull.

cordially,
Scofflaw

pH

robindch wrote:

...still waiting for an answer on the Unicorn

I'm all for more unicorns, though Scofflaw seems to be on a crusade to rid this forum and other of all mythical creatures, having also shown a particular hatred for dragons, Wicknight's pixies and faeiries also. His crusade to rid us all of already non-existant creatures shows a certain quixotic zeal eh?

Scofflaw wrote:

In other words, if we have to assign probabilities to the system, we should assign equal probabilities

In what meaningful way does anyone 'have to' assign probabilities? Is there a man with a gun forcing anyone?

And no, even at gunpoint assigning equal probabilities are no more correct than any other guess.

Alex S.

The point is not what's correct or not, PH, as none of us know. The point is what is what can be deduce.
If you deduce that the P(God(s)) exists is 50 / 50 or it is unknown, it doesn't matter both are logical arguments for agnostism, not athesim.
Athesim stipulates there is definetively no God, that is the difference between athesim and agnostism. There is no logic, which supports that athesim is correct.