Originally posted by EcstremeVenomNevertheless most of us can understand him and not you making the probability of you being thick much higher than the probability of it being him that is thick.
theres a misunderstanding here, i know i don't understand what you're trying to say and you don't understand what I'm trying to say.
Probability theory is all about information. Given a random choice between two possible things where the only known fact is that one is true and the other is not, the probability is 50/50. However that is not the case with your specific example. More information is available. Once you specify that the two choices are 1) a random thing exists, 2) a random thing does not exist or in the case you are giving 1) a random set of things, one of which exists, 2) a random set of things none of which exist. Then based on our knowledge that the number of things that do not exist is infinitely greater than the number that do we can immediately say that the probability for choice 1 is infinitely small.
If we go further and specify that the set of things we are referring to is all possible Gods then we immediately have more information to draw on and it changes the probabilities. Here however is where the problem comes in, because each individual person has a different set of information at their disposal regarding the existence of God(s) and thus the probability should be different from each persons point of view and definitely not 50/50 in most cases.
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Originally posted by EcstremeVenomOkay, let's dumb this down even more. Let's go back to rolling dice.
theres a misunderstanding here, i know i dont understand what youre trying to say and you dont understand what im trying to say.
Consider a 20-sided die. I roll the die but do not show you the outcome. I ask, "What is the probability that the number showing on the die less than 7?"
Now you notice that there are many possible numbers that are lower than 7, namely 1,2,3,4,5, and 6. Following the logic you have presented so far, you say, "It's 50/50." After all it's either lower than 7 or it is not, and there are many numbers lower than 7.
Surely, now you begin to see why you have been confused. The probability that the number is less than seven is 0.3 not 0.5. It doesn't matter if more than one outcome belongs to an event and/or if more than one outcome belongs to that event's compliment (i.e. not A). What matters is the form of the probability space.
Originally posted by telerionBut we have no information about the existence of 20-sided dice. It's 50/50.
Okay, let's dumb this down even more. Let's go back to rolling dice.
Consider a 20-sided die. I roll the die but do not show you the outcome. I ask, "What is the probability that the number showing on the die less than 7?"
Now you notice that there are many possible numbers that are lower than 7, namely 1,2,3,4,5, and 6. Following the logic you h ...[text shortened]... t event's compliment (i.e. not A). What matters is the form of the probability space.
Originally posted by DoctorScribblesI say when it comes to gods and other supernatural matters, the whole damn sample space is not measurable in which case the probabilty isn't even defined. At this point, I'm not even concerned with that junk. I'm simply trying to get Venom to realize that if two events form the sigma-algebra over the sample space, the respective probabilities associated with those events need not be .5 and .5, even if each event contains multiple outcomes.
But we have no information about the existence of 20-sided dice. It's 50/50.
I'm just about to write these people off.
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Originally posted by telerionI disagree. Why isn't it defined?
I say when it comes to gods and other supernatural matters, the whole damn sample space is not measurable in which case the probabilty isn't even defined.
We have no evidence of existence but the absence of evidence is evidence of absence. The best estimation is therefore 1 for non-existence, albeit it may be biased for certain types of Gods.
Originally posted by PalynkaIt's not defined because the sample space, which is necessary for a probability to exist, is not clearly defined. In the other examples in this thread, we knew how to characterize all the possible outcomes. Given this sample space, we could construct a sigma-algrebra and a probability measure. From that we have a probability.
I disagree. Why isn't it defined?
We have no evidence of existence but the absence of evidence is evidence of absence. The best estimation is therefore 1 for non-existence, albeit it may be biased for certain types of Gods.
With gods, IPU's, FSM's, Muffy's, and the like we cannot mathematically characterize the set of all possible outcomes (note outcomes, not events). Give me a list of all possible outcomes, and I'm sure we could make up a great many more from our imaginations. That's the silliness of the supernatural. Until the sample space is constructed, a probability measure cannot be assigned to elements of the sigma-algebra, the events, over that space.
Originally posted by telerionThe sample space is not discrete as there are an infinity of Gods. Obviously, I can't explicit the whole space, but that is valid for all non-finite sample spaces.
It's not defined because the sample space, which is necessary for a probability to exist, is not clearly defined. In the other examples in this thread, we knew how to characterize all the possible outcomes. Given this sample space, we could construct a sigma-algrebra and a probability measure. From that we have a probability.
With gods, IPU's, FSM's ...[text shortened]... measure cannot be assigned to elements of the sigma-algebra, the events, over that space.
It's absolutely false that I need to characterize all possible outcomes to estimate a probability. All I need is to have a number of observations and estimate a distribution.
If I only find observations around a mass point (0), then I estimate that the probability of God existing is 0.
Originally posted by PalynkaThe sample space does not need to be discrete. Notice that I used the word "characterize" and not a word like "list." Spin a pointer around a unit circle. There are an infinite number of possible outcomes (anything real number between on the unit interval), but the sample space can still be characterized and a sigma-algrebra placed over it. The probability of a number less than or equal to .2 in this example is .2.
The sample space is not discrete as there are an infinity of Gods. Obviously, I can't explicit the whole space, but that is valid for all non-finite sample spaces.
It's absolutely false that I need to characterize all possible outcomes to estimate a probability. All I need is to have a number of observations and estimate a distribution.
If I only find ...[text shortened]... servations around a mass point (0), then I estimate that the probability of God existing is 0.
Even with a large number of observations, you'll still need to make some explicit assumption about the errors; and that's with natural things. There is an added difficulty with supernatural things because many of these things are considered to be orthogonal to or independent of the natural. They can be anything you like.
If I only find observations around a mass point (0), then I estimate that the probability of God existing is 0.
Generally, you have no reasonable way of mapping observations of the natural into outcomes in the supernatural. Yes, it can work for any of the outcomes for which an explicit natural link is assumed (i.e., a god exists that is incompatible with the existence of fire), but there are an infinite number of other outcomes for which this is not the case. We have no idea what the corresponding measures of the two sets of supernatural outcomes are.
For instance, you can say that you see no evidence of any gods, but then one could always counter that that is exactly what some gods want you to see. Pure insanity really.
Originally posted by telerionThat's what I meant about bias. My estimator may be biased for the existence of Gods who are unknowable. The question is that if they are unknowable, they're also irrelevant and therefore equivalent to non-existence.
If I only find observations around a mass point (0), then I estimate that the probability of God existing is 0.
Generally, you have no reasonable way of mapping observations of the natural into outcomes in the supernatural. Yes, it can work for any of the outcomes for which an explicit natural link is assumed (i.e., a god exists that is incompatib ...[text shortened]... could always counter that that is exactly what some gods want you to see. Pure insanity really.[/b]