The Lost One
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Post by The Lost One on Jul 18, 2017 13:48:18 GMT
I thought I’d use Bayes’ Theorem to try to answer the question “Given that I have never witnessed a miracle, what is the possibility that miracles cannot happen?”
Here, “miracle” is defined as an event that is contrary to the otherwise immutable natural laws.
Bayes’ Theorem can be expressed as follows:
P(A|B)= (P(B|A) * P(A)) / P(B)
I’ll define the terms in the equation thusly:
P(A)=The prior probability that miracles cannot happen
P(B)=The prior probability that I will not witness a miracle
P(B|A)=The probability of not witnessing a miracle if miracles cannot happen
P(A|B)=The probability that miracles cannot happen if I have never witnessed one.
Calculating P(A)
It seems a world where miracles cannot happen is less complex than one in which they can – a world in which miracles can happen requires an additional entity to subvert natural laws. Therefore let us say that it is twice as likely that a world would exist where miracles cannot happen as a world in which they can.
P(A)=2/3
Calculating P(B)
If A is true (P(A)=2/3), then P(B) would be 1 (as you would never observe a miracle if they cannot happen).
If A is false, then it’s hard to know what P(B) would be. However most people who believe in miracles think them very rare – so let’s say you have a 1 in 1,000,000 chance of ever observing a miracle.
P(B)= ((2/3 * 1) + (1/3 * 999,999/1,000,000) = 2,999,999/3,000,000
Calculating P(B|A)
As already stated, this would be 1.
Calculating P(A|B)
P(A|B)= (1 * 2/3) / (2,999,999/3,000,000) = 0.6666669 repeating
So unless I have made a mistake in either my calculations or my assumptions, then it seems that while it is unlikely that miracles are possible, it is not so unlikely for it to be ridiculous to believe they might be possible.
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Post by general313 on Jul 18, 2017 15:09:49 GMT
I thought I’d use Bayes’ Theorem to try to answer the question “Given that I have never witnessed a miracle, what is the possibility that miracles cannot happen?” Here, “miracle” is defined as an event that is contrary to the otherwise immutable natural laws. Bayes’ Theorem can be expressed as follows: P(A|B)= (P(B|A) * P(A)) / P(B) I’ll define the terms in the equation thusly: P(A)=The prior probability that miracles cannot happen P(B)=The prior probability that I will not witness a miracle P(B|A)=The probability of not witnessing a miracle if miracles cannot happen P(A|B)=The probability that miracles cannot happen if I have never witnessed one. Calculating P(A)It seems a world where miracles cannot happen is less complex than one in which they can – a world in which miracles can happen requires an additional entity to subvert natural laws. Therefore let us say that it is twice as likely that a world would exist where miracles cannot happen as a world in which they can. P(A)=2/3 Calculating P(B)If A is true (P(A)=2/3), then P(B) would be 1 (as you would never observe a miracle if they cannot happen). If A is false, then it’s hard to know what P(B) would be. However most people who believe in miracles think them very rare – so let’s say you have a 1 in 1,000,000 chance of ever observing a miracle. P(B)= ((2/3 * 1) + (1/3 * 999,999/1,000,000) = 2,999,999/3,000,000 Calculating P(B|A)As already stated, this would be 1. Calculating P(A|B)P(A|B)= (1 * 2/3) / (2,999,999/3,000,000) = 0.6666669 repeating So unless I have made a mistake in either my calculations or my assumptions, then it seems that while it is unlikely that miracles are possible, it is not so unlikely for it to be ridiculous to believe they might be possible. And if you replace "miracle" with "God" or "Zeus" you come up with the same answer! |
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The Lost One
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Post by The Lost One on Jul 18, 2017 15:41:27 GMT
And if you replace "miracle" with "God" or "Zeus" you come up with the same answer! With Zeus, because he is a specific conception of God, his prior probability would be much lower than 1/3 as you would have to compare his probability with the probability of any other possible God. So Zeus's prior probability would be really really low (suppose there were 1000 possible conceptions of God and Zeus was one of them. Let's say the prior possibility of any God existing was 1/3. Then the prior possibility of Zeus existing would then be 1/3000) . Regarding "God", if you mean Yahweh, then the same would be as true for Yahweh as it would be for Zeus. If you're using the term more generically to mean any possible conception of God, then yes you could probably make an analogous argument to the miracle one to that very broad God concept. |
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Post by general313 on Jul 18, 2017 20:42:05 GMT
And if you replace "miracle" with "God" or "Zeus" you come up with the same answer! With Zeus, because he is a specific conception of God, his prior probability would be much lower than 1/3 as you would have to compare his probability with the probability of any other possible God. So Zeus's prior probability would be really really low (suppose there were 1000 possible conceptions of God and Zeus was one of them. Let's say the prior possibility of any God existing was 1/3. Then the prior possibility of Zeus existing would then be 1/3000) . Regarding "God", if you mean Yahweh, then the same would be as true for Yahweh as it would be for Zeus. If you're using the term more generically to mean any possible conception of God, then yes you could probably make an analogous argument to the miracle one to that very broad God concept. Ok, there's the point that the probability of the existence of any god is higher than that for a specific god. I'll agree to that. But to come up with specific numbers suitable for plugging into a math equation like Bayes', you need to have a meaningful statistical sample to have any kind of accuracy. I don't see how that's possible with things like miracles or God. How can you have a valid statistical sample of something where there's no evidence that that thing even exists? You need countable information to make the probabilities. |
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The Lost One
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Post by The Lost One on Jul 18, 2017 21:46:37 GMT
With Zeus, because he is a specific conception of God, his prior probability would be much lower than 1/3 as you would have to compare his probability with the probability of any other possible God. So Zeus's prior probability would be really really low (suppose there were 1000 possible conceptions of God and Zeus was one of them. Let's say the prior possibility of any God existing was 1/3. Then the prior possibility of Zeus existing would then be 1/3000) . Regarding "God", if you mean Yahweh, then the same would be as true for Yahweh as it would be for Zeus. If you're using the term more generically to mean any possible conception of God, then yes you could probably make an analogous argument to the miracle one to that very broad God concept. Ok, there's the point that the probability of the existence of any god is higher than that for a specific god. I'll agree to that. But to come up with specific numbers suitable for plugging into a math equation like Bayes', you need to have a meaningful statistical sample to have any kind of accuracy. I don't see how that's possible with things like miracles or God. How can you have a valid statistical sample of something where there's no evidence that that thing even exists? You need countable information to make the probabilities. Sure. I'm not saying that my estimations for P(A) or P(B) are all that accurate but they seem at least reasonable estimates that most wouldn't think outlandish. And yet these reasonable numbers would seem to suggest, perhaps contrary to what many would think, that absence of evidence is only fairly weak evidence of absence so long as it is maintained that miracles are rare. |
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Post by 🌵 on Jul 24, 2017 2:36:38 GMT
Therefore let us say that it is twice as likely that a world would exist where miracles cannot happen as a world in which they can. Why should we think that it's twice as likely, rather than three times as likely, or 10^30 times as likely, or any other arbitrary number? |
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The Lost One
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Post by The Lost One on Jul 24, 2017 8:14:52 GMT
Therefore let us say that it is twice as likely that a world would exist where miracles cannot happen as a world in which they can. Why should we think that it's twice as likely, rather than three times as likely, or 10^30 times as likely, or any other arbitrary number? My thinking was it's only one extra complication, therefore there wouldn't be a massive difference in likelihood. But yeah I might be very wrong there. But the more interesting point is that the lack of evidence doesn't seem to modify the prior probability very much. Even if we take the prior probability as being unknowable that would just make the probability of miracles essentially unknowable. |
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Post by Terrapin Station on Jul 24, 2017 12:53:03 GMT
I’ll define the terms in the equation thusly: P(A)=The prior probability that miracles cannot happen P(B)=The prior probability that I will not witness a miracle P(B|A)=The probability of not witnessing a miracle if miracles cannot happen P(A|B)=The probability that miracles cannot happen if I have never witnessed one. The only one of those we'd have any hope of attaching a non-arbitrary number to is P(B|A), and that's only if we interpret it non-phenomenally. (If we interpret it phenomenally, then we have no way of attaching a non-arbitrary number to it.) Or in other words, just because it looks like mathematics doesn't imply that there's any merit to it whatsoever for arriving at ontological claims. |
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Post by 🌵 on Jul 25, 2017 0:23:51 GMT
Why should we think that it's twice as likely, rather than three times as likely, or 10^30 times as likely, or any other arbitrary number? My thinking was it's only one extra complication, therefore there wouldn't be a massive difference in likelihood. First, I'm not sure there's any non-arbitrary way of specifying whether some state of affairs counts as one extra complication, rather than two or three or four etc extra complications. Suppose I put a spade outside in my garden. I go to bed and wake up the next day and I find it in the same place I put it. Here are two hypotheses: (1) after putting the spade out yesterday, it remained there untouched until today; (2) after putting the spade out yesterday, it was stolen and then put back after the thief had a change of heart. (2) includes just one other entity - the thief - so maybe that's only one extra complication. Or we might say that the initial theft and the change of heart both count as extra complications. Or we might say that the thoughts that motivated the thief to commit the crime, the method by the which the thief entered the garden, the method by which he left the garden, the thoughts that caused the change of heart, etc etc, all count as extra complications. Second, even if there were a non-arbitrary way to enumerate complications, why should we think that the probability of X relative to Y increases proportionally to how many extra complications Y has relative to X? Surely we'd need to look at the specific details of those complications. If we were to try to evaluate the probabilities of (1) and (2), we'd need to consider the crime rate in my area, the probability of a person changing their mind while committing a theft, plus facts about my garden such as how attractive and accessible it may be for thieves, etc. But yeah I might be very wrong there. But the more interesting point is that the lack of evidence doesn't seem to modify the prior probability very much. Even if we take the prior probability as being unknowable that would just make the probability of miracles essentially unknowable. You tried to determine the probability that miracles cannot happen given that I have never witnessed one. But if you're evaluating the relevance of lack of evidence, then you'd need to consider the fact that nobody has ever provided a reliable report of a miracle. Taking your figures that if miracles do occur then there is a 1/3,000,000 chance of witnessing a miracle, then I suspect that the fact that there are no reliable reports of miracles would become somewhat surprising on the assumption that miracles do occur. |
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lava-rocks
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Post by lava-rocks on Dec 1, 2018 4:32:08 GMT
Complete bollocks.
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The Lost One
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Post by The Lost One on Dec 3, 2018 11:49:36 GMT
After reading it back (I can't even remember starting this topic), I'm inclined to agree... |
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