Cont: Proof of Immortality VIII

jt512 said:
That's the case of E you have been using. So, you have now conceded that your argument has been incorrect (that's a huge step). Your observing E cannot be evidence for H over ~H or vice versa.
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Jabba said:
jt,
- So far, I don't see how that makes any difference.
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:dl:

You don't see what difference it makes that your argument is invalid?
 
Jabba said:
*provided by #404
jt,
- Why does P(E) = P(E|H)P(H) + P(E|~H)P(~H)?
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Seriously, Jabba? That is a rather basic part of conditional probabilities and Bayes inference.

It is, in fact, the denominator in the right-hand side of the formula you continually proffer. Did you not wonder how Bayes Theroem:
P(H|E) = P(E|H)(P(H) / P(E)​
gets transformed into:
P(H|E) = P(E|H)(P(H) / (P(E|H)P(H) + P(E|~H)P(~H))​
?
 
Mojo said:
Jabba, where do you get the factor of 10-100? You say that the probability of your brain existing is 1, and under H this is all that is required for your existence. Where does the 10-100 come from?
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Mojo,
- The brain is a given in both H and ~H. I equated that to P(E) = 1 in both cases, trying to explain why the conjunction fallacy did not apply to our situation -- multiplying a probability by 1 doesn't make it smaller.
- I'm not sure that P(E) = 1 is appropriate terminology, and seems like I just created more confusion by using it...
- 10-100 expresses how likely you are to currently exist if you have only one finite life to live at most -- and, you don't have to ever exist...
 
Jabba said:
I'm not sure that P(E) = 1 is appropriate terminology, and seems like I just created more confusion by using it...
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You keep being unsure of and incorrect in your terminology and formulation. What are the odss that this, not some imagined bias on your critics' part, is why your proof doesn't work?

10-100 expresses how likely you are to currently exist if you have only one finite life to live at most -- and, you don't have to ever exist...
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That doesn't explain where the value of that number came from. You're giving us a finite number as a likelihood. How did you determine its value?
 
Jabba said:
- Yes.
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That's now the second time you've responded to this post answering the rather pointless question and ignoring the vastly more important question.

Where did the number 10-100 come from? How was it computed?

Shall we assume at this point, given your assiduous avoidance of that question, that it's something you're deliberately trying to conceal from the reader?
 
Jabba said:
- 10-100 expresses how likely you are to currently exist if you have only one finite life to live at most -- and, you don't have to ever exist...
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Ah! Good for you to have finally admitted it's a number you just made up and it's not based on anything rational or logical.

You agree then that you're simply wrong and this can be written on your website as your concession.
 
Jabba said:
Mojo,
- The brain is a given in both H and ~H. I equated that to P(E) = 1 in both cases, trying to explain why the conjunction fallacy did not apply to our situation -- multiplying a probability by 1 doesn't make it smaller.
- I'm not sure that P(E) = 1 is appropriate terminology, and seems like I just created more confusion by using it...
- 10-100 expresses how likely you are to currently exist if you have only one finite life to live at most -- and, you don't have to ever exist...
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Your current existence requires your body to exist in both cases. The sequence of events required to produce your body is the same in both cases. In one case your body is all that is required. Your existence in the other case cannot be more likely than it is in that one.
 
Jabba said:
Why does P(E) = P(E|H)P(H) + P(E|~H)P(~H)?
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Along with jsfisher I'm similarly aghast that this has to be explained to you. This is a foundational concept in statistics. It's one of several foundational concepts you seem to have forgotten, which makes it more likely that the failure of your proof is best explained by your incompetence, not by some imagined bias, ignorance, or mean-spiritedness on the part of your critics. You throw equations around not because you recognize them as tools with which to represent elements of an inference, but apparently just to intimidate the rubes. When asked to explain these concepts, all you seem to muster is the equivalent of the old "The mitochondria is the powerhouse of the cell" recitation.

The probability of an event E happening is the sum of the probabilities of all the ways it can happen. That in turn is a convolution of the probabilities with which various reasons arise, with the probabilities with which those reasons explain the event. P(E|H) is the ability of some reason (or cause) H to explain an event (or effect) E. P(H) is the propensity of that reason to arise. That's all there is to it. A very likely reason H contributes to the event likely happening. A reason that leads more or less inevitably to the event contributes to the event likely happening.

The formulation of "all the ways it can happen" here is H and everything else. ~H obviously isn't a singular hypothesis. It's a set of them having nothing in common other than not being exactly H. P(E|~H) doesn't have any conception meaning beyond "everything else." It does have a value, though -- 1-P(E|H). Given E, the probability that H explains it and the probability that one of ~H explains it must sum to 1. It happened, so we have to explain it If not by H, then necessarily by something else. "Something else" is a member of, but not identical to, "everything else."

Another formulation is the one I gave you a couple weeks ago, which you ignored. That's to treat the problem as true likelihoods and to compare the likelihoods of a few individual hypotheses to each other, not to 1. Jt512 gave you a shorthand to that formulation a week or so ago. The key difference is that given E, the likelihoods that each of the few reasons we consider explains E doesn't sum to 1. We just compare their values to each other to see whether one stands taller than the pack. The event happened, but we don't have to explain it by any of the few hypotheses we consider. Explanatory power is relative in this case.

P(E|H) and P(E|~H) sum to 1. But P(E) is not 1. It's not guaranteed to happen. What determines whether the effect happens is whether any of the causes arises. P(E|H)P(H) combines the ability of reason H to explain event E with the propensity of reason H to arise. P(E|~H)P(~H) is simply the complement under E. It's the ability of a disjunction of all other reasons to explain E and the propensity of a disjunction of all other reasons to arise. Figuring P(H) and P(E|H) takes brains. H is a specific thing, and its specificity must be reckoned against the specificity of E. P(H) is a tractable problem. P(E|H) is a tractable problem. That doesn't mean they have certain values. But it does mean you can talk rationally about them. P(~H) and P(E|~H) are no-brainers. Complements require no brains to devise because they result simply from subtracting our wok above from 1. Because they have no rationale -- merely algebraic existence -- they have almost no explanatory power. Your proof, in contrast, relies upon trying to give it meaning and explanatory power beyond its ken.
 
Jabba said:
- Yes. Yes.
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And you don't see the problem there?



If the likelihood of your body is the same under both hypotheses, and in one of the hypotheses (~H) you add another factor with its own likelihood (the soul), then you REDUCE the odds of your existence under that hypothesis.
 
Jabba said:
Mojo,
- The brain is a given in both H and ~H. I equated that to P(E) = 1 in both cases, trying to explain why the conjunction fallacy did not apply to our situation -- multiplying a probability by 1 doesn't make it smaller.
- I'm not sure that P(E) = 1 is appropriate terminology, and seems like I just created more confusion by using it...
- 10-100 expresses how likely you are to currently exist if you have only one finite life to live at most -- and, you don't have to ever exist...
Click to expand...

How did you arrive at that number? Especially since you've shown the likelihood of H to be 1.
 
MRC_Hans said:
I think were on to something basic here.

Do you mean that while your self is perceived through your current brain, it could be perceived through any brain, and thus whichever physical appearance you might be in, you would somehow be YOU?

In that case I think we are at a more basic caveat:

Just because one hypothesis has a higher likelihood than another it needs not be the true one.

An example: I give you a nice, fresh ripe apple. I inform you that it comes from a tree in my garden.

Now, we can make two hypoteses:

H : Apples grow seasonally on the three and it carries fresh ripe apples for a period of about five weeks every year.

~H : Apples do not grow seasonally but are available any time of the year.

The likelihood of getting a ripe apple under H is about 1/10.
Under ~H it is 1.

However, apples still grow seasonally on my tree.

Hans
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Hans,

- I think that you left out a couple of important words.
- H : Apples grow seasonally on my tree and it carries fresh ripe apples for a period of about five weeks every year.
- ~H : Apples do not grow seasonally on my tree but are available any time of the year.
- The likelihood of getting a ripe apple from my tree under H is about 1/10. Under ~H it is 1.
- I got a fresh apple from my tree. - The likelihood of getting a fresh apple from my tree is greater Under ~H than under H -- but the prior probability of H is much greater than the prior probability of ~H.
- I don't know much about the prior probabilities here, but my best guess is that the Bayes formula would include the following numbers:
- P(H|E) = .10*1/((.10*1) + (1*.01)) or .10/.11 or 91%.
- In other words, the posterior probability that your tree is seasonal is 91%.
 
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