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Originally Posted by Ken G
It looks like you and I are all that remain in this debate for the time being, so it's up to us to get to the bottom of it.
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Or to abandon it as an argument that's going nowhere, to be frank.
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Originally Posted by Ken G
So yes, of that set, 5% are in the first 5%, it's well defined. But the same must be true of any statement of confidence. Therefore, if you claim that "I am 95% confident that humanity will not outlive 200 billion", you must also produce such a set (even if idealized) or it is a meaningless statement.
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The same set provides confidence for both claims. The mathematical linkage between the first claim and the second claim is trivial.
(A paediatrician tells you that your son's height is in the 98th centile for his age. You go home and measure your son's height - he's 120cm tall. That immediately tells you that 2% of kids your son's age are over 120cm tall. You don't need to doubt that proportion just because you've now measured the height.
It's the same proportion, with or without the numerical knowledge.)
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Originally Posted by Ken G
Could the supporters of that probability view simply say...
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Originally Posted by grant hutchison
There is no such set.
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as if it saved their argument? The fact that there is no such set is exactly why the argument is wrong. |
Or this imaginary set has
no relevance to the argument, which is my position. The set of relevance is the set of humans who make a claim about the likely total number of human lives, using their birth-number to make the calculation. 5% of them are wrong.
The set of people who make the specific claim that there will be 200 million humans, of which 5% are wrong, doesn't exist, as I said, for exactly the reasons you've set out. But it's just a non-issue for this problem.
Are you going to claim that there is a set of children 120cm high who are
not in the 98th centile for their age, and so measuring your child's height invalidates the paediatrician's assessment?
Here's another way of looking at it. Saying you're 95% percent certain you're not in the first 5% of human lives is just shorthand for saying "If only 100 humans lived, I'm 95% certain I wouldn't be in the first 5." Inserting your birthnumber merely introduces a constant of proportionality into that claim. Each individual inserts their own birth number, and comes up with their own estimate of the total number. The claim stays the same because the proportion is the same, just as it would have done if you'd decided to express your claim as a fraction or a per-mil, rather than a percent.
Grant Hutchison