SIA should be suspect because ultimately probability is just a fancy way of counting and if you phrased this just as a matter of counting possibilities this isn't really convincing.
I think the problem here is, much like with sleeping beauty, ultimately just a confusion about what it is you are counting. If you are trying to count the fraction of experiences that are like being woken up for beauty where the coin is heads divided by all such experiences that gives you one result -- and could be called probability in a sense. OTOH if you count the number of configurations of the whole world divided by the number where the coin is heads you get a different result.
Same thing here. You are just counting two different things.
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More generally, if you accept the kind of reasoning a la SIA you end up having to say that you should be certain that theories which predict infinite numbers of people are infinitely more likely than ones which don't. And then what about uncountable cardinalities (nothing about these theories require the observers to be in same 'universe').
>. They are currently 50/50 between humanity having tons of people and it having just two people, but reason in the following way: “if civilization lasts super long, it’s unlikely that we’re the first two people—for we could be any of the people. In contrast, if there are only two people in total, then we’re guaranteed to be the two people. Therefore, if we ever discover that we’re the first two people we’ll get extremely strong evidence that humanity doesn’t last long.”
This is just accepting the reasoning of SIA. All you've done here is combine the reasoning that you take to establish SIA with the assumption of it's falsity so of course you can derive absurd conclusions.
While I admit that I don’t care too much about this, I appreciate that you care. 🙂
SIA should be suspect because ultimately probability is just a fancy way of counting and if you phrased this just as a matter of counting possibilities this isn't really convincing.
I think the problem here is, much like with sleeping beauty, ultimately just a confusion about what it is you are counting. If you are trying to count the fraction of experiences that are like being woken up for beauty where the coin is heads divided by all such experiences that gives you one result -- and could be called probability in a sense. OTOH if you count the number of configurations of the whole world divided by the number where the coin is heads you get a different result.
Same thing here. You are just counting two different things.
--
More generally, if you accept the kind of reasoning a la SIA you end up having to say that you should be certain that theories which predict infinite numbers of people are infinitely more likely than ones which don't. And then what about uncountable cardinalities (nothing about these theories require the observers to be in same 'universe').
>. They are currently 50/50 between humanity having tons of people and it having just two people, but reason in the following way: “if civilization lasts super long, it’s unlikely that we’re the first two people—for we could be any of the people. In contrast, if there are only two people in total, then we’re guaranteed to be the two people. Therefore, if we ever discover that we’re the first two people we’ll get extremely strong evidence that humanity doesn’t last long.”
This is just accepting the reasoning of SIA. All you've done here is combine the reasoning that you take to establish SIA with the assumption of it's falsity so of course you can derive absurd conclusions.