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').

Yes, you should think the universe is infinitely big. I agree with this and in fact defended it in this very article. In this article I gave an argument for SIA which is, I think, convincing. Not sure what you mean about probability just being a fancy way of counting or why that discredits SIA.

Regarding the infinite universe the problem is that for any specific cardinality you get that the universe is essentially certainly larger than that.

But now you can't even talk about the set of all people since it's not going to be a set but a proper class with virtual certainty and something seems wrong about that.

Ahh but now you get into a paradox because the whole notion of probability -- which you used to reach this result -- is defined into terms of a probability space which itself takes every outcome to be a set. So probability reasoning can't be used to talk about the probability of results like this.

What? Why? Like, if you think Beth 2 existing is possible you should have some view about how to reason about that. Can you spell out what the paradox is?

>. 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.

What, no? If you know that there are a lot of people but don't know your birth rank, you should split your credence across the possible birth ranks and think it unlikely that you're late.

Wait if you are thinking of it that way you can't simultaneously have them think it's likely that there aren't many people and that conditional on them procreating there will be many people.

This example seems kinda poorly defined so maybe you could explain it in more detail.

stage 1: they don't know their birth rank. So they think it's super unlikely they're the first two people if the first two people have lots of offspring

stage 2: they find out that they're the first two people. Because that's guaranteed if the first two people don't have offspring but unlikely (per stage 1) if they do, they have strong evidence that the first two people won't have many offspring. But now they know they're the first two people, so they get strong evidence that they themselves won't have many offspring. From this, lazy adam and such follows.

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').

Yes, you should think the universe is infinitely big. I agree with this and in fact defended it in this very article. In this article I gave an argument for SIA which is, I think, convincing. Not sure what you mean about probability just being a fancy way of counting or why that discredits SIA.

Regarding the infinite universe the problem is that for any specific cardinality you get that the universe is essentially certainly larger than that.

But now you can't even talk about the set of all people since it's not going to be a set but a proper class with virtual certainty and something seems wrong about that.

That's why you should think it's bigger than any cardinality--just like there's no cardinality of all truths because there's no set.

Ahh but now you get into a paradox because the whole notion of probability -- which you used to reach this result -- is defined into terms of a probability space which itself takes every outcome to be a set. So probability reasoning can't be used to talk about the probability of results like this.

What? Why? Like, if you think Beth 2 existing is possible you should have some view about how to reason about that. Can you spell out what the paradox is?

>. 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.

What, no? If you know that there are a lot of people but don't know your birth rank, you should split your credence across the possible birth ranks and think it unlikely that you're late.

Wait if you are thinking of it that way you can't simultaneously have them think it's likely that there aren't many people and that conditional on them procreating there will be many people.

This example seems kinda poorly defined so maybe you could explain it in more detail.

stage 1: they don't know their birth rank. So they think it's super unlikely they're the first two people if the first two people have lots of offspring

stage 2: they find out that they're the first two people. Because that's guaranteed if the first two people don't have offspring but unlikely (per stage 1) if they do, they have strong evidence that the first two people won't have many offspring. But now they know they're the first two people, so they get strong evidence that they themselves won't have many offspring. From this, lazy adam and such follows.