I don't think this is correct. If we're going to allow actual infinities, we should allow infinitesimals. So the probability of you existing in any given century is infinitesimal, but non-zero.
> it is reasonable to suspect that things did not just appear in this unusual state for no reason.
Okay, but ... um ... how can there be an infinite past? The state of the universe at every point in time depends on the state at the time just before that. It simply doesn't make sense to say that there is no initial state. Because without a first state, the universe cannot determine its second state.
It's not like a number line in which every number is *independent* so we are free to imagine a negative infinity (and note that negative infinity isn't proven to exist in any physical sense; it's only a mathematical idea).
It's not relevant to your thesis, but I also disagree about the future being infinite. My model is that although the edges of space and time are both unimaginably vast and unreachable,
1. time is physically finite (rationale: it must have a beginning in *some* sense because causality exists, and "year infinity" will never happen, so clearly every future point in time is a finite point) and
2. space might well be finite also (under a Wolfram-like model of spacetime, which is hard to prove but has nice intuitive properties for us computer engineers). It's simple enough for space to be finite while having unreachable and invisible edges: it just needs to have an outer surface that always expands at the speed of light. So just like time, space can go on and on forever without literally being infinite.
> The doctrine of Eternal Recurrence is the belief that everything that occurs will repeat itself in the future
It doesn't look like the universe will collapse and produce another big bang.
> If time is infinite, the probability of you existing in any given century is 0.
I think this is where your reasoning went off the rails. Sure, it's wrong in my model where time is finite, but it's also wrong in general.
Suppose X is unknown to you, but its value actually happens to be 7^51 trillion googolplex. Since you don't know the value of X, and it could be anything on an infinite number line, you reason that the probability that it is any particular number (including 7^51 trillion googolplex) is zero. But actually X = 7^51 trillion googolplex, so you were wrong to discount that possibility.
Treating 'some permissive view of persons is correct' as a true statement about the universe doesn't seem right to me. What would the object-level differences of a universe where personhood was restrictive vs. permissive look like?
They feel more like statements about an individual person. (e.g. I might have a much more permissive view of whether another mind would be me or not than most people. I can't say their restrictive view is /false/ exactly, but I can say that the reasons they usually give to justify it would lead to a MUCH more restrictive view than they actually want to have.)
You'd probably find Max Tegmark's _Our Mathematical Universe_ of interest - ttps://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307744256
(Tegmark - https://physics.mit.edu/faculty/max-tegmark/ - is *the* Cosmic Microwave Background guy and knows his cosmology.) He makes the case, based on cosmology, that infinite copies of each of us not only exist but exist via multiple independent mechanisms (each adding to the number of subjective copies). It's not rigorous (it's a popular book) but I found it pretty convincing (more so than I do Huemer's argument). Google can find you his papers if you don't want to buy the book.
That all said, I think "reincarnation" is the wrong, and misleading, word for what you're describing. That word conjures up a lot of ideas from Eastern religion involving souls, judgement, karma, etc., which I think neither you nor Huemer (nor Tegmark) are arguing for.
The fact that there are (probably) infinite numbers of *copies* of each of us, and infinite small and large variations on each of us, and infinite worlds, doesn't mean there is karma or justice for good and evil.
Per Tegmark (and I think Huemer if I understand your post), multiple copies exist. None of them are "reincarnations" of previously existing people - each is an independent version arising independently via local mechanisms.
I don't think this is correct. If we're going to allow actual infinities, we should allow infinitesimals. So the probability of you existing in any given century is infinitesimal, but non-zero.
> it is reasonable to suspect that things did not just appear in this unusual state for no reason.
Okay, but ... um ... how can there be an infinite past? The state of the universe at every point in time depends on the state at the time just before that. It simply doesn't make sense to say that there is no initial state. Because without a first state, the universe cannot determine its second state.
It's not like a number line in which every number is *independent* so we are free to imagine a negative infinity (and note that negative infinity isn't proven to exist in any physical sense; it's only a mathematical idea).
It's not relevant to your thesis, but I also disagree about the future being infinite. My model is that although the edges of space and time are both unimaginably vast and unreachable,
1. time is physically finite (rationale: it must have a beginning in *some* sense because causality exists, and "year infinity" will never happen, so clearly every future point in time is a finite point) and
2. space might well be finite also (under a Wolfram-like model of spacetime, which is hard to prove but has nice intuitive properties for us computer engineers). It's simple enough for space to be finite while having unreachable and invisible edges: it just needs to have an outer surface that always expands at the speed of light. So just like time, space can go on and on forever without literally being infinite.
> The doctrine of Eternal Recurrence is the belief that everything that occurs will repeat itself in the future
Is this like the Futurama episode? https://futurama.fandom.com/wiki/Forwards_Time_Machine
It doesn't look like the universe will collapse and produce another big bang.
> If time is infinite, the probability of you existing in any given century is 0.
I think this is where your reasoning went off the rails. Sure, it's wrong in my model where time is finite, but it's also wrong in general.
Suppose X is unknown to you, but its value actually happens to be 7^51 trillion googolplex. Since you don't know the value of X, and it could be anything on an infinite number line, you reason that the probability that it is any particular number (including 7^51 trillion googolplex) is zero. But actually X = 7^51 trillion googolplex, so you were wrong to discount that possibility.
Also, zero and one are not probabilities: https://www.lesswrong.com/posts/QGkYCwyC7wTDyt3yT/0-and-1-are-not-probabilities
Treating 'some permissive view of persons is correct' as a true statement about the universe doesn't seem right to me. What would the object-level differences of a universe where personhood was restrictive vs. permissive look like?
They feel more like statements about an individual person. (e.g. I might have a much more permissive view of whether another mind would be me or not than most people. I can't say their restrictive view is /false/ exactly, but I can say that the reasons they usually give to justify it would lead to a MUCH more restrictive view than they actually want to have.)
You'd probably find Max Tegmark's _Our Mathematical Universe_ of interest - ttps://www.amazon.com/Our-Mathematical-Universe-Ultimate-Reality/dp/0307744256
(Tegmark - https://physics.mit.edu/faculty/max-tegmark/ - is *the* Cosmic Microwave Background guy and knows his cosmology.) He makes the case, based on cosmology, that infinite copies of each of us not only exist but exist via multiple independent mechanisms (each adding to the number of subjective copies). It's not rigorous (it's a popular book) but I found it pretty convincing (more so than I do Huemer's argument). Google can find you his papers if you don't want to buy the book.
That all said, I think "reincarnation" is the wrong, and misleading, word for what you're describing. That word conjures up a lot of ideas from Eastern religion involving souls, judgement, karma, etc., which I think neither you nor Huemer (nor Tegmark) are arguing for.
The fact that there are (probably) infinite numbers of *copies* of each of us, and infinite small and large variations on each of us, and infinite worlds, doesn't mean there is karma or justice for good and evil.
Per Tegmark (and I think Huemer if I understand your post), multiple copies exist. None of them are "reincarnations" of previously existing people - each is an independent version arising independently via local mechanisms.