If you're interested in videos about big numbers like Tree 3, I would recommend https://youtu.be/kmAc1nDizu0. It's about the Busy Beaver function, which grows faster than any other function that can be defined in a finite number of steps.
From Olum's abstract it seems that he is just appealing to the doomsday argument. Well, yes, SSA is stupid in this case and SIA just so happens to produce a correct answer. This, however, is not a sufficient argument in favor of SIA in general.
The actual common sense solution to domsday argument is that you are not randomly sampled among all people that have ever existed, nor all the possible people. Your existence is the result of specific causal process: your parents having sex, about nine months of pregnancy and then your mother giving birth. This process couldn't have created any other person but you or, arguably, your twin.
> as does Carlsmith.
This I've read in full several years ago and since that I can't stop wondering how any person can treat either SIA or SSA as candidates for being true. It probably was the greatest inspiration for the anthropic sequence that I'm working on now.
Carlsmith explains in details how both SSA and SIA lead to obviously stupid conclusions, implying that people have psychic powers to blackmail reality, and then sides with SIA anyway. And the core reason why he is ready to bite all the SIA's bullets is that they are inevitable conclusion of thirdism in Sleeping Beauty. He mentions this point several times but apparently doesn't understand that it's a reason to re-investigate his commitment to thirdism.
> A quick route from mathematics to metaphysical necessity
Ha. I see some people are still trying to apply the sleight of hand from Critique of Pure Reason. I'll let the readers find the exact fallacy themselves and simply present a general proof:
Either Alexander Pruss's line of reasoning is logically coherent or it's not. Let's assume that it is. Then it's a logical proof that Peano Axioms are consistent. But then, according to Godel, Peono Axioms are not consistent - thus a contradiction. Q. E. D. This line of reasoning is logically incoherent.
//From Olum's abstract it seems that he is just appealing to the doomsday argument. Well, yes, SSA is stupid in this case and SIA just so happens to produce a correct answer. This, however, is not a sufficient argument in favor of SIA in general.//
//This I've read in full several years ago and since that I can't stop wondering how any person can treat either SIA or SSA as candidates for being true. It probably was the greatest inspiration for the anthropic sequence that I'm working on now.//
Most of the results of Carlsmith follow from every view other than SIA.
> In fact, as I show elsewhere, only SIA avoids weird results in Doomsday
I've just explained how to "avoid weird result in Doomsday" without SIA. Unless there is a mistake in my reasoning that you can point to, your claim that only SIA avoids Doomsday is, therefore, wrong.
But sure, I'll read the whole paper, even though I don't expect anything interesting from it. I'll let you know if it surprised me.
> Most of the results of Carlsmith follow from every view other than SIA.
Not other than SIA. SIA as well. He is very explicit about it
And yes, most of the theories on any specific question are wrong. This is a completely not surprising result. There is only one true theory of anthropics and I'd rather search for it, discarding every other as soon as I find them implying wrong things, instead of trying to rationalize why having psychic powers might be okay.
//I've just explained how to "avoid weird result in Doomsday" without SIA. Unless there is a mistake in my reasoning that you can point to, your claim that only SIA avoids Doomsday is, therefore, wrong.//
You haven't addressed my modified doomsday case or argument for why any solution will straightforwardly neglect Bayes theorem.
//Not other than SIA. SIA as well. He is very explicit about it//
He thinks, like I do, that this result of SIA is not weird. Contrary to your indication, you have no causal power or ability to influence the future in non-kosher ways. Instead, your credence in past events is affected by your existence. But that's perfectly ordinary. There isn't a single counterexample to SIA that I find remotely compelling.
> argument for why any solution will straightforwardly neglect Bayes theorem.
As you point out yourself, SIA agrees with SSA about Domsday inference. It just adds an extra reasoning counterbalancing it. And it's true that if you accept 1) doomsday inference and don't accept 2) some counterbalancing consideration like in SIA - then you should agree with Doomsday Argument.
But a completely obvious third way is to deny both 1) and 2), which is exactly what I'm doing in the commons sense solution to Doomsday argument. Instead of accepting silly premise and then putting a band aid onto it, you can just deny the premise in the first place.
I'm not randomly sampled among all the people who existed or will ever exist. There are correlations and causality between people existences, previous and next ones do not happen independently. I couldn't possibly be born in year 30000, because my parents would have already been long dead at that moment. Nor could I've been born in middle ages because my parents were not alive yet. The causal process that led to my existence was quite specific, not allowing me such "reference classes".
> You haven't addressed my modified doomsday case
The one with either a lot of people spontaneously coming to existence in a room in a sequence, or just one person? Here I don't understand the specifics of causal process that led to my existence and therefore it's not impossible that the doomsday argument analogue would be correct. For example if I was meant to always be created at a random place among all the created people, then finding myself at place one is a strong evidence in favor of outcome with only one person. I can't just dismiss such possibility a priori. But SIA does exactly that. Out of nowhere, it makes an assumption about the causal process that led to my creation - that it's necessary a random sample among all possible people - and, therefore, fails dramatically in situations where this assumption is wrong.
//But a completely obvious third way is to deny both 1) and 2), which is exactly what I'm doing in the commons sense solution to Doomsday argument//
Conditional on you existing, the odds you'd be very early are low. That's why the doomsday inference is trivial. The way to see this is in the case I gave: if you don't know your birth rank, you should think in a universe with many people it's unlikely that you're early. Then, if you find out that you're early, because that's predicted on the hypothesis that there are few people and not on the other, you get the doomsday inference--and same with the Adam and Eve inference and all the other ones.
//I couldn't possibly be born in year 30000, because my parents would have already been long dead at that moment.//
But you're conflating metaphysical possibility with epistemic possibility. It's true that--if origin essentialism is true--you couldn't have been born any time other than which year you were. But the epistemic probability of you being born in an early year conditional on the small universe hypothesis is 1, while it's lower if the universe is big. This is like in response to getting a bunch of royal flushes in poker, having your explanation be "Everything that happens is necessary, so it's necessary that I got those royal flushes."
//I'm not randomly sampled among all the people who existed or will ever exist. There are correlations and causality between people existences, previous and next ones do not happen independently. //
When assigning priors you don't look at the evidence of the world. Obviously you update in favor of thinking that you being some possible people with your evidence is more likely than you being some other possible person with your evidence--but that's based on non-anthropic evidence.
> Conditional on you existing, the odds you'd be very early are low. That's why the doomsday inference is trivial.
Only if we accept the premise that my existence is randomly sampled among all people who are meant to exist. As if God is selecting a soul from a limited stock to instantiate in the world every time a new human is born. I don't see any reason to accept this premise considering our modern state of knowledge about the way universe works.
> The way to see this is in the case I gave: if you don't know your birth rank, you should think in a universe with many people it's unlikely that you're early.
I think you confuse "not knowing your birth rank" and "having to reason as if your birth rank was assigned at random". Not unlike Sleeping Beauty, where people confuse "not knowing the exact awakening the Beauty is experiencing" with "Beauty should reason as if she is experiencing random awakening". I'll make sure to write in details about it after I'm fully done with Sleeping Beauty.
> But you're conflating metaphysical possibility with epistemic possibility.
"Metaphysical possibility", is supposed to be approximated by epistemic possibility as with any map-territory relation.
Let's for simplicity sake assume that we live in a deterministic universe and, therefore all possibilities are epistemic. Whether I get a royal flush in such universe is completely determined by a specific causal process. So, in what sense is getting a royal flush in a poker game has probability 0.000154%? The answer is, that according to a mathematical model which treats every card placement as *randomly sampled* the probability is 0.000154%. And so the question is, whether or not I can apply this mathematical model to the problem at hand, whether or not the causal process can be approximated as random sampling of cards. And the reason why we think that we can is because of the shuffling mechanics that is supposed to "randomize" card placement - put them into such positions, so that no player could systematically predict the next card better than chance.
It's easy to see that without shuffling, the mathematical model is not applicable anymore. If the same cards a dealt again and again the probability to get royal flush may be as high as 1. We do not get to simply assume that cards are inherently random. That getting a specific card has a fixed prior in any circumstances. We need to make sure that the shuffling happens.
The same logic applies to anthropics. And as there is no reason to assume the "shuffling mechanics" throughout time, there is no reason to accept the prior of random sampling.
> When assigning priors you don't look at the evidence of the world.
Technically true. But in practice, we hold multiple theories in mind, which may have different priors. And we can notice that some of these theories produce counterintuitive results and discard them, deciding that their priors are not correct.
That's exactly what is going on. I'm ready to entertain the idea that I should use equiprobable prior for my existence as any person through time. Then I see that it leads to the ability to predict the future which seems absurd. Now there are two alternatives. I can either decide that this prior is wrong or that the prior is right but I didn't update on all the available evidence, for instance maybe I'm supposed to update in favor of more people existing in the universe based on my existence. I'm ready to entertain the idea of such update and see where it leads. Oh well, apparently it means that you can blackmail reality into winning a lottery.
This seems even more absurd. So i decide that the prior is wrong.
Now, if you, for some reason, think that blackmailing reality into winning a lottery is fine - then it's less clear cut for you. You still don't have sufficient reasons to discard the prior. But neither you get to say that this prior and the update are the only conceivable possibility. The possibility that the initial prior is wrong hasn't gone anywhere.
Pruss' short argument isn't an attempted proof of PA's consistency, and moreover the incompleteness theorems don't say that no such proof can exist (they just say they'll require sufficiently different/strong axioms than PA, if PA is consistent).
Pruss uses logic (a subset of PA) to reason about PA's consistency, arriving to a conclusion that PA is necessary consistent. This means that either PA is definetely inconsistent or Pruss's reasoning is logically incoherent. In any case his claim about metaphysics is unsound.
Lots of mistakes there. First, Pruss' conclusion is not "PA is consistent," it's "I already believe PA is consistent, and if that's the case it's metaphysically necessarily consistent despite lacking 'logical necessity'." Mere belief in the consistency of PA is not remotely something Gödel's theorems rule out (in fact, practically everyone believes it's consistent), nor is reasoning from its consistency. Second, there are well known consistency proofs of PA, like Gerhard Gentzen's; they may or may not be satisfactory since the formal systems they employ are vulnerable to their own Gödel sentences, but they're certainly not pathological. Finally, logic is not a subset of PA.
> Pruss' conclusion is not "PA is consistent," it's "I already believe PA is consistent, and if that's the case it's metaphysically necessarily consistent despite lacking 'logical necessity'."
No, not just If X then Y. He makes a stronger statement:
X - because otherwise Z - therefore Y.
And if we investigate the weaker version:
"I don't know whether PA is consistent or not, but if it is then it's necessary consistent"
The problem with the statement becomes very clear. If PA is necessary consistent how comes you do not know whether it's consistent or not? The whole point of necessity is that there is no other option. So an obvious contradiction.
Of course we can define new category "methaphysical necessity" meaning "not really necessary" but I'm not sure what's the point to do that.
>Of course it is. Or are you under the impression that PA can't deal with zeros and ones?
I don't know what this means. It's true that you can encode first-order statements in PA, but not all logic is first-order logic.
The rest of your comment seems to be suggesting that we can't positively affirm the statement "PA is consistent" for Gödelian reasons. I don't know what to tell you, that's just false, and is contrary to what nearly every logician believes. You can think it's consistent based on the consistency of some other formal system you believe in, you can think your intuitions about metaphysical possibility (which Gödel's theorems are completely silent on/irrelevant to) present philosophical evidence for PA being consistent, you can be a subjective Bayesian and think it's OK to just give it a high prior, etc.
> The rest of your comment seems to be suggesting that we can't positively affirm the statement "PA is consistent" for Gödelian reasons.
You are missing the point.
>It's true that you can encode first-order statements in PA
Glad that we agree on it. Now the question is: Does Pruss use second order logic in his argument or just first order logic? Because if it's only first order logic then my initial claim that he is using PA to prove PA consistency is true, with all that follows.
If you're interested in videos about big numbers like Tree 3, I would recommend https://youtu.be/kmAc1nDizu0. It's about the Busy Beaver function, which grows faster than any other function that can be defined in a finite number of steps.
Hinduism link is to your response to Neil, not Amos's article
Fixed thanks.
> Olum has a good piece arguing for SIA
From Olum's abstract it seems that he is just appealing to the doomsday argument. Well, yes, SSA is stupid in this case and SIA just so happens to produce a correct answer. This, however, is not a sufficient argument in favor of SIA in general.
The actual common sense solution to domsday argument is that you are not randomly sampled among all people that have ever existed, nor all the possible people. Your existence is the result of specific causal process: your parents having sex, about nine months of pregnancy and then your mother giving birth. This process couldn't have created any other person but you or, arguably, your twin.
> as does Carlsmith.
This I've read in full several years ago and since that I can't stop wondering how any person can treat either SIA or SSA as candidates for being true. It probably was the greatest inspiration for the anthropic sequence that I'm working on now.
Carlsmith explains in details how both SSA and SIA lead to obviously stupid conclusions, implying that people have psychic powers to blackmail reality, and then sides with SIA anyway. And the core reason why he is ready to bite all the SIA's bullets is that they are inevitable conclusion of thirdism in Sleeping Beauty. He mentions this point several times but apparently doesn't understand that it's a reason to re-investigate his commitment to thirdism.
> Adam Elga is right about sleeping beauty
No he is not. https://benthams.substack.com/p/elga-proved-13/comment/51980818?utm_source=activity_item
> A quick route from mathematics to metaphysical necessity
Ha. I see some people are still trying to apply the sleight of hand from Critique of Pure Reason. I'll let the readers find the exact fallacy themselves and simply present a general proof:
Either Alexander Pruss's line of reasoning is logically coherent or it's not. Let's assume that it is. Then it's a logical proof that Peano Axioms are consistent. But then, according to Godel, Peono Axioms are not consistent - thus a contradiction. Q. E. D. This line of reasoning is logically incoherent.
//From Olum's abstract it seems that he is just appealing to the doomsday argument. Well, yes, SSA is stupid in this case and SIA just so happens to produce a correct answer. This, however, is not a sufficient argument in favor of SIA in general.//
Well, maybe you should read beyond the abstract :). In fact, as I show elsewhere, only SIA avoids weird results in Doomsday https://benthams.substack.com/p/alternatives-to-sia-are-doomed
//This I've read in full several years ago and since that I can't stop wondering how any person can treat either SIA or SSA as candidates for being true. It probably was the greatest inspiration for the anthropic sequence that I'm working on now.//
Most of the results of Carlsmith follow from every view other than SIA.
> In fact, as I show elsewhere, only SIA avoids weird results in Doomsday
I've just explained how to "avoid weird result in Doomsday" without SIA. Unless there is a mistake in my reasoning that you can point to, your claim that only SIA avoids Doomsday is, therefore, wrong.
But sure, I'll read the whole paper, even though I don't expect anything interesting from it. I'll let you know if it surprised me.
> Most of the results of Carlsmith follow from every view other than SIA.
Not other than SIA. SIA as well. He is very explicit about it
https://joecarlsmith.com/2021/09/30/sia-ssa-part-2-telekinesis-reference-classes-and-other-scandals#vi-does-sia-imply-telekinesis-too
https://joecarlsmith.com/2021/09/30/sia-ssa-part-4-in-defense-of-the-presumptuous-philosopher
And yes, most of the theories on any specific question are wrong. This is a completely not surprising result. There is only one true theory of anthropics and I'd rather search for it, discarding every other as soon as I find them implying wrong things, instead of trying to rationalize why having psychic powers might be okay.
//I've just explained how to "avoid weird result in Doomsday" without SIA. Unless there is a mistake in my reasoning that you can point to, your claim that only SIA avoids Doomsday is, therefore, wrong.//
You haven't addressed my modified doomsday case or argument for why any solution will straightforwardly neglect Bayes theorem.
//Not other than SIA. SIA as well. He is very explicit about it//
He thinks, like I do, that this result of SIA is not weird. Contrary to your indication, you have no causal power or ability to influence the future in non-kosher ways. Instead, your credence in past events is affected by your existence. But that's perfectly ordinary. There isn't a single counterexample to SIA that I find remotely compelling.
> argument for why any solution will straightforwardly neglect Bayes theorem.
As you point out yourself, SIA agrees with SSA about Domsday inference. It just adds an extra reasoning counterbalancing it. And it's true that if you accept 1) doomsday inference and don't accept 2) some counterbalancing consideration like in SIA - then you should agree with Doomsday Argument.
But a completely obvious third way is to deny both 1) and 2), which is exactly what I'm doing in the commons sense solution to Doomsday argument. Instead of accepting silly premise and then putting a band aid onto it, you can just deny the premise in the first place.
I'm not randomly sampled among all the people who existed or will ever exist. There are correlations and causality between people existences, previous and next ones do not happen independently. I couldn't possibly be born in year 30000, because my parents would have already been long dead at that moment. Nor could I've been born in middle ages because my parents were not alive yet. The causal process that led to my existence was quite specific, not allowing me such "reference classes".
> You haven't addressed my modified doomsday case
The one with either a lot of people spontaneously coming to existence in a room in a sequence, or just one person? Here I don't understand the specifics of causal process that led to my existence and therefore it's not impossible that the doomsday argument analogue would be correct. For example if I was meant to always be created at a random place among all the created people, then finding myself at place one is a strong evidence in favor of outcome with only one person. I can't just dismiss such possibility a priori. But SIA does exactly that. Out of nowhere, it makes an assumption about the causal process that led to my creation - that it's necessary a random sample among all possible people - and, therefore, fails dramatically in situations where this assumption is wrong.
//But a completely obvious third way is to deny both 1) and 2), which is exactly what I'm doing in the commons sense solution to Doomsday argument//
Conditional on you existing, the odds you'd be very early are low. That's why the doomsday inference is trivial. The way to see this is in the case I gave: if you don't know your birth rank, you should think in a universe with many people it's unlikely that you're early. Then, if you find out that you're early, because that's predicted on the hypothesis that there are few people and not on the other, you get the doomsday inference--and same with the Adam and Eve inference and all the other ones.
//I couldn't possibly be born in year 30000, because my parents would have already been long dead at that moment.//
But you're conflating metaphysical possibility with epistemic possibility. It's true that--if origin essentialism is true--you couldn't have been born any time other than which year you were. But the epistemic probability of you being born in an early year conditional on the small universe hypothesis is 1, while it's lower if the universe is big. This is like in response to getting a bunch of royal flushes in poker, having your explanation be "Everything that happens is necessary, so it's necessary that I got those royal flushes."
//I'm not randomly sampled among all the people who existed or will ever exist. There are correlations and causality between people existences, previous and next ones do not happen independently. //
When assigning priors you don't look at the evidence of the world. Obviously you update in favor of thinking that you being some possible people with your evidence is more likely than you being some other possible person with your evidence--but that's based on non-anthropic evidence.
> Conditional on you existing, the odds you'd be very early are low. That's why the doomsday inference is trivial.
Only if we accept the premise that my existence is randomly sampled among all people who are meant to exist. As if God is selecting a soul from a limited stock to instantiate in the world every time a new human is born. I don't see any reason to accept this premise considering our modern state of knowledge about the way universe works.
> The way to see this is in the case I gave: if you don't know your birth rank, you should think in a universe with many people it's unlikely that you're early.
I think you confuse "not knowing your birth rank" and "having to reason as if your birth rank was assigned at random". Not unlike Sleeping Beauty, where people confuse "not knowing the exact awakening the Beauty is experiencing" with "Beauty should reason as if she is experiencing random awakening". I'll make sure to write in details about it after I'm fully done with Sleeping Beauty.
> But you're conflating metaphysical possibility with epistemic possibility.
"Metaphysical possibility", is supposed to be approximated by epistemic possibility as with any map-territory relation.
Let's for simplicity sake assume that we live in a deterministic universe and, therefore all possibilities are epistemic. Whether I get a royal flush in such universe is completely determined by a specific causal process. So, in what sense is getting a royal flush in a poker game has probability 0.000154%? The answer is, that according to a mathematical model which treats every card placement as *randomly sampled* the probability is 0.000154%. And so the question is, whether or not I can apply this mathematical model to the problem at hand, whether or not the causal process can be approximated as random sampling of cards. And the reason why we think that we can is because of the shuffling mechanics that is supposed to "randomize" card placement - put them into such positions, so that no player could systematically predict the next card better than chance.
It's easy to see that without shuffling, the mathematical model is not applicable anymore. If the same cards a dealt again and again the probability to get royal flush may be as high as 1. We do not get to simply assume that cards are inherently random. That getting a specific card has a fixed prior in any circumstances. We need to make sure that the shuffling happens.
The same logic applies to anthropics. And as there is no reason to assume the "shuffling mechanics" throughout time, there is no reason to accept the prior of random sampling.
> When assigning priors you don't look at the evidence of the world.
Technically true. But in practice, we hold multiple theories in mind, which may have different priors. And we can notice that some of these theories produce counterintuitive results and discard them, deciding that their priors are not correct.
That's exactly what is going on. I'm ready to entertain the idea that I should use equiprobable prior for my existence as any person through time. Then I see that it leads to the ability to predict the future which seems absurd. Now there are two alternatives. I can either decide that this prior is wrong or that the prior is right but I didn't update on all the available evidence, for instance maybe I'm supposed to update in favor of more people existing in the universe based on my existence. I'm ready to entertain the idea of such update and see where it leads. Oh well, apparently it means that you can blackmail reality into winning a lottery.
https://www.lesswrong.com/posts/y7jZ9BLEeuNTzgAE5/the-anthropic-trilemma
This seems even more absurd. So i decide that the prior is wrong.
Now, if you, for some reason, think that blackmailing reality into winning a lottery is fine - then it's less clear cut for you. You still don't have sufficient reasons to discard the prior. But neither you get to say that this prior and the update are the only conceivable possibility. The possibility that the initial prior is wrong hasn't gone anywhere.
Pruss' short argument isn't an attempted proof of PA's consistency, and moreover the incompleteness theorems don't say that no such proof can exist (they just say they'll require sufficiently different/strong axioms than PA, if PA is consistent).
Pruss uses logic (a subset of PA) to reason about PA's consistency, arriving to a conclusion that PA is necessary consistent. This means that either PA is definetely inconsistent or Pruss's reasoning is logically incoherent. In any case his claim about metaphysics is unsound.
Lots of mistakes there. First, Pruss' conclusion is not "PA is consistent," it's "I already believe PA is consistent, and if that's the case it's metaphysically necessarily consistent despite lacking 'logical necessity'." Mere belief in the consistency of PA is not remotely something Gödel's theorems rule out (in fact, practically everyone believes it's consistent), nor is reasoning from its consistency. Second, there are well known consistency proofs of PA, like Gerhard Gentzen's; they may or may not be satisfactory since the formal systems they employ are vulnerable to their own Gödel sentences, but they're certainly not pathological. Finally, logic is not a subset of PA.
> logic is not a subset of PA.
Of course it is. Or are you under the impression that PA can't deal with zeros and ones?
https://en.wikipedia.org/wiki/Boolean_algebra
> Pruss' conclusion is not "PA is consistent," it's "I already believe PA is consistent, and if that's the case it's metaphysically necessarily consistent despite lacking 'logical necessity'."
No, not just If X then Y. He makes a stronger statement:
X - because otherwise Z - therefore Y.
And if we investigate the weaker version:
"I don't know whether PA is consistent or not, but if it is then it's necessary consistent"
The problem with the statement becomes very clear. If PA is necessary consistent how comes you do not know whether it's consistent or not? The whole point of necessity is that there is no other option. So an obvious contradiction.
Of course we can define new category "methaphysical necessity" meaning "not really necessary" but I'm not sure what's the point to do that.
>Of course it is. Or are you under the impression that PA can't deal with zeros and ones?
I don't know what this means. It's true that you can encode first-order statements in PA, but not all logic is first-order logic.
The rest of your comment seems to be suggesting that we can't positively affirm the statement "PA is consistent" for Gödelian reasons. I don't know what to tell you, that's just false, and is contrary to what nearly every logician believes. You can think it's consistent based on the consistency of some other formal system you believe in, you can think your intuitions about metaphysical possibility (which Gödel's theorems are completely silent on/irrelevant to) present philosophical evidence for PA being consistent, you can be a subjective Bayesian and think it's OK to just give it a high prior, etc.
> The rest of your comment seems to be suggesting that we can't positively affirm the statement "PA is consistent" for Gödelian reasons.
You are missing the point.
>It's true that you can encode first-order statements in PA
Glad that we agree on it. Now the question is: Does Pruss use second order logic in his argument or just first order logic? Because if it's only first order logic then my initial claim that he is using PA to prove PA consistency is true, with all that follows.