>TT worries next that perfection isn’t simple. It’s just one word in English, but a single word can express a complicated concept. But perfection just means unlimited goodness, and goodness is simple and fundamental, so perfection is simple. The fact that something can be described easily in English doesn’t mean it’s simple, but the fact that it has an unlimited amount of some fundamental property does.

Based on the moral realism post you link to in this paragraph, this is again confusing moral goodness with the sort of "goodness" - i.e., what some philosophers call "greatness" - that involves knowledge and power. Maximal quantities of the former might be simple (though I doubt it, since moral realism is in fact false), but maximal quantities of latter definitely aren't, and it's what you need to get most of your theistic arguments off the ground compared to competing hypotheses.

The second isn't simple because there's arguably no unique maximal set of abilities/known facts, and in fact probably any such set is not recursively enumerable. So a property (maximal greatness, rather than maximal moral goodness) all of whose realizations are monstrously, uncomputably complex seems pretty darned complicated. And it's *this* property you need in most theistic abductive arguments, because all of them crucially rely on God having lots and lots of power rather than just having the right moral inclinations.

I'm not sure I understand how that's responsive to my comment. Whether they're better or not (and again, that word is ambiguous between morality/axiology/"greatness"), the "maximal greatness" conception of God is very complicated (thus low-prior), and there is furthermore no non-complicated view of God on which he clearly has enough power to shoulder the burdens that theistic abductive arguments place on his abilities in order to be sound.

That doesn't help you, since there's not a unique maximal collection of axiologically good attributes for exactly the same reason, and again any such collection will be uncomputable.

Why doesn't your view collapse to modal realism? Seems like if an unboundedly infinite number of people exiost, one would expect an unboundedly infinite number of people to exist who have had the exact same experiences as you but for whom induction suddenly implodes.

To answer the question properly you need to show why the implication from SIA to modal realism is wrong.

I suppose, you can say that SIA is confident in the existence of the worlds with other people but is indifferent to worlds where no people exist while according to modal realism all worlds (even unpopulated ones) exist. But this doesn't really help with the induction, does it?

>But even if two actions both involve creating the same cardinality of people, if one of them involves creating a proper subset of the people of the other, then the other is better.

Haven't made my way through the whole post but it's littered with nonsense statements like this. The odd numbers are a proper subset of the integers, but there's no coherent sense in which the infinite set of odd numbers is "more odd" than the infinite set of integers. Their cardinality is the same, so any multiplicative operation performed on both sets will be equivalent. That's just what cardinality is and how it's used to construct measures of things. I.e the measure of oddness of the odd numbers is infinity * 1 = infinity, and the measure of oddness of the integers is infinity * .5 = infinity.

Suppose that God has created aleph null people. Then he could create aleph null more people. My claim is that even though it's the same cardinality of people, he has a moral reason to create the other, because though they're the same cardinality, there are some people who now exist, who wouldn't have otherwise existed.

I instantiate all of the odd numbers. Then I instantiate all of the integers. Did the second instantiation produce more odd numbers overall than if only the first instantiation happened?

If it did, then the odd numbers in the set of integers must have a larger cardinality than the odd numbers in the set of odd numbers, because the cardinality of infinite sets is determined via bijection. If we can't biject each member of set A with each member of set B, then one of A or B must have a larger cardinality than the other.

If it didn't, then there's not more odd numbers in existence because the cardinalities are equivalent. Every odd number is already instantiated after the first instantiation.

I think your intuitions about infinities are flat out wrong and probably the biggest hole in the argument. I don't see how you can conclude that googolplex/infinity is actually different from 1/infinity. If you're going to claim that then I think you need a lot more explanation.

Similarly, your argument hinges on the claim that even though the number of possible people is too large to be a set, it's still possible for God to create "all" of them. This seems pretty incoherent to me. And this isn't just a random throwaway statement, you insist that there is a point where God could not possibly create more. I'm no mathematician so maybe I'm wrong, but I would really like to see what a mathematician would say about this specifically.

Agreed. I think Majesty of Reason points out similar flaws in William Lane Craig's Hilbert's Hotel arguments against infinity. If I recall correctly, WLC thinks that 1) Hilbert's Hotel instantiates an infinite number of occupied rooms, but 2) you can create more occupied rooms by kicking a tenant out to replace with a new tenant, and propagating this chain onwards to each of the infinite set of rooms in Hilbert's Hotel. And the putative contradiction is that we've added 1 more occupied room to the collection, which was previously infinite and so must have had all occupied rooms, therefore actual infinites can't be instantiated. I could be on crack, but the error is that aleph null isn't a regular cardinal, meaning it's either meaningless to "add 1" to the infinite collection, or if it's meaningful adding 1 doesn't alter the cardinality of the set (because by stipulation that's not how infinity is defined in set theory).

Sorry if I'm missing something in your argument here, but your reliance on unrestricted SIA and perfect being theism feels... far too speculative. USIA seems to predict that I would know of existence of much more being that I currently do, that our universe would be full of life, which I don't observe. Perfect being theism makes even worse predictions. I can't imagine a perfect being creating a world of suffering like ours.

I know a part of your argument is that we should believe those things with probability one. But if such an argument contradicts everything I know about this world, I don't throw out my empirical observations, even though I'm less than absolutely sure of them. I suspect the argument is wrong, even if I don't know how exactly. There prior probability of the argument being somehow wrong, after all, is pretty high.

The argument doesn't rely on perfect being theism--it's an argument for perfect being theism. It also doesn't rely on USIA. USIA butresses one very small point but is largely inessential.

USIA predicts that all possible people would exist but you don't know if they do. It doesn't predict anything about how dense the distribution of them would be.

> Objections to SIA (most of these he claims are not objections to SIA, but if they were right they would imply that one shouldn’t reason in accordance with SIA).

> Reasons that theism wouldn’t predict a huge number of people being created.

> But this means that even if most of what he says is probably right, as long as you have some credence that God would create either all possible people or some huge number, theism is majorly supported on anthropic grounds.

I don't see how this makes sense. If TT arguments are correct, then you shouldn't have high credence that God would create all possible people and should think that SIA is a wrong approach to anthropics. Either of this points would be enough to refute the claim that theism is supported on anthropic grounds. Were you trying to say that your prior in favor of SIA and its implying theism is so high that no argument can persuade you otherwise?

> TT’s argument, if successful, would totally jeopardize anthropic reasoning. If SIA is correct but impossible to do if there are infinite possible people, and there are infinite possible people, that means all anthropic probabilities end up being undefined and anthropic reasoning becomes impossible. Clearly, this is wrong!

It would jeopardize SIA in particular, not every possible approach to anthropic reasoning. And considering that SIA implies that you can blackmail reality into winning a lottery by creating copies of yourself, can be born with arbitrary high probability if your parents are infertile at the moment of your conception, and, apparently, also implies the existence of God for the mere fact that a particular human exists, it's very much not clear that discarding SIA is wrong.

The fact that SIA simultaneously implies that infinite people existing is the most probable case and breaks in this case, in particular, is a huge problem. You can't dismiss it by saying that many other theories also break in infinity cases - these theories can still be true if infinities are impossible. But SIA can't. Either it's wrong because there actually are infinite number of people and then all of SIA's math stop making sense or it's wrong because there are not infinite number of people, while SIA is very confident that there are.

> If TT arguments are correct, then you shouldn't have high credence that God would create all possible people and should think that SIA is a wrong approach to anthropics.

I agree with this. The original motivation for SIA is supposed to be it fitting our intuitions correctly on various firing squad-like (and other) thought experiments. But if all possible people exist with high certainty and SIA is correct, then we should in fact reject our intuitions about all of these cases, realistically speaking. There's an infinite number of people in your epistemic situation who miraculously survive the firing squad by freak accident, and an infinite number who survive because the firing squad missed on purpose. Thus, it's plausible SIA recommends indifference if you discover that the firing squad unexpectedly missed. (Now, there are ways to make the SIA still work with infinite cardinalities of possible observers who have your evidence in certain cases where expected values - and conditional expected values - are still finite, but it's hard to see how that would apply here.)

Higher cardinalities of infinity are larger in the way relevant to probability. There are more reals than naturals because you pair all of the naturals with the reals but not all the reals with the naturals.

My point about Beth 2 was that I know that there is a procedure for a bijection even if I don't know off the topic of my head what it is. It's generally not intuitively obvious what the bijection between two things would look like.

I didn't give no reason to think there's such a bijection--I cited the proof by Lewis, where possible worlds are a function over the Beth 1 possible points, and thus the cardinality must be at least the powerset of Beth 1.

My view is that there can't be a set of all possible people but if there is such a set it must have at least Beth 2 people. The claim about there being unsetly many people is a bit controversial--the one about there being Beth 2 people at least is less controversial, so I was suggesting that the argument works even if we grant it.

I'm not sure what the problem is supposed to be with writing articles quickly. Of course, if the arguments are bad, then that's a problem, but they're not--you've just misstated what the arguments I made were and then gotten mad.

//what is that way? How do you take probabilities over infinite sets?//

I don't have a foolproof way for doing it in all cases but there are certain cases where the judgments are obvious.

// How do you know what there is procedure for a bijection if you don't know what the bijection is?//

Because we have a proof of the lower bound of the cardinality.

I've never claimed to be an expert on set theory though I do know what a bijection is and have at least passing knowledge. That's why before writing about it--and the bit about infinites sets and unsetly many--I asked two of my friends who are very informed about it.

Not interested in defending the claim that I'm a good philosopher to you, but worth pointing out that various professional philosophers like Mike Huemer and Richard Chappell have said good things about my philosophical ability, with both going to far as to recommend my blog. I have no doubt I get a decent amount wrong--my bar for posting an article is it being something interesting I've thought about not my being sure about it--but I think I didn't make any of the errors you accuse me of.

Well I gave a case where the judgment is obvious. Your credence in Graham's number rooms in Hilbert's hotel being painted red if you're in a red room should be Graham's number times higher than your credence in just one room being painted red. My view is that in lots of probabilistic reasoning about infinites your credence should be vague. There isn't agreement about how to do probabilistic reasoning in infinite cases.

"How do you take probabilities over infinite sets?"

It's fairly well-understand you can take probabilities over such infinities. For example, with non-uniform probability distributions. In case of continuous normalisable probability distribution over an infinite interval, you simply integrate from 0 to infinity then derive whatever property you're interested in. Huemer gives an example of taking a probability over an infinity to derive more complex theories tend to have a lower probability than simpler theories:

> if we suppose that degree of complexity is a continuous variable

rather than discrete, the probability density function over the possible degrees of

complexity should integrate to 1 over the interval from 0 to 4, which requires that

the probability density approach 0 as degree of complexity increases without bound.

> For any set of possibilities that is ordered and unbounded in the upward direction,

any normalizable probability distribution over the possibilities must generally

assign decreasing probabilities to later members of the set.

Hard to believe we actually had to educate you on this. Especially given you posture as if you're knowledgeable.

Also noticed you dodged my question. Why posture about "intellectual virtue" if you lack honesty to admit error? Simple yes/no question: Do you admit your claim is false?

"there is no such thing as "all truths" on pain of contradiction."

Oh man. This that "Truth" Teller guy? Guy who dropped the ball claiming "there is no such thing as "all truths" on pain of contradiction." Which Matthew corrected:

> This is not what the Grim proof says—it says there’s no set of all truths but not that there is not such thing as all truths.

Good one, Einstein. Can't live that one down. Just brutal. 🤦

Maybe you'll restore faith in humanity coming clean admitting error. Do you admit your claim is false?

"there is no such thing as "all truths" on pain of contradiction."

edited Apr 25>TT worries next that perfection isn’t simple. It’s just one word in English, but a single word can express a complicated concept. But perfection just means unlimited goodness, and goodness is simple and fundamental, so perfection is simple. The fact that something can be described easily in English doesn’t mean it’s simple, but the fact that it has an unlimited amount of some fundamental property does.

Based on the moral realism post you link to in this paragraph, this is again confusing moral goodness with the sort of "goodness" - i.e., what some philosophers call "greatness" - that involves knowledge and power. Maximal quantities of the former might be simple (though I doubt it, since moral realism is in fact false), but maximal quantities of latter definitely aren't, and it's what you need to get most of your theistic arguments off the ground compared to competing hypotheses.

I think god has a maximal degree of the first kind of goodness—I’m less sure if the second is joint carving

The second isn't simple because there's arguably no unique maximal set of abilities/known facts, and in fact probably any such set is not recursively enumerable. So a property (maximal greatness, rather than maximal moral goodness) all of whose realizations are monstrously, uncomputably complex seems pretty darned complicated. And it's *this* property you need in most theistic abductive arguments, because all of them crucially rely on God having lots and lots of power rather than just having the right moral inclinations.

But things are better if perfect beings have more power

I'm not sure I understand how that's responsive to my comment. Whether they're better or not (and again, that word is ambiguous between morality/axiology/"greatness"), the "maximal greatness" conception of God is very complicated (thus low-prior), and there is furthermore no non-complicated view of God on which he clearly has enough power to shoulder the burdens that theistic abductive arguments place on his abilities in order to be sound.

Oh my claim is that God is what you get when a being has maximal axiological goodness.

That doesn't help you, since there's not a unique maximal collection of axiologically good attributes for exactly the same reason, and again any such collection will be uncomputable.

Why doesn't your view collapse to modal realism? Seems like if an unboundedly infinite number of people exiost, one would expect an unboundedly infinite number of people to exist who have had the exact same experiences as you but for whom induction suddenly implodes.

Modal realism undermines induction.

So why doesn't your view collapse to modal realism and, therefore undermine induction?

edited Apr 27Cuz it doesn't say every possible world exists. More concisely, because it's not modal realism.

To answer the question properly you need to show why the implication from SIA to modal realism is wrong.

I suppose, you can say that SIA is confident in the existence of the worlds with other people but is indifferent to worlds where no people exist while according to modal realism all worlds (even unpopulated ones) exist. But this doesn't really help with the induction, does it?

>But even if two actions both involve creating the same cardinality of people, if one of them involves creating a proper subset of the people of the other, then the other is better.

Haven't made my way through the whole post but it's littered with nonsense statements like this. The odd numbers are a proper subset of the integers, but there's no coherent sense in which the infinite set of odd numbers is "more odd" than the infinite set of integers. Their cardinality is the same, so any multiplicative operation performed on both sets will be equivalent. That's just what cardinality is and how it's used to construct measures of things. I.e the measure of oddness of the odd numbers is infinity * 1 = infinity, and the measure of oddness of the integers is infinity * .5 = infinity.

Suppose that God has created aleph null people. Then he could create aleph null more people. My claim is that even though it's the same cardinality of people, he has a moral reason to create the other, because though they're the same cardinality, there are some people who now exist, who wouldn't have otherwise existed.

I instantiate all of the odd numbers. Then I instantiate all of the integers. Did the second instantiation produce more odd numbers overall than if only the first instantiation happened?

If it did, then the odd numbers in the set of integers must have a larger cardinality than the odd numbers in the set of odd numbers, because the cardinality of infinite sets is determined via bijection. If we can't biject each member of set A with each member of set B, then one of A or B must have a larger cardinality than the other.

If it didn't, then there's not more odd numbers in existence because the cardinalities are equivalent. Every odd number is already instantiated after the first instantiation.

Yup.

I think your intuitions about infinities are flat out wrong and probably the biggest hole in the argument. I don't see how you can conclude that googolplex/infinity is actually different from 1/infinity. If you're going to claim that then I think you need a lot more explanation.

Similarly, your argument hinges on the claim that even though the number of possible people is too large to be a set, it's still possible for God to create "all" of them. This seems pretty incoherent to me. And this isn't just a random throwaway statement, you insist that there is a point where God could not possibly create more. I'm no mathematician so maybe I'm wrong, but I would really like to see what a mathematician would say about this specifically.

Agreed. I think Majesty of Reason points out similar flaws in William Lane Craig's Hilbert's Hotel arguments against infinity. If I recall correctly, WLC thinks that 1) Hilbert's Hotel instantiates an infinite number of occupied rooms, but 2) you can create more occupied rooms by kicking a tenant out to replace with a new tenant, and propagating this chain onwards to each of the infinite set of rooms in Hilbert's Hotel. And the putative contradiction is that we've added 1 more occupied room to the collection, which was previously infinite and so must have had all occupied rooms, therefore actual infinites can't be instantiated. I could be on crack, but the error is that aleph null isn't a regular cardinal, meaning it's either meaningless to "add 1" to the infinite collection, or if it's meaningful adding 1 doesn't alter the cardinality of the set (because by stipulation that's not how infinity is defined in set theory).

Sorry if I'm missing something in your argument here, but your reliance on unrestricted SIA and perfect being theism feels... far too speculative. USIA seems to predict that I would know of existence of much more being that I currently do, that our universe would be full of life, which I don't observe. Perfect being theism makes even worse predictions. I can't imagine a perfect being creating a world of suffering like ours.

I know a part of your argument is that we should believe those things with probability one. But if such an argument contradicts everything I know about this world, I don't throw out my empirical observations, even though I'm less than absolutely sure of them. I suspect the argument is wrong, even if I don't know how exactly. There prior probability of the argument being somehow wrong, after all, is pretty high.

The argument doesn't rely on perfect being theism--it's an argument for perfect being theism. It also doesn't rely on USIA. USIA butresses one very small point but is largely inessential.

USIA predicts that all possible people would exist but you don't know if they do. It doesn't predict anything about how dense the distribution of them would be.

edited Apr 24> Objections to SIA (most of these he claims are not objections to SIA, but if they were right they would imply that one shouldn’t reason in accordance with SIA).

> Reasons that theism wouldn’t predict a huge number of people being created.

> But this means that even if most of what he says is probably right, as long as you have some credence that God would create either all possible people or some huge number, theism is majorly supported on anthropic grounds.

I don't see how this makes sense. If TT arguments are correct, then you shouldn't have high credence that God would create all possible people and should think that SIA is a wrong approach to anthropics. Either of this points would be enough to refute the claim that theism is supported on anthropic grounds. Were you trying to say that your prior in favor of SIA and its implying theism is so high that no argument can persuade you otherwise?

> TT’s argument, if successful, would totally jeopardize anthropic reasoning. If SIA is correct but impossible to do if there are infinite possible people, and there are infinite possible people, that means all anthropic probabilities end up being undefined and anthropic reasoning becomes impossible. Clearly, this is wrong!

It would jeopardize SIA in particular, not every possible approach to anthropic reasoning. And considering that SIA implies that you can blackmail reality into winning a lottery by creating copies of yourself, can be born with arbitrary high probability if your parents are infertile at the moment of your conception, and, apparently, also implies the existence of God for the mere fact that a particular human exists, it's very much not clear that discarding SIA is wrong.

The fact that SIA simultaneously implies that infinite people existing is the most probable case and breaks in this case, in particular, is a huge problem. You can't dismiss it by saying that many other theories also break in infinity cases - these theories can still be true if infinities are impossible. But SIA can't. Either it's wrong because there actually are infinite number of people and then all of SIA's math stop making sense or it's wrong because there are not infinite number of people, while SIA is very confident that there are.

edited Apr 24> If TT arguments are correct, then you shouldn't have high credence that God would create all possible people and should think that SIA is a wrong approach to anthropics.

I agree with this. The original motivation for SIA is supposed to be it fitting our intuitions correctly on various firing squad-like (and other) thought experiments. But if all possible people exist with high certainty and SIA is correct, then we should in fact reject our intuitions about all of these cases, realistically speaking. There's an infinite number of people in your epistemic situation who miraculously survive the firing squad by freak accident, and an infinite number who survive because the firing squad missed on purpose. Thus, it's plausible SIA recommends indifference if you discover that the firing squad unexpectedly missed. (Now, there are ways to make the SIA still work with infinite cardinalities of possible observers who have your evidence in certain cases where expected values - and conditional expected values - are still finite, but it's hard to see how that would apply here.)

Comment removedYou're quite confused.

Higher cardinalities of infinity are larger in the way relevant to probability. There are more reals than naturals because you pair all of the naturals with the reals but not all the reals with the naturals.

My point about Beth 2 was that I know that there is a procedure for a bijection even if I don't know off the topic of my head what it is. It's generally not intuitively obvious what the bijection between two things would look like.

I didn't give no reason to think there's such a bijection--I cited the proof by Lewis, where possible worlds are a function over the Beth 1 possible points, and thus the cardinality must be at least the powerset of Beth 1.

My view is that there can't be a set of all possible people but if there is such a set it must have at least Beth 2 people. The claim about there being unsetly many people is a bit controversial--the one about there being Beth 2 people at least is less controversial, so I was suggesting that the argument works even if we grant it.

I'm not sure what the problem is supposed to be with writing articles quickly. Of course, if the arguments are bad, then that's a problem, but they're not--you've just misstated what the arguments I made were and then gotten mad.

Comment removed//what is that way? How do you take probabilities over infinite sets?//

I don't have a foolproof way for doing it in all cases but there are certain cases where the judgments are obvious.

// How do you know what there is procedure for a bijection if you don't know what the bijection is?//

Because we have a proof of the lower bound of the cardinality.

I've never claimed to be an expert on set theory though I do know what a bijection is and have at least passing knowledge. That's why before writing about it--and the bit about infinites sets and unsetly many--I asked two of my friends who are very informed about it.

Not interested in defending the claim that I'm a good philosopher to you, but worth pointing out that various professional philosophers like Mike Huemer and Richard Chappell have said good things about my philosophical ability, with both going to far as to recommend my blog. I have no doubt I get a decent amount wrong--my bar for posting an article is it being something interesting I've thought about not my being sure about it--but I think I didn't make any of the errors you accuse me of.

Comment removedWell I gave a case where the judgment is obvious. Your credence in Graham's number rooms in Hilbert's hotel being painted red if you're in a red room should be Graham's number times higher than your credence in just one room being painted red. My view is that in lots of probabilistic reasoning about infinites your credence should be vague. There isn't agreement about how to do probabilistic reasoning in infinite cases.

Yo Matthew, you already banned this clown? Was about to write utter destruction of the latest sophistry.

Hey you fucking scumbag, we already answered the Pop Quiz questions about Infinities. Why are you dodging our questions?

"How do you take probabilities over infinite sets?"

It's fairly well-understand you can take probabilities over such infinities. For example, with non-uniform probability distributions. In case of continuous normalisable probability distribution over an infinite interval, you simply integrate from 0 to infinity then derive whatever property you're interested in. Huemer gives an example of taking a probability over an infinity to derive more complex theories tend to have a lower probability than simpler theories:

> if we suppose that degree of complexity is a continuous variable

rather than discrete, the probability density function over the possible degrees of

complexity should integrate to 1 over the interval from 0 to 4, which requires that

the probability density approach 0 as degree of complexity increases without bound.

> For any set of possibilities that is ordered and unbounded in the upward direction,

any normalizable probability distribution over the possibilities must generally

assign decreasing probabilities to later members of the set.

Hard to believe we actually had to educate you on this. Especially given you posture as if you're knowledgeable.

Also noticed you dodged my question. Why posture about "intellectual virtue" if you lack honesty to admit error? Simple yes/no question: Do you admit your claim is false?

"there is no such thing as "all truths" on pain of contradiction."

Oh man. This that "Truth" Teller guy? Guy who dropped the ball claiming "there is no such thing as "all truths" on pain of contradiction." Which Matthew corrected:

> This is not what the Grim proof says—it says there’s no set of all truths but not that there is not such thing as all truths.

Good one, Einstein. Can't live that one down. Just brutal. 🤦

Maybe you'll restore faith in humanity coming clean admitting error. Do you admit your claim is false?

"there is no such thing as "all truths" on pain of contradiction."

Comment removedAre you "Truth" Teller or just some random triggered sophist?