Contra Truth Teller on the Anthropic Argument For Theism

Your existence points to God's existence

1 Introduction

Doubt thou, the stars are fire,
Doubt, that the sun doth move,
Doubt truth to be a liar,
But never doubt I love the anthropic argument.

—Hamlet

Anthropic reasoning concerns how one reasons about their existence. I adopt the view of anthropics known as the self-indication assumption, according to which given that you exist, you should think more people exist (for that makes it likelier that you, out of all the people that could exist, would happen to exist). A theory that says 10 people exist is 10 times better than a theory that says one person exists, all else equal. For reasons to endorse SIA, see here, here, here, here, here, here, here, here, here, for instance.

Once we accept SIA, there’s a very powerful argument for the existence of God. God would be very likely to make a huge number of people—potentially every possible person. Because creating a happy person is good, God would create a huge infinity worth of people. That means that theism predicts the existence of many times more people than atheism does, and is thus much more plausible on SIA. Because theism makes it pretty likely that every possible person exists, it’s decently likely that you, in particular, would exist.

This is an argument I’ve given before—see here. Truth Teller—who I’ve previously debated about utilitarianism and had a discussion on YouTube with about the anthropic argument—yesterday wrote a very long response to the anthropic argument. It’s an interesting piece, and I’m glad someone has engaged with the anthropic argument in depth. That said, I don’t find any of the objections remotely convincing and think some of them are downright misleading. I thus thought a response would be appropriate. Truth Teller (henceforth TT) says that the argument doesn’t move his credence in theism one bit. So he doesn’t think that his objections are merely enough to give an atheist an escape hatch—he thinks it’s enough to totally defang the argument. I’ll show, I think convincingly, that even if most of what he says is right, the argument should majorly raise your credence in theism.

There’s something exciting about having someone write a lengthy response to you—it means people are actually engaging with and thinking through the things that you wrote. But there’s a downside to it—if their response is sufficiently long, it’s easy for third parties to throw up their hands and say “this stuff seems complicated,” and not form a view. I hope people don’t do this about Truth Teller’s article—I’d encourage you to actually read through the exchange rather than throwing up your hands because it’s complicated.

Despite appearances, I claim that my anthropic argument relies on only one controversial claim—that SIA is true. Truth Teller’s objections almost all fall into three categories:

1. 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).

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

3. Objections to some claim I made or way I’ve formulated a point, but that, even if right, don’t threaten the argument.

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. It’s easy to just see a wall of arguments and throw up your hands, but when you look through them in detail, very few of them threaten the argument in any major way.

2 Who misstates set theory?

In my article, I argued that there is no set of all possible people but nonetheless it would be possible for God to create all possible people. I analogized this to truth—Grim famously proved that there is no set of all truths but, nonetheless, all truths do exist.

Note that my argument doesn’t depend on this. SIA says that views according to which more people exist are more likely relative to how many times more people they say exists. So whether or not you think there’s a set of all possible people, as long as theism predicts way more people existing than atheism, theism will have a major advantage in explaining your existence.

However, I think I’m right about this point. I give a few different arguments for why there can’t be a set of all people—most of which Truth Teller ignores (I’ll tell you about the one he addresses in a minute). But he claims that it’s incoherent to talk about a collection of things that’s not a set, saying:

I'll also note that the claim that there is 'a number of things too large to be a set' is devoid of any coherent meaning. A set is any well-defined collection of things of any size. In standard ZFC set theory, for any n, you can have a set of n elements.

The claim that there is a number of things too large to be a set is not at all true. A set has a well-defined formal definition. This isn’t controversial—the Wikipedia page on limitation of size, describes inconsistent multiplicities “that cannot be sets because they are "too large".” That there are classes too big to be sets was axiomatized by Von Neumann—famously no slouch. That’s why classes that are sets are sometimes called small classes—there’s an important sense in which they’re smaller than classes that aren’t sets. In fact, I gave a quite clear explanation of the sense in which it’s too big to be a set—for any set of any size, one can construct a larger set from subcomponents of the collection of all truths.

Take, for instance, the class of all sets. There’s an important sense in which it’s bigger than any set (for any set of any cardinality, it contains a set of higher cardinality—namely, the power set of the original set). Similarly, the collection of truths is not a set for the reason described by Grim.

In response to this worry about there being no collection of all truths, Truth Teller claims “that there is no such thing as "all truths" on pain of contradiction.” 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. Obviously, there are all truths—for if each truth is true, then all of them are true, by definition. It’s coherent to quantify over truths, saying things like there are more truths than marbles in my bedroom.

One of my arguments for why there could be no set of all people was that for every subset of a set, it seems there could be a distinct mind thinking only of that subset. But that means the cardinality of the set of all agents must be greater than any set. TT attempts to derive a contradiction from that, writing:

1. Suppose there is some God-actualizable state of affairs A wherein all possible people are made to exist (assumed for reductio)
2. We can perform an operation, parallel to forming the powerset of a set, in which we form a collection of every conceivable world segment of A (ex. the world segment that just has Billy, the world segment that has Billy & Sandra, the one that just has Sandra, the one that has Sandra & Joe & Ethan and so on.). Call this collection P(A)
3. There is a unique possible mind that each individually thinks about a proposition pertaining to some distinct element of P(A) where a set of such minds would have a cardinality equal to P(A). (BB's argument)
4. All those possible minds must be injected into A (by stipulation all possible minds are in A)
5. Thus, P(A) can be injected into A (3, 4)
6. But for any X, P(X) cannot be injected into X (Cantor's theorem, contradiction 1,5)
7. So, 1 is false. A is not a God-actualizable state of affairs

I reject 2 because Cantor’s theorem only applies to a set and there are unsetly many world segments. I also reject 3, because once every possible agent is created, you can’t just make new ones to think about things.

3 The SIA applies to infinite sets

Truth Teller suggests that SIA applies in cases where the number of possible people is finite but not infinite. If there are, say, 100^100 possible people then it’s easy to do the math around them—a theory that predicts 100^100 possible people is 100x as likely to contain you as one that predicts 100^99 possible people, for the other theory predicts only 1% of possible people exist. However, if there are infinite possible people then no matter how many people are created, 0% of possible people are created.

But let’s just be clear on what SIA says. It says—and this is what’s supported by all of the arguments I’ve given for SIA (read through any of the arguments here, for instance)—that more people existing is more likely. It says nothing about the percent of possible people existing (in fact, part of the motivation for adopting this formulation of SIA is that it avoids trickiness about counting up percentages of infinity). That’s one way to formulate it, but it’s certainly not required, and does generate trickiness for the reasons TT describes.

Maybe the objection is that SIA is unintuitive unless one thinks of you as randomly selected from possible people. I don’t think this is right—we can say that you’re more likely to exist if more total people exist even if it doesn’t affect the share of possible people that exist.

For another, there is an important sense in which a greater share of possible people exist if ten people out of infinity exist than five. Sure it’s still either zero or infinitesimal, but it will be, in some intuitively important sense a bigger infinitesimal. Suppose that you’re in Hilbert’s infinitely big hotel and your room is red. You’re considering between two possibilities—either googolplex rooms were painted red or only one was. You should think the first hypothesis is more likely, even though they’re both probability of either zero or infinitesimal. The math around this is tricky and there’s no agreed upon way of doing it, as TT notes, but there are still certain clear results.

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!

Furthermore, even if you think the odds are either zero or infinitesimal of your existence unless all possible people exist, given that they’re 1 if all possible people do exist, this just gives you a reason to be very confident that all possible people exist. To go back to the Hilbert’s hotel analogy, if your room is painted red, you get infinitely strong evidence that an infinite number of rooms are painted red. TT addresses this, writing:

the claim that God would be specifically interested in creating the set of all possible observers rather than a set with the same cardinality of possible observers, looks deeply unmotivated to me. Recall that the reason given to think that God would create all possible persons is that it is good to create a person and give them a happy life, and the more people that are created and given happy lives, the better. But there's a problem with that reasoning. If God creates all possible people instead of any set of ℶ2 people He wouldn't have created more people than otherwise. In both cases He'd have created ℶ2 people.

ℶ2 for the record is a large infinite. ℶ0 is the smallest infinite, ℶ1 is bigger than that, and ℶ2 is bigger than that. ℶ2 is also called Beth 2 and ℶ1 is called Beth 1.

So TT says that God would just create ℶ2 people—assuming there are ℶ2 possible people—but not necessarily all possible people. He says that creating all possible people involves creating the same number of people as just creating ℶ2 people because it’s the same cardinality.

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. If you’ve already created aleph null people, but then you can create Suzie and give her a good life, you should do so. It’s good to create a happy person—as I’ve argued elsewhere—and that doesn’t depend on whether an infinite number of people already exist.

Suppose that the future is infinite and someone will get stabbed once a day forever. That’s infinitely bad. Yet surely it would be worse—even though it would involve the same cardinality worth of pain—if they got stabbed twice a day forever. That’s because it would add extra badness, where the badness of the original is a proper subset of the original badness. In a similar way, even if God has made ℶ2 people, why in the world would he stop short of creating new people to whom he could give good lives?

If anything, TT’s view seems like the kind of naive value receptacles view Richard argues against in this paper. One should care about utility because they care about people being well off—but then making more people well off is better even if it doesn’t show up in the math.

TT objects to my betting argument for the unrestricted self-indication assumption. This argument isn’t relevant to the broader point so I’ll address it in an Appendix. My objection to the claim that SIA doesn’t work if there are infinite possible people is that there are, in fact, infinite possible people and SIA clearly works, on pain of various absurd results. Even if you think there are only finite possible people (a very weird claim according to which you can know a priori that the universe won’t be infinite in size because then it would have too many people), it seems like if there were infinite possible people, none of the weird consequences of SIA should be right.

TT accuses me of inconsistency in that I rely on intuition at various points in the argument (for example, in arguing for USIA I claim that it seems that one’s credence and betting odds should be the same—e.g. if you’re two-thirds confident in a proposition you should bet in favor of it at up to 1:2 odds), but ignore the counterintuitiveness of my position. Yet why is my position counterintuitive? I grant that the existence of infinite people sounds weird, yet there’s a big difference between a position sounding weird and genuinely seeming wrong. To me it seems strange that we would have bare intuition about the number of people.

TT claims this is counterintuitive because it’s unclear how we would map the actual people onto the set Beth 2. It’s true that there isn’t an obvious procedure for doing this, but they can be shown to be the same cardinality (Lewis showed the number of possible people across worlds was at least Beth 2). I don’t know exactly how you would design a procedure to map the reals onto the powerset of the naturals either, but I know there is a bijection to the two because they’re both cardinality Beth 1. He notes we can’t list the real numbers, but that doesn’t rule out a possible bijection between them and some set equal in size.

4 Against the spirit of SIA

TT raises another broad objection to the argument that argues that even if the SIA update is justified, it’s canceled out by another update in the opposite direction. Suppose that there are two theories, one of which says that two people exist and the other says that one person exists. TT claims that while the theory that says there are twice as many people might make it twice as likely that I’d exist, it makes it half as likely that I’d be me (for there are now more people that I might be). So therefore the SIA update is cancelled out.

I have two problems with this. First of all, it is wrong as a matter of probabilistic reasoning, for reasons I’ll explain in a moment. Second, and more importantly, it is not SIA in any real sense, and as a result, every argument given for SIA is an objection to this view. I will not repeat the arguments for SIA as I’ve already given them in a million different articles and everyone is sick of them, but all the arguments given here, for instance, are fully applicable in exactly the way they are to every alternative to SIA. To avoid the result described in section 3, one has to think that one should think the world has a lot of people given that they exist, which they shouldn’t if the update is cancelled out.

It’s also wrong as a matter of probability. I’ve made this point before, but it’s a tricky one, so I’ll repeat it. Suppose a coin is flipped. If it comes up heads, a random person is going to be created in room 1 and if it comes up tails a random person is going to be created in room 1 and another random person is going to be created in room 2.

Upon being created in a room my credence should be 2/3 in T2. That’s because I’m twice as likely to exist on tails. So now I split my credence three ways—there’s a 1/3 chance I’m created in room 1 and the coin came up heads, 1/3 room 1 and it came up tails, and 1/3 room 2 and it came up tails.

If I knew I was in room 1 then it would cancel out the update. But I don’t—I might be in room 2, which straightforwardly confirms tails. Therefore, when one accounts for the uncertainty about which agent I am in which world, there’s no second update. It’s true that if there are twice as many people the odds I’d be one of the first few people are half as great, but if I don’t know if I’m one of the first few people, then there’s no update in favor of views on which I’m likelier to be one of the first few people.

Because I don’t know which location I’m in, I can’t update in favor of a greater likelihood of being in the particular location I’m in—with my skin and such—without taking into account the probability of my existing with my current evidence. But that’s just determined by the number of people with my current evidence the theories predict. So there’s no update that cancels out the SIA update.

5 The goodness of creation

I’ve argued elsewhere that it’s good to create a happy person—here, here, and here, for instance. If this is right, then God would create every possible person, for each person he could create he could give a good life to. In fact, even if you think that this is probably wrong, so that there’s only a 10% chance of it, that still means theism makes the odds you’d exist 10%, which is much higher than naturalism.

TT first says the argument “assumes the falsity of anti-natalism and person-affecting views in population ethics, both of which are live views defended by intelligent philosophers.” First of all, even if it did assume that, that wouldn’t be a problem because those views are extremely improbable (see my articles linked above, also Thornley’s excellent paper—I have a paper that I’ve sent to a journal that has, I think, a totally decisive argument that I’ll write about when it’s published). Second of all, as I described above, we’re here considering the relative probabilities of different views—even if you think the odds of anti-natalism are pretty high, as long as there are nonzero odds of pro-natalism, your existence will favor theism.

I also think that even if this is right, it doesn’t affect the relative force of the argument. If anti-natalism is true then theism can’t be (for God wouldn’t have created at all). So that means the probability of theism equals the probability of theism + pro-natalism. Thus, given that that’s the only plausible theistic hypothesis before one examines the argument, if the argument raises the probability of theism + pro-natalism, then it raises the overall probability of theism (this is the double-counting charge that TT objects to later).

TT suggest that even if it’s good to create a happy person, there might be exceptions. For instance:

Consider a conceivable entity that I will call an R-goblin. R-goblins are conscious persons, who, by their very nature, at all times have twisted, perverted thoughts, and wickedly evil desires to rape, torture, and pillage other conscious beings. They spend every waking moment of their existence attempting to cause the most amount of horrific agony possible.

Worst of all, I’ve heard they half in sleeping beauty!

I reject that there are such things as natures that constrain who a person is across worlds. Thus, I don’t think that R-goblins are conceivable. For any particular R-goblin in a world, it seems conceivable that they’d eventually come to have different dispositions. You are a soul, after all. And even views of personal identity that deny the existence of souls generally don’t hold that there are these robust evil-doing cross-world essences. So on nearly every view of personal identity, this is impossible.

Furthermore, even if this is possible, it’s totally irrelevant. Perhaps if this is right not all possible people will be created, but all possible people with non-corrupt essences will be. But I don’t have a corrupt essence, and I don’t think you do either. So therefore my existence is very likely on theism and very unlikely on atheism. I’m not an R-goblin!

6 Recap

Let’s take a moment to recap because a lot has been said. TT has made a lot of objections. I contend that they’re all wrong. But the important point is they’re mostly irrelevant to the main argument. So far the arguments have been:

1. Challenging my claim about set theory. But the claim about set theory isn’t needed for the argument.

2. Challenging the SIA’s applicability to infinite sets. But remember, the number of possible people is infinite on basically everyone’s view. So this amounts to claiming SIA is false. Thus, if one has good reason to accept SIA, this second challenge can’t work. The reason I’m harping on this point is that I want to be clear: the anthropic argument for theism only needs one controversial philosophical view—the truth of SIA. If that’s in place, while one can quibble around the edges, something like SIA is clearly established. Furthermore, as TT admits, if God would create every possible person, then even if this objection is right, theism is out of the woods—but the argument for why God wouldn’t was, as we saw, very unconvincing.

3. The claim that there’s another update that cancels out the SIA update. Again, this is just rejecting SIA (in spirit if not technically given how it was worded). So if one finds the many, many arguments given for SIA convincing, then they will reject this.

4. The claim that God wouldn’t make every possible person, just some of them. Crucially, however, even if this is right, this just shows God would make people with irreversibly fucked essences but that doesn’t affect the probability he’d make us. Additionally, even if it’s probably wrong, if there’s even a low chance it’s right, theism makes your existence more likely than naturalism.

So TT has said a lot of things. But they’re all either things that we can grant and the argument would still succeed or challenges to SIA. Thus, while we’ve gotten very bogged down in the weeds, it is simply not the case that the argument requires lots of tricky and controversial assumptions. For all the views like anti-natalism on which the view is false, theism is already committed to the falsity of those views, and the argument can still work even if you think there’s only a 10% chance those views are false.

7 Would God create?

Truth Teller thinks that God wouldn’t create anything at all. I find that very implausible, for reasons I’ll explain in a moment, but even if it’s right, while it would be a challenge for theism, it would not reduce the evidential significance of the anthropic argument.

Stuff was created. So if theism is true it has to be that God would create. This means that the only type of theism that was plausible prior to thinking about the anthropic argument was one on which God would create. Thus, if theism is already committed to that, it won’t affect the degree of the update. For Truth Teller to justify his claim that the anthropic argument doesn’t raise his credence in theism one bit, he’ll have to do more than raise this objection, because this doesn’t affect how big of an update he should get in favor of theism.

Furthermore—and this is a common theme—even if you think God probably wouldn’t create, as long as there’s a, say, 5% chance he’d create, your existence still massively favors theism. Thus, if one is at all uncertain about whether God would create, the anthropic data will still massively favor theism. I think it would be hard, on the basis of contested arguments, to get anywhere much below a 50% chance of God creating, meaning that the odds of your existence on theism is still much higher than on naturalism.

The other problem with TT’s argument is that it’s false—God would have a reason to create. Creating a happy person is good, and so God would create every possible person he could. TT explains:

For one, God is morally perfect and so He would plausibly bring about a perfect world or at least the best world He could create. On theism, however, the world is perfect, and maximally good sans creation, as it contains God, an absolutely perfect, and maximally good being. God could not increase the world's goodness or perfection by creating more goods, since, prior to creation, the world already contains God, and thus already contains the property of maximal goodness and perfection of being.

God is the single maximally best thing but that doesn’t mean that a world with God alone is the best possible world. A world with God and other good things is better because it has extra good stuff. Having a single perfect thing in a world doesn’t make the world perfect—the world would be improved by adding more people.

Denying this violates the Pareto principle. Creating a person is good for them, as the arguments I’ve given before show. But then a world with an extra happy person is better for one person and worse for no one—God isn’t harmed by the existence of extra people and the extra person is well off.

Here’s another analogy (credit to John Buck for it). Consider the anti-god, the most terrible possible entity. Maximally evil, pernicious, and powerful. Would a being like that create? Of course—it would create huge numbers of people to torture. Yet one could reason in the same way: the world already has the maximally evil thing, so it can’t be made worse. Any argument for why this is wrong will explain why a good God would create.

TT further explains:

One cannot add to a world’s goodness by adding more goods, if the property of maximal goodness is already contained in it, in much the same way that one cannot add to the world's snake-length if the world already were to contain a maximally long snake.

But we have to distinguish maximal goodness in objects contained in a world from maximal goodness in a world. The world doesn’t have maximal goodness but it has a maximally good singular entity. It has the best single thing but it’s not a maximally good world because a world is improved by having more stuff good stuff. Compare: a architectural team where each architect designs one room, and there are five rooms total, might have maximal goodness in one room, but not maximal goodness overall if there’s one perfect architect and four bad ones.

Further, a popular theistic meta-ethic famously pioneered by Robert Adams (Adams 1999), and supported by others like William Alston and William Lane Craig, is the view that what it is for something to be good is for it to stand in a resemblance relation to God, or God's nature. If such a view is right, it follows that anything other than God could at most be a lesser good, the goodness of which is solely derivative from God and could not add to the goodness of a world with God, who of course already resembles Himself to a perfect degree. Even if one doesn't accept the meta-ethical view that goodness is constituted by resemblance to God's nature, at the very least it's plausibly a commitment of perfect being theism that entities are good only if, and to the extent that, they resemble God.

I don’t find this view at all plausible. Even the second more limited view that is “plausibly a commitment of perfect being theism,” isn’t plausible—a spirit version of me resembles God more in that he’s immaterial but is no better. Furthermore, even if goodness=resemblance to God, the world with more things that resemble God is better, having more total goodness.

However, if you conceive of a being for which objects or events can be good without resembling the goodness of said being at all, you can conceive of a greater being, one for which objects or events are good only to the degree that they resemble her, for whom all possible goods are exemplified in her, fully, unsurpassably and perfectly.

But such a being is metaphysically impossible. Goodness is the way it is necessarily—it can’t be contingent in that way.

TT next worries that God wouldn’t bring the world from pure perfection to imperfection. But the world wasn’t perfect—it was lacking lots of good things. After creation, it now has more good things!

TT next objects to the notion that God might make people so that it benefits them. He first notes that this assumes that the axiological asymmetry is false. Yes, it does, but that’s not a problem given that it is false (see the links above about population ethics—TT just keeps double counting the “if you don’t think there’s anything good about creating people then God won’t create people,” argument). Again, even if you think it might be false but aren’t sure, the argument still massively favors theism.

TT next argues that God wouldn’t create imperfections. He appeals to the following principle:

A morally perfect person M will actualize some state of affairs S that contains or entails some moral imperfection or evil E only if S is a greater good and it's not the case that there is a possible state of affairs S* which is a yet greater good M could choose to actualize instead of S, and S* does not contain or entail E.

I accept this. God would only create imperfections if they serve greater goods. But then if one thinks there’s a solution to the problem of evil they’ll think the world’s various imperfections serve greater goods. Obviously if the problem of evil kills theism then the argument wouldn’t work—but this is just double counting the problem of evil. Because theism assumes that the problem of evil doesn’t work—otherwise it would have to be false—pointing to the problem of evil doesn’t affect the relative evidential force of the argument.

However, I think one can reasonably reject the principle, though I lean towards it. Suppose there are an infinite range of options each better than the last. It wouldn’t be wrong for a perfect being to create one of them, even though there are better options. At some point, one simply needs to pick

TT says that this implies God wouldn’t make imperfect creatures. But perhaps making temporarily imperfect creatures serves a greater good—say, providing free will, or putting us in a broadly indifferent universe to strengthen our relationship with God. Remember, this is just the claim that people make when they deny the problem of evil, so if TT’s objection assumes that the POE works, it will already assume theism is false, and thus not give an additional reason to reject the argument.

One last reason would be an appeal to God's impassibility, together with God's existence as a sole entity prior to creation. Since God is the only existing entity pre-creation, any divine action, such as creation, cannot be for the sake of something else that exists.

But it can be for the sake of someone that will exist. Just as it would be wrong for God to create a miserable person because it would harm them, it would be right for God to create a happy person because it would benefit them (see here for elaboration on the point). TT says that God in his unchanging nature can’t create without it affecting him and thus that creation conflicts with impassability. This isn’t a topic I’ve thought about at all, but worst case scenario, that just means you shouldn’t accept divine impassibility (which I already don’t). Obviously if divine impassability is incompatible with God creating then theists shouldn’t accept divine impassability, so this if the argument is right, it just gives a reason to reject divine impassability.

8 The duplication objection

TT next suggest that even if God wants to create, he wouldn’t create us. TT says that he has no reason to create us when he could instead create Godmen—beings way better than us in every way. This argument has five big problems:

1. I know I’m repeating this a lot but it’s important—even if you think there’s only a, say, 20% chance he’d make us, your existence still favors theism because the odds of your existence is so minuscule on atheism.

2. If this is right then theism is false. Thus, the argument—for the reason I’ve now explained several times—doesn’t affect how much the anthropic considerations should raise our credence in theism. It just provides a separate objection to theism.

3. I think it’s plausible that God does make creatures like that. We are Godmen in the next life. However, as argued by the theodicy I’ve given, we have limited goodness and power temporarily in this life because it strengthens our eventual relationship with God and might achieve various other great goods.

4. If this is right, then God could never create because for each creature he could create there’s some other better creature. As a result, he just has to pick some creatures to create, even if they’re not the best creatures he could create. A morally perfect person is perfectly justified in creating a very good state of affairs, even if there’s a better one, as long as there’s an infinite continuum of options of increasing goodness.

5. God does create those Godmen—he just creates them and us as well. He creates every possible person and gives them the best life he can, on my view.

TT anticipates this response and objects, “First, there are surely some constraints on the beings God would and would not create, since we've seen that not all beings are all-things-considered worth creating, such as R-goblins.” I addressed that before, but even if he’s right about that, then God wouldn’t create beings whose happy existence is bad by their essence, but that doesn’t apply to us. TT notes that the “distance in moral impressiveness between us and God and the very best God could create is plausibly at least as great as the distance in moral impressiveness between us and R-goblins,” and claims that this implies that it would be wrong to make us instead of God men. But the things that make creating R-goblins bad is that their existence is bad, not that their existence is comparatively worse than other beings. God would also be expected to create, say, lizards, whose existence is much less impressive than ours, because their existence is good on the whole (at least if you buy that these robust essences are possible).

Further, though the world with us, and with more impressive beings than us may have more people, it's far from clear, by my lights, that God is doing more good by actualizing the world W3 that contains us and more impressive beings than the world W4 with only godmen who have richer lives, and capacities to more deeply appreciate goods. Perhaps, as I think plausible, the value of worlds is not fixed by the amount of people who are given happy lives in them, but by the kinds and quality of goods realized.

But this violates the Pareto principle. It’s good to create humans, even if there are already Godmen, because it makes the humans better off and no one worse off. To see this, suppose you found out that there were Godmen a galaxy away. Would that make it less good to have kids, because you dilute the goodness of the Godmen universe? No, of course not! The goodness of creating a person has nothing to do with the presence of other unaffected people. And all the arguments for creating happy people apply even if there are Godmen. So TT is just repeating over and over again that you might be an anti-natalism of some sort, or an anti-natalist in world with Godmen. It’s easy to find a lot of different motivations for anti-natalism but one must argue for their plausibility rather than just state that they’re a conceivable view one might hold. TT next says:

Leaving those concerns aside, there's a direct reason the objection goes wrong. For any human God creates, it looks like He could create a duplicate of a godman instead.

A few problems:

1. Let’s call Godmen+ the beings better than Godmen and Godmen++ the beings better than Godmen+. By this standard he’d never create anything, because for anything he could instead create a better being.

2. This assumes that one can keep cloning people indefinitely. But this is contentious. If every person is their own unique soul, he can’t create new people because there is no extra uncreated person who could be created (all the possible people exist). This will also follow if one accepts Willliams’ necessitism.

3. This argument assumes that creating Godmen trades off with creating people. But he could create both. He could make as many Godmen as he once and people. It’s at least not terribly improbable that he’d create beings of all good kinds in infinite numbers—if there’s even a 1% chance of that, say it with me now, that massively favors theism.

Remember that this is all a response to just the fifth point—so even if I’m wrong about this, it wouldn’t jeopardize the argument overall. TT says “Since there's no contradiction in doing so, it seems to me there isn't an upper bound on the universe's God can create and the duplicates He can put in them.” But the scenario is impossible—every possible person has been created and yet new people are being created. A person is being created who is not a possible person. But clearly impossible people can’t be created!

To spell out the contradiction:

1. In the scenario God has created every possible person.

2. In the scenario after this God creates new persons.

3. For God to create a new person they would have to be possible.

4. So God would have to create people that he’s already created.

5. If a person is created they can’t be created again.

TT objects that this “assumes soul theory.” It doesn’t—various views of haecceities imply it, as does necessitism, as does soul theory. But as long as you have, say, 10% credence in soul theory, it will still massively favor theism, because theism+soul theory predicts your existence much more than other theories. Even if you reject soul theory, you should just think God will create a huge number of people.

TT spends some time addressing the double-counting charge. But his responses all miss the point. If an objection, if true, means theism is false, then while it might be a good objection to theism, it won’t affect the evidential significance of some evidence for theism.

9 Another recap

So far all the arguments have either rejected SIA, been irrelevant to the main point, or been about why God wouldn’t create creatures like us. The first category could sink the argument if successful, but it’s not successful, and given the abundant evidence for SIA, we can be confident it’s wrong. The second category doesn’t affect the argument. The third category also doesn’t affect the evidential force of the argument because for theism to be right, God must create people like us. Thus, the only part of TT’s objections that affect how much one’s credence in theism should rise as a result of the argument is the part that objects to SIA—but those objections aren’t any good. His general objections to theism, about why God wouldn’t create, also aren’t any good, but even if they were, it wouldn’t threaten the broader argument: if there’s only a 5% chance God creates huge numbers of creatures like us, theism still massively beats naturalism in predicting your existence.

10 Explaining the data

Next TT tries to argue that naturalism can have various extra hypotheses to explain your existence. I agree it can do that, but because the probability of those things conditional on naturalism are super low, naturalism starts to look really improbable. TT’s first naturalistic hypothesis is Nd:

On Nd, there is an initial state, perhaps an initial singularity or a quantum field, that is disposed to lead to your existence as an inevitable consequence, or perhaps that is heavily weighted to make your existence likely.

The problem is that this has a prior probability of zero. Because you’re not special, a theory where the universe picks you out has no higher of a prior than a theory that it picks out any of the other infinite possible people, so it has a prior of zero.

TT doesn’t address this worry. The rest of his section is just arguing that theism is improbable. Now, you can read my response to that if you want, but that’s not a response to the anthropic argument—it’s just raising a bunch of other arguments against theism.

Of course, it might be very mysterious why and how a naturalistic initial state is causally disposed to lead to your existence in particular. But I contend that the theistic hypothesis is no less mysterious. Mystery is a central feature of theism. Why does the divine being at the foundation of reality decide to create a universe with you in particular? You can say it's because He is motivated by certain moral reasons, but why is He motivated by those reasons and not infinitely other reasons He might be motivated by?

He’s maximally motivated by moral reasons. He brings about the best possible world or, barring that, some very good world. He’d create either all possible people or some huge number of people. What other moral reasons is TT talking about? God would do the best thing or some very good thing if there is no singular best thing. That entails creating either every possible people or a huge number of people, which, on SIA, makes your existence much more likely.

How does the divine being at the foundation of reality create a universe and ensure that you will be in it anyways? You can say they can because they are omnipotent, but that doesn't at all tell me what the causal mechanism is.

There’s no extra mechanism. God has the property of omnipotence meaning that which he wills happens. Once there is a being like God, there’s nothing extra needed for him to be able to create. Now, maybe TT thinks that the prior probability of God is near-zero. But why in the world would one think that? God is very simple—having just one essential property—might be provable, lacks arbitrary limits, and is ontologically unique. All of that makes it hard to have a super low prior in theism.

TT talks about things in terms of mystery. But that’s not the way to do it. Think about things in terms of conditional probabilities—the odds of theism start out decently high and theism predicts that you exist which has a very low prior. Applying Bayes theorem, we get very strong evidence for theism.

Suppose you think there’s a 1% chance that something like the Godellian ontological argument or the contingency argument works. Well then the prior in theism can’t be too far south of 1%—before looking at the evidence one should think there’s a decent likelihood that God exists necessarily.

TT objects that there are a lot of different possible Gods, so perfect being theism starts with a low prior. But only perfect being theism has these attractive features—simplicity, provability, ontological uniqueness, and lacking arbitrary limits. Thus, if there is a God, it’s probably a perfect one.

TT worries that perfect being theism isn’t much likelier than Nd. But if, as I’ve argued, Nd has a prior of zero, then theism is much more likely. TT says:

Theism fits very poorly with our background information, since all persons we know are embodied, all persons we know are limited in power, knowledge and goodness, all persons we know are located at particular points in space and time.

I don’t think that just looking around and seeing if beings around you have some property tells you very much about whether the foundation of all of reality has that property. This is especially so if, as I’ve argued, we have a plausible story of why that view of ultimate reality would produce conditions like the ones we observe. TT worries that theism is less simple than naturalism because “naturalism only commits to natural concrete entities, and causal relations between those entities, and theism posits a supernatural entity.”

Simplicity, however, is about fundamental entities. It would be absurd to say one should think God wouldn’t create because that would be simpler. Theism, then, does very well, positing just one fundamental entity with one unlimited property—perfection. TT next remarks:

Indeed, the history of science is replete with examples of phenomena we previously thought to have supernatural explanations being displaced by natural ones.

It’s also replete with us discovering things that point to the supernatural, like fine-tuning, the presence of laws, psychophysical harmony, and anthropics. Furthermore, the theodicy I’ve given explains why that would be—God puts us in a broadly indifferent universe. God supernaturally intervening all the time would be the byproduct of poor design.

TT objects to the idea that arbitrary limits is a vice of a theory, saying that he doesn’t share the intuition. By this standard, then, the speed of light being unlimited starts out no more probable than it being, say, 100,000,323 miles per hour and there’s nothing wrong with thinking the universe stops somewhere for no reason. This is very implausible, and the history of scientific inquiry shows us discovering many unlimited things.

He next worries that even if it’s somewhat of a virtue, that doesn’t mean it’s enough of a virtue to outweigh the combined probabilities of all the limited theisms. But theories that have extra arbitrary limits and are less simple tend to be much worse than theories that don’t, not just a bit. That’s wh a being that knows all things is way more likely than the combination of all infinite beings, each of whom knows every fact but one. Dustin Crummett’s given a helpful analogy: the odds that nature is uniform is much higher than the odds that it’s randomly disuniform in one small region because, though there are many more ways for it to be disuniform, each of those have arbitrary limits and are less simple.

TT objects that perfection isn’t simple because it assumes the existence of various disunified parts. One is perfect in part because they have infinite power, so perfection isn’t simple. I’ve objected to that in various places. Consider an analogy: modal realism says every possible world exists. That’s a simple theory, even though modal realism depends on lots of different worlds existing. Modal realism serves to explain why the worlds exist, which is why it’s more probable than a theory according to which a bunch of random worlds just happen to exist. Perfection is similar.

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.

TT next argues that naturalism can explain the data by positing a multiverse. The problem is that a multiverse doesn’t predict the existence of Beth 2 people, just aleph null, so your existence is infinitely more likely on theism than on multiverse naturalism. TT responds to this:

One might be tempted to object that there are not enough physically realizable outcomes to lead to the existence of ℶ2 people, and yet there are ℶ2 possible people. But even if that's right, it doesn't follow that multiverse naturalism doesn't make your existence likely. You are a physical body (perhaps with some soul or spooky ectoplasm that supervenes on those physical states) and on multiverse naturalism, we should expect all physically possible outcomes to be realized. Given that an outcome involving your physical body is physically possible, we should expect it to be realized in some universe given many-worlds theory. Sure, it may not predict all possible people, since perhaps some of them are not physically possible, but it still predicts that you, a physically possible person, would exist in some universe.

TT claims that every physically possible outcome gets realized. He notes that if this is so then you exist. But on SIA, the number of people created matters. Any other view violates the conservation of evidence and Bayesian updating, for reasons I’ve described here and here (the general arguments for SIA given here or here can be made into objections to the argument). The thing that matters isn’t the share of experiences had but the number of experiences had.

To see a particularly weird example of the implications of the view, modal realism says that every possible world—every way things could be—actually exists. On this view, then no matter what one experiences, it gives them evidence for modal realism because it predicts your experiences being had. But every second, they should expect induction to implode, because worlds where induction implodes are more numerous than other worlds. So then with each passing second one should expect induction to implode if modal realism is true, and then when they observe it doesn’t, they still get confirmation of modal realism. On such a view, your credence in modal realism predictably goes up over time, necessarily confirmed by whatever you experience.

That’s utterly crazy.

11 Final recap

TT raised a lot of arguments in his piece. Yet most of them are just generic objections to theism which, if true, would require the falsity of theism. This means that they don’t actually affect the evidential force of the anthropic argument, because if they work, theism is already out of the race. Furthermore, the objections are mostly wildly unconvincing. All of the ones that threaten the core of the argument just involve objecting to SIA, yet failing to realize that he is objecting to SIA, and consequently failing to engage with the mountain of evidence for SIA.

In section 2, I covered TT’s claim that I butchered set theory. It turned out that he was just straightforwardly, unambiguously wrong about set theory. Sections 3-4 addressed objections to SIA, which were wildly unconvincing, in part because TT didn’t engage with the arguments for SIA. Sections 5-8 addressed claims that God wouldn’t be likely to create many beings like you—but if those are right then theism is already out, so they’re not additional evidence against theism. Additionally, those arguments were wrong, and if one has any uncertainty about their correctness, they’ll just mean theism doesn’t entail your existence, but still predicts it with much higher likelihood than naturalism.

Section 10 addressed some naturalistic explanations of the anthropic data. There were two. The first one had a prior of zero and the second assumed the falsity of SIA. Thus, when considered as a whole, every single one of his arguments that lowers the relative evidential force of the anthropic data challenged SIA. So as long as you accept SIA, even if you agree with the rest of TT’s points, you should think this massively raises the likelihood of theism. His random swipes at theism if successful might show that theism is overall unlikely—though I obviously don’t think they show that—but doesn’t show anything interesting about the argument.

Furthermore, TT never deals with the arguments for why even if SIA is false, anthropic evidence favors theism. Thus, even if you reject SIA—and especially if you’re uncertain about it—your existence majorly favors theism. Ultimately then, while I applaud TT for the effort and appreciate the engagement with the argument, his responses are, when considered as a whole, a total failure.

12 Appendix

There are two different versions of SIA. I’ve explained the difference between them here:

There are, however, two different ways of thinking of SIA. The first one we might call the restricted self-indication assumption (RSIA). On this view, one should think there are more people because that would mean that a larger share of possible people exist. The other is the unrestricted self-indication assumption (USIA), which says that one should simply think there are more people, not merely because it means a larger share of possible people are created.

This is a rather confusing distinction, and must be illustrated with a slightly complicated example. Let’s begin by noting that some infinites are bigger than others. The smallest infinite is aleph null, Beth 1 is bigger than that, and Beth 2 is bigger than that. Suppose that there are two theories that are otherwise supported by identical evidence. The first claims that there are aleph null possible people and all of them exist. The second claims that there are Beth 2 possible people and all of them exist.

RSIA would be indifferent between these two views. After all, both of them predict every possible person existing. USIA, in contrast, should think that, because the second hypothesis means more people will exist, I gain very strong evidence for the existence of Beth 2 people.

No part of the anthropic argument hinges on USIA (well it slightly buttresses one minor point, but it’s basically irrelevant). However, TT objected to my argument for USIA, so I thought responding would be fruitful. The argument is:

1. If one should bet in accordance with USIA rather than ~USIA, USIA is correct.
2. ~USIA instructs one to, if they’re 50% sure that the number of people both actual and possible is Beth 1 and 50% sure that they’re both Beth 2, and if they’re given a choice between getting 2 dollars if there are Beth 1 people or 1 dollar if there are Beth 2 people, accept the offer that gets them 2 dollars if there are Beth 1 people.
3. If there are two possible events each with some probability, your betting between them shouldn’t depend on whether they’re impossible or merely non-actual if that doesn’t affect your payouts.
4. Therefore, ~USIA instructs one to, if they’re 50% sure that the number of actual people is Beth 1 and 50% sure it’s Beth 2, and if they’re given a choice between getting 2 dollars if there are Beth 1 people or 1 dollar if there are Beth 2 people, accept the offer that gets them 2 dollars if there are Beth 1 people
5. If the case described in premise 4 were repeated over and over again, people would get less total money by accepting the offer that gets them 2 dollars if there are Beth 1 people than accepting the other offer.
6. Following the right betting advice would not result in getting less money, if the situation were iterated, than following the wrong betting advice.
7. If ~USIA is true then one accepting the offer that gets them 1 dollar if there are Beth 2 people in the scenario described in premise 4 is following the wrong betting advice.
8. So USIA is true.

TT objects that 1 is false. But this is a contentious view of probability. Probability theory tells you what credence you should have in some proposition. Once you have a credence in some proposition, you should obviously bet in accordance with that probability. If your credence in some proposition is .5, you should take a bet if that offers you payouts twice as good with if the proposition is true. This might even be part of the definition of a credence, as various people have argued. TT has no objection to this or counterexample, so I’m not sure why he rejects it.

2. is also false. In order to reject the USIA (and I think everyone should because it's false) one need not take a particular decision theoretic view on what to do in cases where you're asked to bet on what uncountably infinite cardinality of people there are.

But you should bet in accordance with your credence. If the anthropic data doesn’t favor either theory then you should bet at 1:1 odds between the two theories.

Finally, 5. is also false, as it assumes that one is more likely to end up being an observer in a world with ℶ2 than a world with ℶ1 observers.

It just assumes that more people get money if ℶ2 people get a dollar than ℶ1 people. Which is true, obviously.