I Talked With The Most Prolific Critic of the Anthropic Argument

It was a great chat! Here's the progress we made.

Summarizing the anthropic argument

In the early days of the internet, I’m told, there were often extended, weeks-long back and forths, spanning hundreds of pages. These blog wars were epic and ranged across topics, though they were often about evolution vs. creationism, or broader philosophy of religion topics.

The anthropic argument has restarted the blog wars.

It all started when I began writing about the anthropic argument. My view on the argument: it provides extremely strong evidence for theism, and nothing approaching a convincing response has yet been given. Furthermore, the arguments supporting the various premises are strong enough that we know that nothing approaching a convincing response will be given.

The argument, for those who don’t know, goes as follows.

1. You exist.

2. Your existence is more likely if there are more people. E.g., if a coin gets flipped that creates one person if heads and ten people if tails, you should think it’s ten times likelier that it came up tails than that it came up heads. A theory that says there are N times as many people that you might presently be, predicts your present existence N times as well.

3. If this is right, then you should think that tons and tons of people have been created. If ten people get created, your existence is ten times as likely, if a hundred people get created, then your existence is a hundred times likelier. By this logic, if infinite people get created, your existence is infinitely likelier. So, you should think, from the fact that you exist, that there are infinite people.

4. The train doesn’t stop at infinity. There are bigger and smaller infinities, as mathematicians have agreed for many decades. So, not only should you think that there are infinite people that exist, you should think the number of people that exists is one of the really big infinities. You should think the number of actual people that exists is equal in size to the maximum number that there could be. Note, this doesn’t require thinking every possible person exists, for reasons I’ll explain in a footnote¹, but just that the number of people that exists is the biggest number there could be.

5. The number of people that there could be is at least a very large infinity called Beth 2. I think it’s more, but let’s be generous to the naturalist, and say it’s Beth 2.

6. Beth 2 is a giant number. It’s more than the number of natural numbers (1, 2, 3, 4, etc) more than the number of real numbers (this includes every number on the number line, including infinite non-repeating decimals). It’s really big! On naturalism, it would be super weird if there were that many people. If the universe is infinitely big, you only get aleph null people, which is way smaller than Beth 2. To get a multiverse to produce Beth 2 people, you need a great deal of chicanery and gerrymandering. Standard naturalist multiverses don’t do that.

7. In contrast, if God exists, he’d be likely to create at least Beth 2 people. It’s good to create. Why’d he stop at 10 billion, or even aleph null? If he can keep creating more, why’d he ever stop. Thus, on theism, it’s likely that the number of people that would exist would be the maximum number it could be.

8. So to recap: from the fact that you exist, you should think there are more people. Just like it’s ten times as likely you’d exist if there were ten people, and a hundred times as likely if there were a hundred, it’s infinitely likelier that there are infinite people. This doesn’t stop at infinity; thus, you should think there a—pardon my French—shit-ton of people! At least a giant infinity called Beth 2. Too many for naturalism to be able to plausibly produce. In contrast, an omnipotent God would be able to create them, and have every reason to.

I know, a lot of this sounds weird and controversial. In reality, I think the only philosophically controversial premise that bears on the truth of the argument is the second. But I think that premise is supported by lots of extremely powerful argument (at the link, I’ve compiled every argument I’ve discovered for SIA, with links to papers defending them), some of which I’ve published on. Nothing approaching a convincing response has been given to that premise. You might think the seventh premise is controversial—for reasons that I’ll explain later, that premise is immaterial to the force of the argument (though it is, of course, relevant to what your credence in theism ought to be).

Anyway, Truth Teller wrote a long response of around 10,000 words. I wrote a long response of around 10,000 words. Truth Teller wrote a long response that was the size of a small book. I made a two-part YouTube stream that lasted about four hours in total.

Finally, we decided to have a dialogue about our disagreements. Truth Teller didn’t want it to be recorded, so it was not.

While you might expect from the barbs we’d thrown back and forth that it would be hostile, it was a really good and friendly conversation. Truth Teller is a smart and honest guy, and I’d suggest you check out his blog. Chalk up our previous (slight) hostility to “the internet makes it easy to say mean things without consequence, and few of us resist that temptation, especially when responding to a piece that we find to be deeply wrong.”

Progress regarding understated evidence

The first important agreement: Truth Teller’s argument about understated evidence doesn’t work. What Truth Teller suggested in his original piece was that while more people existing makes it likelier you’d exist, it’s less likely you’d be you. When I walked through the probabilistic analysis I’ve provided here in section 2.3, as well here, and here—Truth Teller agreed that his objection failed.

In short, suppose that John is created. A coin is flipped. If it comes up tails, Jack is also created. You get created through this scheme, not knowing if you’re John or Jack. What should your credence be that the coin comes up tails when flipped? Note: I use the phrase “comes up” to note that you’re not sure if the coin already has been flipped or that it will be flipped in the future.

SIA answers: 2/3. Twice as many people get created if the coin comes up tails, so you should think the coin came up as 2/3rds odds. Alternatives answer 1/2. But if we’re precise about what you know, we can show that SIA’s credences are right. To see this, I claim you should think:

1. It’s just as likely that you’re John and that the coin will come up heads as that you’re John and the coin will come up tails.

2. It’s just as likely that you’re John and the coin will come up tails as it is that you’re Jack and the coin has come up tails.

3. Therefore, tails is twice as likely as heads.

The third premise obviously follows from the first two—tails, after all, entails that you’re John and the coin will come up tails or that you’re Jack and the coin has come up tails. Heads, in contrast, entails that you’re John and the coin will come up heads. If each of the tails outcomes are as likely as the one heads outcome, then tails is twice as likely as heads.

Now, when we’re precise about this, understated evidence worries don’t arise. Yes, it would violate understated evidence concerns if you being John and the coin coming up heads is only half as likely as you being John and the coin coming up tails. While tails means that it’s twice as likely that you’ll exist, it’s only half as likely that you’d be John if you exist. But with the premises as stated, there’s no violation of understated evidence.

Crucially, SIA doesn’t give you reason to think that there are more people that you know you’re not. It only gives you reason to think there are more people that you might presently be. From the fact that I exist, SIA gives me direct evidence that there are more Matthews—people that I might be—but no evidence (except indirectly) that there are more, say, shrimp. So long as we keep that in mind, no understated worry evidence arises.

Truth Teller has thus retracted the objection. Yay! He also thought that my response might have some purchase against his set theory worries, but would have to think more about it.

What to have in the background?

One other major subject that we talked about was what to put in the background. Suppose that we’re evaluating the likelihood of evil on theism vs. naturalism. Well, in order to come to any all-things-considered judgment about whether naturalism or theism best predicts the evils of our world, we’d need to consider:

• Would God create? Would anything at all exist on atheism?

• How likely is there to be contingent stuff on theism vs. atheism (evil is contingent after all).

• Would the universe have begun to exist on atheism? Would it on theism? Did it? Did evils begin to exist?

• Would there have been a finely-tuned universe on theism vs. naturalism?

And so on through a dozen more questions. But this makes it impossible to ever make progress—every time you raise one point about evil, you’re left talking about half a dozen fairly unrelated arguments for the existence of God. To avoid this, what you should do is hold other extraneous considerations in the background. Imagine that you already were aware of those other considerations, and ask: how likely is it that the thing we’re specifically debating about would exist on theism vs. naturalism, after granting all the background assumptions.

So, for example, when evaluating the problem of evil, you should imagine that you already knew that stuff existed, there was a contingent universe, that we have our basic cosmological evidence, and so on.

Now, in response to the anthropic argument, Truth Teller made the following arguments:

• God likely wouldn’t create at all because a world with him alone is maximally perfect.

• Even if it’s not, he has no reason to create.

• If he creates, he’d create really awesome beings, rather than creatures like us.

I argued that this was unfairly bringing in stuff that should be in the background. Specifically, when evaluating the anthropic evidence, we should hold fixed that there are creatures like us. What we update on is learning that there are uncountably infinite creatures like us, rather than just a few creatures like us. I had several points in favor of this:

1. This is specifically the focus of the anthropic argument. Just like it’s cheating to bring in evil when talking about contingency, it’s cheating to bring in arguments about whether God would create, when addressing an argument that is specifically about how many creatures God would create.

2. When evaluating an argument, and whether it raises the likelihood of a view, you should take as background the stuff that you ought have already considered even if you’d never heard of the argument. This is why it’s cheating to bring up the existence of contingent stuff in response to the problem of evil; perhaps contingency favors theism, but it’s a separate consideration that you ought to have considered even if you’d never heard of the problem of evil.

3. What determines if an argument is successful is whether it would convince a reasonable agnostic. If an argument would convince someone who was on the fence, or even a person who thought your view was probably false but wasn’t sure, it’s a pretty good argument. Like, sure, the problem of evil isn’t going to convince someone who is otherwise certain of theism, but it’s a good argument because it should convince someone who was on the fence and had never heard of evil. But crucially, a person who was on the fence should have considered the various other arguments about whether or not God would create at all. Thus, these considerations don’t affect its success—whether it would convince a reasonable agnostic.

4. When evaluating the success of an argument, you should look at how many times likelier a person would think the view that the argument is in service of is after hearing the argument than before. This is called its Bayes factor. An argument from evil might be successful, even if it doesn’t ultimately convince someone, if it makes them think theism is less likely than it was before. But once again, before considering the anthropic argument, you should have already thought about whether God would create beings like us. Given that the theistic hypothesis that you ought to have considered before thinking about the anthropic argument should necessarily have included the supposition that God would create, none of the considerations affect how much you should update from the anthropic argument.

5. Perhaps most worryingly, if you’re going to consider the arguments for why God wouldn’t create creatures like us, then you should also consider the arguments for why creatures like us wouldn’t be created if atheism is true. But that means that before figuring out if the anthropic argument is good you have to decide on whether each of the following arguments are successful: the fine-tuning argument, nomological harmony, the argument from consciousness, psychophysical harmony, evil, the existence of the physical world, and much more! That’s totally unwieldly and makes it impossible to ever conclude that an argument is good.

Now, let me be clear: of course if you are figuring out how likely it is that theism is true, you should take into account all the evidence. But when evaluating whether any particular argument succeeds, you should try to hold other unrelated things in the background. Otherwise, you can never figure out whether an argument is good without considering every other argument.

Truth Teller agreed that if we hold the fact that there are creatures like us in the background, then the considerations he mentioned about whether God would create, and whether if he created he’d make creatures like us, don’t affect the force of the anthropic argument. He said that maybe then multiverse arguments undermine the argument, but would have to give more thought to it (I don’t think this is right because even granting that there’s a multiverse, as already described, it’s highly unlikely that the multiverse would be big enough to have Beth 2 people). He also said that he’d have to give more thought to whether it was fair to have the existence of creatures like you in the background.

Now, one interesting point that he did raise was: if we keep the fact that there are creatures like us in the background, why not keep in the background the fact that you exist? Hopefully what I’ve said so far heads off this worry. In short, when evaluating the force of an argument, you want to hold in the background the evidence that is irrelevant to the argument, that presents other considerations. Other arguments in the theism vs. atheism debate bear on whether creatures like us would be created, but none of them bear on whether you specifically would be created.

When evaluating evil, you should hold in the background that a contingent universe exists, but you shouldn’t hold in the background that there is evil. Keeping your existence in the background doesn’t meet any of the 5 desiderata listed above, and is particularly perverse when the entire anthropic argument is that your existence is really surprising given atheism, for reasons that have nothing to do with any other consideration given by any other argument for theism.

For a bigger infinity

We didn’t resolve all of our disagreements. There were still concerns about normalizability worries (infinity wreaks havoc on anthropics, as it does on pretty much everything else). I additionally argued that the following formalization of the update can avoid such problems:

Single infinite universe=there is some universe, universe 1, that is infinite in size, and contains infinite people that you might presently be.

Infinite infinite multiverse=there are Beth 2 universes, each of which are infinite in size and contains infinite people that you might presently be Each individual universe has aleph null people

Let's call the one universe that will exist on single infinite universe universe 1.

Infinite infinite multiverse predicts universe 1, universe 2, universe 3...through Beth 2

SIU=single infinite universe

IIM=infinite infinite multiverse

1. P(SIU and I'm in universe 1)=P(IIMN and I'm in universe 1)

2. P(I'm in universe 1)|(IIMN)=0 or infinitesimal.

3. Therefore, IIMN is infinitely likelier than SIU

The less mathy version is this. Suppose that there is one universe that’s infinite in size, containing aleph null people. In that universe, a coin will be flipped. If it comes up heads, no other universes get created. If it comes up tails, Beth 2 other universes get created.

Suppose that you get created and you don’t know whether you’re in the first universe or a later universe. Then you learn you’re in the first universe. Now suppose that you reject the version of SIA that favors bigger over smaller infinities. You being in universe one is infinitely surprising if Beth 2 universes are created. Thus, from the fact that you are in universe one, the relative odds of the coin coming up heads go up by a factor of infinity. Because you were previously indifferent, you should now think the coin is certain to come up heads. Note: SIA cancels that update, because while it agrees that you should think the odds of Beth 2 universes being created goes down by a factor of infinity, it started out infinitely likelier that Beth 2 universes would get created—that predicts infinitely more people than merely aleph null people getting created.

But this is weird! This means you should think that a fair coin that hasn’t been flipped yet is 100% certain to come up heads. Worse, if you replace the coin with a game of poker, and Beth 2 universes are only created if the fair poker game turns up ten royal flushes, the views that deny that the multiverse with Beth 2 universes is infinitely likelier than the single universe necessarily will hold that you should be 100% certain that a fair game of poker will, in the future, turn up ten royal flushes. Nuts!

Additionally, nearly every argument for SIA—and there are plenty of arguments for SIA—can be made in defense of the judgment that Beth 2 people existing is infinitely likelier than aleph null people existing. Thus, normalizability worries shouldn’t dissuade you from accepting this judgment, as it’s supported by lots of powerful arguments.

Ultimately, we didn’t resolve everything. We didn’t clear up the normalizability stuff, or discuss the naturalistic alternative to theism in explaining the data. But I think our conversation showed the importance of dialogue on these topics. By having a friendly conversation between two interlocutors who are informed about the subject, you can make a lot of progress!

1. Infinites come in different size. The sorts of infinities that mathematicians talk about are infinite sets. Two infinite sets can be the same size even if it seems like one has more stuff than the other—for example, the set of all natural positive numbers (1, 2, 3, 4…) is the same size as the set of all natural numbers (-4, -3, -2, -1, 0, 1, 2, 3, 4…). So long as you pair each member of an infinite set with a member of another infinite sets, the infinite sets are the same size. Thus, in order to think that God creates a number of people that’s equal in size to the maximum number of people there could be, you don’t have to think he makes every possible person. This is analogous to the number of natural positive numbers being the same size as the number of natural numbers, even though not every natural number is positive. Additionally, if you think that the number of people is too big to be a set, then God doesn’t need to make every possible person—just a number of people too large to be a set.