We Finally Published the Paper on the Anthropic Argument For God's Existence

Plus Joe Schmid, Brian Cutter, Amos Wollen, Dustin Crummett, Philip Swenson, and I are writing a book defending the existence of God

I have written many long pieces about the Anthropic argument for the existence of God. Last year, Amos Wollen and I wrote this up in paper form. A few weeks ago, it was published.

Sadly, philosophy journals penalize ambitious arguments. Thus, to get it in publishable shape, the piece had to be castrated and lobotomized. The original title was “A Presumptuous Proof of Theism.” The new—less interesting—title is A Presumptuous Path to Theism, Modal Realism, or axiarchism. The published paper on the topic is significantly less comprehensive than my blog post on the subject. There’s much less about why the main rivals to theism are implausible.

I’ll tell you about the paper. But first: book announcement. Joe Schmid, Brian Cutter, Amos Wollen, Dustin Crummett, Philip Swenson, and I are writing a book defending the existence of God. One of the chapters will be about the Anthropic argument and will be the most comprehensive presentation of the argument to date!

Our aim is to popularize and defend all the insanely strong Bayesian arguments for theism that nobody aside from like ten philosophers and some of my blog readers has ever heard of. We’ll talk about the prior probability of theism, a priori fine-tuning, nomological harmony, psychophysical harmony, and some new arguments that have yet to see the light of day! Rumor has it that it will strike the fear of God into the hearts of atheist readers and illustrate that there are many different powerful arguments that substantially raise the probability that God exists.

The book probably won’t be out for a year or more. It’s in its early stages. But when it comes out, finally the theism question will be resolved, and philosophers can move on to other philosophical questions, like whether there are chairs. If I had to hand-pick a power team to defend God’s existence, my coauthors would be some of the first people I’d pick. It’s amazing to have such a stacked group of coauthors, providing such stacked arguments, for the best possible news—that there is a being of limitless perfection with an infinitely amazing plan for the universe who loves each and every one of us.

Here’s the Anthropic argument in a nutshell. The self-indication assumption claims that your existence favors theories on which there are more candidates for being your present self. So, for example, imagine a coin gets flipped. One person is created if it comes up heads and ten people are created if it comes up tails. You get created by the coin flip. SIA says you should think it’s ten times likelier the coin came up tails than that it came up heads. Because tails leads to ten times more people being created—and you could be any one of them—it makes your existence ten times likelier. SIA in an oversimplified sentence: your existence is likelier if there are more people. (If you want the most precise definition which doubles as an argument for SIA, see here).

Oh and here’s another thing about the SIA: it’s the correct view. The other views are, to use technical language as a Real Scholar™ who has just published a paper on the subject and will one day be the Jacob Urowsky Professor of Philosophy at Yale University, totally whack. There are a bunch of very strong arguments for SIA and no good responses to them. I’ve published another paper arguing for the SIA and have various blog posts that are more detailed.

If the SIA is right, then your existence favors theories on which there are more people. A theory on which there are 10x more people makes your existence 10x likelier—a theory on which there are a trillion times more people makes your existence a trillion times likelier. But then by the same logic, a theory on which there are infinitely more people makes your existence infinitely likelier.

Conditional on the correctness of the SIA, your existence gives you infinitely strong evidence for the existence of infinitely many people. There are also smaller and larger infinities. So if the SIA is right, then your existence confirms that the number of people that exists is the very largest number of people that there could be. Maybe this is some infinite cardinal like Beth 2 (ℶ2)—more likely, it’s absolute infinity (Ω). As Menzel describes it:

Cantor recognized that some collections — notably, the collection of all ordinal numbers — are themselves “too big” to be assigned a definite size, a definite cardinal number. This idea led to the development of the limitation of size approach to the set theoretic paradoxes that focuses on over-largeness per se as their source. I am of course strongly challenging that view — it is only when a collection is over-large due to unboundedness that paradox can arise. However, it seems to me it is quite intuitive to say that the “size” of a set that cannot be measured by the cardinals that emerge in the course of the set formation process represents an unsurpassable — albeit mathematically indeterminable — limit, what Cantor called the “absolutely infinite”: an “absolute quantitative maximum” that is larger than any set with a definite cardinality and is incapable of either determinable measure or any definite form of increase; no two absolutely infinite sets can differ in size in any mathematically definite sense.

So if SIA is right then you should think the number of people that exists is this giant infinity that’s way more than the number of numbers. Standard atheistic multiverses don’t get you anywhere near that number of people. You need chicanery to get more people than numbers. So if there’s no God, the odds there’d be that many people are very low. In contrast, because it’s good to create, if there is a God, it’s reasonably likely he’d do a lot of creating. Thus, the fact that there’s a ridiculously large infinity worth of people—confirmed by the SIA—is strong evidence for theism.

Here are the basic steps in the argument:

1. SIA is right.

2. If SIA is right, then the number of people is a very large infinity (if it can even be called a number).

3. The odds of the number of people being a very large infinity are vastly higher given theism than atheism.

4. Thus, the fact that the number of people is a very large infinity is strong evidence for theism.

The paper didn’t argue for 1. Instead, we simply argued that if you accept the self-indication assumption, then you should start thinking that the number of people is some giant-ass infinity (that’s a technical term for an infinity that is very large). If you think that, then you should be inclined toward some pretty exotic picture of reality. The main options we discuss are axiarchism (some generic force of limitless power that compels good things to happen), theism, and modal realism (the view that every possible world concretely exists). All of these have the potential to produce some ridiculously large number of people. Standard atheism has much more trouble.

Why? Well, the number of possible people is very large. To explain how large, I’ll have to tell you a bit about infinities. The smallest infinity is aleph null (ℵ0). It’s the number of natural numbers: 1, 2, 3, 4, etc. Bigger than that is Beth 1 (ℶ1)—the number of real numbers, which includes every decimal number, even infinite non-repeating decimals. Bigger than that is Beth 2 (ℶ2). All of these describe the size of sets. But there are some collections that are too big to have an associated cardinality. For example, you can prove that there can’t be a cardinality of the collection of all truths.¹

So how big can we prove the “collection” of possible people is?²

Here’s an argument that there are at least ℶ1 possible people. There are ℶ1 positive real numbers. It seems you can create a copy of me with a height for each of the positive real numbers. Thus, there are at least ℶ1 possible people.

There are ℶ2 ways of arranging space-time points. If a region contains ℶ1 spacetime points and each point admits at least two relevant states, there are ℶ2​ binary arrangements of those points. So if there’s a version of me with each of the points in his hand scrambled in any way they can be scrambled, then there are at least ℶ2 possible people.

So long as you can clone a person N times, where N is any distinct cardinality, then the number of possible people must be absolute infinity (Ω); it must be too big to have a cardinality. And so long as you buy the right version of the SIA, on which your existence favors the presence of more people, rather than the existence just of a larger share of possible people, your existence confirms that the number of possible people is Ω (for more on this, see section 4.3). After all, there are more total people if Ω people exist than some smaller number.

Thus, if SIA is right, then your existence gives you arbitrarily strong evidence that the number of people that exists is the most it could be. Probably that’s Ω—too large to have a definite cardinal ranking. The odds of so many people existing are high (or at the very least not very low) if God exists. If God is going to bother creating at all, he has no reason to stop after one universe, or ten, or one hundred. If creating is worth doing, there’s no reason to stop before creating Ω universes. Thus, conditional on God creating anything at all, it seems very likely that he’d create the very most people he could.

Contrast that with atheism: what is the plausible atheistic story on which you get even ℶ2 people, much less Ω people? Standard atheistic multiverses like eternal inflation just get you ℵ0 people. The many worlds can maybe get you a bit more, but not enough³—and certainly not Ω. To the best of my knowledge, there has never been a theory of physics proposed that gets you enough people.

So if the argument is right, standard non-exotic “physics is all there is” pictures of reality are out. You’ll need to believe in something very weird like modal realism. And modal realism probably undermines induction: if there are infinite concretely-existing worlds that are like ours up until one second from now and then chaotically break, it’s hard to see on what grounds I can rationally trust that our laws won’t break.

That’s basically what the paper argues. If you buy SIA, you can’t be a moderate. You have to think ultimate reality is much weirder—and much bigger—than you thought before. There are a few non-theistic theories that aren’t automatically ruled out, but if the argument single-handedly wipes out 99% of atheistic probability space, then that’s a reasonable success!

1. On standard views, there is no set of all truths. On Menzel’s view, there would be a wide set of truths.

2. Note: I call it a collection. If it’s not a set, it’s not clear that it’s really a collection. But I’m going to call it that for ease of exposition. It also might be a set.

3. It can’t get you enough for the following reason. Assume there are K branches (on some way of precisifying). There are 2^K ways to subcollect K branches, so there are 2^K possible people across branches. By Cantor’s theorem, 2^K>K. Put more simply: you could make more people by taking every arrangement of wave function branches.