The Anthropic Argument For Theism
This is probably the best argument for theism
For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things have been created through Him and for Him.
—Colossians 1:16
Descartes, in his quest to disprove scepticism, endeavored to first prove that he himself existed, then that God existed, then that others existed (he made sure to do his proof in order of importance). This argument is similar—it starts with the assumption that I exist, then goes on to show that infinite other people exist, then goes on to show that God exists. I’ve already discussed this argument with Joe Schmid and have briefly described it in a previous article, but seeing that it’s the argument that moves me most in favor of theism, I thought it would be worth discussing in more detail. I’m also writing a paper on this argument with my friend Amos Wollen, which makes it especially worth discussing.
The argument is fairly simple. I exist. If there were a God, my existence would be very likely, but if there were no God, I almost certainly wouldn’t exist. So the fact that I exist is very strong evidence for God.
Why think that my existence is very likely if there’s a God? Simple: God would create all possible people. It’s good to create a person and give them a good life. There’s nothing stopping God from creating any person, so he’d make them all. God would make anything that’s worth making, and every person is worth making, so God would make every person.
I don’t claim to be totally certain of this. Maybe God can’t make all people for some reason. Maybe I’m wrong about population ethics and the anti-natalists are right (that’s very unlikely though). Or maybe, as some have supposed, God is permitted to just create some of the people, because he can satisfice. But none of these things are obvious. So at the very least, my existence conditional on theism is pretty probable—say 50%. I think it’s much higher, but this is a reasonable estimate.
In contrast, what are the odds of my existence conditional on atheism? Roughly zero. There are at least Beth 2 possible people. Beth 2 is a very large infinite—it’s much more than the number of natural numbers or real numbers (it’s the size of the powerset of the reals). Wikipedia helpfully explains that it’s the size of “The Stone–Čech compactifications of R, Q, and N,” which really helps you get a sense of the size :).
So on atheism, it’s really hard to see how Beth 2 people could possibly exist. But if fewer than Beth 2 people exist, then 0% of possible people exist, which would make the odds of my existence in particular zero. I’m not special—if 0% of possible people exist, it’s ridiculously unlikely I’d be one of the lucky few that exist.
The problem is, I think, even worse. There aren’t just Beth 2 people—there is no set of all people—there are too many to be a set. I think there are two ways to see this:
There is no set of all truths. But it seems like the truths and the minds can be put into 1 to 1 correspondence. For every truth, there is a different possible mind that thinks of that truth. So therefore, there must not be a set of all possible people.
Suppose there were a set of all minds of cardinality N. It’s a principle of mathematics that for any infinity of any cardinality, the number of subsets of that set will be a higher cardinality of infinity. Subsets are the number of smaller sets that can be made from a set, so for example the set 1, 2 has 4 subsets, because you can have a set with nothing, a set with just 1, a set with just 2, or a set with 1 and 2. If there were a set of all minds, it seems that there could be another disembodied mind to think about each of the minds that exists in the set. So then the number of those other minds thinking about the minds containing the set would be the powerset (that’s the term for the number of subsets) of the set of all minds, which would mean there are more minds than there are. Thus, a contradiction ensues when one assumes that there’s a set of all minds!
If this is true then it’s a nightmare for the atheist. How could, in a Godless universe, there be a number of people created too large for any set? What fundamental laws could produce that? If it can’t be reached by anything finite or any amount of powersetting, then the laws would have to build in, at the fundamental level, the existence of a number of things too large to be a set. How could laws like that work?
I only know of one way and that’s to accept David Lewis’s modal realism, according to which all possible worlds are concretely real. On this view, Sherlock Holmes exists just as concretely as you or I—he’s just not spatiotemporally connected to us. This view is, however, very improbable for a bunch of reasons including that it undermines induction and gives no reason to think reality is simple. Also, the standard reasons for supposing it’s true are bunk, for there’s no way we could come to know about the possible worlds in our modal talk.
There are a few technical objection to the theory that Amos and I address in the paper which I won’t address here because this is a popular article and none of you are reviewers of papers, and as such you won’t raise complaints like “you didn’t address this niche objection given by a random person in 1994 to a different argument that’s sort of like yours and as such you didn’t successfully engage the literature and consequently your familial line will be cursed for ten generations.” But there’s one big objection to the argument which proceeds by noting that it assumes a controversial theory of anthropics.
Anthropics is the study of how to reason about one’s own existence. The doomsday argument and the sleeping beauty problem are part of the broad subject matter of anthropics. Some people have this view of anthropics called SSA (the self-sampling assumption), where you’re supposed to reason as if you’re randomly selected from the set of observers like you. Thus, you should think that there aren’t lots of people like you not on Earth, because it’s unlikely that you’d be on Earth. On SSA, you should think the world has few people like you, rather than many.
I am not at all moved by this objection for three reasons (strap in, this will get a bit technical). The first one is that SSA is very clearly false. Notice how the argument so far has proceeded by observing that I exist and then asking for the best explanation of that. This is how probabilistic reasoning is supposed to work. You look at some data and use Bayes theorem. But SSA doesn’t do that—it asks you to randomly pretend, for no reason other than that it makes sense of anthropic intuitions, that you’re like a jar being randomly drawn from your reference class. Thus, SSA is a bizarre deviation from how probabilistic reasoning is supposed to work. Furthermore it—and all other alternatives to SIA—imply utterly bizarre results, including that one can guarantee a perfect poker hand by making a bunch of copies of them unless they get a perfect poker hand, that are enough to totally sink the view.
Second, suppose you’re not sure if SIA is right (SIA is the view that this argument relies on that says that from your existence you have a reason to think there are many people). If SIA is right and theism is true, it’s likely that I’d exist, for the reasons described. If SIA is right and atheism is true then it’s unlikely that I’d exist. If SSA and theism are true, the odds of my existence aren’t that low but are sort of low (I’ll describe that more later). But if SSA and atheism are true, my existence is ridiculously unlikely, because the universe has to be finely tuned to make my reference class small. If the universe is infinite in size, then my reference class is infinite, and the odds of my existence here are zero. The same is true of every universe that isn’t in a small goldilocks zone—just big enough to have life, just small enough to have a small reference class. Thus, given that you exist, probably theism is true, given that on every view of anthropics, your existence is very unlikely on atheism.
Third, while I think it’s pretty obvious that on theism God would make every possible person, it’s not totally obvious. Lots of theists disagree. So let’s say that SSA is true and there’s a 1% chance God would make only humans. Well, given how low the odds of my existence are conditional on atheism and SSA, this is still very strong evidence for theism.
I think this argument is probably the best argument for God, just narrowly beating out the argument from psychophysical harmony. Now, maybe if you’re unsure about anthropics this should move you less than it moves me. But I’m very very confident that SIA is right. And I think, for the reasons described, even if you’re not sure about SIA being right, or even if you think SIA is wrong, the argument is still ridiculously strong evidence for theism. I literally cannot think of a single way that atheism could accommodate the existence of a number of people too large to be part of any set.
Apologies for the late post. But I found this argument fascinating and wanted to share my thoughts. Also sorry to see the reception you got on the reddit page. I took a peek at the comments, and they seemed especially dull and mean-spirited. Just a reminder of how much we should cherish philosophical blogs like these I suppose!
Before I get into the meat of your argument, let me make a minor quibble about your points that there is no set of possible observers (the observer reference class is greater than Beth 2):
1. As mentioned already in the comments, not all truths are knowable. So it seems dubious that truths can be put in 1-to-1 correspondence with observers.
2. This assumes that infinite minds count in the set of possible observers. But maybe it doesn't make sense to include such minds in the reference class of possible observers one can be. If so, then (assuming every mind is decomposable into a computational structure with finite parts), we won't be able to construct a diagonal proof showing that there is a mind not in the set of all possible observer-minds, since that mind would have to be describable by a real number (i.e. infinite).
Now into the meat of the argument:
A) It seems to me that there is a lacuna in your argument which has to do with the construction of one's reference class. Endorsing SIA doesn't obviate the need for constructing a reference class, since we still need to define what we think an observer is. Reasonable people can disagree about what constitutes an observer. Particularly, if we accept SIA then we accept that we should reason as if we were sampled from the reference class of all possible observers we could have been. But what constitutes an observer that "we could have been"? Maybe a physicalist might argue that an observer can only be a physical entity which is composed of some finite computational structure (related to point 2 above). It could also be argued that we should only consider ourselves to belong in the reference class of entities which could be physically constructed according to possible natural theories. If so, then hypothetical entities in the Beth 2 realm won't count as observers. And the multiverse counter still goes through.
B) It's not clear to me that atheism is incompatible with Beth 2 worlds. Just because we reject theism doesn't mean we have to accept some common naturalistic alternative (e.g. multiverse theory). Maybe there exists some metaphysical principle (e.g. simpler patterns reproduce into complex repeatable patterns) which governs the construction of worlds, and which entails that there will exist uncountably infinite number of worlds where induction is sound, and little to no worlds where induction is falsified. I don't see why our prior for such a principle must be lower than our prior for theism.
Alternatively, one could simply accept the existence of Beth-2 observers in uncountable number of worlds as a brute fact. One presumably has to endorse a brute fact at some stage (whether God or something else). So the atheist can simply say that they take on a brute fact one step sooner in the explanatory chain. Perhaps this could be retorted with appeals to simplicity (similar to Swinburne's cosmological argument), so that accepting a simpler explanation (i.e. God) as a brute fact is easier. However, I find such arguments really dubious. It's not clear to me that there are metaphysical reasons to favor simplicity. Maybe there are physical reasons to favor simplicity (our universe is constructed such that simpler theories will be more likely to be true), but why should we think that the success of simplicity in the physical world is explained by the existence of a metaphysical rule in favor of simplicity which applies to cases outside our physical universe?
C) I think the reliance on infinite classes is problematic for the argument here. Infinity is especially tricky, as evidenced by cases like the measure problem and Pascal mugging. The problem with infinites in general suggests to me that the real trouble in such cases is that anthropic reasoning in ordinary cases is not equipped to handle infinites, and we need to make modifications like introducing cutoff thresholds (e.g. regularization).
Just as an example. Suppose I told you that I was an interdimensional being who had been in contact with a superintelligence that had discovered a new physical theory which predicted some staggering super-infinite class of observers but also predicted that theism was false. For simplicity, let's just say that this super-infinite class of observers was larger than Beth omega.
Now obviously you aren't going to believe me. But presumably you should assign some vanishingly small, but still finite, prior credence that what I say is true. But now given the insane posterior shift advantage that my theory, if true, would accrue over the theistic theory, it seems that you must endorse my theory.
I think what this reveals is that we simply can't naively reason on infinities in anthropic cases as we would ordinarily do; we need some cutoff value somewhere. But once we introduce a cutoff value, nothing stops the atheist from asserting that the increase in possible observers from aleph-null to Beth-2 goes beyond the cutoff, and thus does not affect the posterior shift in any way. Hence, theism need not be more probable than multiverse theory.
1. This would also seem to support the evil god hypothesis. If there's only a 1% chance that a good god would create everyone, there seems to be an equal chance that anti-nataliss are right and that there's a 1% chace of an evil god creating everyone as well.
2. This argument defeats psychophysical harmony. If God creates infinite minds, then presumably he will create many minds that are not psychophysically harmonious, and many more which cannot tell the difference. What's to say that you and I are not one of those minds? However, if God really does create every possible mind in a way that's harmonious, then it's unclear why an infinite material universe couldn't do the same. If an infinite universe cannot, why can a (logically constrained) God do so? (Actually this latter point also seems convincing. If there is "no set of all truths" in logic, why can God make one. Are you arguing for some sort of divine transcendence of logic?).
3. This argument seems to also defeat induction in the same way that modal realism does. If an infinite number of actually created minds exists, then surely there are an infinite number of minds where induction spontaniously breaks down, and everything around them turns into cantelopes.
4. One atheist account that solves this argument is to deny that there are other minds exist at all. There is only one possible mind, and it is the mind that is currently experiencing. :P