Richard Carrier Replies To Me On The Anthropic Argument

And makes major errors

Richard Carrier is an atheist, mythicist blogger who goes on at considerable length about the errors of those who argue for God’s existence and Christianity. Carrier writes confidently about numerous topics: philosophy of religion, normative ethics, meta-ethics, history, philosophy of mind, cosmic sperm banks, and more. Recently, he took a break from his busy schedule to respond to various arguments I’d made, including the anthropic argument.

I found Carrier’s responses disappointing because they frequently misrepresented what I said. I can only conclude that Carrier briefly skimmed the article while doing something else (Checking his phone? Cooking pesto? Watching YouTube?), assumed I was saying something very dumb, and called it a day. When he did correctly understand what I was saying, his responses were demonstrably wrong.

Specifically, Carrier addressed an article of mine where I provided a tier list of theistic arguments. In this article, I’ll only respond to the things that Carrier said about the anthropic argument—most of his replies to my other arguments involved saying false things and then linking to various articles of his. I’ll have another article out soon where I address those. Carrier writes of my tier list, where I give some theistic arguments low rankings:

It’s kinda silly. Kudos for them grading the arguments F and D that they do (they correctly suss why those are bad arguments). But they themselves get an F for actually thinking the The Anthropic Argument they present is even logical (it is a rank fallacy; and ironically, when restructured to be valid, argues for multiverse theory, not gods: see Six Arguments That a Multiverse Is More Probable Than a God). That even makes me wonder if this article is a Poe.

Regarding this statement, I can only quote the words of Carrier himself “it’s kinda silly.” To explain why this is, I’ll have to provide some context. The anthropic argument, for those unaware, argues roughly the following:

1. You’re likelier to exist if more people exist (e.g. if a coin gets flipped that creates one person if heads and ten if tails, then if you get created from this process, you should think the coin came up tails at 10:1 odds). Note: I didn’t make this principle up. It’s in fact been mostly defended by atheists in other contexts, like the saintly Joe Carlsmith (blog here).

2. By the above logic, you’re infinitely likelier to exist if there are infinite people, so you should think there are infinite people given that you exist.

3. More specifically, you should think the number of people that exists is the most that there could be. Because each infinity is infinitely bigger than the infinities that are smaller than it, you should think that whatever infinity is equal to the number of possible people that exists, is also equal to the number of actual people that exists. So, for example, if there are Beth 2 possible people (that’s a big infinity) you should think there are Beth 2 actual people.

4. Because the number of people that could exist is a very large infinity—far more than the number of numbers—if there’s no God, it’s very unlikely that such a number of people would exist. One needs a very gerrymandered multiverse to produce the right number of people. In contrast, if there is a God, because it’s good to create, it’s expected that the number of people that would exist is the most there could be. Thus, the fact that, as established by 1-3, the number of people that exists is the most there could be, is powerful evidence for theism.

Or, to be more concise: SIA says theories that say there are more people are better, in which case you should think the number of people is the maximum that it could be. This makes more sense if there’s a God who desires to create and has no limits on how much he can create than if there isn’t.

Note: here I have not defended the steps in the argument, I have just explained what the steps are. So if you are thinking to yourself “all these premises are unjustified, and he hasn’t said anything to support them, hasn’t this fellow heard about begging the question,” I suggest that you read what I have written in defense of the argument. You can certainly disagree with the argument, but given that over the years I’ve written probably the length of a book in defense of it, no one can accuse me of leaving the premises unsupported.

Anyway, we now have context to discuss Carrier’s claims. He first says the argument “is a rank fallacy.” Unsurprisingly he does not discuss what about it is supposedly fallacious. I suppose this is just one of those things that one can simply assert!

Next, he says “when restructured to be valid, [it] argues for multiverse theory.” Regarding invalidity, I think he misunderstands what the point of my list was. In the article, I had a list of steps explaining the argument, like the list displayed above. This was not intended to be a deductively valid formal argument but merely an informal explanation of how the argument basically works. Indeed, the argument isn’t even a deductive argument. This is like objecting to a statement from a politician that “we should have Medicare for all because people deserve free healthcare,” on the grounds that it’s not deductively valid.

If you want to be precise about the argument it is a Bayesian argument. It argues that some fact is likelier if theism is true than if it is false. The fact in question is that the number of people that exists is the most there could be. The argument claims that the probability of that is higher given theism than given naturalism. If one wants to make the argument formal:

Let N be the size of the collection representing the number of possible people:

1. There are at least N people (deduced from the fact that you exist).

2. The existence of at least N people is vastly likelier if theism is true than if theism is false.

3. If some fact is vastly likelier if a theory is true than if it’s false, then that fact is strong evidence for the theory.

4. Therefore, the fact that N people exist is strong evidence for theism.

I was particularly amused by Carrier’s statement that the argument “argues for multiverse theory,” as if that was a refutation of it. Um, yes. That is indeed the argument. It claims that your existence gives you evidence that there is an enormous multiverse, and that the probability of such a multiverse existing is much higher given theism than given naturalism. This is like objecting to the fine-tuning argument on the grounds that it points to a fine-tuner. Indeed! That is the point of the argument. Carrier doesn’t engage at all with my arguments for why the existence of a multiverse of the requisite size would be evidence for theism. Carrier’s triumphant declaration that it argues for a multiverse theory not God shows that he has not grokked the argument.

Skipping to Richard’s next commentary on the anthropic argument, he writes:

P.S. If it isn’t clear, the reason their favorite argument (their “Anthropic” argument) is fallacious is so multiple as to be laughable (which is why I struggle to believe they actually intend this seriously, given their acumen in respect to earlier arguments they evaluate):

“Suppose that a coin gets flipped which creates one person if heads and ten people if tails. You should, after being created by the coinflip, think tails is ten times likelier than heads.”

This is false as stated. If it’s a coin flip, it’s 50/50 either way. The number of persons resulting has not been stipulated to affect the probability of a coin landing on tails. So they have started with a blatantly self-contradictory premise. They basically aren’t explaining why the tails side of a coin should get heavier simply because of an effect it later causes. In other words, they have not stated why their premise is supposed to be true.

Richard calls my view “blatantly self-contradictory” because I hold that in the case described you should think the odds that the coin came up heads is not 50%. Now, this problem, or at least a variant of it, has been endlessly discussed in the philosophical literature. It would therefore be surprising if one of the positions—one adopted by the slight plurality of philosophers—was “blatantly self-contradictory.”

The problem with Carrier’s reasoning is that it’s not blatantly self-contradictory to think that the odds a coin came up tails are more than .5. Honestly, this point is sufficiently elementary that it shouldn’t need to be stated. Suppose, for instance, that my parents flipped a coin after meeting. If it came up tails, they agreed to never have sex. Well then I should think at 100% odds that the coin came up heads!

It’s true that you should think a coin will come up heads with 50% probability if you have no other evidence. However, it is claimed by those who adopt my view that from the fact that you exist, you do have evidence that the coin came up tails: you’re likelier to exist if the coin came up tails. Thus, Carrier’s principle is demonstrably false.

Contra Carrier, I obviously do not think that “the tails side of a coin should get heavier simply because of an effect it later causes.” Likewise, I do not think in the case that I just described that my parents’ resolutions affect the weight of the coin. Instead, I presently, from my existence, have evidence that it came up heads.

The self-indication assumption (SIA) is the name of the view that your existence gives you evidence that there are more people. It is thus amusing that, as I’ve shown in various places (see section 3.1), only SIA consistently maintains that before flipping a fair coin, you should think at 50% odds it will come up heads, if the only effects of it coming up heads or tails will be present after the coin is flipped. If Carrier is really wedded to his principle that you should think a fair coin will come up heads with 1/2 probability, then he’ll have to accept SIA, and thus grant that your existence gives you infinitely strong evidence that there are infinite people.

Carrier says that I “have not stated why [my] premise is supposed to be true.” Well, perhaps he would have done well to consult the article where I defend the argument, rather than the article briefly summarizing it. In fact, in the brief summary article, I tell people to consult the other article if they want to know more about the argument. The tier list article which Carrier drew on was a summary of the arguments I like, not an in-depth defense.

Carrier’s claims get even more confused with his next volley:

“If 10 people existing makes your existence ten times likelier and 100 people existing makes your existence 100 times likelier, infinity people existing makes your existence infinitely likelier.”

This gets closer to a correct intuition, but gets probability arithmetic wrong.

First, it is not possible, in the sense required, for the probability of your existence to be infinite. Probability is analytically bound to a finite limit of 100%. You can’t be “more” than 100% likely to exist. So once you get to, say, a 99% chance, going to infinity can only get you to 100%, which is only 1% more likely. That is not enough to conclude the base number should be infinite.

Dear reader, did I say that the probability of your existence was infinite? If I had, that would indeed be a rather embarrassing error. But if one reads carefully, they’ll notice that I did not say that! Instead, I said “infinity people existing makes your existence infinitely likelier.” Now, I can see how one might think that I said that the probability of your existence is infinity if they stopped reading the sentence after the word infinitely (perhaps their pesto was ready) and did not notice the ly at the end. But, in fact, I said that it’s infinitely likelier you’d exist if infinite people exist than if finite people do.

Can one thing be infinitely likelier than another? Indeed it can. For instance, if you’re in an infinitely big hotel, it’s infinitely likelier that you’re not in room 1 than that you are. The odds you’re in room 1 is 0 or infinitesimal, the odds you’re in a later room is infinitely greater.

Especially since the probability that it is one of the finite numbers is the sum of all finite options, which will sum to near 100% (infinitesimally near, in fact), whereas the probability that it will instead be infinite must be the converse of that, which is near 0% (infinitesimally near, in fact). So we should not conclude the population is infinite. It will far more likely be finite.

Carrier here is assuming that you should just brazenly apply the indifference principle across the numbers of people there might be. Because there are infinite finite numbers, and (so he claims) just a single infinite number, it’s infinitely likelier that there will be a finite number of people than an infinite number. This is so badly confused, I almost don’t know where to start.

I mean, first of all, there are actually infinite infinite numbers. Beth 0, Beth 1, Beth 2, etc. So even by Carrier’s logic, the odds of there being finite people wouldn’t be certain. There are many more permutations of infinite sets than finite ones.

Second, Carrier assumes an indifference principle over the number of people there might be. So, for instance, he assumes that it’s just as likely there’d be infinite people as that there’d be exactly 392489743289^355984322 people. But this is a patently ridiculous assumption that implies you should start with a 0% prior in there being infinite people. But you obviously should not assign a 0% prior to an infinite universe.

If you assign a 0% prior to an infinite multiverse, you have to think that no matter how strong the scientific evidence was for an infinite multiverse, you should always reject it. This is clearly ridiculous. Infinite people existing follows from many simple, natural assumptions like those that go into most multiverse models; you shouldn’t assign it equal probability to some highly arbitrary, totally random number of people existing like 392489743289^355984322.

Third, Carrier is totally neglecting the implications of SIA. If your existence is likelier if there are more people, then we won’t assign uniform probability across the numbers. We’ll think that aleph null people existing, for instance, is infinitely likelier than any particular finite number of people existing.

Now you might reply that I’m assuming SIA without justifying it. This is true. I have not argued for SIA in this article, though I’ll briefly sketch one argument for it a bit later. I have done this elsewhere, and have no desire to repeat myself. So if you want to know why I think SIA is true, see here, for instance.

But worse than that, the probability of 1 person existing if 10 do is already 100% (think about it). So increasing the population does not increase this probability at all.

Their premises are badly worded (note the first premise). So they might have meant to say (but failed to say) that they mean the probability of uniquely you existing, and if infinitely many unique people are possible, the probability you would exist is infinity to one, unless all people exist (likewise, if there are instead, say, only one billion possible people, the odds you would be among them do go up the more people there are).

Richard says that my premises (they aren’t premises, but a numbered list of the basic steps in the argument) are “badly worded,” so that he needs to guess if that’s what I’m saying. What I in fact said was “You’re likelier to exist if there are more total people that exist.” No guesswork is needed if you read what I said—the principle is that it’s likelier that you, in particular, would exist if there are more people.

But that would be a Fallacy of Neglected Total Probability.

The probability that some unique person would exist is 100%; so their being unique is not improbable. Since every person who could exist could say the same, there is no improbability to their existing that matters to this equation. In Bayesian terms, the probability that someone would be in that position if ten are is 100%. It is not the probability of that particular person being selected; because that probability is the same for every possible person, none can claim to be less probably the one who would be selected.

Richard accuses me of committing the fallacy of neglecting total probability. Then, in very next sentence, he at considerable length and with great zeal commits the fallacy of neglecting total probability.

The fallacy of neglecting total probability occurs when one fails to fully take into account all the probabilistically relevant features of a scenario. For instance, you’d commit the fallacy if you said that a person committed the murder on the grounds that they were found near the crime scene with a knife, but neglected to mention that it was a butter knife and the person was shot with a gun.

Richard notes that the probability that some person would exist is 100% as long as at least one person exists. Thus, he claims, you cannot infer that lots of people exist from the fact that you exist. But treating your evidence only as “some person exists,” neglects your total evidence. You don’t just know that some person exists, but that you exist! That’s likelier if there are more people. The principle of total evidence says that you should take into account the most specific version of your evidence; you include that the person was found with a butter knife, not just that they were found with a knife. Carrier violates this principle and commits the fallacy of understated evidence by neglecting that your evidence is quite specific: you know not merely that someone exists but that you do.

An analogy should help illustrate the point. Suppose everyone in the world is put to sleep. Then a coin is flipped. If it comes up heads, one person wakes up at random. If it comes up tails, everyone in the world is woken up. If you wake up, you should think that the coin almost definitely came up tails. Both theories predict that someone would wake up, but only the theory that it came up tails predicts that YOU would wake up.

Or, to give another analogy, suppose that everyone in the world is given a number. A coin is flipped. If it comes up heads, a random one of the numbers glows red. If it comes up tails, all the numbers glow red. If your number glows red, you should think it probably came up tails. Both predict that some number would glow red, but only tails predicts that your number, in particular, would glow red.

Carrier notes that if someone is created, then necessarily there is some particular person who will exist. But it is not necessary that you would be the particular person that exists. You are much likelier to exist if more people do.

Here’s one way to see this that I’ve expounded on at length before. Suppose that one person is created. Then a coin is flipped. If it comes up tails, one other person gets created. Now suppose that you get created from this process but don’t know your birth rank. In other words, you don’t know if you’re the first person, the second, the third, etc. What odds should you give to the coin coming up tails when it’s flipped?

The answer: 2/3. The argument for this is:

1. The probability that you’re the first person and the coin will come up heads = the probability that you’re the first person and the coin will come up tails. (After all, if you learned you were the first person, you should think it’s equally likely it will come up heads and tails).

2. The probability that you’re the first person and the coin will come up tails = the probability that you’re the second person and the coin has come up tails.

3. Therefore, the probability that the coin came up tails is 2/3 (of the three events with equal probability discussed above, two of them involve the coin having come up tails).

Switch around the numbers and you get the same result in other cases: you’re likelier to exist if there are more people.

Next, Carrier says:

“That’s a really huge number. Theism can nicely explain why that number of people exists, but atheism has no comparable explanation. In fact, because it’s good to create, theism actively predicts that number of people existing, while atheism does not.”

This is a strange conclusion. It would appear to be falsified (and thus prove God does not exist), since infinite people observably don’t exist. So I am not sure what they think they just said.

Oh no! I forgot to check census statistics! I had thought earth had infinite people, rather than 8 billion. How could I have made so foolish an error.

My view, of course, is that there’s an infinite multiverse, not that infinite people are all on earth. I do not think that there are infinite people on earth, obviously. One commenter even pointed this out, saying “They argue that infinite people exist throughout the multiverse, not on Earth.” In response, Carrier replied:

Which is not observed. So it cannot be cited as evidence confirming the theory. That’s my point.

That apologetic doesn’t work anyway because the prediction should be observed in this universe, not unobserved ones. So the prediction failed. Whereas atheism exactly predicts what we observe. So this is evidence against theism.

But it follows from the self-indication assumption—the principle that you’re likelier to exist if there are more people—that your existence gives you infinitely strong evidence for an infinite multiverse. If SIA is right—which I’ve argued for at length—then your existence does give you infinitely strong evidence for an infinite multiverse. Carrier says that the evidence must be in this universe, but it is! The odds that this universe with you would exist is infinitely higher if an infinite multiverse is created, for the reasons I’ve already given (in the brief argument I gave for SIA a few paragraphs back, just replace people with universes containing exactly one person). See also the other arguments I give in the piece arguing for SIA.

Perhaps this is atrocious wording again and they meant why the number should be finite (and not the “really huge number” they just affirmed a premise before), and I suppose, somehow uniquely six billion or so, and not ten or a quadrillion. But of course atheism explains this better: causal history has determined not only how many people there shall be at any given time, but also why it should be bounded (Earth cannot sustain a quadrillion people, much less infinitely many, nor has there been time enough to generate so many people). By contrast, “God” predicts all planets and space should be fully inhabited (and we should indeed see boundlessly many people exist), which prediction has failed, and therefore their own argument refutes the existence of God.

Perhaps if Carrier wanted to know what I meant, it would have been helpful for him to read the lengthier clarification of the argument! I do not mean that there are finite people—that’s why I said there are infinite people. Normally when I mean to say that there are finite people, I do not say that there are infinite people. In fact, of all the sentences in the English language, that is the one least conducive to conveying that there are infinite people. The people are not all on earth, but they exist throughout the multiverse (or so follows from the SIA, which I’ve given arguments for).

Regarding his final claim that theism predicts the entire universe being inhabited, see here for my reply to this.

I appreciate Carrier taking the time to reply to me on the anthropic argument. It’s an interesting argument, and I hope it gets more attention. I’d also be happy to have a debate with Richard about it. Hopefully, though, when he next explains what he thinks is wrong with it, he will actually attend to what I said.