Not too long ago, I had a discussion with Bentham's Bulldog (BB) on his Youtube channel, with regards to his anthropic argument for theism. However, due to time constraints, my drowsiness at the time, and live discussions not being my forte in general, I wasn't able to succinctly express many of my problems with the argument, nor push back as much as I'd like to have. This post will serve as my fully expressed thoughts on the argument, why it doesn't move my credence in theism one bit, why I think it probably shouldn't move almost anyone's credence in theism, as well as a resource for those interested in objections to the argument. This will be a somewhat technical one, so strap in.
Table of Contents
The Anthropic Argument
The Self Indication Assumption and Infinite Sets
1.1 From Googols to Infinites: The SIA Across Different Scales
1.2 Preempting Two Objections
1.3 An Intuition That Cuts the Other Way
1.4 Trading One Improbability for Another
Theism and Possible People
2.1 Is it Always Good to Create a Person?
2.2 God and Creation
2.3 The Duplication Objection
2.4 Double-counting the Problem of Evil?
Naturalism and Your Existence
3.1 Stalking Horse Naturalism
3.2 The Simplicity of Theism
3.3 Multiverse Naturalism
The Anthropic Argument is a novel Bayesian argument for theism conceived of by BB and Amos Wollen. Bayesian arguments for theism are not themselves much new, you have Bayesian arguments from fine-tuning (Collins 2009), Bayesian arguments from the existence of conscious agents (Page 2020), the argument from psychophysical harmony (Cutter & Crummett forthcoming), and so on. What is new about the anthropic argument for theism is the use of anthropic reasoning to argue that, when taking into account the data of one's own existence, one should update heavily in favor of the theistic hypothesis, in particular perfect being theism. Why? The idea, so the argument goes, is that we should hold to an assumption in anthropic reasoning known as the Self Indication Assumption (SIA), which states that, all other things equal, an observer ought to reason as if they are randomly selected from the set of all possible observers. So, when taking into account the fact that I/you, a particular observer, exists, we should update in favor of hypotheses which predict that there will be more observers. This is because, for hypotheses which predict more observers, there would be more "slots" available for one of those observers to be you or me, and since you have an equal chance of filling each observer slot as anyone else, the more observer slots there are, the more likely it is that you will be one of those observers.
Now, here's the kicker. The theistic hypothesis posits that there is an agent, God, that is morally perfect and so desires to act in accordance with their moral reasons, and omnipotent and so has the ability to do so, insofar as it is logically possible. It is morally good to create a person and give them a good life. So, for every possible person God could create, including you and me, He has a strong moral reason to create them and give them a good life and can do so. Thus, we have good reason to think that the theistic hypothesis predicts that all possible observers which would include you will obtain. Oh, and did I neglect to mention that the number of all possible observers, it is argued, is at least ℶ2 which is the cardinality of the powerset of the real numbers (a really big infinite!)? In fact, BB claims it is even greater than that (More on that shortly). So, God would likely create all possible people, a set that has the cardinality of at least ℶ2. Letting T be theism, and Y be the data of one's own existence, we can say that P(Y|T) is high. What about, P(Y|N) where N denotes naturalism? On naturalism, fundamental reality is indifferent, so it's no more antecedently probable that any observers would exist at all over the many ways natural reality might give rise to no observers at all. Worse yet, even if natural reality does give rise to observers it would be indifferent between there being ℶ2 observers, or any finite quantity of observers, or even a smaller infinite quantity of observers such that it would be extremely unlikely that you'd be among those observers. So, on naturalism, it is not likely that any observers exist, and it is extremely improbable that you, of the uncountably infinite possible people that could exist instead of you, would exist. So, P(Y|N) is very low. Taking stock, the argument could be formulated as follows. Where '>' denotes 'is more probable than' '>>' denotes 'is significantly more probable than', and k is our background knowledge.
1, ¬(P(N&k) >> P(T&k))
2. P(Y|T&k) >> P(Y|N&k)
3. Y obtains
4. Thus, P(T|Y&k) > P(N|Y&k)
The first premise says that the prior probability of naturalism together with our background knowledge is not significantly greater than the prior probability of theism together with our background knowledge. I actually think 1. is false and we’ll get to that later, but my critique is not going to hinge on it. Some views that deny the existence of the self might reject 3. I won’t get into that, however. The second premise is the central point of dispute that will be the target of the lion's share of my critique.
Before moving on I'd like to address one of BB's claims in his post on the argument, regarding just how large the number of all possible observers is. He says the following;
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:
1. 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.
2. 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.
BB here claims that there are too many minds for there to be a set of them. Yet there is still some number that is the number of all possible minds, and God could create that number of possible minds. Unfortunately this is incoherent, and indeed the fact that there is no set of truths or persons is, if true, a nightmare for the theist, not the atheist.
Why is there no set of all truths? Because if there were a set of all truths T, there would be a powerset of T, P(T), which is the set of all subsets of T. However, for each subset S of T there would be a unique corresponding truth f(S) where f(S) = T1 is in S and f(S) would have to be in T. This means that you could have an injective function which maps elements of P(T) to elements of T. But, as proven by Cantor's Theorem, for any powerset P(X) of any set X there cannot be an injective function mapping elements of X to P(X). So the notion of a set of all truths is contradictory. This doesn't mean that there is some amount n, that is the number of all truths and that n simply cannot be reached by 'powersetting'. It means there is no such n. So, if there is no set of all truths, then for any n, no matter how large an infinite, that n could not be the amount of all truths. I'll also note that this doesn't mean there cannot be true propositions, but it does in fact mean that there is no such thing as "all truths" on pain of contradiction. It also implies that omni-theism is incoherent insofar as God is understood as knowing all true propositions. As it happens, Patrick Grim, who is the one who argued that there is no set of all truths in the paper BB links to, argues that such a consideration renders divine omniscience incoherent (Grim 2000).
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 tantamount to the claim that there is an amount of things too large for there to be an amount of them. Being charitable, the only intelligible thing in the vicinity of what BB might have in mind is that the amount of possible people is an 'inaccessible cardinal' which cannot be reached by taking the powerset of any smaller cardinal number, including uncountable infinities like ℶ2, ℶ3 and so on. But even if there are inaccessible cardinals, which isn't proven by the ZFC axioms, they aren't 'too large to be a set'. Nor are such cardinals closed under the operation of powersets. For any inaccessible cardinal k, its powerset P(k) is still larger than k.
If, as BB argues, for the same reasons, there cannot be a set of all possible minds, that just means, again for the same reasons, that 'all possible minds' cannot exist whether we are theists or naturalists, as the very concept is incoherent. To make this more clear, 'all' quantifies over every element in a domain, the problem is if there is no set of all possible minds there is no 'every element' we can quantify over, because, per BB's argument, for any n amount of elements we quantify over, no matter how arbitrarily large, there are more possible minds than n. Even God cannot make it the case that all possible people exist. Because, for any amount of people God actualizes, He wouldn't have succeeded in actualizing all possible people. To make this even more clear we can even run the exact same set-theoretic paradox, by simply treating God-actualizable states of affairs as sets to show that it isn't logically possible for God to create all possible people given BB's own view!:
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
In conclusion, the suggestion that there is no set of all truths, and in the same way no set of all possible people is a disaster both for the logical coherence of omni-theism as standardly understood, and the prospects of the Anthropic argument. If the concept of a set of all possible people is incoherent, then neither theism nor naturalism can predict an amount of possible people sufficient to make one's own existence probable given SIA, as the very notion of such an amount entails a contradiction. Contra BB, I will henceforth assume there are no devastating set-theoretic problems which provide a priori reasons to reject the argument and that the cardinality of all possible people is ℶ2. Indeed, I take it that BB's argument for thinking there is no set of all minds is dubious and can be safely put aside anyways, as it assumes, without argument, that for any proposition P, there is a distinct possible mind that thinks about P.
The Self Indication Assumption and Infinite Sets
1.1 From Googols to Infinites: The SIA Across Different Scales
One immediate issue one might have is whether the SIA, the anthropic assumption the argument relies on, is correct, and if so if it can be used in cases involving infinites. I will grant that the SIA is the correct account of anthropic reasoning (something I'm agnostic about). BB has many articles on his blog discussing motivations for the SIA and I'd like to avoid getting into the weeds of that debate. What I will dispute though, is the claim that we have reasons to update in favor of hypotheses which predict more possible observers where the total space of possible observers is some higher order infinite like ℶ2. Recall that the SIA as defined by Nick Bostrom says the following;
SIA: All other things equal, an observer should reason as if they are randomly selected from the set of all possible observers.
Given the SIA, and given that the set of all possible observers is some really large finite number, it's clear why we should update in favor of hypotheses which posit that the world contains more observers. Let's say the total amount of possible observers is a googol or 10^100 which, for the record, is orders of magnitude more than the amount of atoms in the observable universe. Suppose you have two hypotheses about the observers the world contains, H1, and H2. H1 says that all observers in the world are just those observers that we know to exist, will exist on our planet, and have existed on our planet. Now, what counts as an "observer" is not entirely clear but for simplicity we'll just assume that humans are the only observers on earth. It's believed that, to date, approximately 117 billion human beings have existed throughout history, and we'll say that according to H1, in the future exactly 117 billion more observers will exist. So, H1 posits that there are 234 billion observers. H2, on the other hand, posits that there are vastly more planets with observers like ours perhaps in some vast multiverse scenario, such that the total amount of possible observers that are at any time instantiated in the world is something like 5 x 10^99 or five duotrigintillion. How do we assess the probability that you exist on both hypotheses? Let's start with H1, which posits there are 234 billion observers. We know that there are googol possible observers, and, given SIA, we reason as if we are just as likely to be any one of those possible observers as any other. So, in a scenario where only 234 billion observers exist, the probability that you would be among those observers is 234000000000/10^100, which is 2.34 octovigintillionths of a percent, a percentage so small that it might as well be 0%. What about H2? On H2 the probability that you would be among the observers that are instantiated is 5 x 10^99/10^100. Which is 50%, in other words your existence given H2 isn't so surprising, it's basically the flip of a coin, whether you will exist or not. So, conditional on the fact, Y, that you exist, you should massively update in favor of H2 over H1. Since, P(Y|H1) is extremely low, and P(Y|H2) is .5.
We've seen how updating in light of the data of one's own existence can work if the set of all possible observers we are working with is finite. What if the set of all possible observers is an infinite set like ℶ2? In that case, both P(Y|H1) and P(Y|H2) would be 0. This is because, while H2 predicts more observers than H1, any finite number no matter how large, is infinitesimally small compared to an infinite set. For both H1 and H2, despite the fact that H2 posits much more observers, the amount of possible observers that are unaccounted for is precisely the same, ℶ2. The same would apply if we construct hypotheses that posit the existence of ℵ0 or ℶ1 possible people, ℶ2 possible people would still be left out. You might think that this can be fixed if you take a hypothesis, H3, that states that there exists an amount of people with the cardinality of ℶ2. Surely, the probability that you would be among the ℶ2 possible people that exist given that there are ℶ2 possible people as H3 says is 1, right?
Unfortunately, while this may seem right prima facie, that's not how infinite sets work. It's true that a finite set can obtain if and only if every element of that set obtains. It's a different story for infinite sets, however. For any infinite set, you could remove any element of that set and still be left with the same infinite cardinality. For instance, the set of all whole numbers {0, 1, 2, 3...} has a cardinality of ℵ0, if you take away the element 0, you are left with the set of all natural numbers, which is still ℵ0. You could go further and remove all even numbers from that set (ℵ0 members of that set) and you'll still be left with a cardinality of ℵ0. With a set of cardinality ℶ2, which is a higher order infinity, the same thing applies to an even greater degree. You could remove any finite number, ℵ0, ℶ1, or even potentially ℶ2 members of that set and still be left with a cardinality of ℶ2. Put another way, even if there are ℶ2 actual observers, we have no idea how many possible observers in the initial possibility space are still left out. It could be 0, but it could also be ℶ2, ℶ1, ℵ0 or any arbitrarily large finite cardinal number. So, it's certainly not the case that there existing a set of ℶ2 observers guarantees that you will exist as a member of that set, nor do we have any reason to think the probability of that is more than 0. Worse yet, standard probability measures don't extend to sets with a cardinality of ℶ2 in a way that allows for useful probability calculations for individual elements of that set, like a specific individual in a set of possible observers. The closest we've got is the Lebesgue Measure, but I won't get into too much detail here as I'm not qualified. Basically, in a set of cardinality ℶ1, you can assign probabilities via a continuous distribution, where probabilities are defined for intervals or Borel Sets. The Lebesgue measure of getting any individual point or element in an uncountably infinite set will always be 0, however. To make matters even more difficult, the Lebesgue measure is specifically tailored to sets with the cardinality of the real number line (ℶ1) in which we have well-defined concepts for "size" like length and volume, not to sets as large as ℶ2. Even selecting a suitable collection of subsets to which our measures are applied (σ-algebra in technical terms) for sets of ℶ2 becomes much harder. While it is no doubt theoretically possible to assign probabilities within sets of any cardinality including ℶ2, there are practical difficulties and no standard way of addressing them as far as I can tell. Even if they are addressed, it remains the case that the probability of getting any individual element in such a set will always be 0. So, P(Y|H3) is either undefined or just 0. Thus, even granting the SIA, there is no reason to update in favor of hypotheses that predict more observers if the set of all possible observers is ℶ2. No matter how many observers a hypothesis posits, the probability that you exist conditional on said hypothesis won't be greater than 0.
1.2 Preempting Two Objections
There are a few objections that might be levied at this juncture. It might be objected that while the probability that you are a member of a set for which all that is known is that it contains a cardinality of ℶ2 observers, is 0 or undefined, we aren't talking about such an unspecified set here. We are talking about a set, the contents of which necessarily include all possible observers. Such a set by definition would contain you as a member since you are a possible observer, and said set just happens to have the same cardinality as any set of ℶ2 observers. This is correct, as far as it goes, I agree that a hypothesis that predicts all possible observers would indeed entail the data of your existence. What is certainly dubious in the extreme though, is that the theistic hypothesis is one such hypothesis. In the next section under the heading "The Theistic Hypothesis and Possible People" I will discuss some reasons why I think it's false that theism predicts that there will be people like us at all. But even if all my objections in that section fail, 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. True enough, He could create me and you, and it may even be that He has more reason to create me and you than to not create at all. What I'm not convinced of, and what has not been justified, is that God has more reason to create a set of ℶ2 people that includes you and me, over any set of ℶ2 people that doesn't include you and me. Neither state of affairs appears to be more intrinsically valuable than the other, since ex hypothesi, both contain the exact same amount of people whom are given happy lives. So, the case that we should update in favor of theism in light of the data of one's existence remains seriously under-motivated.
Another objection is the one BB raised in our discussion and that he discusses here. The idea I take it being that, if you don't update in favor of hypotheses that predict more observers even in cases wherein the universal class of possible observers is an infinite cardinality of possible observers, this leads to unintuitive results in cases where agents are asked to bet on if there is a smaller or larger infinity of observers. BB gives the following argument, where the USIA is the "unrestricted self indication assumption" a principle which says we should always think there are more people when taking into account one's existence even if it doesn't mean a greater share of possible people exist;
1. If one should bet in accordance with USIA rather than ~USIA, USIA is correct.There are quite a few problems here. To start, 1. is simply false. USIA is correct if and only if your existence is always more probable on scenario's which contain more observers. Yet, we've already seen that this is not the case where the set of possible observers is infinitely large. Indeed, in such a case the probability of getting a particular observer given there are ℶ2 possible observers cannot exceed 0 no matter what number of observers are actualized. So, the USIA is false even if there are possible cases where one should bet in accordance with it for practical purposes. 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. In fact, I don't take a view on that because I don't see any reason to think we have reliable access to the best decision-making procedure for highly abstract and complicated cases of that sort if there even is one. 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. That's wrong, as discussed above, the probability of being in either world, given that we don't know how many observers there are, is 0 or undefined. Perhaps BB wants to say that 5. is referring to a case where you know you exist and that the amount of observers in the world is either ℶ1 or ℶ2. But in that case, two points are in order; (i) this would be an epistemic situation utterly unlike ours since we don't start out with knowledge with respect to how many observers our world contains so it is inapplicable to our situation, (ii) even then because of the aforementioned way infinite probabilities work, it's far from clear that 5. is correct. The probability of ending up in either world looks indeterminate as far as our ability to measure probabilities goes since ℶ1/ℶ2 is undefined. So, the argument has at least 2 false premises, and one highly dubious premise. It is therefore unsound and the objection fails.
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.
Maybe BB wants to say that the claim that rational betting behavior does not align with our probabilistic reasoning in infinite cases is highly unintuitive. Or that the claim that one isn't more likely to be in a world with ℶ2 instead of ℶ1 people is 'clearly crazy'. I've had my fair share of disagreements with BB in the past about this sort of intuition-mongering. I'll note that I do not share his intuition here. And even if I did, I think it is wrong-headed to expect infinites to conform to our intuitions. Especially since we in fact know that those intuitions are unreliable. Take Hilbert's hotel, wherein there are infinitely many rooms each with a guest, yet if a new guest comes to the hotel, the manager can accommodate them despite all the rooms being full. She can even accommodate infinitely many new guests. Now, you can imagine someone stamping their feet and saying "No! Clearly if the hotel is full you cannot accommodate new guests even if it's an infinite hotel! I have an intuition that this is the case!". But, of course, this would be to do little more than profess one's ignorance of infinite sets and their intuition-violating properties. I think the case here is relevantly similar, BB might find it unintuitive that assigning probabilities to infinite sets does not work in the way it does for finite sets. But I take it both that this is unsurprising when we take a moment to think carefully about the properties of infinite sets and how distributing probabilities among them would work, and that we have no good reason to think BB's intuition on this matter is truth-tracking.
1.3 An Intuition that Cuts the Other Way
As regards to intuition, I'll also add that appealing to intuition cuts both ways here. For instance, I, and I suspect many others will find the idea that there are ℶ2 people deeply unintuitive, and basically incomprehensible. For how can we map people in the world to correspond to elements in such a set? We would have no problem doing this for any finite set, or even a countably infinite set such as the set of all natural numbers. You could have a bijective function that maps the first person to 1, the second person to 2, and so on. But how could we possibly do this for an uncountably infinite set, like a set of cardinality ℶ1, let alone ℶ2? Presumably, there isn't a 1.354898675...th person. Worse yet, it looks like we literally couldn't map all people to a set of ℶ1, let alone a set of ℶ2. Famously, Cantor proved it is impossible to list all the real numbers, hence its being an uncountably infinite set. Suppose the first element in the set is the number 1 and that we can map the first person to it, what's after that? No matter what you say, you'll have missed a real number. Indeed you'll have missed infinitely many, because between any two real numbers, there are infinitely many other real numbers. So, the idea that you could put real people in the world in one-to-one correspondence with a set of uncountable infinite cardinality seems highly counterintuitive.
Now, of course, this is merely an appeal to intuition, it's far from a knock down rebuttal to the concept of a set of ℶ2 people that I would hang my hat on. I don't think the possibility of ℶ2 people is something that can be a priori ruled out, and, like I said, I don't think our intuitions about infinite cases like this are reliable. The point is if BB wants to appeal to his intuition regarding infinites, which I suspect he will, it should be noted that such a strategy is a double edged sword. Either we think intuitions of that sort are reliable or we don't. If we do, then BB's intuition goes through but so does this one which cuts against the possibility of a set of ℶ2 people. If we don't, then of course we have no reason to trust BB's intuition to track the truth.
1.4 Trading one Improbability for Another
So much for applying the SIA to cases involving infinite sets. One at this point may point out that the Anthropic argument for theism doesn't necessarily depend on the claim that there are ℶ2 possible people. One could in principle run the argument while assuming a finite possibility space of possible observers, albeit the probability judgment wouldn't be quite as strong. So, I'll finalize this section by providing an objection that leads me to be skeptical of the general prospects of an anthropic argument for theism based on the SIA.
Recall that on the SIA when you take into account the data of your own existence, Y, you should update in favor of hypotheses that predict more observers because there are more available slots for one of those observers to be you. I'll grant this, if H1 is a hypothesis that predicts many observers, and H2 is a hypothesis that predicts much fewer observers, then P(Y|H1) > P(Y|H2). However, this does not mean P(H1|Y&k) > P(H2|Y&k) if we take into account the total evidence. Let's now put the data of your existence in our background knowledge k, and take the further data, that your observations take place relative to a certain body, with a certain perspective, and various experiences that are unique to you. Among the people that exist there's a bunch of others you could have been, but you're you, and not anyone else. Call this data O. What effect does O have on H1 and H2? On H1 there are more people that you can be, so it's less probable, of any one of those people taken individually, that you will be that person. If we suppose you're a priori equally likely to be any one of those then the probability that you are the particular person you are, say Chad, (because you're reading my blog) is 1/n where n is the number of people H1 posits. What about H2? On H2, there are much less people, and so less people for you to be, so it's more likely of any one of the people that exist, that you are that person. It would be 1/n* where n* is the number of people given the truth of H2. Long story short, P(O|H2&Y) > P(O|H1&Y). So, the idea is, we don't have an all-things-considered reason to accept hypotheses on which there are more observers when taking into account one's total evidence. Positing more observers accounts for one improbability, in this case the improbability of Y, at the cost of another, in this case the improbability of O.
We can see using simple math, that these likelihoods P(Y|H1) > P(Y|H2) and P(O|H2&Y) > P(O|H1&Y) will cancel each-other out if we assume a uniform probability distribution, which is what the SIA itself assumes. Let's simplify this and suppose the space of possible observers includes 1 million observers, and that H1 predicts that there are 1 million observers and H2 predicts that there are 100 observers. We can see that P(Y|H1) = 100% or 1, because H1 predicts 1 million observers and there are 1 million possible observers. P(Y|H2) on the other hand would be 100 in 1 million since H2 only posits 100 observers of the million possible observers, which is 0.01% or .0001. P(O|H1&Y) is 1 in 1 million which is 0.0001% or .000001 since there are 1 million observers on H1 and I'm equally likely to be any given one of them. P(O|H2&Y) is 1 in 100 which is 1% or .01, since there are 100 observers on H2 whom I'm equally likely to be. Now, to calculate P(Y&O|H1) we multiply 1 by .000001 to get .000001, and to calculate P(Y&O|H2) we multiply .0001 by .01 to once again get .000001 or 0.0001%. Bingo bango, there you have it, the probabilities counterbalance, and this same general principle would extend to the anthropic argument for theism. Theism, we can grant, makes your existence more likely than naturalism given that theism predicts more observers, but only at the expense of drastically decreasing the probability that among the observers that exist, you are that specific one. We thus have no reason to distribute more of the overall weight of the probabilities to theism than we initially did. The total evidence gives us no reason to update in favor of one hypothesis over the other.
One possible, but ultimately confused objection might be that once we have the data of your own existence in the background, there's nothing left to account for. You are identical to Chad. Once we know that you exist, we already know that Chad exists and that you are Chad. This is false, and commits the familiar error of mistaking intensions for extensions. When I say "you" or you say "I" that designates the same extension, Chad. But importantly, "You" and "I" are indexical terms, they don't have a fixed referent, it can refer to Chad or it can refer to anyone else. "Chad" however does have a fixed referent, it always refers to the same individual. So you can know that when you say "I" you're referring indexically to yourself, without knowing that "yourself" picks out the particular person, Chad. An easy way to see this is that you could have a severe case of amnesia where you end up forgetting who you are, but you'll still know that you are yourself in a trivial sense.
Another way to resist this is to argue that the fact O, that you are yourself and not some other observer that exists is not data you can update on, as it's simply epistemically necessary for you, that you are Chad and not anyone else. Unfortunately, this is unavailable to the proponent of the anthropic argument because we can make this same move to say that the data of your own existence is not data that you can update on, since, from your perspective, your existence is epistemically necessary. This would be to endorse a weak anthropic principle on which you cannot calculate the relevant likelihoods of different hypotheses conditional on your existence at all, as your existence isn't something you can conditionalize on, it's simply a given. Perhaps there's some sort of relevant asymmetry between the epistemic necessity of you being Chad and not Brad, and the epistemic necessity of you existing at all, such that we can't update on the former but we can update on the latter. I'll just note that I don't see what that is, and, as far as I can tell, any motivation for thinking O is not data we can update on, is in turn a reason to accept a weak anthropic principle which is devastating to the anthropic argument for theism.
2.1 Is it Always Good to Create a Person?
In the first section I've considered whether the inference from one's own existence to scenarios in which there are much more observers works for cases involving an infinite set of possible observers. I argued that it does not. I also considered if the SIA can at least be used if there are finite possible observers to show that the theistic hypothesis gets an all-things-considered probability boost, given one's existence and that theism predicts all possible observers exist. I argued that it can not. In this section, rather than targeting the general inference that underlies the anthropic argument for theism, I'll target a specific probability judgment the argument makes, that P(Y|T&k) is high, or at least much higher than a hypothesis that is indifferent to your existence. I take it that what motivates this assumption is (a) that it is always prima facie good to create a possible person and give them a good life, and (b) that there aren't more reasons for God not to create you. It may be alleged that (a) & (b) are jointly plausible, and together make it likely that God will create you, and perhaps all possible people.
It's far from immediately obvious that (a) is true. For starters, it assumes the falsity of anti-natalism and person-affecting views in population ethics, both of which are live views defended by intelligent philosophers, see in particular (Benatar 2006). But even if those views are false, it is not obvious, without further justification, that it is always prima facie good to create someone and give them a good life rather than most of the time prima facie good. Even worse, (a) seems to be subject to counterexamples. 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. Is it prima facie good to create an R-goblin if they end up having a life that is good for them? I, and I think most people, will say no. Importantly, this does not imply a commitment to thinking actual people have intrinsically corrupt natures. Just that some possible people can. There isn't any logical contradiction, as far as I can tell, entailed from the concept of an R-goblin, so it looks like R-goblins are logically possible people that God could create. So, we have a counterexample to (a), and thus (a) appears to be false.
In response (a) might be amended to (a*) in some way or other. Perhaps (a*) is that it is always prima facie good to create a certain kind of possible person and give them a good life. Or maybe we interpret "good life" in an objective-list-theory sense, which precludes R-goblins from having good lives. These suggestions at least concede that there are some restrictions on the possible people it is good to create. But even that's not enough: in order for your existence to be likely given theism, it must be all-things-considered good for God to create you. If there are any better reasons not to create you, or if there are many other equiprobable acts that preclude your existence that are equally or incommensurably good, then it is not at all likely that God would create you. Both (a*) and (b) must hold, it is not enough that we are possible people. It has to be, instead, that it is likely that we are a subset of the kind of possible people that are good to create, and that it is likely that it is all-things-considered good for God to create those people. But why think this? I take it that the case for this is under-motivated and what little justification for this that has been so far proffered by BB is completely insufficient. Further, I think, upon carefully reflecting about what to expect given theism, there are actually good reasons to think it is false that God would create us. I will now provide two independent arguments to motivate this claim.
2.2 God and Creation
The first reason to think it is false that God would create you is that there are reasons to think God would either not create at all, or at the very least not create any imperfect beings like us. Why think this? Here are some reasons:
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. 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. 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. Perfect being theism posits that God is a maximally great being, a being for which no greater is conceivable, or at least, metaphysically possible. 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. So plausibly, you wouldn't have conceived of the greatest possible being, God. This is sufficient to generate the conclusion that for any good God actualizes, no matter how great, the world would not have been better than it was prior to God's creative act. So it looks like God doesn't have a reason to create.
Worse yet, if God were to create any imperfect entities or worldly blemishes, it would appear that the world will have been moved from a state of absolute perfection and goodness, to a state of absolute goodness plus some blemishes or bad stuff. Prima facie, it is utterly mysterious if not inconceivable that God, a being motivated out of pure moral goodness, would move the world from a state of perfection, to a state that contains imperfections. Indeed, it's hard to imagine how imperfection could at all arise, metaphysically, from a state of pure perfection. My concept of pure perfection is one that can only give rise to more perfection otherwise it wouldn't be pure perfection. I'll admit perhaps this is just incredulity or some kind of lack of imagination on my part, but that remains to be seen, and at the very least it's the theists job to motivate the prima facie implausible claim that God would create imperfections.
It may be argued that while God is maximally good or perfect qua being and thus unimprovable, this does not mean a world with God alone is perfect, or maximally good qua world and thus unimprovable. This is the most common objection, and I must admit I find it perplexing. If the world, W1 we are talking about is a world where God exists sans creation, then W1 is coextensive with God, the very same object is being picked out when I refer to W1 as when I refer to God. So, I must ask the rhetorical question, what sense can be made of the claim that W1 can be improved, and yet God cannot? One might be tempted to argue that the possible world where God creates, W2, contains a diversity of beings whereas W1 does not, and diversity of beings is good qua world, and so that is what is meant by good qua world. However, as already argued, since God exemplifies maximal goodness and absolute perfection qua being, the existence of other good beings would not increase the goodness of the world where maximal goodness of being already exists—a point which is further compounded by the fact that things are good only to the extent that they resemble God.
Another possible objection might be that God's reasons for creating people are not grounded in the fact that it leads to a greater world, but out of consideration for the persons He's creating, and the knowledge that it would be good for those people to share in His glory. One issue with this response is that it appears to undermine divine impassibility, a point which I'll expand on shortly. A further point is that this assumes controversial ethical assumptions—if we, for instance, accept that there is an axiological asymmetry, e.g. while it is good in general for there to be an absence of suffering, it's not bad for there to be an absence of well-being or good experiences unless there is someone to be deprived of them, then this point fails to go through. Most crucially, even if we accept that it's good for there to be good experiences even if no-one is deprived of them, it is unclear to me what that judgment is grounded in except for the principle that a world with good experiences would be a better world than a world without them. Yet we’ve seen that the world W2 with imperfect people with good experiences, is not better than the world W1 where God exists alone. Indeed in creating imperfect people, it looks like God must move the W1 from a state of absolute perfection, to a state that contains some imperfections which is, if anything, plausibly all-things-considered worse.
Related to the last point is the next reason to think God would not create. There is, I think, a plausible condition on what an omnipotent, morally perfect and all-knowing being would do which entails that God would not create if said creation involves any evil or blemishes. A couple years back on my blog I defended a version of the logical problem of evil making use of something like this condition, it can be revised for our purposes to state the following;
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.
Now, this condition entails that God would not create morally imperfect or sinful creatures. This is because even if the creation of morally imperfect creatures is an overall good, it still entails moral blemishes or evils E, and per our condition, a morally perfect being would only permit E if E entails a greater good, and there is no even greater good that does not entail E. However, we can see that for any overall good that entails E, there is a greater good which does not entail E. God Himself is such a greater good, indeed, He is the greatest possible good, and God does not entail E, or any evils (I argue for this more in depth on my aforementioned blog post). So God would, being morally perfect, not create any imperfect or sinful creatures.
Why accept this condition? To start, when we simply analyze what is entailed from the concept of a morally perfect being, it's a plausible candidate for a conceptual truth. Why would a morally perfect being intentionally permit some evil E? Upon deeper analysis, a morally perfect being M would have a perfect moral resume, so they wouldn't permit much less actualize an evil E needlessly. It's not enough that E entails or leads to a greater good, if M could bring about the greater good without E, which would of course be a more impressive moral resume. It's also not enough that E is entailed by a greater good, as E is trivially entailed by the conjunctive good G&E where G is a greater good that outweighs the badness of E. Once again, this is because it might be possible for M to bring about G without actualizing E. This plausibly leads us to the analysis that M would not intentionally permit or actualize E, unless permitting or actualizing E is the only way they could bring about a greater good G*, and there is no greater good G which does not entail E, which they could have brought about instead of G*. Furthermore, it explains our judgments regarding ordinary cases. For instance, we ordinarily think a mother needlessly harming her young child is wrong, unless it involves bringing about some greater good, such as a net benefit to the child in such a way that this good could not be brought about without permitting the child's suffering. An obvious example might be forcing the child to take a painful vaccine to prevent a painful or fatal disease. If the mother had access to a procedure that is painless and also guaranteed prevention of the disease, yet chooses to force her child to endure the painful vaccine regardless, we'd think she's doing something wrong. This is because, while forcing the child to take the vaccine would be an evil that leads to a greater good, a greater good is readily accessible to her that doesn't involve forcing the child to suffer. Certainly we would at least think, were the mother morally perfect, she'd pick the option that involved less suffering, all-else equal.
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. Classical theism, and indeed most perfect being theisms, posit God's impassibility. As a perfect being, creation cannot enhance or diminish God's nature. God's actions are understood as intentional and purposeful but not influenced by any external compulsion or need but purely as an act of free will. Consequently, God cannot benefit from creation, He doesn't have any need or desire to create. So, we have a dilemma. If human good is distinct from God’s good, then we have no reason to think God would create humanity, as God is unaffected by human good. Alternatively, if human good isn't distinct from God’s good, the lack of divine benefit from creation still leaves it a mystery why God, a perfect and self-sufficient being, would have any reason for creation (See Mullins 2020) for more on this point). It might be objected that God might still have reasons to create, even if He is unaffected by them. But I can't make sense of this claim. Reasons are if nothing else something which moves an agent’s will. It may also be objected that God may freely choose to create, even though it's not a feature of His nature or an external compulsion, it's simply a free choice as an expression of His love. But this is a point I can grant, it's possible that God would freely choose to create. However, it remains completely unclear why, antecedently, we'd expect God to create, let alone create us. Ex hypothesi, it's equally consistent with God's existence sans creation, that He doesn't create at all, or the infinitely other possibilities wherein God creates but not in such a way to give rise to us. Such a point is quite enough to undermine the probability judgment that P(Y|T) is not low. If we accept that P(Y) is intrinsically very low, the truth of theism does absolutely nothing to raise its posterior probability, it seems to me.
2.3 The Duplication Objection
So much for God creating an imperfect world. However, suppose we hold it in our background knowledge, k*, that God does create, and would create some imperfect entities for the sake of their good. Conditional on T&k*, is it likely that your existence obtains? You might think such a move is justified on the basis of a Bayesian argument where the datum is the existence of conscious moral agents generally (Again, see Page 2020). If God were to create, it may be argued, God would create other conscious agents in virtue of Him being all-loving and all-good. However, conditional on God creating, is it likely that God would create you and beings like you, though? Not so, I would argue. Granted, God might have some reason to create you and others like you, if we accept certain axiological assumptions. However, if there are two mutually exclusive actions God could take, A1 and A2, and A1 entails all the known relevant goods of A2 and is overall more valuable; Necessarily, God would do A1 over A2, since doing so would be a greater action which leads to an overall more impressive moral resume, and God is necessarily morally perfect. Is there something better God can create over us? Yes. God could create far more impressive beings than us. Humans like us are severely limited in various respects related to cognitive ability, moral reasoning and knowledge, and overall quality of character and dispositions to do good. Here's an excerpt, discussing Mark Walker's anthropic argument for theism (Walker 2009), from my friend's fantastic blogpost which nicely summarizes some ways in which human beings like you and me are unimpressive creatures relative to what could exist:
“Firstly, while we are certainly constituted to be selectively altruistic in some ways, our moral characters are highly flawed and often deficient. We are extremely prone to violence, bias, barbarism, jealousy, greed, and a litany of other vices. Secondly, we are highly intellectually ignorant beings that succumb to many cognitive limitations and are more likely to rely on cognitive shortcuts than think rationally. Thirdly, there are clearly many levels of flourishing we are simply incapable of experiencing quantitatively. For instance, imagine life whose architecture is such that their experiences of all positive emotions are hundreds of times more intense than our own. Fourthly, and most importantly, we are unable to realize the deepest level of and essential qualitative aspects of the most important values. Anyone who has been in altered states of consciousness knows that even within our limited biological architecture there are states of experience whose valuable aspects are far deeper than what can possibly be achieved in the course of normal human life [7]. Imagine the kind of experience that organisms with much more impressive capacities could engage in. I will provide three examples…”
To add on to this, even BB must agree that humans in general are pretty bad at moral reasoning, or otherwise lack moral motivation and thus have poor characters. Most people eat factory farmed products either because they are ignorant, they don't care about animal welfare, or they have really bad reasons like "it's the natural order" or "animals are stupid", or they simply aren't motivated enough to change their ways, all of which BB thinks are grave moral errors. Or consider that most people aren't motivated to get involved with causes which improve lives, such as donating to charities or effective altruist organizations. There are possible moral agents with much greater capacities that don't have such flawed moral characters.
The question then becomes, why did God create us instead of conscious agents, which we can call godmen, that are more impressive than us in all the various ways listed above? After all, if given the choice between creating humans like us or creating godmen who can experience the deepest forms of pleasure, moral and intellectual enlightenment, and have greater dispositions to cultivate virtue, love, and appreciation of the glory of God creating godmen looks clearly all-things-considered better. Recall that the reason given to think God would create us is that it is good to create a person and give them a good life, but that is also a reason to create godmen instead of us. When choosing whether to create humans or to create godmen, considerations of the creature’s good are present in both cases, the only asymmetry being that creating the godmen achieves a much greater degree of person-based goods without the blemishes and moral faults implied by the existence of much worse beings like humans. It becomes completely puzzling, practically inconceivable, then, that a morally perfect being would choose to create us instead of godmen.
There are potential objections that can be made here. Many rejoinders therein are covered by my friends aforementioned post in the section on humans, and I won't repeat them here. I will cover what I take to be the most relevant consideration for the anthropic argument, which is that, in fact, God does create godmen, and indeed, all other such possible conscious beings that are much more impressive than us. But he also creates us. There is no choice God has to make between creating godmen on one hand, and creating us on the other, He simply does both.
There are immediate concerns with this. 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. Indeed, if a scientist were to intentionally create R-goblins instead of more morally virtuous entities we'd think that is seriously unethical. So why think we are the type of persons that are all-things-considered worth creating for an all-knowing and all-powerful being, instead of only beings greater than us in the order of impressiveness? 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. 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. Yet W3 already realizes the best kinds of goods, such that the addition of lesser creatures does nothing to enhance the value of such a world. This might be rejected on the basis of accepting some crude utility-maximizing conception of God. God creates W3 because it maximizes the value of the world quantitatively by having more happy people in it. But I see no reason to accept such a conception of God, and it runs headfirst into serious issues such as the problem of no best world (See Rowe 1994). Further, it looks like there's a lot of disvalue and horrendous evil present in W3 that is not present in W4, in virtue of having creatures with much weaker moral dispositions, limited cognitive powers, etc. Why think the value of creating W3 by creating humans in addition to godmen, outweighs the value of creating W4 which, while lacking the value of created humans, contains none of the entailed badness in W3?
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. God has the property of omnipotence, which is typically understood as the ability to actualize any logically possible state of affairs. So, if God can actualize possible people of some cardinality n, God can create n many duplicates of godmen where the only different thing pertaining to each duplicate D1, D2, Dn.. could perhaps be the universe they're in U1, U2, Un.. 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. For instance, He could create otherwise identical universes with duplicates of godmen, DU's for short, for which the only difference between each DU may be that He gives them a different name, such as U1, U2, U784342454646, Uω, Uω+1 and so on. Or the only difference between each DU might be the amount of duplicates He puts in them, e.g., n, n+1, n-1 and so on. Both of these options do not violate Leibniz' Law, and do not, as far as I can tell, entail a contradiction. So, for any number of persons God can create, there are at least as many corresponding DU's God can create. He could always create another duplicate instead of a much less impressive entity, in the sense that there is nothing stopping Him from doing so. Therefore, for every act of creation God performs, there is a choice between creating a duplicate of a godman in some DU, or creating a less impressive being, like a human. Yet, creating a duplicate of a godman always looks more valuable than creating a human for the same reasons that creating a godman is more valuable than creating a human. So, when presented with the choice, He would always create a godman, or a duplicate of a godman instead of a human.
One objection might be that once original copies are created, creating duplicates doesn't add to the value of the world. But what could be the motivation for thinking this? Afterall, suppose you are not already inclined to nihilism, or a feeling of worthlessness, would finding out you have a duplicate in some other universe make you think that your existence no longer adds to the goodness of reality? I wouldn't think so. Duplicates add to the goodness of reality by increasing the world's total utility, there are more instances of good experiences in the world. Perhaps the idea is that what matters is the types, not specific tokens of goods that are instantiated in the world. But as we've seen above that same motivation motivates the claim that God would only create godman, and not humans, since the very same types of goods humans realize are realized to a greater degree in godman.
The objection that BB appealed to in our discussion is that God could only create another duplicate if there is another soul for God to create. Once God creates all the godmen, there aren't any more duplicates for God to create. There would have to be another godman soul for God to create, but there isn't. One problem with this response is that it undermines BB's objection to multiverse naturalism’s ability to account for the data, but we'll get to that in the next section under the heading "Naturalism and Your existence". Another is that it assumes soul theory, which I don't find plausible. Most crucially, I think we can see that no matter one's views on the essential characteristics of souls, there isn't any reason to think that creating duplicates is impossible. Either we accept that it is logically impossible for a duplicate to have the same soul as an original, in virtue of it being entailed from the concept of a soul that it is singular and cannot animate multiple beings across universes, or we don't. If the former, all this means is that if God were to make duplicates they couldn't have the same soul, but this does not entail that God cannot make qualitatively identical duplicates and put them in different universes. It just means that if there are duplicates in different universes, then this entails that those duplicates must have different souls since the same soul can't exist in two universes at once. But, unless demonstrated, there's no logical contradiction in God creating duplicates in different universes. If the latter, and duplicates could have the same soul despite being in different universes, then God could create endlessly many duplicates inhabiting different universes that share the same soul since, again, there isn't a contradiction entailed from doing so. Either way, this objection does not undermine the possibility that an omnipotent deity could create godman duplicates in different universes, nor does it diminish the eminently plausible notion that creating said duplicates would always be better than creating us. The objection therefore fails.
2.4 Double-counting the Problem of Evil?
One last objection I'll consider, which BB raised in our discussion and can be charged to both objections I've defended in sub-sections 2.2, and 2.3 is that all these objections do is double-count the problem of evil. I find this objection stupefying. It's certainly false that the objections I've laid out to the anthropic argument here can be reduced to the claim that it doesn't get off the ground because theism is off the table in virtue of considerations of evil we observe in the world. Rather, what I am doing is teasing out what, antecedently, we should expect to see given the truth of theism. "Antecedently" being the operative word here—I'm putting aside my knowledge of evil in the actual world to examine the conditional probabilities of certain observations given theism. This is exactly how we'd assess likelihoods such as P(Y|T&k). Perhaps the objection is that we must hold it in our background knowledge that theism has a satisfying, theodicy or solution to the problem of evil. Yet, in doing so we find that solutions to the problem of evil would undermine the objections laid out in 2.2, and 2.3, and thereby license us to make the judgment that P(Y|T&k) is high.
This objection is wrong twice over. Firstly, even if it's true that the objections in 2.2, and 2.3 only work given there is no successful solution to the problem of evil. It remains perfectly kosher in this dialectical context to leverage the theist lacking any successful solution to the problem of evil, if it undermines the argument brought to the table. The proponent of the anthropic argument is the one with the burden to motivate the claim that P(Y|T&k) is significantly higher than P(Y|N&k). Yet if this claim only has purchase if we already suppose that within our background knowledge is a successful solution to the problem of evil, and yet there isn't one, then there isn't any good reason to think the claim is true, and a crucial premise of the argument is unjustified if not outright false. For those interested, I have a blogpost on various of what I take to be the strongest theodicies on offer wherein I argue they all fail. Secondly, the claim that any solution to the problem of evil saves the argument from the above challenges is unmotivated. There is no prima facie incompatibility between there being lots of suffering and impressive beings, or conversely, there being little suffering and highly unimpressive beings. The way Walker & Montesions lay out their arguments is such that for (almost) all of the capacities described, the two facts are independent. Therefore, the burden is squarely on BB or any proponent of this objection to demonstrate that, in offering a theistic explanation of evil, we have thereby explained why God would create unimpressive beings. Further, we have good reason to think it is false that holding any theodicy or response to the problem of evil in the background would address my objections. In order for a solution to the problem of evil to successfully address my objections, it must simultaneously (i) undermine the judgment that God has better reasons not to create or that God has better reasons to create godmen/duplicates of godmen than create creatures like us, and (ii) not undermine the judgment that it is likely that God would create us. But, in fact, I know of no solutions to the problem of evil that satisfies both (i) & (ii). For illustrative purposes I'll examine some standard solutions to the problem of evil and argue that they fail to satisfy either (i) or (ii).
First, the free will theodicy. This theodicy states that the reason God permits evil in the world is that God creates creatures and gives them morally significant freedom. But in order to do so agents must have the capacity to choose evil. Does this satisfy (i)? It does not, because, per stipulation, godmen instantiate all relevant goods humans instantiate to a greater degree, and this would include morally significant freedom. Indeed, godmen, in virtue of having greater capacities, could even have a more impressive degree of freedom than humans. They may be created with more power over the world they inhabit, and the ability to deliberate among a much larger variety of reasons for actions than humans can. Even if the free will theodicy is successful, this in no way undermines the claim that God has more reason to create godmen than humans.
Next, skeptical theism. Skeptical theism (ST) is the thesis that we have no good reason to think that the perceived weight of God's reasons resembles the actual weight of God's reasons. So, any inference we make from the known God-justifying reasons for some horrendous evil E to the total God-justifying reasons for E that there are, fails. Since the known reason's are all we have, we are in the dark about what God's reasons are, and thus whether God is likely to permit E. Does this satisfy (i)? Yes, because we only have access to God's known reasons to create godmen over us, but any inference from God's known reasons to His actual reasons fails under ST. Does ST satisfy (ii)? No, for precisely the same reason. Since we are completely in the dark about the actual weight of God's reasons, we are completely in the dark about whether God has all-things-considered reason to create us. So, we cannot be justified in believing that God is likely to create us. We've seen that BB appeals to known reasons God might have to create us, like it being generally good to create a person. But per ST, we have no good reason to think this known reason reflects God's total reasons, and so the inference to it's being likely that God would create us, fails under ST. ST therefore refutes the duplication and imperfect creation objections, only at the cost of also doing the hard work of undermining the underlying probability judgment of the anthropic argument for me. Maybe BB would appeal to a weaker ST that permits us to reason about divine psychology. But I contend that if it's weak enough to permit justification for the claim that God would create humans, then it is also too weak to undermine my objections in 2.2 and 2.3, which serve as defeaters for that justification.
Lastly, soul-making. The soul-making theodicy says that God permits horrendous evil so that creatures can cultivate virtuous characters through their hardships and suffering. Does this satisfy (i)? No, if anything, soul-making seems to provide a strong basis to think God would create godmen instead of us. I've already stipulated that godmen have far greater capacities for moral development and for learning from their experiences than us and so would instantiate the good of soul-building to a much more impressive degree than us.
But perhaps that's not all there is to the story. Perhaps God creates unimpressive beings like us so that we may, in the afterlife, go through some deification process to become more impressive beings like godmen eternally, and it is necessary that we start out as humans in this process. But this is a very bad explanation and doesn't satisfy both (i) & (ii). If God has the choice between creating a human that becomes a godman at some point in the future or in heaven, or creating a godman from the outset, we should expect God to create a godman from the outset. This is because for any time t, it's better to be a godman at t than a human at t, so God has more reason to create a godman at t than a human at t. So prima facie at least, it looks like (i) isn't satisfied. Perhaps what's being said is that one could tell some unmotivated but logically coherent just-so story about how the most valuable world, logically necessarily, must include humans at some point in addition to godmen or that humans evolve into godmen, and so God would create that world. Certainly such a story could be told, but there are numerous other logically coherent just-so stories one can tell which rule out God creating humans, or at least rule out a world with humans at this point in time. We can tell the story that God would create a world where only cheese exists at this point if we were to observe an only-cheese-world, and that the cheese eventually evolves into godmen in line with God's ultimate purpose. Why not? That's no less antecedently plausible by my estimation. But if we can just attach any unmotivated just-so story to the theistic hypothesis, it becomes empirically vacuous and we would have no reason to think any particular story, including the one where God creates humans, is true, unless we explicitly use the fact that we exist to update on what God would do, but then we couldn't also use that data as evidence for theism. In which case (ii) fails to be satisfied. Therefore, until such time as BB provides a plausible story that satisfies (i) and (ii), this consideration provides absolutely no evidential counter to my argument.
An additional note is also worth making here. If we spend a tiny portion of our existence as humans on earth but the vast majority of it as much more impressive beings in heaven. Then this implies that, for any time t that we observe ourselves persisting, we should expect to be more impressive beings in heaven at t, since there are infinitely many times we spend as impressive beings in heaven, and a proportionally 0 amount of time spent as humans on earth according to this theodicy. So, our observation that we are not deified in heaven and are instead human beings on earth would have an epistemic probability of approximately 0 on this picture. So even if this soul-making+ theodicy did explain why God creates humans like us, it would also entail that the probability of our observations given theism and this theodicy would be pretty much 0.
Now, maybe there is some other theodicy that satisfies (i) & (ii). But I'm not aware of what that is, and if there is one it is BB's burden to provide it. We've already seen that the standard responses to the problem of evil do not satisfy (i) & (ii). We either 1) pick a theodicy or solution that satisfies (i), yet which in turn sabotages the predictive content of theism and thereby implies that we have no reason to expect to observe created humans given theism, or 2) we don't, in which case my objections go through and we still have no good reason to expect to see humans given theism.
3.1 Stalking Horse Naturalism
In the previous section we've assessed P(Y|T&k) and found that we have no good reason to think it is not very low, and, if anything, we have good reasons to think it is pretty low. But it might be asked, even if P(Y|T&k) is pretty low, is it at least higher than P(Y|N&k)? I think not. I see no good reason to think P(Y|T&k) is higher than P(Y). Equally, I also see no good reason to think P(Y|N&k) is lower than P(Y). But to motivate this point further, I'll put forth Dr. Alex Malpass's stalking horse objection.
There are many versions of N which is the broad "naturalistic" hypothesis. One version of N is a chance-based naturalism we can call Nc, which is essentially a cosmic lottery ticket. The idea being that all outcomes that are physically realizable, and which require similarly complex antecedent conditions are equally likely. Certainly P(Y|Nc) is very, very low. However, consider another version of N, which we can call 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. Given that the content of Nd entails or makes it highly likely that Y obtains, we can see that P(Y|Nd) is not very low, in-fact, it is quite high. 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? 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. Both the theistic hypothesis and the hypothesis that there is a mysterious naturalistic disposition look at least equally mysterious by my lights.
There might be other reasons to prefer the theistic hypothesis to the stalking horse naturalistic hypothesis, however. Perhaps the stalking horse hypothesis starts out with an astronomically low prior probability—significantly lower than the theistic hypothesis. But why think this? Perhaps the idea is that we start out giving a roughly equal credence to the bare theistic hypothesis and the bare naturalistic hypothesis. But stalking horse naturalism is a very specific sub-hypothesis of the bare naturalistic hypothesis, one which takes up a very small initial portion of the probability space. There are infinitely many equally a priori likely conflicting naturalistic sub-hypotheses that do not posit the existence of an initial state causally disposed to eventually produce you in particular. So the stalking horse naturalistic hypothesis on offer, while also being ad hoc and transparently constructed to accommodate the data, has an extremely low epistemic probability, if not 0. Something like this is plausibly right. However, a parallel problem afflicts the theistic hypothesis.
Suppose we take the bare theistic hypothesis T to be the bare proposition that there exists a supernatural agent at the foundation of reality. The bare version of T does not at all make probable the data Y of your existence. For starters, T does not specify the causal powers the supernatural agent has. For all we know, they might not have sufficient causal power to create a universe with you, let alone a vast multiverse that contains all possible people. More importantly, T does not specify the contents of the supernatural agent's desires. For all we know, the supernatural agent might not desire a universe with any people at all, let alone you. So, for this reason, T, when understood as the bare theistic hypothesis is just as uninformative with respect to Y as N. For T to predict your existence, we must appeal to a sub-hypothesis within T, call it Ti, which says that the supernatural agent at the foundation of reality has sufficient causal power to create a universe with all possible people, and that they have the desire to do so, and no outweighing reasons or desires against it. But there are infinitely many versions of T that conflict with Ti which are a priori equally probable. For example, you can imagine versions of T where the supernatural agent only desires to create an empty aesthetically beautiful universe (of which there are plausibly infinitely many), or any universe with lots of people but not you (again of which there are plausibly infinitely many). So, just as Nd takes up a small portion of the initial probability space of N, the same looks true for Ti vis-a-vis T. To put the point another way, since Ti entails T in virtue of being a subset of T, it follows that P(Ti|Y) is less than or equal to P(T|Y). Further, since we've seen that T in virtue of it's lack of specificity does not predict Y any better than N does, we can reasonably infer that P(Y|N) = P(Y|T). From this it follows that P(Ti|Y) must be less than or equal to P(N|Y). Here is a good blogpost which makes the same point vis-a-vis fine-tuning.
3.2 The Simplicity of Theism
It may be objected that the version of theism being appealed to, perfect being theism, call it Tp, is intrinsically very simple via some appeal to arbitrary limits, or theoretical elegance. So, Tp takes up a significant portion of the initial probability space for T. Yet, P(Y|Tp) is much higher than P(Y|N). But then my assumption that P(Y|N) = P(Y|T) is wrong. In fact P(Y|N) < P(Y|T) since one of the most plausible versions of T predicts Y, and no correspondingly plausible version of N predicts Y.
There's a lot to say about this objection. Firstly, as I take myself to have convincingly shown in the previous section, it is not the case that perfect being theism predicts Y, and in fact it is very implausible that, antecedently, we would expect to observe Y given Tp. It's certainly not entailed for free from perfect being theism that God would desire to create all possible people, one needs to accept controversial axiological assumptions to make that case, and even taking those assumptions for granted, I've argued that there is still no good reason to think God would create all possible people and there are powerful reasons to think He wouldn't. One can of course cook up a perfect being theism+ by conjoining Tp to the further proposition, 'God intends to create all possible people', but this would be an analogous ad-hoc move to conjoining the naturalistic hypothesis with the proposition 'there is an initial state disposed to lead to the production of you', both of which drastically decrease the prior probabilities of their respective hypotheses.
Secondly, even if we grant that Tp predicts Y, it is far from clear to me that Tp is intrinsically more probable than Nd. To start, I take it that perfect being theism flunks on a set of theoretical virtues, where a mysterious naturalistic explanation scores better. 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. All causes we know are between physical objects or mechanisms (this is controversial if you accept interactionist dualism, but I think interactionist dualism is false), all causes we know that occur on universal and galactic scales are non-intentional causes, indeed most causes we know in general are non-intentional causes. Theism is ontologically unparsimonious compared to naturalistic explanations. Since naturalism only commits to natural concrete entities, and causal relations between those entities, and theism posits a supernatural entity in addition to natural entities, and causal relations between the supernatural entity and natural concreta. Naturalistic explanations which appeal to underlying physical causes and law-like regularities are embedded in a successful research program with theories that have generated novel predictions like general relativity and natural selection, theism is not, not once has theism generated anything like a novel prediction. Indeed, the history of science is replete with examples of phenomena we previously thought to have supernatural explanations being displaced by natural ones. For instance, in some ancient civilizations solar and lunar eclipses were thought to be signs of divine displeasure or omens of significant events, and we now know that they are simply caused by the orbits of the Earth, moon, and sun. So we have plenty of a posteriori reasons to expect a naturalistic explanation for any given phenomena over a theistic one. In fact it isn't very implausible to me, and oughtn't be very implausible to any card-carrying naturalist, that my existence is just a consequence following the natural initial state of the universe initiating a causal chain which eventually leads to a history of various stochastic evolutionary mechanisms and reproductive outcomes up until my parents combining their genetic material, and that is all there is to the story.
Of course, I’m not endorsing this story nor do I think it is independently justified, but I see no reason whatsoever to think it more implausible than perfect being theism a-priori, especially since there are also reasons to think perfect being theism is highly unlikely a priori. Years back, I've argued on my blog that most orthodox conceptions of God, including perfect being theism, are incoherent, and there are many other arguments to that effect that I did not cover. My credence in at least one such arguments being successful is at least respectably high. Tp is also maximally specific with respect to the powers, knowledge and goodness of the supernatural agent. There are infinitely many 'limited god' hypotheses wherein god is limited in some respect or other, to some degree n or other, and there is only one 'unlimited God' hypothesis which entails that God is not limited in any respect, to any degree n. There are thus infinitely many ways for perfect being theism to be false, in the same way it may be argued there are plausibly infinitely many equiprobable rival naturalistic hypotheses to Nd.
I suspect BB and some of my theistically inclined readers might be screaming at me at this point that some argument for the high intrinsic probability of theism works. I'll address a few as briefly as I can. One is the argument from arbitrary limits. This argument depends on the intuition that limits of some degree n are less intrinsically probable than no limits, and that limits call for a deeper explanation in a way that unlimitedness does not. This is an intuition I do not share. But even if I did share the intuition, it would only show that unlimited being theism is more probable than any given limited being theism. It would not show that unlimited being theism is more likely than the disjunction of all possible limited being theisms, of which there are infinitely many. So, even if I thought that unlimited being theism was, say, a billion times more probable than any individual limited being theism, it would still come out extremely unlikely. I'll also note that, while it makes perfect sense to speak of limits in terms of power and knowledge, it's far from clear that limits are the right way to think about goodness of character. If a being is unlimited in ability yet has a complex set of desires and psychological constitutions which entail that they are not morally perfect, are we supposed to think said being is more arbitrarily limited than a being with a complex set of desires and psychological constitutions which entails that they are morally perfect? Why believe that?
Another approach might be to just stipulate God as a perfect or unlimited being and from this simple conceptual characterization all God's properties are entailed for free. I've taken issue with such a strategy in the past. I think it gets the order of logical priority wrong, in order for an entity to have the property of being perfect or unlimited they must first have a highly complex set of properties. Such complexities are baked into the concept of perfection or 'unlimitedness', and so those are not simple properties. Another way to see where this goes wrong is that this sort of point treats contingent features of our language as if they get at some underlying truth about epistemic probabilities. We can imagine a species of aliens who have the predicate 'Y-limited' where the property of being Y-limited entails a complex set of limits to some degree n in knowledge, power etc. You can also imagine such aliens insisting that explanations which involve Y-limited entities are intrinsically simple, since all the complex entailments come for free by simply specifying that some entity has the property of being Y-limited. We happen to have a notion of 'perfect' instead of 'Y-limited', but that doesn't appear to get at anything important.
Lastly, one might appeal to ontological arguments which seek to a priori demonstrate the existence of a perfect being from the concept alone. I've already written an extensive blogpost on what I take to be the most sophisticated ontological arguments, and have argued that they all fall prey to decisive objections and are dialectically inert, so I won't waste time talking about it more here. I'll also note that for almost every ontological argument I know, you can run parodies of them to demonstrate the existence of, say, a perfect atheistic universe, or a limited god.
3.3 Multiverse Naturalism
I've already argued that an ad hoc stalking horse naturalistic hypothesis fares at least as well as the theistic hypothesis on considerations of theory-selection. But I also think we can do better than an ad hoc stalking horse naturalism. In particular, by appealing to many-worlds theory in quantum mechanics. Briefly, a well-known mechanism in quantum mechanics is known as the 'wave function collapse', wherein a particle is in a superposition of states, but, upon being measured it collapses into one of those specific states. The Many-Worlds theory eliminates the need for this collapse by postulating that all possible outcomes of quantum measurements are realized, but in different branches of the universe. This is considered virtuous because it removes the special status of measurement and treats it as a natural, deterministic process governed by the same quantum laws that control all other events. Rather than relying on a somewhat arbitrary division between the quantum and classical worlds, the MWT asserts that the quantum laws apply universally. Further, decoherence provides a mechanism explaining how quantum superpositions appear to collapse when interacting with the environment, such as air molecules or photons. In MWT, this interaction doesn't cause the wave function to collapse, but causes the universe to branch into different worlds, each representing a different possible outcome of the quantum interaction. MWT is also arguably parsimonious by positing that the universe’s wave function evolves in a straightforward way according to the Schrödinger equation, without needing ad hoc rules for collapse. Finally, MWT makes quantum mechanics more consistent with the theory of general relativity (GR). One foundational aspect of GR is the principle of locality, which states that an object is only directly influenced by its immediate surroundings. However, this looks to be challenged by quantum entanglement, which implies instant correlations over potentially vast distances at faster than the speed of light ( ie. "spooky action at a distance"). MWT however posits that each branch of the universe evolves locally, and so does not violate the local realism upheld by relativity.
All this is not to say that you should accept MWT, I'm no physicist, I'm not qualified to make that judgment. It is, however, to say that MWT is independently motivated, and is at least a somewhat antecedently plausible theory. It is not a mere stalking horse. How, you may ask, does it relate to our discussion of the anthropic argument? Simple, on MWT we can say that from the initial state, the universe evolves deterministically and branches off into all possible universes consistent with the laws of physics, all physically possible outcomes consistent with the initial quantum state of the universe are realized. However, since a scenario involving 'you', a material being, obtaining is a physically possible outcome consistent with the initial conditions of the universe, this multiverse scenario virtually guarantees your existence will obtain in some universe or other. So, it looks like the naturalist has a theory that doesn't invoke God, and that theory is both theoretically virtuous and pretty much entails your existence for free. Even if we think that a certain causal history is essential to you, given that your causal history is physically possible, it's pretty much guaranteed that it will obtain in some universe.
Notably, we also avoid one of the strongest objections to the multiverse solution to fine-tuning which is the inverse gambler's fallacy. For, the proponent of the anthropic argument could not charge the inference from the existence of a physically possible person to a multiverse scenario where all physically possible outcomes are realized with the inverse gambler fallacy, without thereby also admitting that the inference from the existence of a particular person to the existence of all possible people also commits the fallacy. As it happens BB himself rejects that the multiverse solution to fine-tuning commits the inverse gambler's fallacy.
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. If we can do this without ontologically committing ourselves to a higher-order infinite cardinality of ℶ2 people, then I say all the better!
Perhaps this is too fast however, and the idea is that while your physical body and the set of temporally continuous decisions, attitudes, experiences and functional states which constitute, or supervene on said body must exist in some universe, that body might not be you. So, multiverse naturalism does not predict that you will exist, just some guy who is qualitatively like you in all respects except perhaps in a different universe or with a different haecceity or soul. This was the objection BB raised to me. There are, however, numerous issues with this objection:
First, it's unclear why we should think that a being qualitatively identical to me in all respects in some universe, is not me. If we are physicalists, and the same material body, causal history, and continuance of physical states through time exists in that universe, then that person just is me. Even if we are dualists, and think the mind supervenes on the physical, given the same set of physical properties must be instantiated in some universe or other, we should think that the same requisite mental properties will necessarily also be instantiated. Maybe BB can appeal to some wacky scenario where it is supposed to be intuitive that, even though the exact same physical states obtain, you don't exist. But I'm not at all inclined to take intuitions so disconnected from our ordinary practices seriously. Even if I was, given the data of my existence and that there’s at least a small chance the qualitative duplicate would just be me, I would just update in favor of the view that a qualitatively identical duplicate is me in conjunction with multiverse naturalism. Why not? Afterall, BB has asked me to update on the conjunction of theism, and soul theory, and certain axiological assumptions. But multiverse theory and the view that qualitative duplicates are me, even if pretty implausible, is closer to my views, and requires far less damage to my web of beliefs. All I'm doing is following the maxim of minimum mutilation!
Secondly, even if it's right that a qualitative duplicate of me in some universe is not me, that can't count as data. The reason is because the scenario where I'm me, and where I'm a qualitative duplicate, are empirically indistinguishable. I couldn't possibly know that I'm not the qualitatively identical duplicate, I don't know what universe I'm in, and everything I could possibly point to, such as my body, my experiences, my memories, my causal history, my qualitative duplicate can point to as well. Since it's not known that the data even obtains, it's not data we can use as evidence for theism over a naturalistic multiverse.
Thirdly, if this response were accepted, it looks like it's straightforwardly falsified that all possible people exist. There are lots of people who could have been born on earth that weren't due to contingent circumstances. I suspect BB would argue that God creates those people in other universes, but if we take this objection seriously those would just be qualitatively identical duplicates in a different universe, not them.
Finally, if this response were accepted, and an identical duplicate of me isn't me, then it looks like BB's response to my duplication objection in section 2.3, which is that there comes a point where God runs out of souls to create, is directly undermined. God could indeed keep creating duplicate universes with qualitatively identical duplicates of godmen instead of universes with creatures like us sans contradiction. They would have different souls, but this just means that He won’t at any point run out of godman souls to create even if He keeps creating duplicates.
One last objection might be that the multiverse itself is unexpected on naturalism, and so this merely pushes the problem back a step. I'll just say two things here. To start, I don't see any reason to think that's true. We've seen that many-worlds theory is an independently motivated scientific theory that doesn't at any point require postulating the existence of God, it only involves the kinds of quantum interactions we've observed. I don't see why we should think it is a priori unlikely, given naturalism, that this is how the world would be. Afterall, on this view, the quantum state of our universe evolves over time in a completely deterministic way. I also don't see why we should think God would create a deterministic multiverse governed by physical laws. It's the theists job to make that argument. This brings us to the second point. Suppose the theist can make the argument that the multiverse is more expected on theism. Fine, so be it. But that would be a separate argument. We can say that when we update on the data of a multiverse, theism 'wins that round'. But then, once we have a multiverse, my existence just falls out of it for free, or so I've argued. Thus, once we hold the data of the multiverse in our background, the data of my existence would not count as any further evidence of theism.
Conclusion
To sum it all up, while if nothing else the anthropic argument for theism raises interesting questions concerning anthropic reasoning, and infinite cardinalities of possible people, I think it simply fails as an argument for theism, and is prone to far too many issues for me to find it at all convincing. Firstly, there's no good reason to think probabilistic reasoning about infinite cardinalities works in a way amenable to the argument, and even if it does, it appears to do little more than trade one massive improbability for another. Secondly, the case for theism predicting all possible people is not only insufficiently motivated as it stands, but is implausible upon careful reflection. Finally, even if theism can be shown to predict all possible people, there are naturalistic explanations of the data of one’s existence that the naturalist has good reasons to think are at least on a par if not outright superior to the theistic explanation on offer. So the argument is, at the very least, completely non-decisive.
To finish this off, it is worth clarifying my views. I am, perhaps unsurprisingly, a staunch atheist, but I do think there is some evidence for theism. For example, the existence of conscious agents probably provides at least some evidence for theism. But once the data of conscious agents is held in the background, I do not think the existence of you, as a particular conscious agent, constitutes any further evidence for theism. If anything, I'm inclined to think that, at the end of the day, anthropic considerations about the kinds of conscious agents there are, probably favor naturalism over theism. Ultimately, I am of the view that natural theology, and the project of treating theism as some robust explanatory hypothesis is dead in the water. That's not to say that I think all theists are necessarily epistemically irrational. I do not think the role theism plays in people's lives is that of a belief justified by robust arguments that ought to rationally compel everyone, or as a successful scientific theory. Rather the role it plays is one of faith, of moral guidance, of hope for a better future and that the world is ultimately good, of seeing God in one's own experiences and in the value and beauty of the world. To quote William James; 'Faith means belief in something concerning which doubt is still theoretically possible ... faith is the readiness to act in a cause the prosperous issue of which is not certified to us in advance.'
You write, "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."
ReplyDeleteI am puzzled by this line, because it seems straightforwardly false. You have ZFC set theory, with all its sets. If you wanted to make statements about "all sets," you can't say "the set of all sets," but luckily for us another kind of collection exists called, "classes" which can hold all sets. The class of all sets contains too many things to be a set. So, it seems perfectly meaningful to say the number of things in the class of all sets is too big to be a set.
But proper classes don't have cardinalities since those are only defined for sets. So, strictly speaking, on my understanding at least, they aren't a "number of things too large to be a set", since they aren't a 'number of things' at all.
DeleteThey're collections of things. So what's wrong with phrasing it as "there are collections of things too large to be a set that exist nonetheless."
DeleteYou can say that. Mathematicians often do. But you need to exercise caution. For one, proper classes aren't 'entities' like sets are, they are theoretical constructs defined in such a way that they do not behave like sets and cannot participate in operations that lead to paradoxes. Essentially it serves the useful conceptual role of allowing us to talk about 'all sets', even though there isn't actually a 'thing' that is the collection of all sets in any ontologically committing sense. All its 'members' can't actually be collected into a single whole that is itself an object in the universe of set theory (otherwise it would be a set).
DeleteFor two, when we say 'too large to be a set' we aren't saying that there is a size S such that S > C for any arbitrary cardinality. More precisely, we are saying that the axiomatic structure used for sets doesn't allow us to have a set of all ordinal or cardinals on pain of contradiction. So we construct the idea of a 'proper class' that fails to meet the criteria of a 'set' which does allow us to talk about 'all ordinals' or 'all cardinals' without contradiction.
"Essentially it serves the useful conceptual role of allowing us to talk about 'all sets', even though there isn't actually a 'thing' that is the collection of all sets in any ontologically committing sense."
DeleteWhether you are a realist about abstracta or not, it would seem that classes and sets would have the same ontological status.
"All its 'members' can't actually be collected into a single whole that is itself an object in the universe of set theory (otherwise it would be a set)."
This is true, but there is nothing incoherent about an object which is a collection that exists outside the universe of set theory, but nonetheless has the same status as sets.
With regards to the second point, "size" means different things in different contexts. (For example, the size of an interval [a, b] can be defined as b - a instead of ℶ1 depending on the context.) In our present discussion, we are discussing objects too big to be sets, so I don't think we should restrict our notion of size to cardinalities. Instead, we should probably just talk about injections and bijections (e.g., there is an injection from any set to the class of all sets, but there is no bijection between them, so the class of all sets is bigger than any set).
Disagree with the first point. I'm a nominalist, but a mathematical platonist need not be committed to the existence of proper classes, sets are well-defined objects that can be members of other sets, have specific properties and are governed by the axioms of set theory, but proper classes aren't, treating them as objects looks odd to say the least because it's not clear what properties they would have if they did exist, nor what explanatory role they would play as objects in our ontology. You probably wouldn't even be able to successfully refer to them, since, for any collection of sets that could be your referent, you can construct further sets from those sets by taking powersets, unions, intersections etc. The only role proper classes serve, so far as I can tell, is a linguistic role, they allow us to talk about "all sets" or "all ordinals" in such a way that we don't contradict ourselves in doing so.
DeleteI don't understand your second point. If we treat classes as having the 'same status as sets', how do we circumvent the paradoxes that they're designed to avoid?
For the last point, that's fine. I was just taking size to denote the amount of things contained in a given collection which would be the cardinality. If you're not talking about that, then you're talking about something else that wasn't what I meant by "size". When talking about the size of collections of concrete things in the world, like people, I take it we are talking about the actual amount of things in that collection, not merely some abstract set-theoretic functions you can perform.
Here's my reply https://benthams.substack.com/p/contra-truth-teller-on-the-anthropic
ReplyDeleteThanks for writing this, I had many of the same objections and you explained them basically perfectly, far better than I could.
ReplyDeleteNo problem! Thanks for the kind word!
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