Catholic miracles are nothing new.1 But these miracles have recently taken a more prominent place than ever before in the internet religion discourse (or, more specifically, the Substack religion discourse). The person responsible for launching this new round of discussion is Catholic convert and rising apologist superstar Ethan Muse. Muse is a PhD student at Rutgers. Muse’s work on Catholic miracles played a significant role in the recent Catholic conversion of two Princeton PhD students, Noah McKay and Joe Schmid.

McKay and Schmid are both incredibly brilliant people, so their conversion is nothing to be sneezed at. Schmid’s conversion, in particular—from arch-agnostic to committed Christian—is something Protestants like myself ought to be happy about. But what’s going on with these miracles? How come someone like Schmid, who previously had numerous substantive objections to Roman Catholicism, was pushed to convert by phenomena like Fatima, Lourdes, and Padre Pio?

Indeed, we see the makings of an intellectual movement forming, and one that I don’t think I’m premature in supposing will significantly influence the shape of online Christian apologetics over the next few years. Though Muse is not a Princeton student, both McKay and Schmid are, and given their broad argumentative alignment I shall be referring to their movement as the Princeton school.

So what is it about the miraculous evidence that’s supposed to be so powerful?

In a nutshell, the biggest reason I see for it is the following. Objections to Catholicism rest on some combination of abstract theological argumentation and armchair moral theorizing. We have independent reason to suppose those to be unreliable means of acquiring truth. Miracles, however, if evidentially well-supported, give us very strong reason to think God exists, and miracles that take place in Catholic contexts that play on Catholic assumptions and motivate Catholic piety (combined with the alleged absence of such miracles in other traditions) are safely inferred as divine vindications of the Roman Catholic Church. Perhaps you don’t like the doctrine of hell, or have reservations about the church’s moral teaching, or think Rome has strayed from the clear Word of God: your flimsy intuitions should bow the knee to the overwhelming evidence that God has attested to us this church, his church, by signs and wonders.

Members of the Princeton school have defended such reasoning at greater length, but the substance is clear: the evidence from miracles is so strong that it overwhelms any lingering objections to Roman Catholicism. This is a form of epistemic routing, in which one grounds their justification of a controversial belief in justification for another proposition which implies it.2 In other words, Catholic miracles imply Catholicism, and Catholicism implies certain doctrines, and since we’re justified in believing those miracles, we’re justified in believing those doctrines.

There are two questions one should be asking here:

1. Is the evidence for these miracles strong?

2. Do they vindicate Catholicism?

The first question, if answered in the affirmative, justifies the supernatural inference. The second question, if answered likewise, justifies the vindicatory inference.

An atheist will not grant the supernatural inference. And no one should be quick to grant any miracle. Each needs to be assessed on a case-by-case basis.

But I’m a Protestant, so I can do something super edgy and simply grant that the Princeton school’s choice cases (Fatima, Lanciano, Lourdes, Padre Pio, in particular) are well-evidenced, such that we can safely conclude something supernatural happened. For the sake of argument, that will be my position in this post.3

However, I don’t yet feel compelled to abandon the Thames for the Tiber. I think there’s a problem.

The epistemic routing problem

Recall how the argument is supposed to go. Someone points to objectionable Catholic teaching. Call this set of teachings O. Again, this could be anything, but since I assumed above that these miracles represent real supernatural activity, let’s run it from the Protestant perspective. The Protestant fills O with all of his objections to Catholicism: alleged doctrinal accretions, magisterial issues, theological errors, and so forth.

Let C denote Catholicism. Now, C implies O, clearly enough. The Protestant is running a basic modus tollens—if ~O, then ~C (the ~ here means “not”).

In comes the Catholic. The Catholic could choose to engage the Protestant’s objections to O, but that gets very involved, very quickly. There are simply far too many rabbit holes to handle. Instead, the Catholic brings up M—the miracles. M implies C, and C implies O, so as long as the reasons to accept M are stronger than the reasons to reject O, Catholicism wins.

The Catholic goes on to argue that the evidence for M is so convincing—skeptical witnesses and medical committees and photographs and blood samples—that it beats O pretty handily. The miracles clearly happened.

But here’s the catch. M alone isn’t enough to support C. We need the other half, namely, reason to think these miracles are vindicatory. Call the collection of vindicatory principles V. V includes information about the kinds of miracles God would and would not perform, what kinds of miracles demons are capable of, how God would attest miracles, and so forth. It’s just the sum total of everything the Princeton school needs to assume to get the vindicatory inference working.

From here, we see that it is not M alone that justifies C, but the conjunction of M and V. So the argument looks like this:

(EDIT: keeping the LaTeX because it looks nice when it works, but the app struggles with it, so here: M&V ⇒ C ⇒ O)

The evidence for M, we’ve granted, is very strong. But how about the evidence for V? Rather than engage specifically with the Princeton school’s approach, I want to point out something more fundamental. V is capped at the level of certainty we can derive from reason alone about God’s vindicatory system and the level of causal power he grants to other supernatural beings.

And there’s a hard limit to how much support for any proposition we can get from armchair theology. We can speculate and formulate arguments, but V just is structurally suspect. And (crucially) it’s independent of M. Piling on more and more evidence for M doesn’t boost V.

What this means is that there’s a critical gap in the extent to which evidence for miracles can overwhelm objections to Roman Catholicism. The idea is supposed to be that more and more evidence for M exerts such a strong epistemic vector in support of C that it overwhelms the vector in the opposite direction coming from ~O.

But ~O doesn’t have to face the evidence for M at all! Rather, the counter-evidence can flow through C, bypass M, and eliminate V. Note the last implication here follows from DeMorgan’s Law and the fact that we’re granting M.

(EDIT: without LaTeX: ~O ⇒ ~C ⇒ ~(M&V) ⇒ M&~V)

What does this mean, exactly? It means that the Protestant with weighty objections to Catholicism doesn’t need to weigh them against the evidence for the miracle. They can weigh them against the strength of the vindicatory inference. If the objections are strong enough, they simply reject the vindicatory inference.

In other words, the Catholic can’t rout epistemic justification exclusively through M. They have to rout it through M&V, and if the second conjunct is weak, the routing won’t work very well. Justification for C is capped at whatever justification we can get for V.

This is the epistemic routing problem.

What it means to reject V

Rejecting the vindicatory inference (but affirming the supernatural inference) gives the Protestant three broad options. We can organize these as a logical partition:

1. If the miracle was worked by a benevolent supernatural force (God, angels, Mary, etc.), we have the divine accommodation hypothesis.

2. If the miracle was not worked by a benevolent supernatural force, and instead it was worked by a malevolent supernatural force, we have the demonic hypothesis.

3. If the miracle was worked by neither a benevolent or malevolent supernatural force, then it was worked by some sort of “neutral” supernatural force (think ghosts, poltergeists, humans with parapsychological abilities), and we can call this the paranormal hypothesis.

Now, maybe you don’t think one or more of these refers to actual beings or ought to be taken seriously. That is fine; the point is to map out the space of Protestant supernatural options.

When the Protestant denies V (but again, affirms M) he is committed to one of these three options or a combination of them.

Here the Catholic may object. Each of these theories is so implausible! Are we really supposed to think that demons worked a miracle with such obviously good fruit as Fatima? Or that Padre Pio was just a psychic? Or that God let people claim to speak for him and work miracles in attestation of it?

If the Protestant’s objections are sufficiently weighty and well-motivated, though, he doesn’t need to pick a specific supernatural theory. He can simply affirm the disjunction of all non-vindicatory supernatural theories and leave it unspecified exactly what was operative in a specific case.

But suppose our Catholic interlocutor isn’t happy with that approach. He insists the Protestant defend a specific theory. Fair enough. So the Protestant picks a theory: Padre Pio’s charisms were the result of subconscious paranormal abilities, not divine favor.

The Catholic then raises objections to this particular theory. Would God let someone “forge his signature” by manifesting supernatural abilities and claiming to speak for him?4 Or, for a demonic hypothesis: why would demons be interested in motivating Catholic piety?

There’s legitimate discussion to be had about these objections. It’s not obvious that Catholic piety is an amazingly good thing from a Protestant perspective, especially if it involves bowing down to created beings and sowing confusion among the body of Christ.5 The Catholic can hit back.

Eventually, though, and I don’t think I’m being unfair in saying this, the debate boils down to some form of appeal to general theological principles, the weighing of various goods, and biblical/patristic theology on miracles. Justification for V must be grounded in that, not in scientific evidence, and there’s a fundamental limit to how convincing such an argument can be. The vindicatory inference can never reach the overwhelming support possible for the supernatural inference.

And wait. Appeals to intuition, arguments about God’s nature, and abstract theology are precisely the mechanisms the Princeton school urges is unreliable in adjudicating O. But those mechanisms are pretty much the only way to defend V.

So what are we left with? Abstract theological arguments for V, abstract theological arguments for ~O, and we’ve come full circle to a generic theology debate.

So the Princeton school can have their miracles, and we’ll just discuss whether it’s more plausible that God is using them to vindicate Roman Catholicism or that the Roman Catholic Church can be inferred wrong on other grounds and there is another explanation for the miracles. Piling on more evidence for M won’t help.

This, I think, is a structural limit to how strong the argument from miracles can be. The inference to Catholicism requires shaky theological assumptions, and those assumptions may well be shakier than the other arguments marshaled against Catholicism. The flip side, of course, is that if the arguments against Catholicism are not very good, and the vindicatory principles fairly solid, then Catholicism does win the day. I do grant that miracles contribute some evidence for Catholicism. Recognizing the limits of miraculous evidence doesn’t resolve the discussion in favor of Protestantism; rather, it reverts the conversation back to the theological one we’ve had with us for centuries.

To conclude, while Roman Catholic miracles are fascinating and will rightfully be discussed with renewed fervor for years to come, routing everything else through them is not going to work.

I could conceivably change my mind on the strength of the vindicatory inference, and look forward to continued discussion. For now, though, it will prevent me from swimming the Tiber.

Yes, the keyboard warrior stereotype is not exactly flattering. I asked ChatGPT, trained on the contents of the internet, to create an image from the prompt “cultural perception of a keyboard warrior, in one image.” If you can stomach the slop (sorry), this just about sums it up:

In many ways, I think the critique is fair. But I don’t think it’s the case that every means of discussing controversial ideas online is a waste of time or an outlet for moral vice. In fact, when done well, arguing online can be a great use of time!

Consider reasons keyboard warriors might give for their behavior. Perhaps they think the positions they defend are important, and that attempting to convince people online will increase the number of people who hold those positions. Secondarily, they may hold that arguing online increases their own competence at defending their position.

These seem like pretty bad reasons. But when we abstract and refocus them, I think they’re actually fairly good.

There are broadly two categories of reasons to argue online, mapping onto the those given by the keyboard warrior: to change minds, and to form one’s own.

The issue with the keyboard warrior’s proposal for changing people’s minds is that it’s ineffective.

Thinking back to the number of internet debates I’ve had, I don’t recall ever convincing someone to change their mind on a major topic. I, too, have never done an epistemic 180 after a conversation with someone on the internet.

This illustrates the broader human tendency of reluctance to admit oneself wrong, but it’s amplified by internet debate dynamics. The keyboard warrior goes for the killshot: the brash, confident statement of his views he thinks is likely to win the most converts to the cause. And that’s extremely ineffective.

Okay then. Perhaps it’s best to be subtle. State one’s views modestly, ask honest questions, and use a respectful tone. That’s a lot better, and it will win one more respect from opposing ideological camps. But is it really more effective?

I’m not sure that it is. I try to be respectful in my internet conversations (apologies if I’ve failed in this regard!), but while leading with a friendly tone helps to make the conversation more enjoyable, it doesn’t make people more likely to change their minds (at least, not on major points).

So is it a losing proposition to use the internet to boost the number of people who hold your view? I don’t think so. The internet is an ineffective means of shaping the views of your interlocutors but an underrated means of shaping the views of spectators: those who read internet conversation from the sideline rather than engaging with it themselves.

For every person you interact with online, there are several more who read the conversation, assess it, and consciously or subconsciously update their credences. Those people are your primary audience.

When I first got into philosophy of religion, I spent little time engaging people on the internet and quite a bit more time surveying conversation threads to assess how well certain views could be defended.

Whether it should be this way or not, many people’s opinion of the strength of a particular argument is influenced heavily by how defensible they perceive that argument to be. If someone is able to think of many competent defenders of the argument and only a few who oppose it, they will be inclined to think more highly of it than if they can think of only a few competent defenders and many who oppose it.

In fact, even just knowing one competent defender of a given view can be enough to nudge someone’s Overton window a little bit closer to that view. Perhaps they didn’t think any version of it compelling, and now they think one modified form of it is at least defensible. When a large number of members of some internet space adjust their credence in your view slightly upward, not only is your view taken more seriously (and is more likely to attract newcomers) but uncertain people may end up on your side of the fence.

For example, Substack introduced me to the idea of shrimp welfare. While I can’t say I’m fully on board, seeing thoughtful defenses of the notion has at least made me take it a little more seriously.

So while arguing online may not be a good way to change the mind of a specific individual, it has untold effects on how people perceive the credibility of the view you defend. Moving your view from the fringes of someone’s consciousness to the interior of their Overton window is progress, and it can happen at decent scale on the internet.

This can cut both ways, of course. A poor defense of your view can cause people to lose confidence in it. But a view defended well subtly steers the opinions of onlookers and can even nudge fence-sitters over the edge. This is all the more true if you have a large platform, of course, but even those of us without one can have much the same type of effect by actively participating in internet spaces, especially where a particular view is under-represented.

All right then, perhaps online discussions can be effective at changing minds. But that’s far from the only reason to engage in them. There’s another significant reason: forming one’s own mind and character.

The keyboard warrior’s second stated reason for engaging in debate, as listed above, is to sharpen his arguments and become a more competent defender of his view. In practice, however it rarely amounts to anything intellectually virtuous.

If you begin every conversation with the assumption that the only thing that you could possibly have wrong is how you defend your positions, not your positions themselves, then that’s just confirmation bias and motivated reasoning at their finest.

That mindset, in fact, will serve only to entrench you in whatever positions you hold. As you perceive yourself to be winning more and more internet arguments, you will assume your views really are just that defensible. Maybe you got lucky and happen to have the right views by accident, but even if that were true, you should want to cultivate an intellectually virtuous character equipped to form true beliefs on future topics.

If you approach your internet conversations with a spirit of epistemic humility and a readiness to learn from others, and if you choose to engage primarily with thoughtful critics rather than those you can easily dunk on, you’ll be benefiting greatly.

LLMs can be somewhat helpful as an ideation partner, but you’ll need to talk to real people if you want something more than just “Your argument is a thoughtful one, and it carries weight. But there’s one part where I’d push, and it’s worth being honest about.” Other people, especially critics, are best positioned to draw your attention to flaws in your thinking or recommend niche resources you’d otherwise miss. Some part of their epistemic universe collides with yours, and you’re both better off.

Further, every message you send in an online conversation is a test of moral virtue. You get to choose to be charitable or snarky, clear or opaque, and humble or arrogant. I’m not the most irritable guy in real life, but that’s because I have social norms and the desire to maintain a good reputation. The internet removes those constraints and is thus far more robust as both a test of virtue and a means of cultivating it.

You also benefit from the chance to express your thoughts in a structured, comprehensible form. At times I’ve tried to explain something to someone and realized, in tracing it out, that I had made a mistake in my reasoning. At other times, I’ve explained something and found a much better way to articulate some part of it or ground one of the associated intuitions in a deeper philosophical idea. Much of my best intellectual progress has come in conversations with others.

Thus, disciplined online discussions (that is, ones conducted virtuously with thoughtful people) are valuable for two reasons: they really can have a significant effect on the views people find plausible and on the number of people who hold your view, and they can help draw you closer to truth, both in the propositions you affirm and in the character with which you pursue it.

Some may not be able to jump into the online space without it being morally corrosive, and these people should not take the advice I’m offering here. But to anyone with opinions on important questions and a sincere desire to grow their understanding, arguing online is a very good use of time!

At this point, I would say something like “Bet you didn’t know I’m talking about Mormonism!” except you probably did know that because of the subtitle of the post and the fact that the exordial head fake is a rather common rhetorical ploy. Yes, this is an accurate description of Mormonism, at least as far as the facts themselves are concerned. It sounds rather similar to historic Christianity, perhaps concerningly so. If someone thinks the evidence for the resurrection compels belief, must they also accept the Book of Mormon? After all, to remain rational when miracles when faced with two of equal credibility, one must either accept or reject both.

The Nicene Christian may face this challenge from two sides. On the one hand, the atheist might claim that, if one rejects the Book of Mormon, one also must reject the resurrection. On the other hand, the Latter-day Saint may insist that no, the evidence for the resurrection is quite strong, and really one ought also to accept the Book of Mormon! What one can not do is affirm only the resurrection.

The former tactic is taken by Alex O’Connor in his recent-ish debate with Trent Horn. The latter is advanced in Witnessing Miracles: Historical Evidence for the Resurrection and the Book of Mormon by apologist Joshua Gehly (and one of the few Mormon apologists who chose, in my opinion, the correct branch of Mormonism, the Bickertonite church).

Call the idea that the Book of Mormon and the resurrection are equally supported by eyewitness evidence the Mormon-Resurrection Equivalence Thesis (or MRET). In this article, I will attempt to steelman MRET, unpack a fair methodology for assessing it, and then explain why I think it fails and why the case for the resurrection far exceeds the case for the Book of Mormon.

The case for the Book of Mormon

At the beginning of each copy of the Book of Mormon are printed two signed statements, one bearing the testimony of the Three Witnesses and the other the testimony of the Eight Witnesses. The Three and Eight were associates of Joseph Smith who collaborated with him in the production of the Book of Mormon and the rise of the early LDS church. To set fully before us the facts to be explained, I will reproduce both testimonies here.

Testimony of Three Witnesses

Be it known unto all nations, kindreds, tongues, and people, unto whom this work shall come: That we, through the grace of God the Father, and our Lord Jesus Christ, have seen the plates which contain this record, which is a record of the people of Nephi, and also of the Lamanites, their brethren, and also of the people of Jared, who came from the tower of which hath been spoken. And we also know that they have been translated by the gift and power of God, for his voice hath declared it unto us; wherefore we know of a surety that the work is true. And we also testify that we have seen the engravings which are upon the plates; and they have been shown unto us by the power of God, and not of man. And we declare with words of soberness, that an angel of God came down from heaven, and he brought and laid before our eyes, that we beheld and saw the plates, and the engravings thereon; and we know that it is by the grace of God the Father, and our Lord Jesus Christ, that we beheld and bear record that these things are true. And it is marvelous in our eyes. Nevertheless, the voice of the Lord commanded us that we should bear record of it; wherefore, to be obedient unto the commandments of God, we bear testimony of these things. And we know that if we are faithful in Christ, we shall rid our garments of the blood of all men, and be found spotless before the judgment-seat of Christ, and shall dwell with him eternally in the heavens. And the honor be to the Father, and to the Son, and to the Holy Ghost, which is one God. Amen.

Oliver Cowdery

David Whitmer

Martin Harris

Testimony of Eight Witnesses

Be it known unto all nations, kindreds, tongues, and people, unto whom this work shall come: That Joseph Smith, Jun., the translator of this work, has shown unto us the plates of which hath been spoken, which have the appearance of gold; and as many of the leaves as the said Smith has translated we did handle with our hands; and we also saw the engravings thereon, all of which has the appearance of ancient work, and of curious workmanship. And this we bear record with words of soberness, that the said Smith has shown unto us, for we have seen and hefted, and know of a surety that the said Smith has got the plates of which we have spoken. And we give our names unto the world, to witness unto the world that which we have seen. And we lie not, God bearing witness of it.

Christian Whitmer

Jacob Whitmer

Peter Whitmer, Jun.

John Whitmer

Hiram Page

Joseph Smith, Sen.

Hyrum Smith

Samuel H. Smith

That’s a little weird, right? Here are eleven men claiming to have seen the plates from which Joseph Smith translated the Book of Mormon. Three of them claim also to have seen an angel. All of them claim that their experience provided assurance of the truth of the Book of Mormon.

Further, the experiences are multisensory: the Three claim to have not only seen an angel with the plates, but heard the voice of God (visual + auditory); the Eight claim to have handled the plates themselves (visual + tactile). Further, these were group experiences—not individual episodes.

The gospels report similar experiences: multiple people encountering the risen Jesus in multisensory fashion. Hallucinations? No, the apologist might counter: hallucinations don’t happen to groups, and they are not multisensory. But such responses seem to rule out hallucinations for the Book of Mormon witnesses too!

Were the witnesses insincere? In both cases, it seems unlikely. Both the early Christians and the early Mormons endured some degree of persecution for their claims and we have no evidence of any witness to either event recanting their testimony (a point especially strong in the case of the Mormon witnesses, since we have numerous later statements in which they reaffirm their testimony). Sure, all of the Three later left Smith’s church for political reasons (Cowdery and Harris eventually returned), but they never abandoned their sincerity in the truth of the Book of Mormon.

One might even claim that the evidence for the Book of Mormon is better than the evidence for the resurrection. A skeptic could in principle deny that the gospel resurrection stories represent the apostolic testimony. Perhaps the apostles never claimed multisensory group experiences, and the talking, breakfasting risen Jesus was a legendary invention. This route is not available to the Book of Mormon skeptic: the signatures on the statements leave little room for question that the testimonies trace back to the witnesses. And we have a much greater number of witness testimonies than apostolic testimonies.

So what gives? Do we accept both? Accept neither? Before deciding, let’s see if the parallel is really quite so compelling as it appears on the surface.

Comparing an apple and an orange

Clean comparisons of historical events are hard, especially when one took place two thousand years ago and one merely two hundred. The amount of information available about the early history of Mormonism dwarfs the amount of evidence available for the rise of Christianity.

The early Christian church left us a handful of Greek documents of which scholars have not been able to agree on the eyewitness provenance (whether rightly or wrongly) and which all agree were written decades after the fact. Aside from some passing mentions by later historians that tell us hardly anything we wouldn’t otherwise have known, that’s it.

The early Mormons, by contrast, left us not just their canon but also journal entries, eyewitness interviews, letters, and newspaper articles. The longest surviving member of the Three Witnesses, David Whitmer, left no fewer than 71 recorded interviews—all in English. This is unlike anything we have for early Christianity.

Now, it would be a mistake to hand Mormonism the proverbial W on this basis alone. Of course we would expect a more recent religious movement to have more founding documents to sort through! But we do have to decide how to compare the two cases fairly. It would be a mistake to dig up some odd turn of phrase from one late Whitmer interview as the smoking gun refutation of MRET, since we don’t have any such interviews of the resurrection witnesses where they could have said similarly incriminating things.

One could take this point either way. On the one hand, some of the details contained in these interviews seem to bolster the witness’ claims (e.g., Whitmer’s continued insistence on the physicality of his appearance, often telling his listeners to compare it to the clarity with which they perceived some surrounding physical object). On the other hand, some of the details seem to tell against them (e.g. LDS law student James Moyle’s statement that Whitmer was “not as materialistic in his descriptions as I wished.”) Certainly these details are relevant to determining the truth behind the witness’ claims. But to determine whether the cases are comparable, we must focus on the sorts of evidence common to both.

I thus propose we focus simply on the question of what the witnesses claim to have experienced, broadly speaking (i.e., no hyper-specific details or word choices, just the broad structure of the claim). This isn’t terribly difficult to determine for the Three and Eight Witnesses: we have their signed testimonies and later statements to corroborate them. It’s a bit harder for the apostles since the gospels stand at (potentially) a bit more historical distance from the original claims. But at least in principle this is a fair comparison. If the structures of the claims are significantly asymmetric, MRET falls.

Why the resurrection dominates

Without turning this post into a full-blown historical examination of the resurrection, here’s what I think we can say about the apostolic claims.

The apostolic claim, broadly speaking, was that Jesus preached and taught about the kingdom of God, worked numerous public miracles of various kinds, was crucified, rose, and then appeared to the disciples on multiple occasions, experiences which at least sometimes had a physical dimension (e.g., more than vague visions).

I won’t offer a full defense of this here for reasons of scope, but the only parts I could see being controversial are (a) that the apostles claimed Jesus worked numerous public miracles and (b) that the apostles claimed the resurrection appearances occurred to groups and had a physical dimension.

In defense of (a), the miracles of Jesus are distributed throughout all four gospels and mentioned by at least one apostolic father (Quadratus) with the comment that some of the recipients of Jesus’ miracles had survived into his own time. This should lead us to think it was a central feature of Jesus’ ministry rather than a legendary accretion. Further, if Craig Keener’s meticulous documentation of modern miracles shows anything, it’s that people sincerely claim to witness supernatural events rather frequently, meaning we shouldn’t set a terribly low prior that the testimony in the gospels can be traced back to the eyewitnesses. That doesn’t mean that every miracle narrated therein is authentic, but it beggars belief to suppose that the apostles made no claims about Jesus working miracles during his earthly ministry.

In defense of (b), the sheer number of texts referring to group, physical appearances gives us good reason to think it traced back to the apostolic testimony. As Andrew Loke comments,1

The portrayal of Jesus’ being involved in meals with causal effects left behind and witnessed by two or more disciples is attested in Luke 24:30–31, 35 (causal effect left behind: the broken bread, witnessed by two disciples), Luke 24:39–43 (the eaten fish, witnessed by ‘The Eleven’ and those with them), Acts 1:4, 10:41, and Ignatius Smyn. 3:311 (the food and liquid eaten and drunk, witnessed by a group of disciples), and John 21:12–13 (the bread and fish given, witnessed by seven disciples).

So while we’d need a more thorough investigation to determine what exactly the apostles claimed about the resurrection appearances, it seems we’re on safe ground saying that Peter et al. would have had more in their story than a brief, visual-only appearance.

If the reader isn’t willing to grant these features of the apostolic testimony, no hard feelings—treat the rest of the post as a conditional critique of MRET, that is, if the apostles did claim these things, then MRET is false.

The LDS witnesses’ claim is different, and there are two versions of it. The three claim a single supernatural experience where they saw an angel, heard a voice, and viewed (and possibly handled) a few physical objects. The eight claim only to have handled one physical object (the plates).

And here’s the crux of my argument: it is far easier to see how the LDS witnesses could be mistaken about their experiences than to see how the apostles could have been mistaken about theirs. There are three reasons for this.

First, the claims of the apostles contained far more supernatural content than the experiences of the witnesses. The Eight saw only a set of plates. There’s nothing about a stack of metal plates that cries for a supernatural explanation. One can, as I do, suppose that Joseph forged a fake set of plates (tin or copper) and showed them only on rare occasions when he could count on them being convincing. There’s very little in the experience of the Eight to confirm Mormonism over this skeptical hypothesis. The Three do claim an angelic visitation, but it’s of indeterminate length and uncertain integration with their surrounding physical environment, and so not obviously outside the purview of an ecstasy-induced vision.

Second, the apostles claimed to witness not one-offs but rather diverse phenomena that recurred across time. None of the Three or the Eight were privy to another alleged major, supernatural confirmation of the Book of Mormon.2 A one-off experience leaves open many explanatory options that don’t scale cleanly to experiences repeated across time, and experiences of two different kinds will often require two semi-independent explanations. Plausibly, the apostles claimed nature miracles, healing miracles, multiplication miracles, and the resurrection itself. In their printed testimony the witnesses claimed one substantive experience each. Explaining the apostolic testimony requires accounting for each of these types of things; explaining the witness testimony only requires accounting for one experience.

Third, miracles and a resurrection leave behind verifiable traces in a way that angelic visitations do not. An angel delivering a message doesn’t necessarily leave some physical trace of its presence that could be inspected after the fact to confirm the reality of the experience. Such physical evidence is left behind by the kinds of miracles the apostles claimed of Jesus: miraculous healing leaves behind a restored individual, meals leave traces of food (or the absence of food known to be present), and so forth. This isn’t to say that any particular miracle in the gospels would certainly have left behind these traces, or that they would certainly have been inspected for their evidential value. It’s only to say that, at least in principle, physical evidence grounding the reality of the experience so it was verifiable after the moment of excitement (a fair criterion for bolstering a miracle’s credibility) was present for Jesus’ miracles but not for the visions of the Three and Eight. This means the apostles had grounds available for inferring and confirming supernatural agency that the witnesses did not, and consequently their claims are more credible (even if still wrong).

Thus, it’s easy to see why the apostolic claims are of a totally different class than the claims of the witnesses. Since the plates themselves (and the other artifacts seen by the Three) are relatively easy to account for, all one needs to explain the testimony of the Three and the Eight is some mechanism by which they the Three could be convinced they saw an angel testifying to the reality of the Book of Mormon. And while I don’t know what the Three really saw that day, it’s not that hard to think of non-Mormonism-supporting reasons they could become convinced they saw an angel.

Now, even if one thinks the claims made by the apostles can also be accounted for, it’s at least not so easy of a task. Their claims are to events of a far more substantial, phenomenologically varied, recurring, evidence-producing quality.

One may object here: sure, if the apostles claimed what I’ve said they did, then the two claims are asymmetric—but we don’t have enough reason to suppose they did! Their initial claims may have been far more mundane and in line with the witness experiences.

I disagree, of course, and alluded to some of the reasons for that above, but if this is the claim the critic wants to press, they still ought to abandon MRET unless they can devise a plausible alternative scenario which gets Christianity going with miracles no more impressive than those of early Mormonism. It seems to me that one must at least postulate two classes of miracles (pre-resurrection, done by Jesus, and post-resurrection, done to Jesus) to have any hope of explaining how the church agreed within living memory of eyewitnesses that Jesus was raising the dead, stilling the seas, healing the sick, and returning from the grave. And that starts to push the apostolic claims into a class superior to the witness claims.

As such, I think MRET fails, and one is totally within their rights to accept the evidence for the resurrection without accepting the inspiration of the Book of Mormon.

That’s not to say there’s nothing for resurrection studies to learn from the Book of Mormon witnesses. At the very least, it shows that groups of people can have purportedly supernatural experiences and stick with them for their whole life, and so something more impressive than that is needed to establish Jesus’ resurrection. Fortunately, we have more than that, and so compelling parallels to the resurrection must be sought elsewhere.

But suppose the basic claims of Mormonism were true: an angel really did appear to Joseph Smith, who really did find an authentic record of the history of the Nephites which he faithfully translated as the Book of Mormon. Which of the contemporary LDS denominations has the best claim to being Christ’s restored church? My contention is that it is not the mainstream Church of Jesus Christ of Latter-day Saints. The most plausible Mormon denomination is the Church of Jesus Christ (Bickertonite) in Pennsylvania.

It may surprise some readers to learn that there is more than one LDS denomination. It’s true that the vast majority of contemporary believers belong to the well-known Church of Jesus Christ of Latter-day Saints (henceforth CJCLDS), centered in Salt Lake City, Utah. They have nearly 18 million members. But they are not the only Mormons.

The other LDS denominations have fewer than 500,000 members combined. They’re tiny. Many trace their origins to the succession crisis of 1844, when the death of Joseph Smith left the growing Mormon movement without a leader. The majority of the church followed Brigham Young, who led the westward migration of Saints to the Utah basin. But small remnants followed other leaders: some followed Smith’s son Joseph Smith III, some the recent convert James Strang, and some the First Presidency member Sydney Rigdon, among others. There are other LDS denominations which broke from the mainstream CJCLDS later (like the fundamentalists who preserve polygamy), but they are not the focus of this post.

These remnant groups ended up comprising their own denominations. The second largest LDS denomination after the CJCLDS is the Community of Christ (COC), headquartered in Missouri, with around 250,000 members. The Pennsylvania-based Church of Jesus Christ (Bickertonite), 20,000 strong, is the third-largest, and in my mind has the strongest claim to being the restored church of Christ, conditional on Mormonism being true (which, again, it’s very probably not).

I’ll briefly survey the history of the Bickertonites, then explain why I think their claims are more plausible than the COC and the CJCLDS.

Who are the Bickertonites?

The Church of Jesus Christ (Bickertonite) traces its lineage through Joseph Smith to Sydney Rigdon and eventually William Bickerton, who founded the church in the 1860s.

As alluded to above, the death of Joseph Smith (and that of his likely successor, Hyrum Smith) left the Mormons in a real predicament. They had plenty of fervor but no leader. The power vacuum produced numerous claimants to the presidency of the church, the most successful of whom was Brigham Young. Young was then the president of the Quorum of the Twelve Apostles, and it was that, primarily, on which he based his claim to be Smith’s rightful successor.

Sydney Rigdon, on the other hand, based his claim on his membership in the First Presidency: the primary governing body of the church, consisting of the president and two counselors. Rigdon was a member of the inaugural First Presidency, advising Smith with Jesse Gause. After Smith’s death, Rigdon claimed to have received a revelation appointing him as “guardian” of the church.

Since the First Presidency exerted more executive power over the affairs of the church then the Quorum of the Twelve, a minority of the Saints thought Rigdon was the natural successor and followed him, forming the Rigdonites.

William Bickerton was a Rigdonite evangelist. While Rigdon eventually disbanded his church, Bickerton continued to preach, and eventually reconstituted many of the former members into what is now known as the Church of Jesus Christ (Bickertonite). The church has remained small, but has locations throughout the United States.

The succession debate is complicated and, well, I don’t know enough about it to attempt to summarize it here. Presently, while it seems to me one could make a half-decent case for Young’s leadership, one could also make a good case for Rigdon’s, and the politics of succession are not enough to decide between the churches. The fact of the matter is that Smith did not explicitly designate a successor, and he did not leave a clearly interpretible rule by which to select one. Even if one thinks Young had the stronger argument, I don’t think one should hold that this is so obvious that it could not be controverted by further evidence. So we must turn to other factors to adjudicate between the churches.

When this is done, I think the Bickertonites win pretty handily.

So why the Bickertonites?

There are many very small LDS denominations, including others who left during the succession crisis and some who left after the migration to Utah in an effort to preserve polygamy. The latter I have no desire to defend. The former (Strangite, Cutlerite) I will pass over as well, though their claims to legitimate succession don’t have quite the same institutional backing as Young’s or Rigdon’s. I will focus instead on the two largest LDS denominations—the CJCLDS and the COC.

First, the mainstream LDS church. As is well-known, the CJCLDS did not exactly behave like a restored church. Brigham Young took a staggering 56 wives and openly defended racism. One must wonder whether a divinely restored church believing strongly in the guiding role of the Spirit of God could retreat from moral progress in such a spectacular fashion. This isn’t merely a church failing to make moral advances from their surrounding culture. The mainstream church went backwards. This is precisely the opposite of what one would expect from a restored church!

The Bickertonites, on the other hand, joined the COC in never accepting the validity of Joseph Smith’s polygamy revelations. They also supported racial integration well before the CJCLDS. This is precisely what one would expect from a restored church.

Another serious problem for the CJCLDS is that their metaphysics is totally wack, to use the technical term. Those metaphysical beliefs derive primarily from the Doctrine and Covenants—a book rejected by the Bickertonites, whose canon contains only the Bible and the Book of Mormon. For example, D&C 130:22 says that

The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us.

The affirmation that God has a physical body more or less wrecks theistic philosophy. I’m not bold enough to say that one couldn’t come up with a way to make this tenable, but it seems that such a conception of God implies God can’t be fundamental reality, which is what’s supposed to make theism a metaphysically satisfying theory in the first place. Someone convinced of certain arguments against traditional theist metaphysics may actually find this a reason to favor the CJCLDS, but I reckon most readers will not be willing to say that the CJCLDS conception of God is more plausible than the traditional Christian one, even if they see problems with both.

Thus, the Bickertonites avoid both the moral and the metaphysical problems with the mainstream LDS church. Now, one may pose a meta-historical objection here: isn’t the success of the CJCLDS evidence of its divinely favored status? How can a church as small as the Bickertonites claim to be of God?

I don’t think this objection works. The notion of a small faithful institution set apart from a corrupt mainstream is, well, a very Mormon idea! That’s the entire premise of the restoration movement, and remember, we are assuming for the sake of argument that restoration theology is true—that God raised Jesus from the dead, let the church fall away quickly after the death of its first leaders, and waited to restore it for almost 1800 years. If we’re already assuming that happened, then why is it so surprising that corruption might seep in again after the restoration? Under Mormon theology, God has no issue letting the masses obscure and corrupt his revelation. In fact, one begins to suspect that the corruption of the mainstream LDS church is precisely what one might expect given Mormonism’s assumptions about the fidelity of the church.

Why the Bickertonites, though, and not the Community of Christ? The COC has many of the advantages of the Bickertonites: rejection of polygamy, support for racial integration, and more traditionally Christian metaphysics. The main difference between them and the Bickertonites (aside from size) is that the COC is theologically and socially progressive (many taking a non-historic view of the Book of Mormon, for instance) whereas the Bickertonites remain staunchly conservative. The COC is very ecumenical, for instance, and in many ways resembles mainline Protestantism.

But it seems unlikely that God would restore his church from the established ones only for them to become like the very churches they left. Before claiming the discovery of the plates, Smith claimed a revelation in which God told him that all of the existing churches were corrupt. That’s the whole reason the church needed to be restored in the first place. It’d be somewhat strange for God to restore a church only for that church to argue that all the other churches which motivated its restoration are actually just fine and we should all try to get along. The primitive, exclusivist outlook of the Bickertonite church is more consistent with the tenets of restoration theology: the original message is of the utmost importance, fragile, and must be guarded at all costs.

The Bickertonites thus proclaim a theology which may not be very plausible on the whole, but makes sense internally and avoids some key problems. God raised Jesus from the dead, establishing a church which was soon corrupted. God re-established his church in the 1800s, but even that re-established church quickly repeated the pattern of the 1st-century church, and now only a remnant faithfully preaches the true gospel. It’s a fairly consistent set of claims, and while as a grand theological theory it really leans on “the road is narrow and few find it,” it’s far more coherent than the messy pseudo-restoration of the Church of Jesus Christ of Latter-day Saints.

And that is why, if I were ever convinced of Mormonism, I would strongly consider joining the Bickertonites.

Now, the obvious downside of this is that the naive masses can delude themselves into thinking they’ve mastered the field and are worth taking seriously. The obvious upside is that the field attracts contributions from a wider slice of people, and more meaningful contributions means more intellectual fruit.

Why do I distinguish the naive masses from the thoughtful outsiders? To dissolve any pretension that I have the slightest idea to which of these categories I belong as I engage the magnum opus of the man who, in my present opinion, is the most intellectually formidable atheist in the modern academy, at least among those working in the analytic philosophical tradition: Paul Draper, professor of philosophy at Purdue University. Draper is well-known for his work on Bayesian arguments from evil and his contributions to philosophy of religion more broadly.

Last year, he published a tour-de-force defense of atheism entitled Atheism and the Problem of Evil. Shout-out to Oxford University Press on the exceptional cover. “Don’t update your credence in a book’s epistemic force by conditioning on its cover design,” as the saying goes, but it sure is a beauty:

I, a theist seeking to take the methods of philosophy seriously, felt obliged to read this book. I have done so, and I remain a theist, and these are my disagreements. I am not a trained philosopher. I have, at present, no intention of becoming one. As such, my critiques are somewhere between perceptive and naive, and probably not all of them at the same place on that spectrum. Fortunately, Substack provides an optimal venue for exactly these kinds of musings.

Since I’m already busy hedging at the all-you-can-caveat buffet (as I am wont to do), I’ll mention that this critique is aimed more at challenging what appear to me to be a few chinks in the armor of Draper’s arguments rather than mounting a complete response to them. There’s much more to be said, on both sides, and I intend this as a contribution to the discussion rather than an attempted conclusion of it.

Draper’s contentions

Draper’s book takes a probabilistic approach to evaluating the evidence for theism. While he discusses deductive arguments in a few places, the meat of his contribution is the use of Bayesian reasoning to construct two arguments against God’s existence.

I won’t rehash Bayes’ Theorem here. I’ll refer the interested reader to my series of articles on the subject, beginning here. But briefly, Bayesian reasoning places particular weight on two features of a hypothesis: its prior probability and its posterior probability. Speaking loosely, the prior probability is how your hypothesis holds up before looking at any evidence, and the posterior probability is how it fares afterward. These terms are somewhat slippery because you can condition on anything and call it a prior probability so long as it’s compared to a probability derived by conditioning on something further, but that’s the basic idea.

Draper uses the notion of intrinsic probability to mean “epistemic probability independent of all data” (52). We can think of this as the prior probability of a hypothesis when conditioning on no contingent facts. It’s a kind of prior probability, but in a sense the “most prior” probability. It’s simply a property of the hypothesis.

To get a rough intuition for this, we can think about the fact that some hypotheses are much more likely to be true, a priori, than others. For example, the hypothesis that a man is currently walking in front of my house is more likely to be the case than the hypothesis that, say, Keir Starmer is currently walking in front of my house. Similarly, the hypothesis that it didn’t rain last night is more probable intrinsically than the hypothesis that it rained torrentially but dried up by 8 am.

What determines this, though? What makes a hypothesis more intrinsically probable than another? Draper argues that intrinsic probability is a function of two (and only two) features: modesty and coherence. Modesty concerns how much a hypothesis claims to be true. Coherence concerns how well the different parts of the hypothesis fit together.

Applied to the first example above, we can see that the first hypothesis (a man is in front of my house) is more modest than supposing that Keir Starmer is in front of my house. The latter is making a very specific claim, whereas the former is making a much more general claim which would be true if Keir Starmer were in front of my house but also if any other man were in front of my house. This is the criterion of modesty.

The “rained torrentially but dried up by 8am” hypothesis, on the other hand, exhibits a notable lack of coherence. Extreme precipitation doesn’t usually correlate with the high heat necessary for rapid drying. As such, the different parts of this hypothesis don’t work well together, so the first hypothesis (it didn’t rain at all) is more coherent. One could also argue the first hypothesis is more modest, since it postulates just one common event rather than two less common ones.

Draper argues that other candidates for determinants of intrinsic probability (e.g. simplicity) are either not relevant or reduce to either modesty or coherence. I’m willing to grant that modesty and coherence are the only determinants of intrinsic probability—I tentatively think Draper’s arguments here were convincing. Draper uses the notion of intrinsic probability (and particularly the twin virtues of modesty and coherence) heavily in his discussion of theism, so it’s worth keeping in mind.

Draper proceeds to construct two arguments against theism. He calls the first argument a decisive evidence argument and the second argument a decisive priors argument. The basic idea is simple. A decisive evidence argument finds a competitor hypothesis to theism that is of roughly equal intrinsic probability and yet much more strongly favored by the evidence. A decisive priors argument finds a competitor hypothesis which is much more intrinsically probable and is at least equally supported by the evidence. The structure here is sound: if there’s either a hypothesis which is just as intrinsically probable as theism and better supported by the evidence, or a hypothesis which is far more intrinsically probable than theism and no worse supported by the evidence, than theism can’t win the evidential race. There is at least one option on the table which bests it.

I have some concerns with both arguments, and I will address them in turn. First, though, it is worth setting out the terms that Draper uses throughout the book. “Core theism,” the hypothesis that “there exists an omnipotent, omniscient, and loving agent who created the cosmos for good reasons” (17), is the primary version of theism Draper engages. “Core atheism” is simply the denial of core theism.

“Indifference deism” is the competing hypothesis Draper considers in his decisive evidence argument, defined to be the hypothesis that “there exists an omnipotent and omniscient agent who created the cosmos for good reasons and who is indifferent to the well-being of the sentient creatures in that cosmos” (77).

Finally, “anaxiarchism” is the competing hypothesis that Draper considers in his decisive priors argument, defined to be the hypothesis that “either (i) some entities are causally fundamental and aimed neither at goodness nor badness, or (ii) no entities are causally fundamental but, for some time t, no entity prior to t was aimed at goodness or badness” (96). It’s called anaxiarchism to contrast with axiarchism, the hypothesis that fundamental reality is (generally non-agentically) aimed at goodness.

The decisive evidence argument

Draper begins with his decisive evidence argument. I will reproduce the full statement of the argument here (78-79):

Let “QUALITY” stand for a statement reporting what one knows about the quality of the lives of sentient beings on earth—that is, about how good or bad those lives are for the beings living them. My decisive evidence argument for core atheism can be formulated as follows.

(1) Indifference deism and core theism have roughly equal intrinsic probabilities.

(2) Indifference deism and core theism fit the background evidence—that is, the total evidence excluding QUALITY—roughly equally well. In other words, the background evidence favors neither hypothesis over the other, at least not strongly.

(3) QUALITY is known to be true and, relative to the background evidence, very strongly favors indifference deism over core theism—that is, its antecedent probability given indifference deism is many, many times greater than its antecedent probability given core theism.

It follows from (1), (2), and (3) that
(4) Indifference deism is many times more probable than core theism.

It follows from (4) that
(5) Core theism is very probably false.

It follows from (5) that
(6) Core atheism is very probably true.

Recall that for the decisive evidence argument to work, the core atheist must simply identify one competitor to core theism which is roughly equal with it on prior probability and is much better supported by the evidence. If this can be done, then core theism is not the best option on the table, and it must be less probable than core atheism. Note that because of how Draper has defined the terms, indifference deism is actually a form of core atheism. This may not be the sort of atheism most people envision, but it works for the purpose of the argument, since most contemporary theists do not believe in the deity of indifference deism (and that deity is incompatible with the teachings of the major world religions) and so a good case for indifference deism is a major blow to core theists.

Draper argues, correctly, that the inferences to (4), (5), and (6) are sound. Obviously, language like “very probably” and “many times more probable” requires us to slightly relax our standards of rigor, but he provides a convincing derivation for its prudence in the book. The key premises, then, are (1), (2), and (3).

Premise (2) is questionable. As Draper explains, the reason God creates anything is because it is good that those things exist: it is good that, for example, consciousness, moral agency, and beauty exist. Draper’s indifferent deity is likewise interested in creating things that are good (see the “for good reasons” stipulation), but not in the welfare of sentient life. Further, Draper argues the theistic God’s concern for the welfare of sentient creatures does not give him additional reason to create consciousness, moral agency, or beauty, and so that we would expect those things equally on either hypothesis.

My biggest concern with premise (2) is that this argument only goes through if you assume that the “good reasons” which motivate the indifferent deity provide the same degree of motivation as the “good reasons” which motivate the theistic God. If they do not, then we have no grounds on which to make the claim that equally predict the evidence. Draper admits that “good reasons” is a broad justification which can refer to reasons that are good for the creatures, reasons that are good for the creator, or both, or some other kind of good entirely. But if indifference deism predicts consciousness on the ground that it is good for the creator that it exists but theism predicts it because it is good for the creator and because it is good for the creatures, then the theistic God has more reason than an indifferent deity to create consciousness, and so the probabilities are unequal.

One could argue that our ignorance of which hypothesis gives us the best reasons to expect the phenomena we observe means we should assume a symmetry between the two for the sake of argument. To this I say: fine. But I suspect one could press the objection further.

That said, there is at least one category of theistic evidence which would boost theism without boosting indifference deism: miracles. Draper admits as much (83):

Finally, arguments from benevolent miracles would be helpful to the core theist if it could be established that such miracles have occurred (good luck with that).

That is in fact all he says about miracles here, and readers hoping for a more detailed discussion elsewhere in the book will be disappointed. While Draper must scope his book somehow, I find “good luck with that” rather unsatisfying. I’ll leave the point here.

My biggest concern with the argument is premise (1). Recall that, according to Draper’s analysis intrinsic probability depends on modesty, coherence, and nothing else. In Draper’s view, while one could make an argument that indifference deism is more modest since it doesn’t specify the sorts of goods in view, and while one could make an argument that indifference deism is less coherent since it makes more sense for the creator to value all sorts of goods rather than just some, neither argument is going to justify believing that one of the hypotheses is substantially more intrinsically probable than the other, and so premise (1) holds.

I don’t think Draper has adequately defended the coherence of indifference deism. A hypothesis is coherent to the extent that its pieces fit well together. Indifference deism postulates the existence of a deity who cares about some good things but not others (like the welfare of sentient beings). But this is puzzling. Concern for one sort of good seems to fit way better with concern for other sorts than with indifference toward them. Postulating that God is motivated by all sorts of good (theism) is to postulate a clean, unified motivational suite rather than an inconsistent and piecemeal one.

One could hash out this concern in terms of modesty, as well. Theism postulates one type of attitude toward goods: value of them. Indifference deism postulates multiple types of attitude toward goods: value of some and indifference toward others.

It’s not clear how one should weight these concerns, but it’s also not clear that Draper is correct in supposing that modesty/coherence concerns from indifference deism and theism balance each other out. It seems that more work needs to be done to establish premise (1).

Finally, premise (3). The heavy lifting here is done by the phrase “many, many times greater.” Draper aims to justify this by discussing many categories of evil and suffering which, he argues, are mostly (though not completely) independent of each other. These include facts about pain and pleasure and about flourishing and languishing.

Here I will briefly make a conditional objection. The assumption of independence seems to mostly dissolve if the theist adopts some kind of regularity theodicy, namely one where God more or less lets the world play out and only occasionally intervenes. Done properly, this could provide an evolutionary explanation for facts about pain and pleasure, and explain numerous other apparent theistic counterevidence as a result of God entrusting stewardship of his world to his creatures (a supposition not terribly far from the teachings of a particular religion to which I may or may not adhere). If one is convinced that such a theodicy is not terribly improbable, then the claim that QUALITY is “many, many times greater” on indifference deism than on theism is far less obvious. It is not my intent to defend a regularity theodicy here, but this strikes me as a reasonable line of attack.

Wrapping up the decisive evidence argument, then, I think premise (1) is questionable, premise (2) is very questionable, and premise (3) is possibly questionable. So while the decisive evidence argument may, for all I know, be sound, I cannot say that I find it persuasive.

The decisive priors argument

Draper defines another proposition, VIRTUE, to stand for “what we know about the moral qualities of human beings, both positive and negative.” Here’s his decisive priors argument (97-98):

(1) The background evidence—that is, the total evidence excluding QUALITY and VIRTUE—does not favor core theism over anaxiarchism more than QUALITY and VIRTUE together favor anaxiarchism over core theism.

It follows from (1) that
(2) The total evidence does not favor core theism over anaxiarchism.

(3) Anaxiarchism is many times more probable intrinsically than core theism.

It follows from (2) and (3) that
(4) Anaxiarchism is many times more probable than core theism (all things considered).

It follows from (4) that
(5) Core theism is very probably false.

It follows from (5) that
(6) Core atheism is very probably true. [emphasis in original]

Recall that anaxiarchism is the hypothesis that “either (i) some entities are causally fundamental and aimed neither at goodness nor badness, or (ii) no entities are causally fundamental but, for some time t, no entity prior to t was aimed at goodness or badness.” This is, roughly speaking, the idea that ultimate reality is indifferent toward good and evil. Draper has a clever argument for premise (3) that I, an intellectual chicken, will not discuss here. I want to focus on premise (1).

Draper wants to show that anaxiarchism starts the race far ahead of theism and that theism doesn’t have enough evidence to catch up. To make this claim, of course, he must consider the broad categories of theistic evidence, which he does at this point in the book.

Here I want to press just one objection. When Draper considers the probability of consciousness, agency, and beauty obtaining on theism relative to anaxiarchism (100-102), he does not factor evidence from fine-tuning into naturalism’s side of the equation. That’s fine, in principle: the order in which evidence is assessed is irrelevant in Bayesian reasoning. But then it’s rather perplexing that Draper’s response to fine-tuning is to argue that, because theism really only gives us reason to expect consciousness is valuable, rather than biological life, the fine-tuning data needs to be assessed together with consciousness:

As explained in Section 6.4, conscious life (at least of the sort with which we are familiar) is valuable and thus is more likely on hypotheses like theism that are “biased” towards positive value than on hypotheses like anaxiarchism, which have no such bias. This is why it is so important to tease apart the fine-tuning data from the datum that conscious life or embodied consciousness exists in our universe… My objection to the fine-tuning argument is that, once we separate these two sets of facts, we can see that fine-tuning is at best a sort of red herring—that is, it diverts attention from the real issue of whether conscious life all by itself strongly favors core theism over anaxiarchism. (122)

The effect of reading Draper’s discussion of fine-tuning was to see it deferred to a section which held that it should have been discussed when it was deferred. So fine-tuning never ends up factoring into his argument. In fact, it seems his argument is completely impervious to whatever the probability of biological life given anaxiarchism is. But this seems incorrect. Suppose I had a dial which let me set the probability of biological life given anaxiarchism to whatever arbitrarily low level I wanted: 1 in 10, 1 in 10^10, or 1 in 10^10^500. If moving the dial had no effect on the the final probabilities of anaxiarchism and theism, then clearly something has gone wrong with the argument.

To make the objection a little more precise, we can use C, G, and B to refer to facts about consciousness, agency, and beauty respectively, and F to refer to data about fine-tuning, with T and A being theism and anaxiarchism. Draper admits that P(CGB|T) > P(CGB|A). He also argues that, given that consciousness exists and that anaxiarchism is true, fine-tuning does not favor theism, since any precise historical outcome is going to be extremely sensitive to perturbations in the initial conditions of the causal chain which led to it (122). In other words P(F|T&CGB) ≯ P(F|A&CGB). But if he’s going to bake F into C such that F is more-or-less entailed by it, then whatever hit anaxiarchism takes from fine-tuning needs to show up in P(CGB|A). As it is, the hit never shows up.

If this is true, then the theist convinced of the evidential weight of fine-tuning has a route around Draper’s argument.

Last section’s conditional objection pertaining to regularity theodicies is salient here as well, and given its power to weaken both of Draper’s arguments, it’s something I want to devote some further study to. For now, though, I will leave things here.

Conclusion

I do not think I have conclusively demonstrated that Draper’s arguments are faulty. I do think I’ve put forth some options for the theist to work with. I’m open to correction on any of these points. Multiple times, as I was drafting this post, I realized that I had failed to understand one of Draper’s contentions or overlooked a part of his book where he addressed my concern. He is an extraordinarily thorough philosopher and his intellectual caliber is something to which I, at present, can only aspire. But philosophy is anyone’s game, and I submit this post in the hope that it can be a worthy contribution to the discourse!

Nonetheless, I am highly critical of most popular-level apologetic work. That should not be taken as a critique of Christianity itself. In fact, the quality of popular apologetics is merely one instance of a general phenomenon: the most popular defenders of any controversial view tend not to be its best. There are doubtless many reasons for this fact, not least of which is that simple, easily repeatable analyses appeal more to the average person than nuanced, philosophically rich ones. Christianity is not unique in this regard at all.

My intent is also not to attack any particular apologist. Deep disagreements notwithstanding, I’m hesitant to focus my critique on any one person, given the pervasiveness of these arguments.

As such, while this post is inspired by a book I read recently for a book club at a family member’s church, I will not be naming the book or the author in question. Admittedly, this limits the amount I can quote or how specific I can be, but I should be able to represent the relevant themes in enough detail for the critique to be fruitful. Suffice it to say, while the author is not one of the most well-known evangelical apologists, he is part of their network, and I consider his book reasonably representative of the flavor of pop apologetic arguments.

Why write a post critiquing bad arguments on my own side? Well, it’s important that all be held accountable, and a critique from someone’s own side lands differently than a critique from someone else’s. It would arguably be petty of me to write a post dunking on Internet atheism, and it’s unlikely to convince anyone in that crowd. A critical post from a fellow atheist would have at least slightly better prospects of raising the level of the discourse. To be constructive, however, I will try to not merely object to that which I find disagreeable but also, when appropriate, propose a better way forward.

Finally, I will here be critiquing “popular apologetics” as a monolith. That’s admittedly a vague category, and there is certainly plenty of variation within it. One may object that I’m painting with too broad a brush. But I think it’s the case that the term “popular apologetics” at least approximately picks out a school of thought and practice which has at least some general epistemic trends worth critiquing. I beg the reader’s forgiveness for any remaining conceptual sloppiness.

I will frame the critique around what I see as perhaps the biggest problem with popular Christian apologetics. I will unpack that first, and then argue that numerous other issues flow from it.

The biggest problem: inaccurately framing the dialectic

Whether we like it or not, much of our thinking is outsourced. There are limits to how much we can investigate even given a whole lifetime. Most of us hold the beliefs we do through some combination of thinking through the arguments for ourselves and selectively trusting relevant authority figures (experts, religious leaders, knowledgeable friends, and so forth) for the rest. I suspect this holds true, with some variation, across intellectual demographics.

This raises the question of how to know which experts to trust. There are many, and in many fields (especially ones dealing with existentially significant questions), they disagree.

To account for this fact, anyone seeking to impart a worldview to other must provide some sort of dialectical frame that explains which people are right, and why, and which people are wrong, and why. This frame can be simple or complex, implicit or explicit. But it’s always there. After all, if your view is correct, there has to be some reason not everyone accepts it!

Generally, unless there is reason to suspect otherwise, I think the most accurate frame is some kind of epistemological symmetry. Largely speaking, people arrive at different opinions on an issue for largely similar reasons: some of them do so via honest evaluation of the evidence, others by motivated reasoning, others simply by inheriting that belief, and some purely emotionally in the absence of evidence. The point is that none of these epistemic paths are distributed to a wildly disproportionate degree on either side (though certainly there’s some variation). Why think this? Well, people are very similar to each other, and we’re all subject to the same cognitive biases. We succumb to biases more often than we adopt beliefs we don’t want to hold or that would require exile from our in-group. There’s obviously a selection effect toward certain schools of thinking, of course, and I wouldn’t want to claim that opposing sides always have the exact same percentage of each intellectual profile. But to the extent one is convinced of the extent to which common reasoning habits and pitfalls are deeply ingrained in human nature, one ought to endorse some sort of epistemological symmetry.

Epistemological symmetry, applied to Christian evidences, would have it that there exist simultaneously the following groups of people:

1. Intelligent Christians, well-informed, sincerely convinced of the truth of Christianity.

2. Intelligent non-Christians, well-informed, sincerely convinced of the falsity of Christianity.

Most participants to serious religious discussions (the kind you see on our glorious Substack, not on their barbarous X or Reddit), I think, would grant that both these groups exist. I certainly do. And there’s nothing wrong with that. To oversimplify the rather interesting puzzle of peer disagreement, the only thing you need in order to rationally hold your view while maintaining the thesis of epistemological symmetry is some reason to suppose that the others have made a mistake in their analysis. So I don’t think epistemological symmetry is something we ought to be hesitant to grant. Doing so doesn’t undermine the rationality of one’s beliefs.

Enter popular apologetics. I was fascinated by popular apologetics in middle school and early high school. My study Bible, mass market paperback copy of The Case for Christ, and homeschool curriculum afforded me a wealth of evidence ostensibly confirmatory of my beliefs. And the dialectical frame I absorbed from this material was something like the following, which we will call Christian Epistemic Dominance (CED): “The evidence for Christianity is incredibly strong. It’s so strong, in fact, that non-Christians are either uninformed or uninterested—they’ve made a prior commitment to not taking Christianity seriously.”

Maybe absorbing CED from the content I engaged was a me problem, but I don’t think it was. In the aforementioned book club reading, that was the driving idea. Rarely do I ever see popular apologetics work acknowledging the existence of honest atheists or climbing any higher up the ladder of atheist thought than its Dawkinsian lowest rung. Combined with a slew of stories from former non-Christians who became Christians after examining the evidence, shallow engagement with atheist thought certainly does give one the impression that the evidence is pretty clearly decisive and that the critics aren’t serious intellectual players.

CED is an egregious violation of the assumption of epistemological symmetry. Further, to my mind, it’s one of the biggest problems with popular apologetics because it leads intuitively to a whole host of other problems I’ll discuss below.

The issues with it will become clearer as I discuss those other problems, but the primary issue with CED is that it’s manifestly false. There are plenty of informed non-Christians who have arrived at their positions via more-or-less rational means. Certainly, all have epistemologically sinned and fall short of perfect rationality—no one will be without reproach. But to my mind, after engaging top atheist thinkers (like Oppy, Schellenberg, Mackie, Draper, and Sobel), it seems obvious to me that many atheists have met at least a baseline standard of rationality and intellectual virtue, certainly far above the minimum to which popular apologists call their readers. Further, many popular apologists present the evidence as capable of convincing even a hardened skeptic (Lee Strobel’s much-cited story a case in point, though it’s not hard to find others). If this is true, then even only-mostly-sincere non-Christians would pose a problem for CED.

I’ve also grown suspicious of the moral fruit borne by a commitment to CED. Love of intellectual neighbor requires that one not impute ill motives to them in service of a sociological presumption. That’s not to say one must believe every atheist’s testimony of their intellectual sincerity. People who claim to be serious thinkers while giving overwhelming evidence of the contrary are, alas, a common sight, and the atheist community is no exception. But one must also not silence their testimony entirely. This becomes particularly concerning in assertions that atheists are simply too attached to their sin to do proper intellectual investigation.

And finally, one of the biggest problems with CED is how it sets Christians up to be totally blinded by serious, sober criticism of apologetic arguments. This was my experience. My CED-addled brain did not have the categories to deal with philosophical atheism. Unlearning and relearning key epistemic principles took a decent amount of time. And many who have gone my way have not emerged with their faith intact. Let me reiterate, again, that I do think the best available resources defending the Christian faith are impressive and meet the atheists’ challenge. But if we think we can meet that challenge, why pretend it doesn’t exist?

The best way forward for the Christian (like myself) is to simply reject CED. One can simultaneously hold that one’s position is strongly supported by the evidence and that the sincere thinkers who don’t hold it have simply made a mistake somewhere in their reasoning. Maintaining CED, on the other hand, leads to a whole host of difficulties. I will note them as I discuss some other issues with popular apologetics.

Issues downstream of CED

Many popular apologists fail miserably to engage the best objections to their arguments.

Now, obviously, one shouldn’t expect, say, a 200-page book designed for a church small group to offer an extended critique of Paul Draper’s decisive priors argument for atheism. There must be popular-level books. But nothing prevents one from engaging strong counter-arguments briefly and accessibly. One could overview the fine-tuning argument and address, in rapid-fire fashion, a handful of serious objections with more advanced material in the footnotes or in a designated “further reading” section. Many books, however, don’t even do this.

This worrying tendency is directly downstream of CED. Seemingly, in the minds of many popular apologists, there simply are no weighty objections to their arguments. They are decisive. This is why someone might present an argument, respond to one objection from Dawkins, and move on to the next. That’s sufficient when one has a sweeping explanation, like CED, for why people object to your argument in the first place. Move on, nothing to see here, because our opponents aren’t serious thinkers!

CED also produces a striking lack of intellectual originality. When one assumes one’s fellow apologists have, like you, landed on the obvious truth, there’s really no motivation to think carefully about the relevant issues from scratch, devise one’s own arguments, or critically assess the arguments of people on one’s own side. And so everything gets repeated. Nearly every new popular-level book approvingly cites its predecessors with little attempt to break new ground. I wager that’s why nearly every popular-level apologetics book contains the following quotes:

“It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door.”

(Richard Lewontin)

“Biology is the study of complicated things that give the appearance of having been designed for a purpose.”

(Richard Dawkins)

“I want atheism to be true and am made uneasy by the fact that some of the most intelligent and well-informed people I know are religious believers. It isn’t just that I don’t believe in God and, naturally, hope that I’m right in my belief. It’s that I hope there is no God! I don’t want there to be a God; I don’t want the universe to be like that.”

(Thomas Nagel)

These quotes are interesting, they’re rhetorically useful, and they clearly fit with CED! And all the other apologists use them, so we’d better do the same. There’s nothing wrong with using these quotes in principle, but they should not be framed as Freudian slips or as the confessions of the rare honest atheist, as if the expressions contained therein are representative of atheists at large. Lewontin’s musings on methodological naturalism may or may not represent the private thoughts of the majority of atheist scientists (I, for the record, reckon that most resistance to a Divine Foot happens subconsciously, when it happens at all), but they alone wouldn’t demonstrate that to be the case.

Another major issue with popular apologetics is the theological gap. Practitioners prefer instead to jump from the resurrection to 20th-century evangelical theology (or perhaps post-Vatican II Roman Catholic theology, as the case may be, though generally Catholics make a slightly more noteworthy attempt to establish their theological distinctives).

Now though the resurrection doesn’t get you all the way to the Nicene Creed since one can cook up any number of weird scenarios in which Jesus rose from the dead but Christianity is false (e.g. simulation theory), it certainly gets you a substantial amount of the way to Christian orthodoxy. But one simply must adduce auxiliary arguments to get to a specific flavor of Christianity. It seems to me (acknowledging my inability to access their mental states) that many apologists seem to think that if they can get to the resurrection and to the authority of Scripture, then their theological package simply comes along for free as the straightforward reading of Scripture. And that’s generally a Billy Graham-style, soterian theological package which is (I would argue) more or less foreign to church history before the mid-1900s. The issue is that the jump from the resurrection to the authority of scripture is at least not totally obvious (though in my mind defensible), and the jump from there to many popular theological frameworks is far less obvious (and in my mind indefensible).

I could say more, but I’ll only make one more point: apologetics should be an activity conducted in service of truth, and accordingly a significant part of the apologist’s task is equipping people with the tools to seek the truth. This means promoting principles of sound practical epistemology (Bayesian reasoning, for example, or tips on avoiding common cognitive biases). But this is often passed over very briefly in the works of popular apologetics which I’ve read in service of a vague notion that “the evidence points” to the truth of Christianity, absent any acknowledgement that perhaps the evidence itself can be ambiguous to certain people (contra CED) and so requires a fuller epistemological toolset to properly think through. This is admittedly present in some popular-level books (J. Warner Wallace’s Cold Case Christianity makes a decent attempt at explaining principles of evidence), but its absence from others is nonetheless concerning.

Conclusion

What ought we do about this? I’ve deliberately focused only on my own side of the aisle, and I will do so again here, but this advice could be inverted for dealing with popular-level atheism.

Christians ought not to be afraid to push for better arguments. We are defending what we are convinced is the truth, and it will not do to defend truth with the armor of falsehood and naivety. Practically, my favorite approach is to swap in a more nuanced, robust version of a bad argument I’m pushing back on. If someone insists that a particular archaeological finding “proves the Bible true,” then one is within one’s epistemic rights (assuming, of course, that the correction is delivered with the humility and grace befitting a servant of truth) to nuance the evidential import of that particular finding but reestablish confidence in the veracity of scripture by mentioning the wealth of other extrabiblical findings which support it.

Non-Christians, for their part, can seek to give broader hearing to the best arguments for Christianity. That’s not to say they can’t critique popular apologetics without caveating every paragraph with references to higher-quality defenders of Christianity. It is to say that if a non-Christian has a large internet presence critical of Christianity and hasn’t once written an article or released a video engaging with the arguments of a rigorous, lesser-known Christian philosopher (i.e., not William Lane Craig), then they are lowering the level of the discourse rather than raising it.

The same, of course, goes for Christians critical of atheism. Raising the level of the discourse is a collective endeavor and requires real effort. But every eager mind we redirect to the deep end is a fresh companion in our mutual quest. May we all, in so doing, draw nearer to the truth.

Discussions of the epistemological and theological assumptions involved in the debate do come to the fore occasionally, but I think there are some things that remain to be said, and so I offer this contribution.

The question

One could easily invest all their free time in exhaustively analyzing every claim of divine healing. But this would probably be absurd. At some point, after one has examined several of whichever examples happen to be popular at a given point in time in a given nook of the discourse, one must zoom out and (inductively, based on the cases they’ve studied) draw some conclusions about the general shape of the evidence. In other words, the question moves from whether a particular miracle is compelling to whether the sort of evidence for miracles in general is compelling. For the sake of argument, I will suppose that the evidence for miracles is (perhaps) suggestive but not conclusive: that is, that one can devise naturalistic explanations of the data which don’t totally strain credulity. Some would doubtless like to challenge this assumption; they are free to do so. But for the rest of this article I will assume a more ambiguous picture presents itself. A skeptically inclined person may offer something like the following assessment:

“Some of these cases may be interesting, but none of them are conclusive. If God existed, I would expect there to be some better cases—not merely ambiguous ones. So the existing miracle distribution is evidence against theism.”

There’s nothing wrong with this kind of reasoning in principle. Certainly, if I investigate ten canonical reports of, say, Florida’s legendary skunk ape and conclude that they are (unfortunately) far from impressive, I am justified in at least slightly lowering my confidence that malodorous, mischievous hominids roam the southern swamps.1

But that conclusion only goes through if we assume another premise, namely that if at least one skunk ape existed, we would expect significantly better evidence of it. Now, in the case of the skunk ape, that assumption seems reasonable. A breeding population of these creatures would be somewhat large, and unless they’re some sort of quasi-supernatural beings (who are of course connected to the UFO phenomenon, a common idea in certain corners of the Internet), there’s no reason to expect them to be undertaking some large-scale effort to conceal evidence of their existence. Sure, they might be wary of humans, but they’re quite large and noticeable, and in between game cameras, drone footage, physical remains, and so forth some decisive evidence would surely have turned up by now.

Reasoning from the poor quality of existing evidence to something’s non-existence is often valid. But not always. Consider the ivory-billed woodpecker2, another animal whose alleged existence draws committed searchers to southeastern swamps. But I find the ambiguous photographic evidence less forceful here, Wikipedia’s spin notwithstanding, and hold out some small measure of hope (though admittedly dwindling by the year) that the ivory-billed woodpecker does in fact survive somewhere.

My credence in the ivory-bill’s existence is much higher than the skunk ape’s, for two reasons: first, of course, we are certain the species did exist at one point (and its much more likely something will exist in the present if it existed in the past), but also more interestingly the ambiguous evidence is less surprising for the ivory bill: it’s a much smaller creature with a known lookalike (the pileated woodpecker) and a much quicker means of escape once noticed by a human. Perhaps, because you are lame and not cool, you find the evidence for the extinction of the ivory-bill decisive. But hopefully you can agree that the evidence is at least less forceful than in the case of the skunk ape. Why? Because there are higher-level factors which influence the extent to which the ambiguous evidence is surprising.

Speaking of the Lord God bird3, we ought to be aware of a similar epistemic dynamic when trying to identify the actions of God. Those convinced that the evidence is ambiguous ought to seriously consider whether theism predicts otherwise. Someone convinced that God would work miracles as a means of maximizing theistic belief may well have different expectations of the evidence than someone with more cautious assumptions, just as one’s expectations of the habits of ivory-bills and skunk apes will influence one’s response to the scarcity of evidence.

I will now drop the gripping subject of legendary southeastern fauna and state my basic thesis: I don’t think ambiguous miracle reports are particularly surprising on theism. I’m not totally confident in this, but I do think a significant portion of the probability space, conditioning on theism, belongs to the idea that miracles would be rare and frequently non-decisive.

I defend this claim in two parts. First, I will argue that there’s compelling reason to suppose that miracles would be rare under theism. Second, I will argue that there’s decent reason to suppose God would work miracles in a way that doesn’t decisively establish theism or Christianity to people not involved in the miracle itself. I will close by discussing the implications of this fact for the miracles debate.

Miracles would likely be rare

Suppose theism is true and there exists a moral arena like the actual one, in which moral agents can make requests of God. Suppose also that God is at least in some cases open to healing them. What kind of frequency might we expect miracles to exhibit?

For two related reasons, I think miracles would be somewhat rare, though how rare is somewhat difficult to determine a priori.

First, a miracle, to be seen as a divine intrusion into the natural order, must stand out from the natural order. This at least puts an upper bound on miracle frequency. An uncontrolled proliferation of miracles would wreck the causal regularity with which they’re supposed to contrast. We can sharpen this observation by pointing out that for any effect which God plans to bring about regularly, it seems more economical to create some causal regularity to reliably produce that effect rather than to intervene to produce it “specially” time and time again.

Further, as has been discussed by many who comment on the subject, for a miracle to serve as an authenticating sign (a common, though not the only, motivation for a miracle) it must be quite a bit different from what ordinarily happens. If God were to raise 10% or 1% or even 0.1% of corpses, any given resurrection wouldn’t be all that surprising. Resurrections would have to be rare to get our attention.

Another reason we might expect miracles to be rare concerns how significantly they would change our approach to interacting with the world if they were not. If we knew God was 50% likely to heal a cancer patient when that patient was prayed for, it seems unlikely we would devote many resources to collaboratively solving cancer. One could multiply similar examples. We would spend nearly all of our time praying and very little of our time doing the other sorts of things we do to solve problems.

Now, one might argue that maybe that’s just the sort of world God would want to create! And I don’t necessarily think that’s unreasonable. It is very difficult to judge such things a priori. But to the extent that the reader is persuaded that there is value in a world where people can work to overcome ills, help others in need, and thereby grow their character, they may find it unlikely that God would set up a world devoid of opportunities to do those things.

One might push back and say that these goods can be realized even in worlds with many more miracles than the actual world. I have two hesitations: first, it’s very difficult for a theist to discern the number of miracles God is performing in the world, especially if those miracles are ambiguous (so the actual number of miracles could be much higher than it appears), and second, it seems more or less impossible to ascertain even an order-of-magnitude estimate of the number of miracles that would perfectly strike the tradeoff between the higher order goods associated with miracles and the higher order goods associated with their rarity.

There are additional reasons to think miracles would be rare (which sharpen the picture to resemble something a bit closer to the actual world), so thither we turn next.

Miracles might well be ambiguous

Imagine, for the sake of argument, a world in which miracles were not ambiguous—a world in which we had, say, definitive evidence of amputee healing. This would be a world in which we’d reach rapid consensus on God’s existence, and probably consensus on some truths about God given the distribution of such miracles.

This would be a totally different kind of world than the current one, and so we ought to be cautious about comparisons between the two.

This ties into a broader concern which may be the subject of a full post, but for now can be stated in brief outline: one can’t assume that a local optimization of a complex system is also a global optimization. Changing “one thing” by just a little bit will often noticeably worsen the functioning of the whole system. Examples include tuning a piano or optimizing a well-trained machine learning model.

Consider two worlds: World A, like the current one, in which miracles, if they happen, are generally ambiguous, and World B in which miracles are not ambiguous. I can certainly understand the intuition behind arguments that World B is more strongly predicted on theism. But so long as someone has some nontrivial reason to think God would favor World A over World B, they will assign a nontrivial probability to World A conditional on theism, and so the fact that miracles are ambiguous wouldn’t afford them much reason to update against theism.

Can we see any reasons God might favor World A? I think we can (and they largely overlap with responses to divine hiddenness in general, for what it’s worth). Bear in mind these aren’t decisive, but in my mind they bring World A and World B to some kind of epistemic parity conditional on theism. Further, while none of them predict the precise degree of ambiguity we see, collectively they provide reason to expect a degree of ambiguity not too far removed from that in the actual world:

1. John Hick’s epistemic distance theodicy. Plausibly, to allow us an adequate degree of individual responsibility for our actions, God chooses not to make his existence totally obvious. To do otherwise would be to encourage souls to build themselves toward pleasing a divine surveillance camera.

2. Diversity among stories of coming to belief in God. I’ve defended this as a response to divine hiddenness in general here.

3. Epistemic responsibility for our fellow humans. This response doesn’t go too far, since assuring us of his existence wouldn’t destroy our ability to epistemically care for others in other ways, but plausibly if it’s good to have that responsibility for some significant truths, then it’s at least a little bit of an extra good to have that responsibility for an additional significant truth.

4. Other higher-order reasons for giving humans maximum responsibility for how the world runs. There’s a biblical idea that humans are tasked with ruling creation on God’s behalf. It doesn’t seem crazy that fully enabling humans to exercise their power requires God to partially conceal his.

If we suppose World A and World B form a partition of possible worlds, and that these reasons (and others) make World A 50% probable on theism, then the fact that miracles are in fact ambiguous doesn’t give us much reason to favor naturalism.

One might object that this merely amounts to cooking the priors: I’ve observed something weird, and I’m now trying to bake it into my theory to avoid falsification. This is a valid concern that theists ought to take seriously, but I’m deliberately stating my conclusions modestly for that very reason. It’s totally justified to reassess the predictions of an otherwise well-evidenced theory in light of apparent counter-evidence, and if the subsequently conceived reasons for expecting the evidence are good, then they are antecedently relevant.

Other thoughts

There’s more one could say here, if I might be permitted to ramble. First, the changes and chances of the spread of information mitigate against the extent to which any given miracle would be globally decisive: a miracle is a firefly, not a signal flare, in the epistemic landscape (alternatively: evidentially speaking, a miracle is like a pebble thrown into a swirling sea). That is, God could raise someone from the dead in India, knowing that such a resurrection would be decisive to those who witnessed it and perhaps those one or two rings removed, but that its supernatural signal would be lost in epistemic noise by the time it leaves the small eyewitness circle. Thus, my argument doesn’t demand that God avoid any but the most mundane miracles: rather, it simply suggests that the frequency with which God performs a particular miracle would be inversely proportional to the “impressiveness” of the miracle. He would do a sufficient number of miracles not to upset the evidential dynamics he has higher-order reason to maintain, not avoid certain classes of miracles entirely.

Second, continuing the thrust of the first, it’s worth remembering that the “ambiguity” of a given miracle is largely socially constructed. Plenty of alleged miracles are strikingly obvious to some and ridiculously weak to others. I’m inclined to think the reason for the divergence is not because one side is relentlessly confirming their priors while the other dispassionately parses the facts, but rather because the conclusions of both sides are tied to the epistemic disposition of their in-group, and the miracle takes on shades of “ambiguity” or “decisiveness” only in that context. So, in theory, the miracle defenders could “win”, convince the world of their criteria, and all would come to accept the obviousness of many miracles. Ambiguity would be destroyed. The opposite is also possible: naturalism could sweep the globe, and collective human cognitive resources be directed toward building a thick wall of unchallenged frameworks and heuristics to shield the masses from miraculous evidence. Ambiguity, then, is not really a property of the miracle itself, but rather is grounded in the miracle’s relation to a group’s epistemic standards, and so is a highly contingent property of the world.

I’m not particularly sure how that would affect my argument here, but it’s worth bearing in mind that miracles don’t come with a fixed “ambiguity score.”

Conclusion

My rather modest conclusion is that God might want miracles to be ambiguous, and so one shouldn’t update too much against theism if that’s how the miraculous evidence strikes them.

Now, there are two ways in which miracles could still be epistemically probative for someone:

1. If I investigate a representative collection of miracles and conclude that all of them permit simple naturalistic explanation, I think I’d be justified in updating against theism (depending on the extent to which one would expect miracles given theism).

2. If instead I conclude that a significant number of miracles resist easy naturalistic explanation, I think I’d be justified in updating toward theism.

So, in some sense, this post really just amounts to “go look at the cases yourself and make up your own mind” but I hope I’ve shown that higher-order arguments about the nature of the miraculous evidence are suspect given our ability to discern somewhat plausible reasons for God setting up the world as it is.

Then he sent them to proclaim the kingdom of God and to heal the sick.

Luke 9:2 (CSB)

I wanted to share some musings about two books I’ve read recently which offer careful rethinking of established Christian practice on related topics. I think the books complement each other in a constructive manner: one supplies the theological motivation for the other, which sketches in the broad outline left by the first.

The two books are N. T. Wright’s Surprised By Hope, which I read last year, and Dominic Roser, David Zhang, and J. D. Bauman’s hot-off-the-press All The Lives You Can Change.

Wright’s book examines biblical data on heaven, hell, resurrection, and the new creation—eschatology, that is, of the kind not concerned with the millennium, the rapture, and the course of recent world history. He concludes that the way the church has preached and lived the gospel, and even the gospel which they’ve proclaimed, has not done justice to the wealth of biblical teaching on the end of all things. We’ve confused new creation with a distant heaven, Wright argues, and the result has spelled disaster for the church’s witness to the world. The actual message at the heart of Christianity is that God calls the church to join him in the renewal of all things through his Son. And that includes much that we traditionally understand as “ministry activities” as well as some which we may not: campaigning for better zoning regulations, or working to end poverty, or anything which brings the order and wisdom of God’s rule to our world.

Roser, Zhang, and Bauman (henceforth RZB), on the other hand, focus not primarily on theology but on practice in their brand new book All The Lives You Can Change. They explain and defend principles from effective altruism to a Christian audience. Effective altruism, for the uninitiated, is a largely secular movement using evidence-based methods to identify and recommend high-return charities or causes. The premise is simple: there are a lot of ways to do good in the world, and since a choice to do good somewhere implies a (usually subconscious) choice not to do good somewhere else, we ought to figure out how to do the most good possible. If Charity A saves a life for the same amount of money Charity B needs to save two lives, then all else being equal, one ought to donate to Charity B. RZB argue that biblical principles (such as “radical empathy”—caring even for people who are geographically far from you) should motivate Christians to be impact-focused with their time, career, and finances.

After reading both books, I started to think that Surprised by Hope supplies the theological framework for the lifestyle and mindset endorsed by All The Lives You Can Change, and the latter provides a concrete, demanding, and radical means of living out the theology expressed in the former. Further, Wright’s work helps resolve some questions one might have after reading RZB’s, and RZB’s demonstrates the practical potential of Wright’s thinking.

How Wright’s theology unifies Christian mission

Imagine you lead an American church.

The church has limited time and resources. You must choose which “churchy” things your church is going to engage in and which ones you’re going to leave by the wayside. Someone in the congregation proposes you run an evangelism training program. Someone else proposes you run a meal drive for the local homeless shelter.

If your church belongs to a conservative evangelical tradition, you will likely favor the evangelism training program on the grounds that meeting eternal, spiritual needs is more important than meeting temporary, physical ones. If your church belongs to a liberal mainline tradition, you will likely favor the meal drive on the grounds that the church is most attractive to outsiders when it is quietly serving and meeting the needs of its community rather than loudly proclaiming its beliefs to a world that may not want to hear it.

Now, most churches would offer some sort of lip service to the value of both activities, and many do both, so the split here is not absolute. But why is there a split in the first place? Why do so many churches seem to separate “doing good” from “saving souls?” How do we decide between the two?

RZB’s book offers some engagement with these questions, but it leaves a little to be desired. Their discussion of evangelism spans about three pages. They explain why someone might want to prioritize evangelism over other causes, and then caution that Jesus did not pursue evangelism to the total exclusion of other forms of doing good (healing the sick, feeding the hungry, etc.), and that doing so is one way in which the church can positively attract the attention of nonbelievers. They also explain how one’s theology will inform one’s take on the importance of evangelism. They even mention N. T. Wright’s support for the idea that our efforts to improve the present world may well last, in some way, into the new creation, and so it’s emphatically not the case that altruism lacks eternal impact.

All this is well and good, but I couldn’t shake the feeling that they had missed an opportunity to detonate some serious theological dynamite that totally reframes the discussion.

Wright argues (very compellingly, in my opinion), along with other scholars like Scot McKnight and Matthew Bates, that Jesus’ ministry and message are fundamentally about the coming of God’s kingdom, and that the gospel proclaimed by Peter, Paul, and the early church ended not with Jesus’ death unlocking an afterlife of heavenly bliss for those who make a verbal confession of faith, but with the resurrection, ascension, and enthronement of Jesus, the King of Israel and of the world, and the right he confers on those who swear fealty to him to join in God’s plan to renew the whole cosmos, and to ultimately participate in the new creation at the end of all things.

This is, in many ways, a total reframe of the essence of Christianity. The mission of the church is not to rush people into lifeboats before the ship goes down but to repair and restore the ship in holistic anticipation of its destination at the new creation. And that will certainly involve guiding people through the fundamentals of Christian doctrine and encouraging them to make their profession of allegiance to Jesus, and it will just as much involve embodying the renewal of creation by working for the good of the world and extending healing and hope to the ends of the earth. These are really two sides of the same coin: doing good and proclaiming the gospel are two different ways of telling people that the King is here.

It is with this foundation that Wright can say the following:

“[M]ission must urgently recover from its long-term schizophrenia. As I have said before, the split between saving souls and doing good in the world is a product not of the Bible or the gospel but of the cultural captivity of both within the Western world.”

Wright, N. T.. Surprised by Hope: Rethinking Heaven, the Resurrection, and the Mission of the Church (p. 265). (Function). Kindle Edition.

What does this look like practically? There is doubtless much still to be worked out here, but as a rough first pass we could say that the church must so fully internalize the gospel of God’s kingdom that doing good in the world and telling people about the King are inseparable. Our altruism should be so totally grounded in kingdom-based living that we cannot speak of our cost-benefit analyses without kingdom principles seeping into our language. We cannot explain to our coworkers why we choose to live simply and donate to effective charities without joyfully bring up the teaching of Jesus. When we can do that effectively, we may well find that evangelism starts to take care of itself. Though not fully tracing out the biblical basis for a unified view of altruism and evangelism, RZB do allude to this:

The early church grew in size and influence not just because of its commitment to evangelistic mission but also because of its tangible care for those in need. In Roman times, Christians were known for rescuing victims of plagues, whom no one else wanted to touch. Catering to the earthly needs of our global neighbors is not only good spiritual practice but is also complementary to a wider evangelistic mission.

Roser, Dominic; Zhang, David; Bauman, J. D.. All the Lives You Can Change: Effective Altruism for Christians (p. 73). (Function). Kindle Edition.

But while RZB mostly just lay out the threads, Wright provides the loom by which they can be woven into a beautiful tapestry.

To return to the hypothetical at the beginning of this section, which should you do: the evangelism training program or the meal drive? Ideally, time and resources permitting, you would do both, but neither in a theologically air-gapped missional context. The best approach is to help your church work toward a unified, thoroughly biblical view of Christian mission, and then pursue both the evangelism training and the meal drive as initiatives of the same kingdom-furthering program. We resolve the tension by collapsing the distinction.

How effective altruism turns Wright’s theology practical

One sometimes walks away from one of Wright’s books with a rather uncertain view of its practical implications. I think this is intentional on Wright’s part. Given the complexities inherent in any missional work, he’s interested less in prescribing a specific set of actions and more in painting, with broad brush strokes, the theological universe which Christians are to inhabit and from which they are to construct their context-adjusted action plans. It’s up to the church to figure out how to apply missional, kingdom-driven living amid the complexity of the modern world.

RZB have taken up that challenge. Multiple factors, they argue, converge to offer Christians (and Westerners, in particular) a unique opportunity to make significant impact: the world is more interconnected than ever, we have tools to research the efficacy of various charities and the tractability of different causes, and many of us have excess income to fund these efforts. When we stop asking only if a given charity is a “good cause” or whether it would be good if a particular problem were solved and begin asking which charities do the most good and which problems are actually solvable with comparably minimal resources, we discover some shockingly feasible ways to impact the world.

First, suppose you were only concerned with saving as many lives, right now, as you possibly could. According to GiveWell, it only costs about $2 to provide vitamin A supplements for one child for one year, and given the health issues prevented by proper intake of vitamin A, donations to vitamin supplementation problems can save the life of a child for as little as $3,500. Assuming the opportunity window remains open and the figure remains constant, if someone made the 2024 median American income of $83,730 and donated just 10% per year over a 40-year career, they could save around 80 lives.

That’s just for saving lives right now. One could potentially have an order-of-magnitudes greater impact by spending their career solving a systemic issue and unlocking welfare gains for millions, or channeling a large amount of their income to organizations seeking to do so. The point that RZB are making is that there’s a lot of good one can do in the world by carefully investing one’s time and resources. This is the cornerstone of effective altruism.

But this isn’t just a book about effective altruism. RZB are interested in motivating the approach from the principles of Christianity (and indeed, at times they point out that some of the causes or emphases of the mostly secular effective altruist movement perhaps do not align very well with Christian principles, and that Christians ought to be discerning and nuanced). The book contains numerous stories of Christians who have invested their lives in ways which RZB deem exemplary, whether by working in neglected cause areas, forgoing minimal local impact for maximum global impact, or living simply in order to donate as much as possible to effective charities. The case studies are practical, compelling, and customized to different cultural backgrounds and skillsets.

The point is clear: there is no one right way to live the kingdom-driven life. That is, I suspect, precisely why Wright devotes relatively little space to exploring practical mission. RZB provide a compelling practical framework through which to embody Wright’s theological task, and so their book is essential reading for Christians who want to fill out Wright’s underdeveloped picture by living high-impact lives.

Conclusion

In summary, Wright’s book outlines the principles which ought to motivate the Christian life, and RZB fill in that outline with advice and examples for the 21st century world. I highly recommend both books.

One question I’m still thinking about is the extent to which one ought to prioritize one’s local community in charitable pursuits. RZB argue mostly compellingly that the answer is “not much, if at all”—we may want to help a homeless person in our city, but if the same amount of money could help ten homeless people elsewhere, why would we choose against helping the ten? My working answer to this is that one ought to prioritize locations of highest impact to the maximum extent one can without hardening one’s heart to the needs of those around them. In other words, if helping those in distant countries requires me to turn a callous, blind eye to the needs of those whose suffering is the most palpable and obvious to me, then perhaps I ought to cultivate the health of my soul by diverting some of my resources to local causes. RZB discuss scenarios like this at some length in their book, but I’d like to reflect on the issue more to solidify my thinking..

Whatever one thinks about this, though, both books are very much worth reading! No life is full of greater purpose than a life motivated by all the hope one can give.

Io non mori’ e non rimasi vivo;
pensa oggimai per te, s’hai fior d’ingegno,
qual io divenni, d’uno e d’altro privo.

I did not die, and I did not remain alive;
think for yourself now, if you have any grain of wit,
what I became, deprived of both.

—Dante, Inferno, Canto XXXIV

Substack has been ablaze with discussion of eternal conscious torment (henceforth ECT). On one side of the aisle, atheists argue that the traditional Christian understanding of hell is literally the most immoral concept it’s possible to contrive. On the other side of the aisle, Christian universalists agree that the traditional Christian understanding of hell is literally the most immoral concept it’s possible to contrive. No one merits damnation, but if anyone does, it’s those responsible for inventing this doctrine and foisting it on humanity.

It’s well known that Christians fall into three main camps on the hell question: ECT, or infernalism; conditional immortality, or annihilationism; and universal salvation, or universalism. The Internet Christian philosophy space has universalist tendencies. Certain segments of the “unshackling the Bible from tradition” crowd favor conditional immortality. And most legacy institutions (seminaries, periodicals, etc.) join the apologetics mainstream in holding ECT.

The Internet tilt toward universalism is understandable. Universalism has both philosophical plausibility and emotional appeal, and many have tried to justify it scripturally.

But while I have not resolved this question firmly in my own mind—and indeed find much to appreciate in all three camps—I wonder if the dismissal of ECT is premature.

“But wait!” you cry. “The traditional Christian understanding of hell is literally the most immoral concept it’s possible to contrive! How dare you suggest it stay on the table!”

Bear with me. There are conceptions of ECT I find gravely immoral. I’m not defending those.

My goal in this essay is to present the most plausible version of ECT I can. You are free to still think it horrifying, but I hope you will at least agree that this conception is a good deal better than others.

I will say nothing here about the positive arguments for annihilationism or universalism. If you think you have independent reason for favoring either of those views, go ahead. The goal here is to push back on some of the negative arguments for those views—that is, arguments from the absurdity of ECT.

Let’s get started.

1. The core difficulty

Eternal conscious torment is a troublesome idea. As C. S. Lewis said,1

"There is no doctrine which I would more willingly remove from Christianity than this, if it lay in my power. But it has the full support of Scripture and, specially, of our Lord’s own words; it has always been held by Christendom; and it has the support of reason."

Someone committed to the authority of scripture and the tradition of church is in a uniquely different place than someone who rejects either of these things. While diversity of opinion can be found among the early fathers, the majority of Christian theologians throughout history have held to some form of ECT.

There’s plenty of debate around key biblical passages. I will not enter it here, save briefly later when I defend my proposal from objections. I want to focus on the philosophical case.

What exactly is it that we find so immoral about eternal conscious torment? What makes it seem so strongly to us that a loving God would never do something like this?

I submit that a large part of it has to do with the fact that consigning an individual to hell confers on that individual an infinite amount of suffering. While it’s possible to imagine God permitting some evils, even significant ones, as long as they are outweighed by a greater good which couldn’t have happened otherwise, this doesn’t seem to work when the evil in question is infinite! How can an infinite evil be outweighed by anything?

Substacker Both Sides Brigade states this point colorfully in a recent note:

Not to harp on it too much, but it really is striking how, from a neutral perspective, the concept of eternal conscious torment really is far and away the most evil position you could ever possibly take. Like, it’s obviously less consequential than many other real-life political or social convictions, and there are sociocultural reasons why people adopt it that don’t necessarily reflect any inherent sadism or callousness. But still, putting aside the interpersonal context and just looking at the basic idea that the best possible world includes billions of people being condemned to endless, infinite suffering, all for the sin of failing to believe in a God who doesn’t even make his existence maximally clear? By any possible measure, that’s a more psychopathically cruel view of the world than anything you’d find in Mein Kampf or The Turner Diaries. If someone told you they thought a Muslim or a Jew deserve to be tortured to death in this life for the sin of unbelief, you’d think they were a raving bigot and a freak. But the majority of American Christians today think that same person should be tortured eternally after death, which is worse!

There’s much to quibble with here, but the basic case against infinite suffering is, at the very least, intuitively plausible. It’s very hard to square with the notion of a loving and gracious God.

And it seems that if hell is a) eternal and b) conscious and c) torment, then an individual experiencing ECT would in fact experience an infinite amount of suffering.

But this isn’t correct.

It’s a well-known idea from calculus that an infinite series can sum to a finite quantity, provided certain conditions. I’ll briefly overview the idea, then explore how it can be applied to ECT.

2. The math of infinite series

Suppose you have $0.

On day 1, someone gives you $1. On day 2, you’re given another dollar, and so on. On the nth day you’ll have n dollars.

As the days go on, the number of dollars you have will increase without bound—that is, there is no number that you won’t eventually surpass if given enough time. If you needed $17,200,322, you’d merely need to wait as many days. For a very large number, you may be waiting long past the heat death of the universe, at which point your available choices for spending those dollars would diminish dramatically, but in principle you would reach it.

Now create a list of the money you made each day—1, 1, 1, 1, 1, …—and you have a mathematical sequence. The sum of all of these terms over an infinite period of time—1+1+1+1+1+…—is a mathematical series.

Suppose we create a new sequence to track our total after each day. We’d denote this sequence 1, 2, 3, 4, 5, … and so on. The 10th term in the cumulative sequence is the sum of the first 10 terms in the original sequence. We’d say that the sequence is a sequence of partial sums.

We’ll use n to denote the number of days that have passed. We concluded that as the number of days increases—as n goes to infinity—the number of dollars you have approaches infinity. Written as a mathematical expression, this is what we showed:

The Greek letter Σ represents repeated addition. We add the number inside the Σ—in this case 1—once for each number between 1 and n, or n times. That sum approaches infinity as n approaches infinity. The symbolism isn’t necessary to understand if the underlying concept is clear.

We often are interested in the convergence of mathematical series. A series converges if the cumulative sum approaches a finite number as you keep adding terms. More specifically, we say the series converges if there is a number the partial sums will never surpass.2

So for the first sequence we considered, the series is the following:

It’s pretty clear that the sum will just keep getting bigger. Name any number—say 17,200,322—and you will eventually reach it if you keep going.

But what if the terms in the sequence decrease over time? Consider the following series:

Here you start with 1, then add a half, then a third, then a fourth, and so on. Will the total sum become arbitrarily large as time goes on, or is there a number we can choose that the series will never surpass?

Perhaps surprisingly, this series does not converge either! The proof for this is somewhat complicated,3 but suffice it to say this series will keep growing toward infinity, though more slowly as time goes on.

But what about this series?

The sequence of terms is decreasing: each term is smaller than the last. Obviously, it’s impossible to manually add an infinite number of terms one by one,4 but we can estimate by checking the sum after adding the first 10 terms, then the first 100 terms, then the first 1000 terms, and so on. If you were to do this, you’d see the sum getting closer and closer to a finite value, namely (and strangely) the square of the number π divided by 6.5 It will never surpass this value.

If that seems weird, that’s because it is. We add an infinite number of things, but they don’t sum to infinity—they get smaller and smaller and converge to some finite number.

So why did this series converge and the other series with decreasing terms did not? The difference is in how fast the terms decrease. If they only decrease a little bit each time, the series will approach infinity rather than converging. But if they decrease significantly each time, the series will converge to a finite quantity.

To solidify the intuition, here are the values of each sum for different values of n (that is, after adding the first 1 term, the first 10 terms, the first 100 terms, and so on):

The first series increases (roughly logarithmically) with n. The second series hits a ceiling.

We could make n as big as we want—as close to infinity as we can possibly conceive—and the second series will never surpass the number 1.64494.

So the core takeaway is simple: a process can go on indefinitely and produce a finite output.

Perhaps you see where this is going.

3. The proposal

My basic idea is that the residents of hell experience suffering that declines over time such that the total amount of suffering they experience is finite.

We can’t really “measure” suffering in a meaningful sense; neither can we measure pleasure. But obviously suffering comes in degrees. Suppose we can speak vaguely of “units” of suffering. Perhaps on day 1 of hell, someone experiences 100 units of suffering. On day 2, they experience 50 units. On day 3, they experience 25 units, and every day half of what they experienced the day before.

This is a geometric series, and it will add to 200. So over an infinite time span, this person experiences no more than 200 units of suffering.

If true, this eliminates the “infinite suffering” objection to eternal conscious torment. There’s a big difference between infinity and 200!

At first blush this may seem like a highly speculative conjecture, but I think it can be motivated theologically—in fact, I think it fits exceptionally well with Christian theology.

Thomas Aquinas famously described God as ipsum esse—being itself. God is not just the source of being, he is being. Communion with God is thus communion with being and thus the highest good.

It seems plausible, then, that existence is experienced in its realest form, with maximum intensity, the closer you are to its source. A light shines brighter, flooding your vision, as you draw near to it, and dims as you recede.

Gregory of Nyssa theorized that heaven involves an unending ascent of the soul upward toward God:

This truly is the vision of God: never to be satisfied in the desire to see him. But one must always, by looking at what he can see, rekindle his desire to see more. Thus, no limit would interrupt growth in the ascent to God, since no limit to the Good can be found nor is the increasing of desire for the Good brought to an end because it is satisfied.

Gregory of Nyssa, Life of Moses II.2396

It’s conceivable then, that hell involves the soul’s unending retreat from God—the soul departs further and further from the source of being, and thus into greater and greater nonbeing.

Souls who have distanced themselves from God are thus separated from the source of being and experience a muted existence.

C.S. Lewis discusses this idea, and is worth quoting extensively. In The Great Divorce the narrator has a conversation with George MacDonald:7

“I saw an infinite abyss. And cliffs towering up and up. And then this country on top of the cliffs.”

“Aye, but the voyage was not mere locomotion. The bus, and all you inside it, were increasing in size.”

“Do you mean then that Hell—all that infinite empty town— is down in some little crack like this?”

“Yes. All Hell is smaller than one small pebble of your earthly world: but it is smaller than one atom of this world, the Real World. Look at yon butterfly. If it swallowed all Hell, Hell would not be big enough to do it any harm or to have any taste.”

“It seems big enough when you’re in it, Sir.”

“And yet all the loneliness, angers, hatreds, envies and itchings that it contains, if rolled into one single experience and put into the scale against the least moment of the joy that is felt in heaven, would have no weight that could be registered at all. Bad cannot succeed even in being bad as truly as good is good. If all Hell’s miseries together entered the consciousness of yon wee yellow bird on the bough there, they would be swallowed up without trace, as if one drop of ink had been dropped into the great Ocean to which your terrestrial Pacific itself is only a molecule.”

And in The Problem of Pain:8

“[H]ell was not made for men. It is in no sense parallel to heaven: it is 'the darkness outside,' the outer rim where being fades away into nonentity.”

Lewis focuses on the ontologically deficient nature of the damned. This is crucial to his project, and it’s underemphasized in popular discussion of Lewis’ view of hell. Contrary to the impression you might get from popular critique of Lewis, his view of hell did not amount merely to “the doors of hell are locked from the inside.” He supplements that insight with the idea that people in hell become, in some sense, less and less real.

If this is true, then it’s reasonable to think that the capacity of a damned soul to experience existence, and so its capacity to experience suffering, would diminish in intensity over time. So while the soul is never annihilated, it grows infinitesimally close to nonexistence, fast enough that the total suffering it experiences is finite, not infinite.

Eternal, conscious, and torment? Yes. Infinite suffering? No.

This view of hell has several advantages.

For one, as mentioned above, it nuances the moral picture of ECT by defusing the “infinite suffering” objection. The suffering is finite—unbounded in duration, but never exceeding some total. That total may even be small!

Second, it preserves the historic testimony of the church to a hell which is simultaneously eternal, and conscious, and torment. For those who think highly of the historic view of the church (Catholics and Orthodox especially, but also high-church Protestants, and anyone who thinks that the church’s historic opinion is evidentially relevant to the truth of Christianity), this comes as a relief.

I could not find anything in my admittedly cursory summary of Roman Catholic doctrine that would definitively preclude the view I’ve sketched here, much less in any official Protestant teaching. More on continuity with historical teaching later.

This means that the limit-based model of damnation enables one to hold a view which has the philosophical relief of annihilationism, but without having to break from the historic opinion of the church. Of course, if you still find conditional immortality unconscionable, this won’t do anything for you. But if you don’t, this option bears consideration.

Third, this view solves what we might call the problem of tainted heavenly joy—how can people in heaven be happy knowing that their loved ones are in hell?

N.T. Wright suggests a possible solution to this conundrum (emphasis in original):9

My suggestion is that it is possible for human beings so to continue down this road, so to refuse all whisperings of good news, all glimmers of the true light, all promptings to turn and go the other way, all signposts to the love of God, that after death they become at last, by their own effective choice, beings that once were human but now are not, creatures that have ceased to bear the divine image at all. With the death of that body in which they inhabited God’s good world, in which the flickering flame of goodness had not been completely snuffed out, they pass simultaneously not only beyond hope but also beyond pity.

A concern I have with this approach is that it doesn’t seem that the image of God is a necessary condition for pity. Humans pity the suffering of animals who lack the imago Dei. Even if humans in hell were so to lose their humanity that they became mere animals, it seems they would not necessarily have fallen beyond the reach of pity.

Positing a rapidly decreasing capacity to experience suffering, on the other hand, preserves the theological insight of Wright’s view—humans can surrender the image of God and separate themselves from God arbitrarily far—while explaining why creatures are also beyond pity. Their suffering is finite, not infinite, and it pales in comparison to the joys of heaven. In the grand scheme of things, it’s nothing.

4. Objections

Several objections could be raised against this account.

“It’s an infinite wrong to deprive someone of an infinite good.”
This is worth considering, but I’m not sure it works. Generally, when we deprive someone of a good, we don’t then think that we’ve inflicted a wrong on them of the same magnitude of the good we deprived them of. This is particularly true if the good they’ve been deprived of is one they chose not to have, in the case of a Lewisian model of hell.

But this objection would work just as well against annihilationism, and it is not my intention to defend conditional immortality here. My objective is instead to show that ECT can be made the philosophical equal of annihilationism. So if you think it would be wrong for God to destroy people, you would find this account of ECT similarly objectionable. That’s beyond the scope of this post.

“That’s just annihilationism with extra steps.”
Yes, and that’s the point. The view of hell sketched here is annihilationism, but asymptotic, and so compatible with the historic teaching of the church. There is never a time at which a human stops existing, but the amount of suffering they experience can be made arbitrarily close to 0.

“That contradicts Scripture.”
There are three ways in which my idea would contradict Scripture: a) Scripture teaches infinite suffering in hell, b) Scripture teaches conditional immortality, or c) Scripture teaches universalism.

I won’t assess (b) or (c) here for reasons of scope. What about (a)? Even supposing contra the annihilationists and universalists that the “hell” passages do teach ECT—is it plausible to claim that Scripture teaches infinite suffering, rather than just unending suffering?

I don’t think so. The closest passage I can think of is Mark 9:47-48 (here the NRSV):

And if your eye causes you to stumble, tear it out; it is better for you to enter the kingdom of God with one eye than to have two eyes and to be thrown into hell, where their worm never dies, and the fire is never quenched.

This imagery is vividly metaphorical, challenging any attempt to figure out what sort of suffering is in view here. But this picture is logically consistent with the view I sketched here: the suffering is unending (the worm never dies, and the fire is never quenched), but of a finite total amount.

For further exegetical insight, we note that Jesus is quoting Isaiah 66:22-24:

For as the new heavens and the new earth,
which I will make,
shall remain before me, says the LORD;
so shall your descendants and your name remain.

From new moon to new moon,
and from sabbath to sabbath,
all flesh shall come to worship before me,
says the LORD.

And they shall go out and look at the dead bodies of the people who have rebelled against me; for their worm shall not die, their fire shall not be quenched, and they shall be an abhorrence to all flesh.

The reference to “dead bodies” seems to fit better with conditional immortality, but since we’re supposing Scripture teaches ECT for the sake of argument, the imagery suggests at the very least some sort of reduced existence. The picture is not one of the new creation humans on the same ontological plane as those outside the new Jerusalem.

Thus, I don’t think the case that the damned experience infinite suffering (as opposed to merely unending suffering) can be supported from Scripture.

“This view is still a significant doctrinal break with church history, so it’s no better on that front than conditional immortality or universalism.”
Dante was (probably) not thinking of the mathematics of infinite series when he depicted hell in the Inferno.

As I argued above, though, my view is highly consonant with broad themes of Christian theology and at least verbally consistent with all the major creeds and statements of faith (at least, I cannot find any with which it’s not). These tend to focus on the unending duration of the punishment, not the fixed nature of it.

The truth of conditional immortality or universal salvation, on the other hand, would mean that many major Christian statements on hell throughout history were flat-out wrong.

This modified view of ECT thus represents not a break from Christian tradition but a refinement of it. So, measured against that standard, it fares better than conditional immortality and universalism.

“It’s wrong to keep such people alive, even if their suffering is trivial.”
This is probably the objection with the best chance of working. That said, I’m not sure what moral principle can be invoked to defend it.

It seems wrong to keep a comatose person experiencing a minor amount of suffering alive for an infinite amount of time, but this would either be because it’s wrong to inflict harm on them at all (not clear in the case of hell as retributive punishment) or because we’re implicitly assuming a constant amount of pain extended over an infinite amount of time, which would total to infinite suffering. Neither is the case in this model of hell.

5. Conclusion

In summary, by positing that the cumulative suffering of the damned behaves like a convergent mathematical series as they pass further from the source of being and into nonexistence, numerous objections to eternal conscious torment—such as the damned experiencing an unconscionably infinite amount of suffering—can be defused, and some advantages of eternal conscious torment—such as historical continuity with the teaching of the church—can be preserved.

I will reiterate once again that I am not claiming this is the correct view of hell. Rather, my claim is that when ECT is thusly reconceived, it ought to be taken at least as seriously as conditional immortality. And that’s a lot more seriously than it is now.

[EDIT: It’s been brought to my attention that this post amounts to an independently-derived rehash of Brian Cutter’s recent paper “Hell and Proportionality,” which I highly recommend reading!]

“You pore over the Scriptures because you think you have eternal life in them, and yet they testify about me.”

John 5:39

For some, the believing scholar is an enigma. For others, he is a truism. For others still, a contradiction.

The relationship between faith and study has puzzled countless minds. One need not venture far into the scholarly waters to know how deep they go. How can we have the faith of a little child amid an onslaught of questions, when the the thick clouds deny even a single ray of clarity?

As we struggle with matters as weighty as these, we must remember that scholarship is not new. We are not the first to ask its questions. Others have wrestled with its implications and purpose for the believing life.

Perspectives on the matter abound. They are complementary. We will survey a few of them, spanning almost three thousand years.

We begin with the conclusion of Ecclesiastes (12:9-14, CSB):

In addition to the Teacher being a wise man, he constantly taught the people knowledge; he weighed, explored, and arranged many proverbs. The Teacher sought to find delightful sayings and write words of truth accurately. The sayings of the wise are like cattle prods, and those from masters of collections are like firmly embedded nails. The sayings are given by one Shepherd.

But beyond these, my son, be warned: there is no end to the making of many books, and much study wearies the body. When all has been heard, the conclusion of the matter is this: fear God and keep his commands, because this is for all humanity. For God will bring every act to judgment, including every hidden thing, whether good or evil.

The Teacher is a gatherer of truth. He scoured the wisdom of the ages to find things to teach his people. He won renown as the wisest man who ever lived. And yet Ecclesiastes does not end with a ringing endorsement of learning. The truth seeker’s journey culminates not at the summit of Mount Knowledge but at the feet of Mount Sinai. The many proverbs which the Teacher gathered were but refractions of a principle so simple that a child could grasp it: fear God and keep his commands, because this is for all humanity. How striking that this was his conclusion!

St. Augustine balanced faith and study in his own way, many centuries later. Book VI of his Confessions narrates a turning point in his intellectual life. Shaken from his Manichaeism and zealous for the truth, he yearned to study. I quote here from E. B. Pusey’s translation:

Lo, things in the ecclesiastical books are not absurd to us now, which sometimes seemed absurd, and may be otherwise taken, and in a good sense. I will take my stand, where, as a child, my parents placed me, until the clear truth be found out. But where shall it be sought or when? Ambrose has no leisure; we have no leisure to read; where shall we find even the books? Whence, or when procure them? from whom borrow them?

Vexed by his lack of resources, he weighs a bold option:

Perish every thing, dismiss we these empty vanities, and betake ourselves to the one search for truth! Life is vain, death uncertain; if it steals upon us on a sudden, in what state shall we depart hence? and where shall we learn what here we have neglected? … Wherefore delay then to abandon worldly hopes, and give ourselves wholly to seek after God and the blessed life?

Though riveted by the thought of forgoing marriage, social life, and all their comforts to chase after truth and wisdom, he holds back, to his later dismay:

Loving a happy life, I feared it in its own abode, and sought it, by fleeing from it. I thought I should be too miserable, unless folded in female arms; and of the medicine of Thy mercy to cure that infirmity I thought not, not having tried it.

Augustine’s regret is palpable. His passions restrain him, for a time, from the wholehearted pursuit of truth. Just like that, years, gone. We catch a glimpse of the truth seeker’s cross. This is not an easy road. It needn’t always lead to forgoing life’s pleasures, but if it does, will we still walk it? Do we love the truth enough to dismiss “these empty vanities?”

Augustine faced an embarrassment of literary riches in his own day. The author of the Imitation of Christ had a thousand years’ more. Book 1, chapter 3 includes a short prayer:

O God, You Who are the truth, make me one with You in love everlasting. I am often wearied by the many things I hear and read, but in You is all that I long for. Let the learned be still, let all creatures be silent before You; You alone speak to me.

The prayer opens with a simple identification: God is the one toward whom all truth-seeking is directed. He is Truth. The pursuit of understanding is empty compared to the thing itself. The author continues:

If men used as much care in uprooting vices and implanting virtues as they do in discussing problems, there would not be so much evil and scandal in the world, or such laxity in religious organizations. On the day of judgment, surely, we shall not be asked what we have read but what we have done; not how well we have spoken but how well we have lived.

Study, properly conceived, flows from virtuous character: love for the true, the good, and the beautiful. Tragedy ensues when truth chokes out the good and the beautiful. Like the Teacher of Ecclesiastes, we must heed this warning. Study will either transform or deform. There is no third option.

Five centuries later, we encounter another perspective on intellectualism, and a Christian motivation for it, from the French Dominican theologian A.D. Sertillanges:

For you, an intellectual, your neighbor is the person who needs the truth, as the neighbor of the good Samaritan was the wounded man by the wayside. Before giving out truth, acquire it for yourself; and do not waste the seed for your sowing.

Sertillanges, A.D.. The Intellectual Life: Its Spirit, Conditions, Methods (p. 43).

Envisioned here is truth seeking as heroic self-sacrifice. The learned believer bravely fights his passions to uncover truth for the benefit of himself and his neighbor. It is service. We help those who whether by negligence or constitution do not discover truth for themselves. To do so, we must secure it ourselves. And yet as we charge toward our books, Sertillanges calls back to us:

Study is intended to bring about the extension of our being: it must not end by making us narrow. If art is man added to nature, knowledge is nature added to man: in both cases we must safeguard the man.

(p. 182)

It is possible to throw ourselves into a good thing so recklessly that we gain it all and lose our souls. We go deliberately yet carefully into study’s cage.

The perspectives of King Solomon, St. Augustine, Thomas à Kempis, and A. D. Sertillanges steer us toward our own. Augustine and Sertillanges remind us of the value of study. Solomon and Kempis remind us of its limits. Error is possible on either side. Truth must be found, grasped, and handled for it to do its transforming work. But nothing less than total transformation, for ourselves and for the world, must be its goal.

We must seek the truth wholeheartedly, so that being unshackled from falsehood, our hearts can love truthfully. Then we will know the truth, and the truth will set us free.

The sea of glowing reviews gives way to a one-star rant about the book’s many perceived flaws. I devote five seconds to a panic-stricken skim. “Ugh. Looks like it’s been debunked.”

I close the tab and do something else, though the icy memory sticks in my mind like a knife.

This is, in fact, how I used to react to rebuttals. I wouldn’t interact with them. I wouldn’t go near them. I would try to forget about them, and take refuge in books whose obscurity protected them from the crosshairs of the debate-me-bros. I was suffering from rebuttal-induced anxiety.

You may have to wait for the DSM-7 or 8 before the term enters popular parlance. But it is a very real affliction. Rebuttal-induced anxiety is characterized by anxiety over and obsession with the mere existence of rebuttals rather than the content of the rebuttals.

A person afflicted by rebuttal-induced anxiety is trapped in the following thought pattern.

First, they notice some piece of content. Suppose it’s a book which supports a view they hold.

Second, they form a positive impression of that content. Perhaps they read the book’s endorsements, the cover blurb, or skim a few chapters. It seems well-researched.

Third, they learn of a rebuttal to the piece of content—perhaps a one-star review with a detailed critique. They don’t necessarily read it.

Finally, they lose their confidence in the value of the content. Why? Because someone of reasonable cognitive means has taken the time to engage with the content, and it did not convince them.

I’m not alone in being susceptible to this kind of thinking. I’ve spoken with others who’ve experienced it.

The faulty premise is the last one: “If someone of reasonable cognitive means is not persuaded by a piece of content, then the argumentation presented in that piece of content is not sound.”

Let’s exemplify its failure with three plausible ways that someone of reasonable cognitive means could engage with a piece of content and not be convinced by it. Etching these into your mind is the most potent antidote to rebuttal-induced anxiety.

First, we must define a touchstone called the Principle of Irrationality:

The Principle of Irrationality: everyone is at least partially irrational.

If you’re convinced, read on. If not, have a look at some of the extensive literature on cognitive psychology. Our cognitive heuristics backfire in all sorts of ways. No one, no matter their education, intelligence, or even metacognitive awareness, is immune. You are not immune, and the author of a rebuttal is not immune. This principle motivates the following scenarios.

Remember, these are plausible explanations of the rebuttal which don’t have any implications for the original content’s value. Note that I am not saying you shouldn’t engage with the rebuttal honestly and remain open to the possibility that it is in fact successful. You should. What follows is not intended as a belief-preservation mechanism. In fact, I’ve found it to have quite the opposite effect: once I internalized these ideas, I overcame my fear of rebuttals and was able to engage them honestly, updating my beliefs as necessary.

Let’s get into the possibilities.

Possibility #1: the detractor didn’t try to understand the content

Sophistry is alive and well on the Internet. The Amazon review or YouTube response video (you should really not be on YouTube at all, by the way) may come not from the mind of a detractor impartially pursuing truth but from that of a sophist writhing in a web of biases.

While the sophist might lean on full paragraphs, grandiloquent verbiage, and credentialism, his critique is merely gilded with glamor, stuffed with straw men. Did you peruse the review? Or did you panic at the sparkle?

The sophist will think he understood the content. He will try to prove this in his review. He’s a sophist, after all. Be careful. Quoting from the book, summarizing the author’s arguments, and referring to other books do not prove understanding. They prove, at most, that the reviewer can read words, fit them to a structure of his own devising, and build on that until he gets something he can critique. But anyone can do that.

I’m not saying you should assume sophistry from the get-go—but be alert. It’s more common than one might think. And it can be subtle.

Possibility #2: the detractor tried to understand the content, but didn’t

Not everyone is a sophist. Some people do reflect on their biases, maintain sober judgment, and engage reasonably. But it’s quite easy to miss an author’s point, especially if it’s subtle and developed over multiple chapters. The detractor may have honestly misunderstood.

Information leaks from each stage of the train of idea exchange, from the author’s thoughts to the selection of words to the perception of words to the interpretation of words and to the construction of larger units of meaning.

I have on numerous occasions read Amazon reviews from people who clearly didn’t understand the fundamental point a book was making. Sometimes this blindness is induced by the reviewer’s sophistry—other times, they may have just missed the point. I’m not immune either—I regularly misunderstand what I read, only to have it corrected for me by a second source. It’s a normal experience.

If the detractor misunderstood the content, then his review of it will be largely misguided, and probably doesn’t refute the content’s core tenets. Without reading the critique (and often the content in question, too) it’s impossible to know whether the detractor understood the arguments.

Possibility #3: the detractor understood the content, but failed to refute it

Finally, it is possible that the detractor did try to understand the content, and they were successful in doing so, but their rebuttal just doesn’t work! Their critique might rely on misinformation or just plain bad epistemology.

One way to challenge your intuition here is to imagine that a third person wrote a lengthy rebuttal of the detractor. Would you assume that the detractor has been successfully refuted? If so, add another rebuttal and repeat the thought experiment. Notice that it becomes a rousing game of “last word wins.” And that’s pretty clearly not how intellectual arguments work.

Keep these three possibilities in your mind the next time you see a critique of any position. Engage the critique, but don’t be scared by its existence. Maybe it’s a successful one, or maybe it’s not. Check it out.

Note, also, that these absolutely cut both ways. A rebuttal I want to agree with could be faulty for the same reasons. Don’t make any assumptions.

If you don’t suffer from rebuttal-induced anxiety, please share this post for the sake of people who do! The mindset hinders the pursuit of truth by inflicting psychological distress, and we would do well to push back on it.

Inevitably, you must prioritize certain topics and set aside others. It’s not always easy to know which ones are worth prioritizing.

Further, you must weigh different factors: your level of confidence in a belief, the importance of the belief, the resources you have available, and so on.

Here’s a decision matrix to help. The first axis corresponds to the level of confidence you have in a belief. The less confident you are in a belief, the less it makes sense to convince others of it. The second is the importance of a belief, where “importance” is determined relative to the proverbial grand scheme of things. It’s more important to convince others of a belief about morality than a belief about the proper way to prepare a salad.

Here’s the matrix:

Unimportant, low confidence: set these aside. You can explore them if you want to, but doing so requires taking time away from more important topics.

Unimportant, high confidence: stand by. It can be worth engaging, but in general, the value of changing someone’s mind on the topic decreases with the importance of the belief. Don’t throw away your time (or relationships).

Important, low confidence: study. These beliefs are worth being right about, so time spent studying them is time well-invested.

Important, high confidence: engage. If you are confident both that a belief is important and that you are correct about it, the rational course of action is to seek to persuade others of it. Bear in mind, of course, that engaging others too confidently will prevent you from seeing that you’re wrong if you are, in fact, wrong. Remain open to being so.

You want to be spending as much of your time in the green squares—the top two—as possible. Dipping into the yellow is fine. The red is not worth your time.

While numerous sources of information populate the Internet—Reddit, blog posts, Discord servers—YouTube is perhaps the most popular. Many people get all of their information about apologetics from YouTube without cracking open a single book.

Now, on the one hand, this is understandable. YouTube is accessible, engaging, and there is a lot of genuinely helpful content there. I often send people YouTube videos that address specific questions. It’s a highly convenient way to share information. So what’s the problem?

There are many. And while the issue is not the use of YouTube per se but rather the exaltation of it to the highest position in one’s hierarchy of research methods, I think many people should stop using it entirely, at least for a time. Here are three major issues with using YouTube to investigate existentially significant questions.

1. The algorithm is the enemy of the truth seeker

The algorithm wants you to waste your time.

Truth seekers are intellectually sober, frugally-minded people. They ingest their content slowly and consider it from different angles before moving on to the next thing. They know that they have a finite amount of time, so they cash it in on high-value forms of information.

What kind of content does YouTube reward?

Drama. Ragebait. Short-form content. Glitzy graphics. Comment section engagement. This is the content that will get pushed to you, even if you start with more serious videos. And unless your discipline and self-control are better than most, you’ll get sucked in, wasting time and cognitive energy—the truth seeker’s most valuable currencies.

As soon as you finish a video, YouTube will happily recommend many more algorithmically selected buffet items in the hope that you will gorge on the next one before stopping to digest the previous one. You will leave full to the point of nausea with far more questions than answers. You will not have gotten your time’s worth. And no one will be refunding that time to you.

The experts who design YouTube’s algorithms are smart. They want you addicted to the platform. They want your time. Don’t let them take it.

2. Superficial platforms don’t produce nuanced thinkers

YouTube tries to keep you in the kiddie pool. Truth is found in the deep end.

Due to the nature of the platform, it is impossible to distill the content of an academic book into a video that will get a non-trivial number of views. While some channels do produce well-researched videos, even they will merely selectively quote sources to support their argument and then refer you to the full book for further information.

And it would be a mistake to form opinions of books by looking only at what people say about them, or even what they quote. You must read the books yourself. That’s the only way to internalize the argument in its original presentation, thereby understanding the author’s intent as well as you can. And intimate comprehension of an argument is the prerequisite for engaging in dialogue about it. Consider Rule 9 of Mortimer Adler and Charles van Doren’s How to Read a Book:

You must be able to say, with reasonable certainty, “I understand,” before you can say any one of the following things: “I agree,” or “I disagree,” or “I suspend judgment.”

Van Doren, Charles; Mortimer J. Adler. How to Read a Book (p. 141).

By rewarding that which holds the attention of the viewer, YouTube promotes superficial summaries of serious subjects. You binge at your peril. A circus parade of caricatures and straw men will overrun your mind. You will surrender your ability to assess your understanding of a given subject.

Books, on the other hand, reward careful consideration and scrupulous engagement. A measured argument must be met with a measured response. The argument stays with you even as the book is laid down, demanding your continued reflection. The author’s ideas soak into your mind as you mull them over. You leave satiated and not stuffed, emboldened and not exhausted. You gain deeper understanding, greater ability to articulate your agreements and misgivings, and a sharper lens through which to distinguish truth and falsehood.

You won’t make progress any other way.

3. Charismatic creators and comment-section choirs distract from intellectual merit

YouTube predisposes you to attend to the way in which a view is presented rather than to the view itself.

You will find a range of things within any YouTube video: the creator’s charisma, the quality of his video, and in the comments section, the ideological missionary-choir to which he preaches. Somewhere in that chaotic, bedazzling mess you will find his arguments. And amidst the distractions, they are very hard to analyze.

It’s much like standing in the center of the dance floor at a disco party and trying to read a syllogism scribbled on a Post-It note. You may not even be able to make out what it says, and you will find it very hard indeed to assess its merit.

YouTube comments, in particular, are a nightmare, especially on popular channels. People who are horrifyingly underqualified to speak on a given topic issue slipshod assessments of the merit of various arguments, often invoking their past experience as a proponent of the view they critique, or using rhetorical flourishes to project an unwarranted aura of confidence.

Let’s take a look at the comments section of a recent video on the resurrection of Jesus produced by Rationality Rules, a large channel with almost 400,000 subscribers at the time of this writing:

The number of philosophical, epistemological, historiographical, sociological, and grammatical miscues here is genuinely quite impressive. About the only thing these statements are good for is crisp, real-life illustrations of elementary logical fallacies and category errors.

For what it’s worth, I’m not trying to defend the claim that atheist channels are uniquely bad in this regard (though I wouldn’t expressly deny that claim either). Plenty of popular Christian YouTube channels come with similarly off-putting comments sections, which only reinforces my point. This is not where serious people come to share their ideas, and if you want to go about this whole truth-seeking thing seriously, you need to hang out with serious people.

All right, so YouTube is not the way to go. What should you do instead?

Suggestions

Restrict your access to YouTube. Perhaps you want to block it entirely, though that may be too far. At the very least, get a plug-in like Unhook to disable features like the recommended video feed and the comments section.

Crack open some books! If finances are a barrier, get a library membership and access books through a platform like Hoopla.

Choose books carefully. Focus on quality over quantity. Try to choose books in which authors state their opinions carefully and keep their rhetoric to a minimum. Note that the most popular books on a given subject are often not the best ones!

Read different perspectives. Don’t shy away from content that challenges your views. If you want to ease into it at first, that’s fine, but don’t put it off indefinitely. Conflicting views are much easier to engage via books than via the Internet.

Find discussion partners. This is where the Internet can be helpful. It may be difficult to find discussion groups in real-life. Search for small, serious discussion groups on platforms like Facebook (or Discord, though they might be harder to find there). Get away from anywhere with an algorithmic stream of unserious opinions.

Eventually, return to YouTube and note the difference. After you’ve studied for a while, you may be surprised at how your perception of YouTube changes. I used to be unsettled by comment-section choirs. I no longer am. You may very well find the same!

Perhaps YouTube has hindered your search for truth for some time. That’s okay. It’s done that to many. But today can be the day you reclaim your mind.

Close the tab and go read a book!

First, we discussed the standard formulation of Bayes’ Theorem, which looks like this:

Second, we introduced the concept of background knowledge and saw how it enables us to track the information we use in making probability judgments.

Then, we introduced the odds form of Bayes’ Theorem, with a particular emphasis on the likelihood ratio:

Finally, we discussed the odds form of a cumulative case argument:

So what’s the point of having covered all this?

Bayesian reasoning is a tool for clear thinking on the road to uncovering truth. I’ve found it to be a powerful one. Let me illustrate what I mean by showing how Bayesian reasoning can be fruitfully applied to existentially significant questions.

To do Bayesian reasoning, we need a hypothesis. In this case, the hypothesis will be whatever religiously or metaphysically significant proposition we wish to investigate. Pick something that you’re interested in learning the truth of.

“The God of traditional theism exists,” “Muhammad was God’s messenger,” or “Jesus of Nazareth rose from the dead” are all hypotheses we may wish to test.

Evidence, as previously, will refer to various observations that bear on the truth of the proposition under consideration. By evaluating the likelihood ratio for each piece of evidence, we can get a clearer handle on where the evidence points.

Let’s briefly sample the sorts of arguments we will be considering. At this point, I will move away from the traditional “E” and “H” notation and use more specific letters. This is totally legitimate, as long as you remember what letters refer to evidence and what letters to hypotheses!

Suppose that our hypothesis is the first one defined above: “the God of traditional theism exists.” Call this T. Suppose we want to argue that the existence of conscious experience—call this C—is evidence for God’s existence. Our work is cut out for us: we will have to show that P(C|T) is greater than P(C|~T).

But suppose we want to show that the existence of suffering—call this S—is evidence against God’s existence. We would have to show that P(S|T) is less than P(S|~T).

The same mode of reasoning can be applied to historical questions. Suppose we take a modest claim called J: Jesus of Nazareth was a historical figure. One piece of evidence, G, is that the New Testament gospels—Matthew, Mark, Luke, and John—attest to Jesus’ existence. Well, if we can show that P(G|J) > P(G|~J), then G is evidence for J.

Let’s broaden our scope—suppose we want to figure out whether Christianity is true. Then, we need to clearly define a hypothesis (that is, specify what we mean by Christianity and what it would take for it to be true) and collect all the relevant evidence we can on the question. We need to think through each piece of evidence through the lens of a likelihood ratio and then combine them into a Bayesian cumulative case.

I invite you to make Bayesian principles the core of your thinking on these topics. You will no longer have to rely on guesswork to determine whether evidence supports a hypothesis. You now have a robust mathematical framework which you can use to support your thinking.

So what next? Try to use Bayesian reasoning and the likelihood ratio in particular the next time you’re trying to figure out whether something is true. See what you find. Use your intuition as a check along the way, but don’t be afraid to override your intuition if you’re sufficiently confident in the value of your likelihood ratio.

If you’re like me, you’ll soon discover an increased confidence in your reasoning ability. You’ll find it easier to think through complicated questions that have numerous arguments for and against. And you’ll find it easier to share your findings with others using the framework of Bayesian reasoning.

Bayes or bust!

Here is a simple case, in which we have two pieces of evidence, denoted by E1 and E2 (Substack, ironically, doesn’t support subscripts, otherwise the numbers would be subscripted). We will use E to denote our total body of evidence. E refers to E1 and E2 together.

The formula looks like this:

Notice that the posterior odds and the prior odds remain the same. However, we now have two likelihood ratios, one for each piece of evidence.

We can keep chaining pieces of evidence in the same way. Suppose we have n pieces of evidence. Here’s what the formula would look like:

You may notice something interesting: each successive likelihood ratio isn’t merely added to the previous one. It is multiplied. This means that if we have three independent pieces of evidence (independent is a technical term, meaning that no piece of evidence entails or increases the probability any other), each with a likelihood ratio (or Bayes factor) of 3, their combined evidential force is not 9 but 27—taken together, they are 27 times more probable on the hypothesis than on the negation of the hypothesis!

This is fascinating. Evidence is not additive! Its cumulative force increases much faster than we might intuitively expect.

This leads to an interesting implication. We may be considering a hypothesis for which there are no particularly strong pieces of evidence. However, if there exist enough weaker pieces of evidence, the hypothesis can still be established with a high degree of probability. Even a hypothesis with a very low prior can, in principle, be supported by a cumulative case.

Let’s return to the courtroom. Recall that we have evaluated the evidential weight of two pieces of evidence: the fingerprints and the witness’ testimony that the defendant was in a different part of town at the time of the murder. Let’s add two more pieces of evidence.

Suppose another witness claims to have seen the defendant pointing a gun at the victim. Suppose further that an article of clothing, conclusively identified as belonging to the defendant, was found at the crime scene.

To calculate the cumulative force of the four pieces of evidence, we must determine the likelihood ratio of each. Let us assume for the sake of argument that these pieces of evidence are completely independent.

For the likelihood ratios for E1 and E2, we will take the values we calculated previously. These are 75 and 1/6.

We will pick some fairly arbitrary numbers for the latter two pieces of evidence. Let’s suppose that the likelihood ratio for E3 is equal to 20 and the likelihood ratio for E4 is equal to 3. Thus, the values of the four likelihood ratios are as follows:

Multiplying these values together will yield the cumulative weight of the total evidence E:

The totality of our evidence is 750 times more likely if the defendant is guilty than if the defendant is innocent. What does this tell us about the probability of guilt?

Let us take the prior probability of guilt, P(H), to be 0.01 and so the prior probability of innocence, P(~H), to be 0.99. We may calculate as follows:

So the guilt hypothesis is about 7.58 times more likely than the innocence hypothesis. Some simple algebra reveals that the probability of P(H|E) ≈ 88.3%.

Voilà! That is how a cumulative case is made.

Now, is 88.3% the exact probability of the defendant’s guilt? Can we use Bayes’ Theorem to obtain accurate probabilities for everything?

Well, no and no. The result you get from Bayes’ Theorem is only as accurate as the numbers you put in, and in a setting as complex as a murder trial, there is no guarantee that you are putting in the right numbers or including all the relevant quantities.

I used this example was merely to illustrate the mathematical structure of a cumulative case. The numbers are not important.

And that’s the basics of Bayesianism! You now have an intuitive understanding of two different formulations of Bayesian reasoning. You’ve seen the power of the likelihood ratio, and you’ve seen how to make a cumulative case. In the final post in this series, we will discuss how to apply Bayesian reasoning to existentially significant questions.

Let’s look again at the likelihood ratio:

This ratio measures the evidential force of E. If the numerator is larger than the denominator, then E is evidence for H. If the denominator is larger than the numerator, then E is evidence against H.

Thus, for any piece of evidence E, we can assess the extent to which it bears on our hypothesis H by estimating the values of the numerator and the denominator. We saw this in the previous post.

In this post, we will look at more examples of the likelihood ratio in action.

Since I’ve run out of interesting things to say about gumballs, we will leave that example and consider a new one.

Example 1: fingerprints on a murder weapon

You are a juror in a murder trial. The prosecuting attorneys draw the jurors’ attention to the fact that the defendant’s fingerprints were found on the gun used for the murder.

Let’s use the likelihood ratio. First, you need to estimate P(E|H). What is the probability that the defendant’s fingerprints would be found on the gun under the assumption that he is guilty?

Well, if the defendant really did commit the murder, then he must have held the gun. Unless he was wearing gloves or had wiped the gun afterward, this would leave fingerprints. Granted, we can’t be sure there would be fingerprints. But it’s at least likely. We estimate that 0.5 < P(E|H) < 1. It’s more likely than not, but not quite certain.

What about P(E|~H)? Under the assumption that the defendant did not commit the murder, how likely is it that his fingerprints would be on the murder weapon? Clearly, this is possible—perhaps he had handled the gun earlier in the day, and then the real murderer had used gloves—but it’s not particularly probable. If the defendant did not commit the murder, it would be very surprising to find his fingerprints on the gun.

Again, you can’t determine an exact value for P(E|~H), but in the absence of any other relevant evidence, you can say that it’s quite low, say less than 0.1. So our estimates are within the following ranges:

• P(E|H), between 0.5 and 1

• P(E|~H), between 0 and 0.1

Let’s choose the values in the middle of each range for the sake of illustration, that is, P(E|H) = 0.75 and P(E|~H) = 0.05. These are likely not the true probabilities, but they will make the point.

Thus, the ratio of P(E|H) to P(E|~H) is top-heavy because P(E|H) > P(E|~H). How top-heavy it is will depend on the precise values of the probabilities. In this estimate, we got a value of 15.

This value is called the Bayes factor.

If the numerator were 0.8, the Bayes factor would be 8, meaning that the evidence is eight times more expected on the guilt hypothesis than on the falsehood of that hypothesis.

For this particular case, it might make more sense to go with more extreme values, such as a value of 0.9 for the numerator and 0.02 for the denominator, resulting in a Bayes factor of 45. The larger the Bayes factor, the stronger the evidence.

Even though you can’t pin down the exact numbers, you reason that the likelihood ratio is top-heavy, and so the fingerprints are evidence for the guilt of the defendant. You’re also able to get a rough handle on how strong the evidence is. It appears to be quite strong.

While the fingerprints provide strong evidence for the guilt hypothesis, they are likely insufficient to convict unless combined with other evidence. A top-heavy likelihood ratio for some piece of evidence is insufficient to show that the posterior odds (the first ratio in the odds form) is also top-heavy. Put differently, just because you have evidence for something doesn’t mean it’s true!

Why is this?

First, we need to clarify the use of the term “evidence.” Some people think of evidence as “whatever demonstrates the truth of a claim.” This not the way the term is used in Bayesian reasoning. Evidence is anything that is more probable on the truth of a hypothesis than on its falsehood.

Second, let’s take this particular case. Why might a piece of strong evidence for the guilt of the defendant be insufficient to issue a guilty verdict?

Look at the odds form again:

The answer is that the prior odds are low. To calculate the prior odds, we need the values of P(H) and P(~H), or more specifically, of P(H|k) and P(~H|k). Recall that k denotes relevant background knowledge, so the values of the probabilities will vary depending on what exactly we choose to include in k. We might include some basic information about the defendant, such as his relation to the victim. But that by itself doesn’t give us much reason to think the defendant is guilty, so P(H|k) is very low and P(~H|k) is very high.

To put it a different way, H starts out with a low probability. Most hypotheses start out that way. Each piece of evidence is going to update the probability either upward or downward based on the Bayes factor. If we have enough evidence, the probability might eventually cross 0.5. Then we would say that the hypothesis is more likely than not. Perhaps we’re interested in a higher threshold, like 0.95. We would need more evidence to reach this, but in principle, we could adduce enough to do so.

Since the odds start out strongly in favor of the defendant’s innocence, the prosecution must bring compelling evidence to raise the posterior odds enough for the jury to render a guilty verdict. This indicates, with some rigor, the sensibility of “innocent until proven guilty.”

Example 2: testimony to the contrary

Let’s consider another piece of evidence. Suppose a witness comes to the stand. She claims that the defendant was in a different part of town at the time of the murder.

This is interesting. It seems to be in tension with the first piece of evidence. We would not expect this to be the case if the defendant were guilty. In fact, if the defendant were guilty, the witness must be either lying or mistaken. But she seems credible.

While you were initially highly suspicious of the defendant due to the fingerprints found on the murder weapon, the witness’ testimony starts to incline you the other way. You intuitively sense that the testimony is evidence against the defendant’s guilt, and you’d be right. But how strong is this evidence?

Let’s call the fact of the witness’ testimony E. P(E|H) must be fairly low. If the defendant is guilty, it’s improbable (though not impossible) that testimony of this sort would be offered.

But what about P(E|~H)—if the defendant is innocent, what is the probability that there would be a claim of the defendant’s alternative whereabouts? This probability is not quite as clear-cut as the others.

We wouldn’t necessarily expect the testimony—the defendant could be innocent and yet no one have this sort of testimony to offer—but it’s at least not too implausible. After all, the defendant must have been somewhere that night, and someone likely knew about it. The defendant would surely want this person to testify, and may take steps to ensure that it happened.

For the sake of argument, suppose that P(E|H) is 0.05 and P(E|~H) is 0.3. Let’s compute the Bayes’ factor:

Then our Bayes factor is 1/6, which is bottom-heavy and so evidence against the guilt hypothesis.

Rinse and repeat!

The same procedure can be followed with any piece of evidence. Suppose it comes to light that the defendant stood to gain from the murder. This is somewhat probable if the guilt hypothesis is true—after all, he had to commit the murder for some reason—but not as probable if the guilt hypothesis is false.

While not as strong as the evidence from the fingerprints, this contributes evidence toward the guilt hypothesis nonetheless.

Let’s recap the implications of reasoning with the likelihood ratio. For one thing, since evidence is simply something that is more probable on a hypothesis than on its negation, there can be evidence for a false hypothesis!

If the defendant is guilty, then E is evidence pointing toward a false hypothesis. If the defendant is innocent, then the evidence of the fingerprints points to a false hypothesis.

Second, evidence need not be entailed by nor even probable on a hypothesis in order to count as evidence for it. The witness’ testimony, statistically speaking, wasn’t particularly likely on either H or ~H, but it was more likely on ~H, so it counts as evidence against the guilt hypothesis.

Finally, we don’t have to quantify the relevant probabilities in order to use the likelihood ratio. Indeed, in real life it is rarely possible to exactly quantify them. Sometimes we can, in fact, supply a rough quantification of both the numerator and the denominator. Other times it is difficult to assess either. In that case, we only need to figure out whether P(E|H) or P(E|~H) is bigger, and by roughly how much.

One question we haven’t yet addressed is how to think through multiple pieces of evidence. How do we combine the forensic evidence with the witness’ testimony, taking both of them into account in arriving at our conclusion? That will be our focus in the next part.

This formulation is useful in some cases. However, there is another formulation of the theorem which, in my judgment, is far more useful in cases of practical epistemology. Known as the “odds form of Bayes’ theorem,” it provides a practical means of evaluating the epistemic force of a piece of evidence. It looks like this:

This is a bit larger! We now have six quantities instead of just four. Why is this an improvement over the original formulation? The short answer is that it tells us whether something is actually evidence for or against a hypothesis or whether it’s irrelevant to the truth of that hypothesis. Let’s look at how that works.

Terminologically, the first ratio is called the posterior odds, the second is called the prior odds, and the third is called the likelihood ratio. The tilde (~) negates a proposition, so ~H means “not H” or “the falsehood of H.” The use of the “odds” quantities—used in statistics to refer to a ratio of probabilities—is why this form is called the odds form of Bayes’ Theorem.

Posterior odds: this is a ratio of the probability of H to the probability of ~H once we’ve taken into account evidence E. If the posterior odds equal 1, then P(H|E) = P(~H|E). This means that the hypothesis is just as probable as its negation. If the posterior odds are top-heavy—that is, if P(H|E) > P(~H|E), then the hypothesis is more probable than not.

The value of the posterior odds represents how much more probable the hypothesis is than not. If the ratio is equal to 9, then the hypothesis is 9 times more likely than not.

Prior odds: this is the ratio of the prior probabilities of the hypothesis and the negation of the hypothesis. Though we didn’t use the term prior probability, we calculated this when we found the value of P(H) in the first post in this series. It represents the probability of the hypothesis before relevant evidence is considered.

Likelihood ratio: this represents the ratio of the quantities P(E|H) and P(E|~H) for some piece of evidence E. This is the most important quantity! It allows us to measure the extent to which a piece of evidence affects the probability of a hypothesis. If the ratio is top-heavy, it means that the evidence is more to be expected under H than under ~H. Thus, the evidence supports H. If it is bottom-heavy, then the evidence is more to be expected under ~H than under H, and so it supports ~H.

A top-heavy likelihood ratio indicates that E supports H to some extent. A bottom-heavy likelihood ratio indicates that E supports ~H to some extent.

We can now figure out when E is evidence for H! We simply need to determine whether the probability of E occurring is greater when we assume H is true or when we assume ~H is true.

Let’s return to the gumball machines. Recall that you drew a green gumball from the second machine, which contained 90 green gumballs and 10 blue gumballs.

First, we’ll go through the entire process of computing the odds form of Bayes’ Theorem, so you can see it done. Then, I’ll zero in on the likelihood ratio and draw some conclusions.

The odds form of Bayes’ Theorem—from the top!

To calculate the posterior odds ratio, we must find four probabilities:

• P(H) – the prior probability of the hypothesis.

• P(~H) – the prior probability of the falsehood of the hypothesis.

• P(E|H) – the probability of observing the evidence if the hypothesis is true.

• P(E|~H) – the probability of observing the evidence if the hypothesis is false.

We’re trying to figure out the probability that we drew a gumball from the second machine (H) given that the gumball we drew was green (E).

Recall that P(H) = 0.5 because the chance of randomly choosing the first machine is equal to the chance of randomly choosing the second machine. That we know. What about P(~H)? Well, what is ~H? Well, since there are only two possible machines we could have drawn from, ~H must refer to the hypothesis that the gumball came from the first machine. So P(~5) will also be equal to 0.5.

We calculated that P(E|H) = 0.9 because the chance of drawing a green gumball from the second machine is 90%. What about P(E|~H)? P(E|~H) represents the probability of drawing a green gumball assuming that you drew from the first machine. Since the first machine contained 100 gumballs and 20 of them were green, the probability of getting a green one is equal to 20 divided by 100, or 0.2.

Thus, we’ve arrived at the following values:

• P(H) = 0.5

• P(~H) = 0.5

• P(E|H) = 0.9

• P(E|~H) = 0.2

Let’s plug these into our equation and see what we get.

The posterior odds (the first ratio) comes out to 4.5. Since 4.5 is greater than 1, the posterior odds are top-heavy. H is 4.5 times more likely to be true than ~H.

Before you removed the blindfold, H and ~H were equally probable to you—you were 50% sure of each. But after considering evidence E, you should now rationally be 4.5 times more confident that H is true than that ~H is true.

Let’s translate this into a probability. If H is 4.5 times more likely to be true than ~H, and their probabilities must sum to 1 (since either one or the other must be true), some simple algebra gives us a value of P(H|E) right around 82%. Sound familiar? This is exactly what we found using the standard formulation of Bayes’ Theorem in the first part of this series. Hurrah! The math checks out.

The likelihood ratio: your new all-purpose epistemological tool

Let’s focus in on the likelihood ratio, the third ratio in the odds form. So you don’t have to scroll back, here it is again:

This, by far, is the most important takeaway. The likelihood ratio is the key to applying Bayesian reasoning in real-life scenarios. To figure out the extent to which some observation supports some conclusion, use the likelihood ratio.

Let’s get practical. Suppose you have a theory that BMW owners tend to be worse drivers than the general population. You’re out driving one day when a BMW attempts to change into your lane right in front of you. Hitting the brakes and recovering your cool, you think your hypothesis has been confirmed.

But wait! How much did your driving experience actually support your hypothesis about BMW drivers? Let’s use the likelihood ratio to shed some light.

E is the fact that a BMW almost collided with you. H is the hypothesis that BMW owners are bad drivers. P(E|H) is reasonably high—bad drivers do often make ill-advised lane changes. P(E|~H), however, is also reasonably high! Even assuming the falsehood of your hypothesis—that BMW owners are no worse at driving than the general population—it’s not at all surprising that a BMW would narrowly avoid a collision with you. Drivers do this all the time, and in this particular case, it happened to be a BMW owner.

Sure, perhaps P(E|H) is slightly higher than P(E|~H). Your experience on the road is some evidence for your hypothesis—a very little bit. Without a more precise way to determine the probabilities, however, it’s best to say that this is only negligible evidence. You need something surer to go on (and, well, that might not be hard to find).

Notice, as a final observation, that we didn’t need to know the exact values of P(E|H) and P(E|~H)! We only need to know which one is bigger. It also helps to have some rough estimate of how much bigger one is than the other—this is what helped us to see that the BMW incident was only negligible evidence for the BMW hypothesis. This is part of what makes Bayes’ Theorem so powerful. We don’t need exact numbers before we can benefit from its logical structure.

In the next post, we’ll unpack the likelihood ratio in more detail with a few more examples. This will set us up for an extremely powerful application of Bayesian reasoning. If you think you have a solid grasp of the likelihood ratio already, go ahead and skip to the next part. If you want to refine your intuitive understanding of the likelihood ratio, read on.

If, despite the enticing subtitle, you want to skip this post, you may do so. The rest of the series will make sense without it.

That said, the notion of background knowledge is critical to a technical understanding of Bayesian reasoning. When we make a probability judgment, we assume certain things to be true about the way the world works. We may also assume some facts specific to the situation we are considering. Those assumptions are part of our background knowledge.

Background knowledge is often symbolized by the lowercase letter k. Using this notation, P(E|H&k) means “the probability of evidence E given our hypothesis H and relevant background knowledge k.” For the sake of simplicity, background knowledge is often omitted from Bayesian notation, and an expression like P(E|H) is understood to include the background knowledge implicitly. This is what Bayes’ Theorem looks like without the letter k:

If you want to retain k in the notation, Bayes’ Theorem would look like this:

None of the math changes. This formulation merely makes explicit the fact that we are taking into account relevant background knowledge when determining a probability.

The simple conjunction “H&k” accounts for everything we use when making a probability judgment. The hypothesis, and the background knowledge. All neatly symbolized.

Cool? Hopefully.

You may want to know what this background knowledge could be. Let’s go back to the gumball example from part 1. Recall that the first value we had to calculate was P(E|H)—or P(E|H&k)—the probability of observing a green gumball if you drew from the machine with mostly green gumballs.

Since that machine contained 90 green gumballs and 10 blue gumballs, you took the probability to be 0.9.

But what did you assume in order to arrive at this number?

One assumption you made is that the gumball you withdrew was truly random. If the gumball machine had somehow been loaded with all the green gumballs on the bottom and all the blue gumballs on the top (thus biasing the machine toward green gumballs), P(E|H&k) would be effectively 1!

To avoid this difficulty, you assume that the gumballs have been well-mixed. This assumption is part of your background knowledge k. Thus, P(E|H&k) refers to (at minimum) the probability of getting a green gumball given that you drew from the second gumball machine and that the gumballs were well-mixed.

It's possible to tease out some other assumptions that you made in arriving at your probability judgment.

For example, you know you live in a world in which objects don’t spontaneously change color on a frequent basis—if that were the case, you may affix different values to some of the probabilities involved. Thus, the fact that objects don’t generally undergo sudden and extreme color change is also part of your background knowledge, and you can include it as a proposition in k. Note that k is a collection of multiple propositions.

Background knowledge may seem trivial, and in the gumball scenario it certainly is. The notion of background knowledge becomes important in more technical applications of Bayesian reasoning in which we have to make judgments about which items should be included in our background knowledge and which should be excluded. For now, just remember that when we make a probability judgment, we are assuming certain propositions as part of our background knowledge.

In the next post, we will look at how to weaponize Bayes’ Theorem for maximum epistemological potency.

Bayes’ Theorem is a mathematical theorem developed by the Reverend Thomas Bayes, an 18th-century Presbyterian minister with a keen interest in statistics. It has many applications in probability theory and is especially helpful in thinking about the role of evidence in confirming or disconfirming a hypothesis. The theorem can be represented by the following equation:

The notation may be confusing at first. P should be read as “the probability of” and the vertical bar should be read as “given.” Thus, P(E|H) means “the probability of E given H,” P(H) means “the probability of H”, and P(E) means “the probability of E.” In this case, H represents some hypothesis we want to consider, and E represents some piece of evidence that is relevant to determining whether the hypothesis is true or false. So, given some piece of evidence E, if we know the values of P(E|H), P(H), and P(E), Bayes’ Theorem allows us to calculate the probability of the hypothesis. Thus, we can measure to what extent a piece of evidence raises the probability of our hypothesis.

When you think about it, this is pretty powerful. We can quantify exactly by how much to raise our confidence in a given belief if we know three numbers. In practice, we may not know all three numbers—no matter. We can still make a lot of headway in assessing our hypothesis if we can estimate the three numbers, or know how big they are relative to each other. For now, let’s look at an example where we know the numbers exactly.

Suppose you are looking at two gumball machines. Each contains 100 gumballs. The first contains 80 blue gumballs and 20 green gumballs, and the second contains 10 blue gumballs and 90 green gumballs.

Now suppose you are blindfolded and instructed to choose a gumball at random. You pick one of the gumball machines, not knowing which one it is, and withdraw a gumball. You now return to the center of the room, remove your blindfold, and observe that the gumball is green.

Which machine do you think the gumball came from?

[pause for reflection]

Obviously, it’s possible that the gumball came from either machine—each had green gumballs. But you notice that the second machine has a lot more green gumballs. If you had to guess, you would say the second machine. But how sure can you be?

Time to apply Bayes’ Theorem. In this case, H and E can be written as follows:

H: “The gumball came from the second machine.”

E: “The gumball is green.”

Now we determine the values of P(E|H), P(H), and P(E).

Recall that P(E|H) means “the probability of E given H.” This refers to the likelihood that you would observe the piece of evidence E under the assumption that H is true. In our example, you want to know how likely it is that the gumball would be green assuming that it came from the second machine. Since the second machine contains 90 green gumballs and 10 blue gumballs, we conclude that there is a 90% chance a gumball withdrawn from that machine would be green. Probabilities compute best on a scale from 0 to 1, so we will say that P(E|H) = 0.9.

Now for the next quantity: P(H). This represents the probability that H is true before you consider any evidence for it. So, pretend you don’t know that the gumball is green—all you know is that you drew from a random machine. What is the probability, in this scenario, that you drew from the second machine? Since you chose randomly, we may assume that the probability is one half. Thus, P(H) = 0.5.

The final quantity is P(E). This refers to the probability of drawing a green marble without knowing which machine you’re pulling from. Since there are 110 green gumballs out of 200 total gumballs, the probability of getting a green gumball at random is 11/20, or 0.55.

Now we have the following values:

P(E|H) = 0.9

P(H) = 0.5

P(E) = 0.55

Thus, we can solve the equation:

Before you looked at your gumball, you were 50% certain you drew from the second machine. But after you saw that the gumball was green, you can be roughly 82% sure that you drew from the second machine.

Can you be certain that you drew from the second machine? No. It’s still possible the gumball came from the first machine—there’s an 18% chance of that. But compared to your 50-50 uncertainty before you looked at the gumball, 82% is pretty good.

But wait. Whether you noticed or not, we had to make some assumptions to arrive at these numbers. We need to at least acknowledge them. Maybe these assumptions were reasonable. Maybe they weren’t. We’ll figure that out in the next post.

A section of Logic and Theism addresses the fine-tuning argument. The fine-tuning argument, for those unaware, infers the likelihood of theism from what we shall call the “fine-tuning fact”—that many of the physical laws, constants, and initial conditions of the universe fall into an extremely small range of life-permitting values relative to the range of possible values they could have taken. Robin Collins and Luke Barnes are two of the foremost defenders of the argument today, and many atheists take it seriously.

Sobel’s comments on the fine-tuning argument are remarkably poor for a philosopher of his caliber. And though I am a theist with a vested interest in the success of the fine-tuning argument, I don’t think all his errors are in one direction: he makes an error that seriously handicaps his own view.

First, Sobel seems to think that the knowledge of physics required to verify the fine-tuning fact is a problem. Note that Sobel previously distinguished the “1776 version” of the argument from design (biological complexity) and the “millennial version” (the cosmological fine-tuning argument), and that Cleanthes is a character in one of David Hume’s Dialogues Concerning Natural Religion:

There is a remarkable difference between the 1776 version and the millennial versions of the argument from design. The evidence for design in 1776 was for all to see: “Look ’round,” Cleanthes could enjoin. The new evidence for design is for all but a very few to take on faith and authority…

[quotation of Peter van Inwagen on fine-tuning)

There you have a general indication of the new evidence, about fourth hand, from me, who got it as you can see from van Inwagen, who probably got it from teachers and reporters of science, who got it from some front-line researchers’ reflections on the significance of some features of contemporary physical theory.

(p. 278)

I don’t see the problem that Sobel does. Perhaps the relative obscurity of the fine-tuning fact makes the intuition less clear, but that says nothing about the strength of the argument. Further, though perhaps information on fine-tuning was harder to come by when Sobel published the book (2003), recent treatments of the fine-tuning argument (see Luke Barnes and Geraint Lewis, A Fortunate Universe) are relatively accessible for someone with one or two undergraduate semesters in physics or chemistry.

Further, one could argue that the evidence of cosmological fine-tuning emphatically is for all to see. Look around the room and notice that things are staying together and not collapsing in on themselves or flying apart. Note that things have stayed this way for a while. Note that the universe permits a bunch of different kinds of things to exist rather than just one kind of thing, and think about all the other ways it could have been. It’s not hard to perceive the strength of the cosmological fine-tuning argument. The technical details merely quantify and add force to what anyone can directly perceive.

Moving on, Sobel discusses the category of “many cosmoi hypotheses”, more commonly called multiverse hypotheses, as alternatives to the theistic explanation of fine-tuning. There are two kinds here: simple many cosmoi hypotheses and evolutionary many cosmoi hypotheses.

Simple many cosmoi hypotheses are those which hold that the values of the fundamental constants in each universe are independent from any other universe. That is, the values of the constants in some universe U are generated randomly without reference to the values in any other universe. Sobel thinks this theory is more intrinsically likely than theism. However, for him, it has very little predictive power. Why is this? Recall that predictive power is a measure of how well a theory predicts that which it’s supposed to explain. Sobel argues that while a simple many cosmoi hypothesis makes it very likely that there would exist, somewhere, life-permitting universes, it does not make it very likely that this particular universe would be life-permitting:

The likelihood of any given particular cosmos, including the one in which we find ourselves, randomly generating for itself the life-supporting parameter assignments (to simplify I am assuming that there is exactly one such assignment), or any other particular parameter assignments, assuming finitely many possible assignments, f, is 1/f, given that, to recall a ‘crucial feature’ of simple many cosmoi theory, assignments for each cosmos are determined by some random chance process operating on the ‘space’ of all possible assignments.

(p. 280)

For Sobel, the fact that needs to be explained is that the universe in which we find ourselves is life-permitting. To make the point a little clearer, let’s suppose that our universe was the 19,880,741st universe generated by some universe-generating mechanism in a simple many cosmoi hypothesis. Sobel claims that a simple many cosmoi hypothesis gives us no more reason to think that the 19,880,741st universe will be life-permitting instead of the 19,880,742nd, or the 19,880,743rd, or so on. The probability of #19,880,741 being the lucky one is still microsopic. Somewhere, in the vast ensemble of universes generated by this mechanism, we would expect there to be a life-permitting universe. But the odds of it being our universe—universe #19,880,741—are not great. Thus, simple many cosmoi hypotheses do not predict our observations, and so they are not a good response to the fine-tuning argument.

Do you see the problem here? Sobel is conflating two different ‘fine-tuning facts’ in a way that, ironically, complicates the atheist’s job. Robin Collins helpfully distinguishes between three fine-tuning facts that need to be explained (this is from his chapter in the Blackwell Companion to Natural Theology):

1. The observer-relative fine-tuning fact: we observe a life-permitting universe rather than a non-life-permitting universe.

2. The indexical fine-tuning fact: that this universe, the one we inhabit, is life-permitting (this here is functioning as an indexical that picks out the universe we inhabit).

3. The existential fine-tuning fact: that a life-permitting universe exists.

Fact 1 is logically entailed by the fact that we exist. Fact 2 is what Sobel is trying to explain. Fact 3 is what Sobel should be trying to explain.

Since it exponentially multiplies the number of universes, a simple many cosmoi hypothesis would prima facie provide a reasonable account of Fact 3. Sobel is right to point out that such a hypothesis doesn’t make any particular universe any more likely to be life-permitting. Where’s he’s wrong is in the significance that he attaches to that fact. We know that we exist, and consequently that our universe is life-permitting. It doesn’t matter “which universe,” indexically speaking, ended up being one of the life-permitting ones. What we’re trying to explain is why we exist at all, and our existence doesn’t depend on the constants in universe #19,880,741. It requires at least one life-permitting universe somewhere.

Suppose instead of universe #19,880,741 it were universe #382,007,227 that ended up being life-permitting. Then we would have found ourselves in that universe rather than the first. No matter. Nothing changes. The indexical fine-tuning fact is not very interesting. It’s the existential fine-tuning fact that requires explanation.

By trying to explain the indexical fact rather than the existential fact, Sobel ends up selling the multiverse hypothesis short, and goes on to relegate it to the same tier as theism (which, in his mind, is not a very good explanation of fine-tuning):

Their advantages of inherent plausibility and disadvantages in would-have-been predictive power to my mind balance to place simple many cosmoi and rational tuner theories about on a par, and equally probable on the evidence of fine-tuning.

(p. 280)

So much for simple many cosmoi hypotheses. Sobel goes on to discuss a different kind of theory, evolutionary many cosmoi hypothesis. In these, the values of the fundamental laws and constants in each universes is dependent on the values of such fundamental laws and constants in logically prior universes. Sobel places the most stock in Lee Smolin’s evolutionary cosmology. As I understand the theory, Smolin argues that the origin of every black hole spawns a new universe. The fundamental constants of a universe spawned from a black hole will randomly deviate from its parent universe within a narrow range of possibilities, leaving child universes which are fairly similar to their parents. Over many “generations” of universes, the universes which “reproduce” the most are those which produce large numbers of black holes, and so those eventually come to dominate the space of possible universes. However, since the constants which allow for black holes are also those which permit stars (the force of gravity, for example), by selecting for black holes, the evolutionary process favors universes with stars. And stars are needed for life. Life is a side effect of selecting for black holes:

Voilà!! Tuning for black holes that is incidentally sufficient for stars, and so for life. What a nice theory!

(p. 280)

Sobel thinks this theory is more likely than either theism or a simple many cosmoi hypothesis, but not quite more probable than not. It certainly sounds nice, though there are outstanding questions, not least of which is why our universe isn’t a wasteland of black holes. There’s also a dearth of empirical evidence for Smolin’s view. Other objections might be raised. For now, I want to jump to Sobel’s conclusions on the fine-tuning argument (here “FT” is theism and “MU” is a simple multiverse):

Were I persuaded that the apparent fine-tuning of which I hear talk cannot be grounded in a ‘deeper theory’, I would put down the appearances of fine-tuning to our dumb luck. Otherwise, supposing a worked-out deep theory of fine-tuning of this cosmos, say a theory along the lines of Smolin’s evolutionary many cosmoi theory, were not only more plausible than FT and MU (as in my view his present largely speculative theory already is by far) but actually acceptable, that is, more probable than not (as in my view his theory presently is not), I would accept it as an explanation of the facts of fine-tuning of this place and put that theory’s fundamental assumptions down to that luck. After all, not everything can be explained, not everything can have a reason (if, it is hardly necessary to qualify, anything is contingent), and a good ‘deep theory’ of ‘parameters for life’ could very well be a place at which reasons and explanations for them run out.

(pp. 284-5, emphasis added)

Let me just be blunt and say that dumb luck is a terrible explanation for fine-tuning. The probabilities in question are so small and the stakes so great that it’s hard to take this response very seriously. So far, I haven’t discussed Sobel’s reasons for discounting the theistic explanation. They center around the “how” and “why” of the theistic hypothesis—what does it really mean for a designer to fine-tune the laws and constants of nature? And why would a designer do so?

Without unpacking potential responses to these questions or Sobel’s elaborations on them, it suffices to say that even if we are unsure of the answers to these questions, we still ought to favor a vaguely-defined design hypothesis to a sheer dumb luck hypothesis.

Sobel’s take on fine-tuning is brilliantly written and fun to think about, but I’m afraid he’s fallen short here in multiple ways, including a significant one that disadvantages his position. I conclude that weighty critiques of fine-tuning will come from elsewhere.