We’re halfway through our analysis of the modal ontological argument, an apologetic argument that’s not accurate and useful so much as weighty. Those of us who are outsiders to philosophy have probably found it to be ponderous and counterintuitive. I certainly did.

In part 1, we saw that premise 1 seemed reasonable and premise 3 seemed crazy, and I promised to swap that critique and show that 3 was reasonable and 1 was crazy.

Here’s the argument again:

Premise 1. It is possible that an MGB exists.

Premise 2. If it is possible that an MGB exists, then an MGB exists in some possible world.

Premise 3. If an MGB exists in some possible world, then it exists in every possible world.

Premise 4. If an MGB exists in every possible world, then it exists in the actual world.

Premise 5. If an MGB exists in the actual world, then an MGB exists.

Conclusion 1. Therefore, an MGB exists.

Conclusion 2. Therefore (since MGB is just another name for God), God exists.

Raising the stakes

Before we complete our attack on the argument, let me show the stakes we’re playing for. Douglas Groothuis in Christian Apologetics (2011) responded to Richard Dawkins’ rejection of the ontological argument in The God Delusion. Critiquing Dawkins, he said:

Without prior knowledge of the history of this fascinating specimen of reasoning, we could conclude from Dawkins’s treatment that the ontological argument was more of a joke than a serious work of philosophy. As a naive empiricist, he simply finds absurd the idea that an argument could prove God’s existence without appeal to empirical evidence. But Dawkins’s glib rejection never engages the richness or subtlety of the argument, a piece of reasoning that has intrigued some of the best minds in philosophy since the argument’s inception by Anselm in the eleventh century.

Richness and subtlety? That’s like complaining that we’re missing the richness and subtlety of the Emperor’s new clothes. Sorry, I’m still stuck on whether the argument is correct or not. Groothuis seems to be promising that it’s a powerful and compelling argument. Let’s see.

Equivocation on the definition of “possible”

In part 1, we saw that premise 3 works, and our problem remains: the conclusion “Therefore God exists” still looks like magic.

Our first challenge was correctly seeing the consequences of an MGB as a necessary being. Now, let’s focus on the word possible. Few people would begrudge premise 1, “It is possible that an MGB exists.” I’ve seen no good evidence, but, sure, maybe an MGB does exist.

But this is the colloquial meaning of possible. We’re saying, “I have no idea—maybe an MGB exists in one possible world or a thousand worlds or none.” This is usage 1: possible as a statement of ignorance. But there’s another usage.

(The modal ontological argument makes use of S5 modal logic, in which necessary and possibly are carefully defined, but there’s no need for our analysis to get bogged down with that. I bring this up only to note that Plantinga used a different definition openly. Unfortunately, it’s easy for other apologists to use these two meanings of possible to take advantage of the reader’s confusion.)

The other usage is possible as a declaration of existence, and we see that in premise 2: If it is possible that an MGB exists, then an MGB exists in some possible world. That is, an MGB exists in one or more possible worlds. Zero possible worlds is not an option.

Now we can see the deceptiveness of premise 1 (again, that deceptiveness wasn’t deliberate for Plantinga, but I doubt that’s true for some apologists). Premise 1 says, It is possible that an MGB exists. In other words (using the appropriate definition of possible), an MGB exists in one or more possible worlds. By accepting premise 1, you’re accepting that an MGB exists somewhere. Not really what you intended, was it?

Let’s rework those first three premises with this new knowledge.

Premise 1′. An MGB exists in one or more possible worlds.

Premise 2.

Premise 3′. Given that an MGB exists in some possible world (premise 1) and that an MGB either exists in all worlds or none (by definition), then an MGB must exist in all possible worlds.

When the implications are laid out, the assumptions become clear, the magic vanishes, and the argument says nothing of interest. When you assume an MGB in your first premise and define it to be either everywhere or nowhere (and nothing in between), it’s hardly surprising that you can conclude that one exists.

This is a circular argument. It logically fails.

Revisit the conclusion

Let’s take a closer look at the second half of the argument.

Premise 4. If an MGB exists in every possible world, then it exists in the actual world.

Premise 5. If an MGB exists in the actual world, then a maximally great being exists.

Conclusion 1. Therefore, an MGB exists.

Conclusion 2. Therefore (since MGB is just another name for God), God exists.

This works except for Conclusion 2. An MGB has a very simple definition, while God (that is, Yahweh) doesn’t. Christians can’t agree on all of God’s properties, and those properties evolved through the Old Testament. The first problem is God’s squishy and ambiguous definition not fitting the simple definition of an MGB.

Let’s focus on one aspect. If God is a Maximally Great Being, then he must be, among other things, wholly good. But read the Bible, and you’ll see that God isn’t wholly good. He supports slavery and demands human sacrifice and genocide. The easy comeback is “Sure, but God could have his reasons,” which simply presupposes God to defend his existence, which is another logical error.

There’s another part of the definition of a Maximally Great Being that doesn’t work, the clash between the conflicting requirements of an MGB’s omni properties. For example, the MGB is omniscient and so knows the future. But he’s also omnipotent, so he can change the future. Which one wins?

And since God has even more superpowers than an MGB, it becomes even weirder with him. Before God created the universe, reality was either perfect or not. It couldn’t have been imperfect, because God wouldn’t have tolerated that. But if it was already perfect, why create the universe? Or how can God be all-just (and give everyone what they deserve) while also being merciful (giving some of us less than we deserve)?

(More on omni conflicts here and a proof that God doesn’t exist because of the suffering in the world here.)

Turn the argument on itself

As with the regular ontological argument (my response to that here), the modal ontological argument can be turned on itself. The argument works because (1) its definition of possible existence is “exists in at least one possible world” and (2) an MGB is necessary, which makes its existence all or nothing—it’s everywhere or it’s nowhere. If you start with premise 1 being “It is possible that an MGB exists,” the wheels of the argument turn to move from an MGB in at least one possible world, to all possible worlds, to the actual world.

But change one cog in the machine, and you get a different prize when you turn the crank. Change every exists to doesn’t exist. It’s still valid, but its cleverness has been turned on itself. Now the conclusion becomes, “Therefore, God doesn’t exist.”

You want to go with this as your argument? Is that your final answer?

This is a caltrop argument, an argument that doesn’t make an offensive point. Its value instead is in slowing down a pursuer. It’s a puzzle. The Stanford Encyclopedia of Philosophy lists eight categories of ontological argument, so there are lots more if the retreating Christian apologist needs to throw out another tar baby.

What kind of god are you defending if you must go to this argument instead of pointing to convincing evidence? What kind of god are you defending if he can’t defend himself?

In fact, Plantinga agrees that the argument doesn’t do much:

Our verdict on these reformulated versions of St. Anselm’s argument must be as follows. They cannot, perhaps, be said to prove or establish their conclusion. But since it is rational to accept their central premise, they do show that it is rational to accept that conclusion.

I’m not sure what he’s saying in that last sentence. My guess is he’s saying that the modal ontological argument reached a conclusion through a flawed logical path, but that’s okay because he knows that conclusion is correct because of other reasoning.

Regardless, we’ve shown that, though the argument concludes, “Therefore, God exists,” that’s not a takeaway for any of us.

Let’s end by returning to Douglas Groothuis, whose challenge mocked us as we began our critique of the argument: “Dawkins’s glib rejection never engages the richness or subtlety of the [ontological] argument, a piece of reasoning that has intrigued some of the best minds in philosophy since the argument’s inception by Anselm in the eleventh century.”

A flawed argument deserves ridicule in proportional to the earnestness with which it is put forward as a serious, useful apologetic argument.

Acknowledgements. Several sources in particular helped me peek behind the curtain to see how the trick was done.

• “Plantinga’s Modal Ontological Argument, Part 1” is an excellent video by Roderic Taylor.
• Richard Carrier’s articles are thorough and insightful but always accessible. He analyzes the ontological arguments here, as part of his series taking down Plantinga’s famous list of “Two dozen or so” arguments.
• Frequent commenters Greg G. and JustAnotherAtheist2 provided useful insights. A particular h/t is due Grimlock, who prodded me to write this post.

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Image from Žygimantas Dukauskas, CC license
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This Christian apologetic argument is the one that I most often see put forward as the one that will put cocky atheists in their place. And for you Christians, once you’ve gotten past the beginner arguments like the Design, Cosmological, and Moral arguments and then master intermediate ones like the Fine-Tuning, Transcendental, and Ontological arguments, it’s time for advanced arguments like the Modal Ontological argument. Or at least that’s how it’s presented.

The best thing I found about this argument was that it was complicated—not that it was correct or informative but that it was so effective a smokescreen that I needed hours of research before I felt that I really understood it. And it’s only five lines long.

While it concludes, “therefore, God exists,” it doesn’t actually tell us that. Not only am I telling you this, but Alvin Plantinga, the author of one popular version, will tell you this as well. And you’ll see it, too, by the end of these two posts.

I’ll try to cover every point thoroughly with simple language, so this may be a little slow for some readers.

The modal ontological argument

First, some definitions.

Definition 1: a Maximally Excellent Being is omnipotent, omniscient, and wholly good.

Definition 2: a Maximally Great Being (MGB) is a Maximally Excellent Being that is necessary (that is, it exists in every possible world).

It’s a little more formal to use MGB rather than “God” for our analysis, but the Christian apologist obviously thinks that they’re synonymous for this discussion. Note also that the MGB is simply the typical list of godlike properties with necessity thrown in. That will be important later.

Here’s the William Lane Craig version of the argument:

Premise 1. It is possible that an MGB exists.

Premise 2. If it is possible that an MGB exists, then an MGB exists in some possible world.

Premise 3. If an MGB exists in some possible world, then it exists in every possible world.

Premise 4. If an MGB exists in every possible world, then it exists in the actual world.

Premise 5. If an MGB exists in the actual world, then an MGB exists.

Conclusion 1. Therefore, an MGB exists.

Conclusion 2. Therefore (since MGB is just another name for God), God exists.

The argument is valid (the formal logic is correct), and premise 1 seems easy to grant, even for atheists. Sure, it’s possible that a maximally great being exists.

However, Premise 3 is crazy—we’re going to go from “Sure, maybe an MGB exists” to “an MGB definitely exists in every possible world.” This is the logical equivalent of the “then a miracle occurs” step in Sidney Harris’s famous cartoon.

You’ll soon see that that initial reaction is backwards—Premise 3 actually works, and 1 is the tricky one.

The prisoner and the surprise sentence

Quick intermission: Did you hear the story of the guy sentenced to execution?

The judge, in a whimsical mood, wondered why sentencing someone to death must always be so gloomy. Can’t we have a little fun with it? “Executions are always at sunrise,” he said to the prisoner. “Your sentence will be one day next week, but you won’t know which day. It’ll be a surprise.”

As the prisoner sat dejected in his cell, he soon realized that the judge’s odd requirement gave him a loophole. After all, if they hadn’t come for him by Thursday morning, then he would know that it would be Friday. And Friday’s out because it would violate the judge’s demand that it must be a surprise.

Looking at the remaining days, he couldn’t be executed Thursday using similar reasoning. And so on, through the days of the week.

The guards woke him from a contented sleep just before sunrise on Wednesday morning to be executed. He was completely surprised.

The Christian’s confidence in the modal ontological argument is like the prisoner’s confidence in his analysis. The Christian probably doesn’t completely understand the argument, but it’s put forward by famous Christians like Alvin Plantinga and William Lane Craig, so must be solid.

Our Christian apologist is in for a surprise.

Take 2: one small change to the argument 

The ontological argument starts with the claim that God is possible and then concludes that he exists. But what kind of black magic is this?! That doesn’t make sense.

Things are clearer if we take the argument exactly as defined above and make one change: replace “Maximally Great Being” with “griffin” (a griffin is a lion/eagle chimera).

Premise 1. It is possible that a griffin exists.

Premise 2. If it is possible that a griffin exists, then a griffin exists in some possible world.

Premise 3. If a griffin exists in some possible world, then it exists in every possible world.

Premise 4. If a griffin exists in every possible world, then it exists in the actual world.

Premise 5. If a griffin exists in the actual world, then a griffin exists.

Conclusion 1. Therefore, a griffin exists.

A griffin doesn’t exist in our world, but (premise 1) it’s possible that it exists. That is, it’s possible that physics and evolution in a different world would be such that a griffin was an outcome. But the argument fails on premise 3. No, even if griffins exist in some possible worlds, that doesn’t transport them to any other non-griffin world.

Then how could the argument work for an MGB?

Premise 3 makes no sense for griffins or indeed for any ordinary thing . . . but it does for an MGB. To understand this, let’s focus on where the action is, just the first three premises.

Premise 1. It is possible that an MGB exists.

Premise 2. If it is possible that an MGB exists, then an MGB exists in some possible world.

Premise 3. If an MGB exists in some possible world, then it exists in every possible world.

The reason that premise 3 works is a word that you may not have taken notice of in the definition of MGB, the word necessary.

Let’s step back. Things are either necessary or contingent. For example, lions and griffins are contingent. Their existence depends on how the world is. In our world, lions exist and griffins don’t, but another possible world could’ve had it the other way around.

Mathematical truths, by contrast, aren’t contingent, they’re necessary. The statements 1 + 1 = 2 and 1 + 1 = 7 aren’t dependent on the way the world is. One is true and one is false, and those truth values are unchanging across all possible worlds.

An MGB is necessary by definition (scroll back up and see). Like mathematical truths, “an MGB exists” is either true or false, but that truth value is unchanged in all possible worlds.

If an MGB is possible (premise 1), then it must exist in one or more possible worlds (premise 2). But if it exists anywhere, it must exist everywhere, since it is necessary (from the definition of MGB). Said another way, an MGB is all or nothing—because it’s necessary, “an MGB exists” is consistently either true or false everywhere. It can’t be true in some fraction of the possible worlds and false in the rest, just like “1 + 1 = 7” can’t be true in some fraction of the possible worlds and false in the rest. Since we’ve shown that if an MGB exists in some possible world, then it must exist in every possible world (and that’s premise 3).

We’ve seen that premise 3 actually makes sense. Next up: we’ll see how premise 1 doesn’t make sense, how the entire argument is circular (and so fails), plus a few other problems.

Concluded in part 2.

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We’ve analyzed New Testament manuscript evidence twice to poke holes in claims for its reliability. In short, the manuscript evidence is pretty good considering that it’s so old, but let’s not pretend that we know with certainty what the originals said.

Let’s review those two analyses and move on to a third. Remembering that the New Testament isn’t a book but is actually a library, our third analysis looks at manuscript support for those 27 books individually.

1. 25,000 New Testament manuscripts sounds more impressive than it is

Yes, there are 25,000 New Testament manuscripts, and that’s more than any other book of antiquity. Homer’s Iliad comes in second place, with 1757 manuscripts. On the other hand . . .

• Only 5800 of those manuscripts are in the original Greek. The rest are translations, are less reliable, and should be discarded in the quest for the best manuscripts.
• Plot a histogram of the creation date of those Greek manuscript copies. There’s an enormous time gap between the original authorship in the first century and most of those copies. On average, it’s over a thousand years. One amusing instance of ignoring this was in the movie The Case for Christ where a priest showed an illuminated page from Homer, emphasizing that it was written 800 years after the original. What he didn’t mention was that 800 years is better than 90 percent of those Greek New Testament manuscripts (my review of that movie here).
• The 5800 Greek manuscripts have now become just the hundred or so from before 400 CE that are closest to the originals.

That argument in detail is here.

2. The chapter-by-chapter dates tell a similar story

Codex Sinaiticus, copied in roughly 350 CE, is our oldest complete New Testament. It is a codex (that is, a book rather than a scroll), and it was written on parchment (rather than papyrus, which was the material used for the earliest copies).

It would be easy to simply point to that manuscript and be done with it, but that would mean a three-centuries-long gap from Codex Sinaiticus back to the original authorship in the first century (as early as the 50s CE for Paul’s epistles to 100 or later for John, Revelation, and many of the other epistles). We can reduce that gap with these early manuscripts but by how much?

I’ve found the date of the oldest manuscript for every chapter in the New Testament and charted the time gap to the original here. Matthew’s per-chapter average from original to oldest copy is 200 years. The per-chapter gap for Mark is a little more and for Luke and John a little less. Note that these early chapters are usually incomplete. If a fragment has only a single verse of a chapter, that counts as a “manuscript.”

The average per-chapter gap for the entire New Testament is close to 200 years. That’s a long dark ages period during a tumultuous time for the Christian message.

(Let me apologize for the upcoming deluge of details in this post. I think you’ll be interested in how the clues fit together, and I’ll try to highlight the conclusions so you can clearly see the finished puzzle.)

3. The per-book number of manuscripts is quite small

And now to the topic of this post: let’s look more closely at that handful of manuscript copies that are Greek and early (made before 400 CE).

New Testament Greek manuscripts are sorted into categories. Papyrus copies, usually scrolls, tend to be the oldest. Parchment copies, usually codices, were written on animal skins. The source data for this table is Wikipedia here and here.

To improve on Codex Sinaiticus, this is what we have to work with. The gospels have a decent number of manuscripts—16 for Matthew and 22 for John—but 16 books have 3 or fewer early manuscript copies, and 3 of those have none.

(I erred on the cautious side when making that table, including all manuscripts from 400 or earlier.)

The Matthew manuscripts

Let’s take Matthew as an example to see how the puzzle pieces come together as we move forward through time. Start with the original Matthew, written in 80. Our oldest manuscript is P104 (papyrus #104), dated to 150. It has 7 fragmentary verses from one chapter of Matthew. Keeping in mind that these dates are just educated guesses, that means that 70 years after the original we have less than 1% of the total.

By 200, we have 4 manuscripts and 3% of the verses of Matthew.

By 250, 9 manuscripts and 13%.

By 300, 13 manuscripts and 16%.

And by 350, we have 20 manuscripts and our first complete one, Codex Sinaiticus. At this point, most verses still have only a single version, but at least we have a copy for each.

The other gospels

The numbers are similar for other books, but there’s a new wrinkle. Early manuscripts of Mark would have just 6 verses (less than 1%) before Sinaiticus except for manuscript P45. Add P45, and now we have 23% of the verses in Mark.

The story is similar with John and Luke. They have a decent number of manuscripts (9 for Luke and 22 for John), but manuscripts P75 and P66 along with P45 probably double their pre-Sinaiticus percentage.

Add in P46, which contains a lot of the epistles, and we see these early manuscripts in a new light. We’re trying to recreate the original book with the oldest manuscripts, and our tools are now one complete codex (Sinaiticus) and four good-sized papyrus fragments (P45, P46, P66, and P75). The remaining 65 manuscripts from before 350 are of secondary importance because they typically hold only a dozen verses or so.

Manuscripts: a closer look

Let’s return to Matthew to look at a couple of manuscripts in more detail. Remember that “by 300 CE, we have 16% of the verses of Matthew” means that we have one or more words of 16% of the verses. Consider Papyrus P62, which has Matthew 11:25–30. That’s it—those six verses are a “manuscript.” But it’s not even that since each of those six verses is incomplete.

And don’t imagine that these early manuscripts do little but boringly validate each other. This summary of the character of manuscript P45 is from E. C. Colwell, a paleographer (expert in ancient handwriting).

As an editor the scribe of P45 wielded a sharp axe. The most striking aspect of his style is its conciseness. The dispensable word is dispensed with. He omits adverbs, adjectives, nouns, participles, verbs, personal pronouns—without any compensating habit of addition. He frequently omits phrases and clauses. He prefers the simple to the compound word. In short, he favors brevity.

This scribe, writing in roughly 250, apparently felt little hesitation to improve the text of the Bible, so we should anticipate that from the scribes of other manuscripts.

If the few manuscripts that we have admit that the early Christian centuries were a turbulent time for the biblical message, we must expect at least the same amount of volatility in the perhaps hundreds of manuscripts that are lost. We can only imagine the changes made in the journey from originals to our best copies.

Conclusions

We’ll pull back from all these details to find some conclusions.

• Let’s review some definitions. “Early” in this domain needn’t be especially early. An early New Testament manuscript could be from 400 CE or earlier, which makes it three centuries or more after the original. “Manuscript” might only be a fragment containing a few verses, and a “verse” need only be a single word.
• Remember that we started with 25,000 New Testament manuscripts and the claim that that’s a far better foundation than any other ancient document. That number became 5800 Greek manuscripts. Then it became the oldest manuscripts, less than 100. And now the focus is on a single complete codex (Sinaiticus, made roughly 300 years after the originals) plus 4 primary papyrus manuscripts with other manuscripts secondary. This is the foundation that scholars use in recreating the New Testament originals. Those scholars do impressive work, but let’s remember the fragmentary evidence they are stuck with. We can’t be certain what any verse originally said. I have a thought experiment that is helpful to make this point.
• Even where we have an impressively old and comprehensive manuscript such as P45, we still have a big confidence gap. P45 was written a long time after the gospels—close to 200 years—and it has a unique voice so that merging it with other sources to recreate the original isn’t a simple process.
• We must be appropriately cautious about manuscript dating. Perhaps you’ve heard about the recent fiasco about a claimed first-century Mark. New Testament scholar Daniel Wallace announced in 2012 that a papyrus manuscript containing a fragment of Mark had been reliably dated to the first century. After six years of rumors (and much bragging by apologists), this manuscript has been re-dated to the late-second/early-third century timeframe. Paleography is a tricky business.
• All this is a process to get back to the original books, but even if we had them, they would still tell an ancient supernatural story with nothing more to recommend it than any other ancient supernatural story.
• Let’s accept the popular apologetic argument that the New Testament manuscripts make a better record than that for any other ancient author—Homer, Thucydides, Herodotus, Sophocles, Julius Caesar, and so on. So what? Nobody much cares if Caesar’s On the Gallic War is full of errors. We don’t take any of their supernatural claims as history, and we certainly don’t use their writings as a template for how to live. A comparison with the Bible is meaningless.

Continue: see this data in visual form here.

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Image from Jakub Kriz, CC license
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