If an argument is unsound, then the claims it makes do not “follow” even though its premises are true.
For example, if I argue, “If pigs cannot fly, then I am the fastest runner on Earth,” the truth value of “I am the fastest” does not emerge “for free” even if pigs are indeed unable to fly.
I’m going to talk about an unsound argument today. The first written evidence we have of this argument is from St. Augustine of Hippo, the most significant (sometimes for better, sometimes for worse) early theologian of his time (the late 4th and early 5th centuries).
Augustine and Endless Hell
In his Enchiridion, Augustine wrote much about his views of hell. Augustine was a proponent of the doctrine of endless hell, as are most Christians today. (It wouldn’t be very reckless to posit that Augustine was the person most evidently responsible for the ubiquity of belief in the doctrine, as well as the Catholic doctrine of Original Sin.)
In Augustine’s day, however, there were a bunch of Christians who didn’t believe in endless hell. These were genuine Christians who were purgatorialists, in the vein of St. Gregory of Nyssa, which means they believed fully in hell — an agonizing, humiliating, to-be-avoided destination — but that it was a remedial punishment.
(One of three major views in the ancient Church, alongside annihilationism and “endless hell.”)
St. Gregory of Nyssa, “On the Soul and the Resurrection,” 4th century:
“… It will be useless to talk of [the contingency upon earthly failures] then, and to imagine that objections based upon such things can prove God’s power to be impeded in arriving at His end.
His end is one, and one only; it is this: when the complete whole of our race shall have been perfected from the first man to the last—some having at once in this life been cleansed from evil, others having afterwards in the necessary periods been healed by the Fire… to offer to every one of us participation in the blessings which are in Him, which, the Scripture tells us, “eye has not seen, nor ear heard, nor thought ever reached.”
… But the difference between the virtuous and the vicious life led at the present time will be illustrated in this way: In the quicker or more tardy participation of each in that promised blessedness. According to the amount of the ingrained wickedness of each will be computed the duration of his cure. This cure consists in the cleansing of his soul, and that cannot be achieved without an excruciating condition, as has been expounded in our previous discussion.”
St. Augustine admitted, in Enchiridion, that there were a great many Christians in his day who were purgatorial universalists like St. Gregory was. He also admitted that they weren’t in outright defiance in Scripture, but opined that their position was driven by soft-hearted “human feelings.”
A purgatorial universalist might ask him, “Why would God blanket-punishment all of the unsaved regardless of their individual infractions?”
Augustine’s answer was that there were a variety of intensities of hell, and that certain folks might get what amounted to “lunch breaks” in hell; “Let them suppose… that for certain intervals in time, the punishments of the damned are somewhat mitigated.”
A purgatorial universalist might ask him, “Why, then, do we pray for the dead, that they might escape a measure of their punishment?” Augustine had some creative eschatology here, and it worked like this:
- Imagine that if you have a “score” of +1 to +10, you’ll be saved.
- If you have a score of -10 to 0, you’ll go to hell forever.
- In life, you merit a score “window” on the bad-good scale like, “-9 to -6,” or “-2 to +2,” or “+7 to +10.”
- Prayers, sacrifices, alms, etc. for the dead could push a person higher in their window.
- If your window wrapped around the midpoint, prayers could potentially push you up into salvation.
- The higher you are, the better off you are, since “hell for -10 people” would be worse than “hell for -1 people.”
“Where they are of value,” Augustine wrote, “their benefit consists either in obtaining a full forgiveness or, at least, in making damnation more tolerable.”
Already, you can probably see how these answers aren’t very satisfying. In my experience, and I think the honest experience even of believers in endless hell, most “creative” formulations of how endless hell might address the difficulties it poses are, indeed, unsatisfying.
Isn’t God, Ultimately, Merciful?
The purgatorial universalist then says, “But Scripture says that he has bound everyone — Jew and Gentile — over to disobedience in order to have mercy on them all (Romans 11:32); he deliberately subjected creation to frustration in the hope of redemption and as part of a creative process (Romans 8:20-22).”
Augustine’s response is that the Bible’s references to God’s ultimate, winning mercy must only be in reference to the few who will be saved from punishment.
This “must” is presented as contingent on the soundness of the following argument, again from his Enchiridion:
“Even so, if they suppose that the text applies to all men, there is no ground for them further to suppose that there can be an end for those of whom it is said, ‘Thus these shall go into eternal punishment.’ Otherwise, it can as well be thought that there will also be an end to the happiness of those of whom the antithesis was said: ‘But the righteous into eternal life.'”
Purgatorial universalists do not translate Heb. olam or Gr. aion/aionios/aionion as “eternal” or “everlasting.” Rather, these words mean “age-pertaining,” often with overtones of significant gravity or broad domain.
This determination proceeds from the variety of olams in the Bible that do not refer to everlasting things, and from the fact that many of these olams are brought across, in the Greek Septuagint, as aion/aionios/aionion.
A few examples:
Isaiah 63:11 (portion)
- From Hebrew: “His people of Moses of the old [Heb. olam] days, he remembered.”
- From Septuagint: “And he remembered days of old [Gr. aionion]; the bringing up from the land the shepherd of the sheep.”
Genesis 6:4 (portion)
- From Hebrew: “In those days in the earth were Nephilim, renowned men of old [Heb. olam], mighty men.”
- From Septuagint: “Those were giants, ones from the eon [Gr. aionos], renowned men.”
Isaiah 42:14 (portion)
- From Hebrew: “I have been still for a length [Heb. olam], held my peace.”
- From Septuagint: “I kept silent from the eon [Gr. aionos], shall I also continually keep silent and endure?”
Here’s the unfortunate reality: Because belief in endless hell is nearly universal among Christians, and has been so for 15 centuries, tertiary translations of the Bible feel no impetus to keep their olams and aions vague; when it comes to the kolasin aionion, they nearly all read, “everlasting punishment.”
But not all translations do this. For example, the literal translations of Young and Weymouth are careful to temper themselves on the issue.
Compare Matthew 25:46 from the NIV, from Young’s Literal, and from Weymouth’s Literal:
- (NIV) “Then they will go away to eternal punishment, but the righteous to eternal life.”
- (Young’s Literal) “And these shall go away to punishment age-during, but the righteous to life age-during.”
- (Weymouth’s Literal) “And these shall go away into the Punishment of the Ages, but the righteous into the Life of the Ages.”
At this point, even staunch believers in endless hell generally admit that the “everlasting” or “eternal” translation is a bit reckless. But they are quick to invoke Augustine’s above argument.
So, without begging the aion question, is Augustine’s argument sound? Does this same-sentence comparison show us that the kolasin and zoen must be of equal time duration?
Can’t Beg That Question? Can’t Reach That Conclusion.
Imagine that “aionion” meant “intense,” just for a moment.
The verse would read,
- “Then they will go away to intense punishment, but the righteous to intense life.”
Would we then argue that the punishment and life must be equal in time duration? No. We’d say, “This verse says they are both intense. It does not say that they are of equal time duration.”
Imagine that “aionion” meant “astounding,” just for a moment.
The verse would read,
“Then they will go away to astounding punishment, but the righteous to astounding life.”
Would we then argue that the punishment and life must be equal in time duration? No. We’d say, “This verse says they are both astounding. It does not say that they are of equal time duration.”
Imagine that “aionion” meant “divine,” just for a moment.
The verse would read,
“Then they will go away to divine punishment, but the righteous to divine life.”
Would we then argue that the punishment and life must be equal in time duration? No. We’d say, “This verse says they are both divine. It does not say that they are of equal time duration.”
Now let’s use “aionion” how it ought to be prudently rendered: “age-pertaining.”
“Then they will go away to punishment of the ages, but the righteous to life of the ages.”
Should a person argue that the punishment and life must be equal in time duration? No. We should say, “This verse says they are both pertaining to ages; it may simply mean that they will both last a long time (finite in one case, infinite in the other). Or maybe it has nothing to do with duration, and simply means that both will take place at the consummation of the ages, the age to come after the general resurrection. Or perhaps it refers to the aionios zoe of the Kingdom of God, the age under which its subjects finally come to know the Father and his Son (John 17:3) and where the self-righteous hold-outs are excluded (Matthew 21:31-32). In any case, it does not suggest that they are of equal time duration.”
Put Very Simply
Here’s a very simple way to understand what’s going on here.
- (1) Given: X has the property A, and Y has the property A.
- (2) Given: X has the property B as well.
- (3) Question: Does that mean that A = B?
- (4) Question: Does that mean Y has the property B?
The answer to both questions is, “No way!”
“Y has the property B” if and only if we have “A = B” as a given.
Thus, Augustine’s argument is unsound, as are unsound all modern repetitions of his argument.
“I Believe the Bible over Xs, Ys, As, & Bs”
Okay. Here’s proof, straight from the Bible, that “forever-ness” does not “pop out” of olam parallelism.
- “He stood and surveyed the earth; he beheld and drove the nations asunder; the everlasting (adah) mountains were scattered, the olam hills bowed low; His ways are olam!”
Keep reading that verse, noble Augustine, until the unsoundness of the argument is ascertained.
(For another exercise that demonstrates this unsoundness, see “The Gift Game & Prudent Hermeneutics.”)
Let’s learn the Mountain Game! It’s the hottest board game around.
The Mountain Game board looks like this:
Its rules are as follows:
- You begin at [START HERE]. This is the “start.”
- You advance upward, one space at a time.
- You must follow all given instructions on visited spaces.
- If you modify the board — or break the rules, or change the rules — of the Mountain Game, including by means of whatever creative semantic or temporal trickery, you lose. That is, there is a “modal spy helicopter” that “sees” any attempt to change the game and declares “This now a different game” upon “seeing” that modification.
A Mountain Game is any challenge defined by the fact that it cannot be met. If someone claims they have won a Mountain Game, you know for 100% certain that they are lying, no matter how powerful they are or what freedom they claim to have.
Let’s say you think you’re playing Five Card Draw, no wilds. You ship some cards and get some back, and end up with a measly pair of deuces.
This isn’t looking so hot. You’ve been bluffing a great hand this round, and don’t have the goods to back it up.
“Oh, we forgot to tell you,” says your friend Harriet, “Bernice is dealer and — while you were in the kitchen — called this round as deuces wild.”
What? Deuces wild? Just as you’re about to complain that the whole round was contaminated, you suddenly realize that with deuces wild, you have a royal flush!
The Utility of Wildcards
Wildcards are extremely useful. They can turn weak hands into kingmakers. They can turn low pairs into royal flushes.
Their power is that they don’t mean anything discrete and coherent unless and until they’re integrated into a final, optimal hand resolution. At that moment, they mutate and solidify into whatever the player pleases.
There is an analogous object, with analogous utility, in logic and rhetoric. Any claim that has no discrete and articulable truth value can qualify, and there are many ways that a claim can be “amorphous” in this manner.
- A claim may be many-faced. “My car is pleasing.” Well, what does that mean? Jake could call his car pleasing, when it doesn’t even work, but looks nice in his driveway. Vera could call her car pleasing, when it looks like junk, but performs great on the road.
- A claim may be nonsensical. “My house is a thing against which there house is no house my house isn’t my house in transcendence, cannot it being.” The preceding sentence probably invokes various images in your mind’s eye, but it does not cohere, and thus can’t have a truth value.
- A claim may be otherwise vague, unclear, ambiguous, or wide open to interpretation.
- A claim may have a hidden referent. The many-faced example above is also a good example here. If the referent is explicated (what pleases Jake versus what pleases Vera), it can cohere. But as long as the question is without its necessary referent, it lacks a truth value. Subjective claims that are mistakenly put into objective language are very often guilty of this referent-lacking problem.
If any of these problems are present and yet are undetected, and treated like coherent and solid claims with discernible truth values, they can mutate and solidify around whatever the hand-holder desires.
Cheryl is late to my party, and I’m worried that she might be lost. In a misguided effort to comfort me, Brent claims the following:
- “Cheryl is flawless at finding a house if she knows its address.
- Thus, Cheryl is not lost.”
Of course, at this point, I think, “But what if she doesn’t know my address?” Brent suspects I might be thinking this, but doesn’t himself know whether she has my address or not. So he tells me something deliberately vague:
- “Cheryl has quasi-panomic knowledge.”
What does that even mean? Further inquiry yields only more such strange statements from Brent, each more unclear than the last, but all in supposed service of clarifying that odd term.
He hopes that I will eventually give up and accept his statement as a bridge. This happens when the images conjured by what he’s saying — a sense of “knowledge” and “full,” at least — come to a rest at some inferred coherent place, like, “She has my address.”
But I refuse to quit, and shout, “Brent! Does she have my address or not?”
“I’m trying to tell you the answer to that!” he says, “You see…” and then continues with the ambiguity.
Now, instead of coming to rest at something vaguely conjured, I can instead say, “Brent, what you’re saying is not cohering. So while it might express some manner of truth, I can’t use it as a premise in service of any conclusion.”
Soon, Brent appears to be drunk. “How many drinks have you had, Brent?” I say.
“Eight,” he says.
“In an hour??” I say.
“Yeah,” he answers.
“You’re drunk,” I proclaim.
“No I’m not! I’ve got a just-firm and nigh-set constitution,” he says.
“A ‘just-firm and nigh-set constitution?'” I ask.
“Absolutely,” he responds. “It means that eight drinks in an hour does NOT mean that I’m drunk. Such a thing would be unthinkable.”
I press him for a more dissected meaning of “just-firm and nigh-set constitution,” in order to determine whether he “has that,” whatever it is, but only ambiguity and dangling references (like circular references) come forth.
How on Earth can I determine whether he has the thing that invalidates my conclusion when the thing’s definition is “that which invalidates your conclusion” and nothing more?
Now, instead of coming to rest at the vaguely-conjured image of someone exceptionally tough who can hold a lot of alcohol without issue, I can instead say, “Brent, what you’re saying is not cohering. So while it might express some manner of truth, I can’t use it as a premise that would stop the accepted premises — how many drinks you’ve had in this period of time — from yielding the conclusion that you’re drunk.”
These examples are rather silly, but in the abstract and confusing worlds of philosophy and theology, Brents abound.
And they’re incentivized to proliferate! Wildcard-loaded hands are “better.” And confusion, “subjective-as-objective,” and ambiguity all yield exciting conversations in fruitless attempts to reach cohesion.
This is especially the case in theology, where it is accepted and acknowledged that various revelatory statements are mysterious and beyond our comprehension. The error comes when those mysteries are treated as non-mysteries for the purposes of bridge-making and bridge-breaking.
As believers, we hold to revealed mysteries faithfully. But we should regard them with enough humble reverence not to treat them like pilons or sledgehammers.
In the meantime, if someone employs some strange term as a premise and refuses to articulate it in a coherent way, treat that term like it’s toxic glowing green and reject their logic until they take a break and figure out what they’re trying to say.
This video, called “The Difficult Ds we Get for Free,” talks about how formal logic gets us “free truth” as corollaries of benign premises, but how the “dirty tricks” of ambiguity can be used as logical wildcards.
“No True Scotsman” is a rhetorical trick where you modify the definition of something on-the-fly to rebut someone’s claim of an exception.
- Let’s say I proclaim, “All Scotsmen love haggis.”
- A person might say, “I’m a Scotsman, and I hate haggis.”
- I could then claim, “Well, then you aren’t a true Scotsman. True Scotsmen love haggis.”
Some Christians pull a version of this maneuver when confronted with the deplorable and regretful actions of various historical Christians.
It works a bit like this:
- Dave says, “Christians always do good things.”
- Jill says, “How can you say that? What about the forced conversions, burning of heretics, and wars of religion we see perpetuated by Christians throughout history?”
- Dave replies, “The people who did those awful things weren’t true Christians.”
This isn’t to say that this is always a trick. Sometimes, the intent isn’t to perform a rhetorical evasion, but to clarify the particular sense of the word they were originally employing.
In the above, it may be that there are two definitions at play:
- Jill’s definition of “Christian” is probably in the sense of outward and visible declarations of belief and/or allegiance. In this way, many people responsible for unimaginable atrocities have declared belief in Christ and themselves to be Christians.
- Dave’s definition of “Christian” is probably in the sense of an inward and relatively invisible state of an individual and her genuine relationship with Christ, which ostensibly prompts her to act charitably as she is being sanctified by his Grace. When a person commits an atrocity, then, it is a spike of evidence that they are not a Christian in this sense.
I believe that Jill’s approach is much better than Dave’s; Dave’s hinges on “unclear genuineness” which is toxic for communication.
EDIT: It’s been several years since writing this, and I now believe both approaches foster communication problems, and the Quiet solution is to use both ways every time and be boringly thorough. Using only one way causes Loudness (which might be your desire; here, spurred engagement at the expense of the clear thinking and relationships of those engaged).
A reductio ad absurdum — I’ll call it “RAA” for short — is when you argue against someone’s claim X by showing that, if X was true, something obviously absurd would also be true.
In other words, as illustrated in the above image, “If the premise was true, the logical implications would be crazy.”
Lisa and George’s Thermometer Collection
Lisa and George are watching it rain.
“Gross, rainy weather lately,” says Lisa. “How cold do you think it is out there?” asks Lisa.
“Maybe 25, 30,” replies George, speaking Fahrenheit.
“What!?” Lisa exclaims. “If it were that cold, it’d be snowing, and we’d be hallucinating! And that’s absurd!”
Pretty straightforward, right? It’s absurd that they’re both hallucinating the rain, and so it mustn’t be 25-30 degrees; 32 is the freezing point in Fahrenheit.
“Alright, let’s check,” says George. They walk out to the back porch and look at the thermometer outside. “See?”
Just as George guessed, it was 29 degrees outside.
“The thermometer must be broken,” said Lisa. “Let’s check the one we have on the front porch.” But, sure enough, the front porch thermometer said 29, too.
Same with the thermometer just outside the kitchen window.
“They can’t all be broken in exactly the same way,” says George. “That’d be absurd.”
It turns out that, from the outset, Lisa was unaware of the fact that temperature can vary in different layers of atmosphere. If it’s warmer above the surface, rainfall may not have time to freeze before hitting the ground, even though it’s passing through a sub-freezing layer.
In other words, learning more about how the world works and doesn’t work can make the difference between some RAA being thought false versus true.
Furthermore, sometimes RAAs are just “non sequiturs,” which means that they don’t logically follow, e.g., “If it was 25-30 degrees outside, all morality would be invalid.”
That’s an obvious one, but non sequiturs are often very subtle. Recognizing non sequiturs where they exist can also make the difference between some RAA being thought false versus true. My own record is spotted with many infractions for criminally using non sequitur RAAs! But I’ve done my share of repentance. (And this is my penance.)
Earlier, I wrote about a specific kind of non sequitur — where you think the world is “too rocked” by a world-rocking revelation — and called it “Kochab’s Error.” Kochab’s Error is often used in an attempt to argue ad absurdum.
Kochab was a cartman who made his living ferrying travelers back and forth between Rome and Constantinople. Each trip took two weeks, but this was much faster than the road by foot, and passengers were eager to pay for his services.
Kochab found the life of a conveyor, while lucrative, rather mundane in and of itself. And so, even though he was an otherwise simple man, Kochab would endeavor to visit and listen to learned people, in both great cities, in order to spark his own imagination and spur contemplation, occupying his thoughts during his back-and-forth journeys.
One day, he attended a lesson by a famous astronomer in Constantinople named Al-Udhi.
“We imagine the Earth as being great in size, and the center of the universe,” said Al-Udhi. “When we look at the starry sky, the cosmos appears as a dome that is not so far away.”
“But these are mere appearances,” explained Al-Udhi. “Through careful observation and mathematical calculation, we have discovered that the earth is not the center of the universe; and the stars are very, very far away indeed; and the size of the earth is very tiny compared to the great size of the cosmos.”
This was startling to Kochab. Al-Udhi was right: Kochab did imagine the earth to be great in size, and the center of the universe. Before, the earth felt very, very large indeed to him. In the eye of his mind, the earth dominated the entirety of the cosmos, filling it up with bright blue and green; but now the artwork of his imagination was full of darkness, littered with stars, with a lonely, miniscule earth in one corner.
To Kochab, it felt as if the earth had shrunk.
So convincing to Kochab was this feeling that he fell into despair, cursing Al-Udhi for spreading this news. “Who now will need my services?” Kochab lamented. “The world is so small, and thus Rome and Constantinople so close together, that one might as well walk!”
A realization about the world, and how it is, or how it works, may prompt a significant paradigm shift in one’s conceptions. When such a jostling happens, it’s human propensity, upon being spurred to re-evaluate, to go “too far.” We might not be as silly as Kochab, but humans conclude non-sequitur conclusions all the time, and especially when their worlds are rocked like Kochab’s.
Furthermore, if that “too far” conclusion is an absurdum, we’ll be extra-likely to reject the paradigm shift at the outset, even though that conclusion is “too far” (a non-sequitur), and that paradigm shift is worth adopting!
In subsequent posts, I’ll talk about difficult conclusions we get “for free” from benign premises. Difficult conclusions often “rock worlds” and prompt non-sequitur absurdums. I’ll be referring to Kochab’s Error in those upcoming posts and linking back here. Keep an eye out!