In brief#
The suggestion made in this appendix is that the sheer horror of the traditional picture of hell can have an effect nobody intends: it can quietly lead people to assume they are unlikely to end up there.
The mechanism is a familiar one from how we read gambles. When we are shown two possible outcomes and told nothing at all about the probabilities, we infer the probabilities from the size of the outcomes. The illustration below makes that mechanism visible, and then applies it.
Four games#
The source document presents four games. In each one you either get Outcome A or Outcome B, and in each one the odds are not stated. The question in every case is the same: what do you assume your chances are?
The original was drawn as a chart, which cannot be reproduced here, so it is rebuilt below as a table.
| Game | Outcome A | Outcome B | Presumed odds of Outcome B |
|---|---|---|---|
| Game 1, "The lottery" | Lose 5 dollars | Win 10,000,000 dollars | About 1 in 2,000,000 |
| Game 2, "The coin toss" | Lose 1,000 dollars | Win 1,000 dollars | 50 in 100 |
| Game 3, "The bad lottery" | Lose 1,000 dollars | Win 10 dollars | About 99 in 100 |
| Game 4, "This is all there is" | Lose nothing | Win nothing | Nothing turns on it either way |
The zero-sum assumption, stated plainly#
The figures in the final column are not measurements of what anyone guessed. They are derived, and the derivation rests on one assumption which is stated here rather than hidden: each game is assumed to be zero-sum, meaning that if enough people played it the total value paid out would come to nothing.
Given that assumption the arithmetic is straightforward. In Game 2, a loss of 1,000 balanced against a gain of 1,000 requires even odds, so 50 in 100. In Game 3, a gain of 10 has to be balanced against a loss of 1,000, so the small gain must come up about 99 times for every one time the large loss does. In Game 1, a loss of 5 balanced against a gain of 10,000,000 requires the gain to come up only about once in every two million plays. Game 4 has nothing at stake, so the question does not arise.
The same reasoning is what makes a lottery intelligible. If a ticket costs one dollar and the prize is a million dollars, nobody has to be told the odds. We assume they are about one in a million, and we assume it from the numbers on the ticket alone.
The mechanism#
That is the whole of the mechanism, and it is worth stating on its own:
When no probabilities are given, people infer them from the size of the outcomes. A very large possible gain is read as a sign that the gain is very unlikely. A very large possible loss, set against a modest gain, is read as a sign that the loss is rare.
Shown Game 3 and asked what will probably happen, most people picture winning the 10 dollars. The 1,000-dollar loss registers as the unlucky case, the exception, the thing that happens to someone else.
The application#
Now put the afterlife in place of the games.
Many people picture it along the lines of Game 3 or Game 4. Either the bad outcome is a rare misfortune reserved for the genuinely wicked while the ordinary case is fine, or nothing much is at stake in the first place. Those who hold a higher view of heaven, and who take the traditional doctrine seriously, are closer to Game 2: a positive infinity set against a negative infinity, equal and opposite. Human beings, though, are not able to think in infinities. What we do instead is read the shape of the gamble.
And that is where the suggestion of this appendix bites. If someone's mental picture is Game 3, then Outcome B is the default. Hell becomes the exception reserved for the unlucky or the very bad, and the person concludes, without ever putting it into words, that they will probably be fine. "I have been a good person" is what that assumption sounds like when it is spoken aloud. The effect is not that they disbelieve the doctrine. The effect is that their sense of needing full repentance and trust in Jesus is dulled, because the outcome they need saving from is one they have quietly filed as improbable.
The question the appendix then puts is: how do things change if reality is shaped like Game 1?
In Game 1 the loss is finite and the gain is beyond comparison. Nothing about that shape encourages anyone to assume the good outcome is theirs by default. The reverse: it is the shape that makes people assume the good outcome is rare and must be sought deliberately. That is also the shape of what Jesus says.
13“Enter in by the narrow gate; for wide is the gate and broad is the way that leads to destruction, and many are those who enter in by it. 14Hownarrow is the gate, and restricted is the way that leads to life! Few are those who find it.
An objection the author raises against himself#
The author anticipates a complaint about his own chart: that Outcome A in Game 1 is drawn disproportionately small, and that this loads the illustration in his favour.
His answer is twofold. First, any finite number is small when set beside negative infinity, and equally small when set beside positive infinity, so the complaint applies to any finite figure one might have chosen. Second, when both options are laid out together, no one is going to look at a loss of 5 dollars standing for finite punishing and a gain of 10,000,000 dollars standing for eternal life and conclude that the loss is an acceptable trade.
It is worth adding one caveat of the same kind. The dollar figures throughout are stand-ins for quantities the rest of this site treats as incomparable to money, and in the case of eternal life as unbounded. The arithmetic should not be pressed. It is there to make the mechanism visible, and it does not survive being taken literally.
What this illustration establishes#
- When probabilities are withheld, the magnitude of the outcomes influences the probabilities people assume.
- That mechanism gives a coherent reason why an extreme picture of final punishment might make some people quietly assume they are unlikely to face it.
What it does not establish#
- Anything at all about what Scripture teaches. This is an analogy, and an analogy is not evidence.
- Any measured claim about what people in fact believe about their own destiny. No such measurement is offered.
- Any claim that defenders of the traditional doctrine intend this effect, or that they are careless about repentance. The suggestion concerns hearers, not preachers.
Related sections and passages#
- Hell is not the opposite of heaven, which is where the underlying point about symmetry is argued.
- Why this question matters.
- The net outcome of humanity illustration, the companion appendix.
Sources and notes#
The games, the figures and the presumed odds are all taken from the source document, whose original charts are not reproduced here. The table above reconstructs them.
[Welch]