In brief#
The argument asks a single question: if you added together everything every human being will ultimately experience, what would the total be?
It sets out four quantities, proposes an equation relating them, and then runs the equation twice, once on the assumptions of eternal conscious torment and once on the assumptions of conditional immortality. The two runs give opposite signs. Whether that means anything is a separate matter, taken up at the end.
The four quantities#
| Term | Meaning |
|---|---|
| Number in hell | How many people end in the destiny of the lost. |
| Number in heaven | How many people end in the destiny of the saved. |
| Value of hell | The overall net value of the experience of the lost destiny, for one person. A negative quantity. |
| Value of heaven | The overall net value of the experience of the saved destiny, for one person. A positive quantity. |
The proposed equation#
In words:
The number in hell multiplied by the value of hell, plus the number in heaven multiplied by the value of heaven, equals the net outcome of humanity.
In shorter form:
(Number in hell × Value of hell) + (Number in heaven × Value of heaven) = Net outcome of humanity
What that means in ordinary language is simply this: all the goodness experienced in heaven, added to all the badness experienced in hell, gives the net result of the whole human experiment.
The premise about the numbers#
One further premise is needed before the equation can be run, and it comes from Jesus.
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.
Few find the narrow way that leads to life; many take the broad road that leads to destruction. Taken at face value that means the number in heaven is smaller than the number in hell.
[Welch]Case one: the assumptions of eternal conscious torment#
On a strongly symmetrical version of the traditional view, hell is the equal and opposite of heaven: a negative experience of unbounded duration set against a positive one.
So the value of heaven is positive infinity, and the value of hell is negative infinity, which is to say it is the value of heaven multiplied by minus one.
Substituting that into the equation, the two terms can be gathered together, and what is left is the difference between the two head counts multiplied by the value of heaven:
(Number in heaven minus Number in hell) × Value of heaven = Net outcome of humanity
Since the number in heaven is the smaller of the two, the bracket is negative. Multiplied by an unbounded positive quantity, the result is negative without bound. On this branch, the net outcome of humanity is negative infinity.
Case two: the assumptions of conditional immortality#
On the conditionalist view the consequence of hell is finite, and the greatness of heaven far surpasses it.
15But the free gift isn’t like the trespass. For if by the trespass of the one the many died, much more did the grace of God, and the gift by the grace of the one man, Jesus Christ, abound to the many. 16The gift is not as through one who sinned: for the judgment came by one to condemnation, but the free gift came of many trespasses to justification. 17For if by the trespass of the one, death reigned through the one; so much more will those who receive the abundance of grace and of the gift of righteousness reign in life through the one, Jesus Christ. 18So then as through one trespass, all men were condemned; even so through one act of righteousness, all men were justified to life.
So the value of heaven is unbounded and positive, while the value of hell, however severe, is a finite negative quantity. The negative of the value of hell is therefore much smaller than the value of heaven, and this remains true even after both are multiplied by their head counts, because a finite number multiplied by a finite value stays finite while the other side does not.
The hell term is therefore negligible against the heaven term, and the equation reduces to:
Number in heaven × Value of heaven, approximately equals the net outcome of humanity
On this branch the net value of the end state of humanity is positive without bound.
The assumptions, stated honestly#
The two branches give opposite answers. It would be easy to present that as a result. It is not one, and the reasons are worth setting out plainly.
- The arithmetic on infinite quantities is informal. Multiplying a finite head count by an infinite value, and subtracting one infinite quantity from another, are not well-defined operations in standard mathematics. The step that gathers the two terms in case one, and the step that discards the hell term in case two, both treat infinity as though it behaved like a large number. It does not. These are illustrations of a shape, not proofs.
- It assumes experiences can be summed across persons. The equation supposes that one person's joy and another person's misery are quantities of the same kind, which can be added and subtracted. That is a substantial philosophical commitment, and many would not grant it.
- It assumes both head counts are finite. Nothing establishes that, and the equation behaves very differently if either is not.
- It assumes the values can be signed at all. Calling the experience of the lost a negative number, and that of the saved a positive one, is a modelling choice, not something Scripture states.
- A net total may not be the right question. Even if every step worked, it is not clear that God's justice is the sort of thing that shows up in a total.
The author's closing note#
The author adds two qualifications of his own.
The first is that it is not all about humanity. The glory of God could be factored in as a further term, though he does not think that term would differ between the two views, so it would not change the comparison.
The second is that a more complicated formula could divide experience into a quality part and a duration part, and could include earthly experience alongside the final state. He expects the resulting equations would simplify the same way, because infinity is involved either way.
What this illustration establishes#
- Under a symmetrical view of the two destinies, and given that the lost are the larger group, the summed outcome is dominated by that larger group.
What it does not establish#
- Anything about what Scripture teaches. The author says this himself, in capitals, at the head of the original.
- That arithmetic on infinite quantities of this kind is well defined, or that the steps above would survive a rigorous treatment.
- That defenders of the traditional view are committed to the symmetry premise the first branch requires. Many are not.
Related sections and passages#
- Hell is not the opposite of heaven, where the symmetry question is argued from Scripture rather than from arithmetic.
- How our view of the outcomes shapes our assumptions, the companion appendix.
Sources and notes#
The definitions, the equation, both branches and the closing note are taken from the appendix of the source document. The statements of assumption above are editorial, so that the argument is not mistaken for a proof.
The source document cites the narrow-way saying as Matthew 7:13-24. That appears to be a slip for Matthew 7:13-14, which is the passage the argument uses, and the corrected reference is given above.
[Welch]