Yesterday, I offered a Toy Model of how God could give infinite chances to someone and they could still reject him. The crucial assumption of the model was that it might take multiple good choices to dig oneself out of the moral hole that one’s wickedness got one into.
But one can also have a model without that assumption. Suppose that every day I make a choice for or against God. If I choose for God, I am saved and God makes me virtuous. If I choose against God, I become habituated into a bit more vice. How much more? Well, we can measure a person’s virtue by how likely they are to choose for God. So let’s suppose that there is some number β strictly between 0 and 1 such that each time I choose against God, my goodness—as measured by the probability of my next choice being for God—is multiplied by β. We can think of β as a kind of wicked habituation constant.
What is the probability that I will always reject God? Suppose my initial level of goodness is α. Then the probability that I will reject God on day 1 is 1 − α. If I do that, then on day 2 my level of goodness will be αβ, and the probability that I will reject God will be 1 − αβ. And if I do that, then on day 3 my level of goodness will be αβ2, and the probability that I will reject God will be 1 − αβ2. So the probability that I will always reject God is:
- P(R∞) = (1−α)(1−βα)(1−β2α)....
Easy mathematical fact: as long as α < 1 (i.e., I am not maximally good on day 1) and β < 1 (the bad choice does decrease my goodness), P(R∞) is bigger than zero. In other words, on this model, I have infinite chances, and each choice has the possibility of resulting in my complete redemption, and yet I have a non-zero probability of choosing badly for eternity.
Let’s make up some conservative numbers. Suppose the infinite chances
regimen starts with death, and that β = 0.99: one gets 1% worse each
time one chooses against God—and that’s 1% of my previous level of
goodness, rather than an absolute 1%. Presumably people die with various
levels of goodness between 0 and 1. Suppose one in a thousand people dies with
a goodness level α ≤ 0.1. Now
if one has goodness level α = 0.1 when one starts the infinite
chances regimen at death, and β = 0.99, it turns out (or so
Mathematica calculates QPochhammer[.1,.99]) that the
probability of damnation is about 0.000035. So with 8 billion people,
there would be 8 million dying with goodness level at most 0.1, and so we might well expect at least
8, 000, 000 × 0.000035 = 280 of them to
be damned even if they got the infinite chances regimen. So on this toy
model, we would expect some people now alive to be damned.
Now it seems plausible that it is compatible with God’s goodness that he would allow one in a thousand people to die with a goodness level of 0.1, and that he would allow a character deterioration of at least 1% per posthumous choice against God—this would give people a real ability to affect their character, while yet being very generous with redemptiveness. In other words, even on an infinite chances model, it is compatible with God’s goodness that hundreds of people be forever separated from God. But if hundreds of people damned is compatible with God’s goodness on an infinite chances model, why wouldn’t hundreds of people damned also be compatible with God’s goodness apart from an infinite chances model, as long as it was also a model where God is very generous in redemptiveness and gives people a real ability to affect their character?
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