Friday, January 18, 2019

Very large multiverses and trans-world depravity

Consider this standard bit of dialectic. One gives a Free Will Defense relying on the logical possibility of Trans-World Depravity:

  1. TWD1: In every feasible world, some significantly free creature sins at least once.

But the response is: “Yes, this shows that the existence of God is logically compatible with moral evil, but since TWD is exceedingly unlikely to be true, this does not help to counter the argument that it is exceedingly unlikely that God would create a world with no moral evil.” (Note: TWD1 is logically weaker than Plantinga’s TWD but does the job just as well. Cf. this.)

Why think TWD1 unlikely to be true? Well, confine our attention to strongly actualizable world cores (i.e., the aspects of the world that God would strongly actualize) containing involving a hundred independent significantly free choices with agential motives balanced between good and evil. For any such world core, the chance that all the choices would go right if the core were strongly actualized is something like (1/2)100. So we would expect one in 2100 such world cores to have the counterfactuals of freedom come out favorably, i.e., with all the choices being right. But there are infinitely many such world cores—each with a different collection of agents (to ensure independence between the counterfactuals holding of each core)—and so the probability that in some core the counterfactuals come out right should be extremely high (namely 1, given real-valued probabilities).

Now here is an interesting next step in that dialectic. Instead of working with the TWD, work with this:

  1. TWD1: In every feasible world containing uncountably infinitely many significantly free choices, at least one of these choices is wrong.

And then add the plausible intuition that it is likely that God would want to create a world with uncountably infinitely many significantly free choices (e.g., because he would probably want to create uncountably infinitely many significantly free people, perhaps in a multiverse).

The improbability response is much harder to make against TWD1 than against TWD1. Remember that the argument against TWD1 worked by generating a sequence of worlds with independent conditionals of free will each of which had a probability of (1/2)100 of being a counterexample to TWD1. But we can’t do that with TWD1. Given an uncountable infinity of significantly free choices, we would expect the probability that all these choices would be right if the world core were actualized is zero: it’s logically possible, but it’s even less likely than tossing a fair coin for every day of an infinite life and getting heads each time (for an infinite life would have countably many days). Granted, there is an uncountable infinity of world cores to try. But if the chance of each one being a counterexample to TWD1 is zero, without some special argument we can’t assume there is a meaningful and high probability that at least one is a counterexample.

Technical note: I opted for worlds with uncountably infinitely many significantly free choices, because if the worlds had countably infinitely many significantly free choices, it might be possible to make the “it’s extremely unlikely” argument go. Imagine a countably infinite sequence of independent significantly free choices, where the nth choice has probability 1 − 2n of going right. Then the probability that all the choices will be right is actually about 0.29. Using worlds like that, one could produce an argument that TWD0 (i.e., what we get when we remove “uncountably” from (2)) is very unlikely to be true.


scott said...

Very cool argument.

Walter Van den Acker said...


"TWDℵ1: In every feasible world containing uncountably infinitely many significantly free choices, at least one of these choices is wrong."

All of these TWDs make the same basic mistake. They assume that God, who is omnipotent, cannot create significantly free creatures who will never sin.
Sure, that is also "logically possible", but given the claim that this God is capable of even absurd things like creating stuff ex nihilo while being immutable, this is extremely unlikely.
What TWD proponents are actually claiming is not just that God would probably want to create uncountably infinitely many significantly free people, perhaps in a multiverse, but that God wants to create free people who can sin and no free people who can't sin.
And the question is: can such a God be called 'good'?

Alexander R Pruss said...

Well, if one is an incompatibilist, it doesn't seem a limitation on omnipotence. To an incompatibilist like me, it seems nearly obvious that no one else can guarantee a particular outcome of a free choice, by the very nature of "free choice". The alleged limit on omnipotence, then, is not very different from that imposed by the fact that God cannot make an uncreated rabbit.

Walter Van den Acker said...


An uncreated rabbit is, given theism, impossible. A significantly free creature who never sins isn't. Unless significantly free entails the possibility to make evil choices, of course, but it clearly doesn't because God is said to be significantly free yet cannot make evil choices.
Making evil choices is due to a defect. Non-defective creatures do not make evil choices.

Alexander R Pruss said...

I am not sure Plantinga would say that God is significantly free in Plantinga's sense of the phrase "significantly free". A significantly free choice is a choice between the right and the wrong. I don't think God chooses between the right and the wrong.

Walter Van den Acker said...


"A significantly free choice is a choice between the right and the wrong" is a question-begging definition. Of course if God wants people to choose between the right and the wrong, then the significant feedom He creates should entail the choice between right and wrong.
But the question is why would a God who is supposed to be perfectly good even "contemplate" "the wrong"?
If God truly is Existence, this kind of anthropomorphism has no place.

Alexander R Pruss said...

Plantinga is clear that his definition is stipulative. Yes, God doesn't even consider the wrong an option, and hence doesn't choose between right and wrong.

The philosophical question then is whether significant freedom, defined as Plantinga defines it, has significant value in creatures. The fact that God lacks significant freedom is evidence to the contrary. But there is a bunch of papers arguing that there are relevant differences between God and creatures such that it's not valuable in God but is valuable in creatures. That's an interesting debate, but not one I am addressing in this post.