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:

2. TWD_ℵ1: 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 TWD_ℵ1 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 TWD_ℵ1. 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 TWD_ℵ1 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 − 2⁻ⁿ 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 TWD_ℵ0 (i.e., what we get when we remove “uncountably” from (2)) is very unlikely to be true.

Against the actual truth of transworld depravity

Here is an interesting result. If the Biblical account of creation is true, then Plantinga’s Trans-World Depravity (TWD) thesis is false. All this doesn’t affect Plantinga’s Free Will Defense which only needs the logical possibility of TWD, but it limits its usefulness a little by making clear that the defense is based on an actually-false assumption. (Quick review: Plantinga uses the logical possibility of TWD to argue for the logical possibility of evil. That argument would survive my critique. But he also suggests that TWD is epistemically possible, and hence could be the heart of a theodicy. That move does not survive, I think.)

I’ll take TWD to be:

1. Every significantly free creature in every feasible world does wrong.

A feasible world is one that would eventuate from God’s strongly actualizing the strongly strongly actualized portion of it.

But now consider this thesis which is very plausible on the Biblical account of creation:

2. At least one human made a significantly free right choice before any human made a free wrong choice.

For the first sin in the Biblical account is presented as Eve’s taking of the forbidden fruit in Genesis 3. But prior to that, indeed prior to Eve’s creation, Adam was commanded to take care of the garden (Gen. 2:15). It would have been a sin for Adam to fail to do that, and since this was before the first sin, it follows that Adam must have done it. Moreover, Adam being a full human being presumably had freedom of will, and hence was capable of refusing to work the garden. Hence Adam’s decision to obey God’s command to work the garden was a significantly free choice before any human made a free wrong choice.

Now, I don’t take the story of Genesis 2-3 to be literally true, but it tells us basic truths about the entry of evil into the world, and hence it is very likely that the structural claim (2) carries over into reality from the story.

I now argue that:

3. If (2) is true, then TWD is false.

Right after the first human made a significantly free right choice, God had the power to prevent any further significantly free choices from ever being made. Had God exercised that power, the world would have contained a creature—namely, the human who made the significantly free right choice—that is a counterexample to TWD. Moreover, the world where God exercises that power is plainly feasible. Hence, (1) is false, since in (1) there is a significantly free creature that does the right thing.

That said, Plantinga’s TWD is stronger than it needs to be for his defense. All he really needs to work with is:

4. Every feasible world that contains a significantly free creaturely right choice contains a free creaturely wrong choice.

And the world where God intervenes and prevents significantly free choices after the first human significantly free right choice is not a counterexample to (4), since prior to the creation of humans there was already sin by angels.

Note, though, that someone who wants to defend (4) by invoking the prior sin of angels needs to hold that the first humans would have sinned in their first significantly free choice had God not created angels or not given angels significant free will, no matter what circumstances the first humans were placed in. In other words, the defender of (4) has to hold that the actual righteousness of the first human significantly free choice has a strong counterfactual dependence on angelic freedom. The only plausible way I know of defending something like this is to say that angelic free choices are a part of human causal history and that essentiality of origins is true. So, interestingly, to hold that the weakened TWD thesis (4) is true seems to require both invoking the sin of angels and essentiality of origins.

Moreover, the defender of the actual truth of (4) would need to hold that the first angelic wrong choice preceded the first angelic significantly free right choice. For suppose an angelic significantly free choice came before any angelic sin. Then, again, God could have suspended free will right after that choice, and not created humans at all, and we would have a feasible world that is a counterexample to (4). Next, suppose that the first angelic significantly free choice was simultaneous with the first angelic sin. Presumably, the two were committed by different angels. But God could have suspended the freedom of those angels who in the actual world sin (this does not even require Molinism: God doesn’t need to know that they would sin to suspend their freedom), and plausible the simultaneous significantly free right choices of the other angels would still have eventuated. And then God could have suspended freedom altogether, thereby furnishing us with another feasible world that is a counterexample to (4).

One can modify (4) in various ways to get around this. For instance, one could say this:

5. Every feasible world that contains a significantly free creaturely right choice and that contains many generations of significantly free creatures contains a free creaturely wrong choice.

But note that if (5) is true, then one needs to invoke more than the value of freedom in saying that God is justified in creating a world with evil. One needs the value of multi-generational freedom.

An argument that Trans-World Depravity is unlikely to be true

Assume Molinism. Plantinga's Trans-World Depravity (TWD) is the thesis that every feasible world--world compatible with the conditionals of free will--that contains at least one significantly free choice contains at least one sin. I want to think about an argument that TWD is likely false.

For consider a world where God creates exactly one intelligent creature with the typical motivations and character of a typical morally upright adult human being. God then forbids the creature from imposing pointless pain on itself, and only ever gives the creature only one significantly free choice: to eat a nutritious food that it likes or to endure five hours of torture. Let's imagine the situation where God creates such a creature and it's about to make that one significantly free choice. Call this circumstances C. Given what we know about decent human beings and their motivations, the creature would very likely eat the nutritious food rather than be tortured. Very well. So very likely the conditionals of free will are such that the world where the creature eats the nutritious food is feasible. But if that world is feasible, then TWD is false.

That was too quick. I jumped between answers to two different probabilistic questions:

1. What is the epistemic probability of the Molinist conditional that were C to obtain, the creature would choose wrongly?
2. Were C to obtain, what would be the chance of the creature choosing wrongly?

It is clear that the answer to (2) is "Very low." But to argue that TWD is very likely false, I have to say that the answer to (1) is also "very low". This leads to a difficult set of questions about the relationship between Molinist conditionals and chances. Lewis's principal principle does imply that if we were to knowingly (with certainty) find ourselves in C, and if we were certain of Molinism, we would have to give the same answer to (1) and (2). The argument goes as follows: given C the Molinist conditional has the same epistemic probability as its consequent, but the epistemic probability of its consequent is the same as its chance by the principal principle. But the answer we should give to (2) in those circumstances where we were knowingly in C may not be the same as answer as we should actually give to (2). Consider this possibility. Our current epistemic probability of the Molinist conditional in (1) is 1/2, but God would be very unlikely to make C obtain unless the conditional were false. He just wouldn't want to create a world where the creature would freely wrongfully choose to endure the torture. In that case, if we were to learn that C obtains, that would give us information that the Molinist conditional is very likely false. And hence the answer to (1) is "1/2", the answer to (2) is "Very low", but were C to obtain, the answer to (1) would be "Very low" as well.

Maybe. But I think things may be even less clear. For the biased sampling involved in God's choosing what to create on the basis of conditionals of free will undercuts the principal principle, I think. I think more work is needed to be done to figure out whether or not there is a good argument against TWD here or not.