Recently in Hell Category

Suppose God gives to each person the greatest equal probability of being saved. It is true, suppose, that there are two, and only two, groups of people. The members of one group will all be saved and the members of the other group will all be damned. The good news is that one of the groups is twice as large as the other. God gives each person the greatest equal probability of being saved only if he saves every member of the larger group. The epistemic probability that you are among the saved is then about .67 or 2/3.

Now suppose God offers to tell everyone whether she is in the larger group or the smaller group. Would it be rational to accept this information? If everyone learns which group she is in, then the greatest equal epistemic probability that each person is saved diminishes to .5 or 1/2. God must now flip a coin to decide which group is saved, the smaller or the larger. That is the only way to give each person the greatest equal probability of being saved. What should you do?

It is a strange problem since, if we refuse the information, many more people get saved! It is also strange since, you are already in one or the other of those groups. The information doesn’t affect which group you’re in.

(Cross-posted to my own blog.)

Some people, I think, are still under the impression that the infinities in Pascal's wager create trouble. Thus, there is the argument that even if you don't believe now, you might come to believe later, and hence the expected payoff for not believing now is also infinite (discounting hell), just as the payoff for believing now. Or there is the argument that you might believe now and end up in hell, so the payoff for believing now is undefined: infinity minus infinity.

But there are mathematically rigorous ways of modeling these infinities, such as Non-Standard Analysis (NSA) or Conway's surreal numbers. The basic idea is that we extend the field of real numbers to a larger ordered field with all of the same arithmetical operations, where the larger field contains numbers that are bigger than any standard real number (positive infinity), numbers that are bigger than zero and smaller than any positive standard real number (positive infinitesimals), etc. One works with the larger field by exactly the same rules as one works with reals. This is all perfectly rigorous.

Let's do an example of how it works. Suppose I am choosing between Christianity, Islam and Atheism. Let C, I and A be the claims that the respective view is true. Let's simplify by supposing I have three options: BC (believe and practice Christianity), BI (believe and practice Islam) and NR (no religious belief or practice).

Now I think about the payoff matrix. It's going to be something like this, where the columns depend on what is true and the rows on what I do:

	C	I	A
BC	0.9X-0.1Y	0.7X-0.3Y	-a
BI	0.6X-0.4Y	0.9X-0.1Y	-b
NR	0.4X-0.6Y	0.4X-0.6Y	c

Here, X is the payoff of heaven and -Y is the payoff of hell, and X and Y are positive infinities. I assume that the Christian and Islamic heavens are equally nice, and that the Christian and Islamic hells are equally unpleasant. The lowercase letters a, b and c indicate finite positive numbers. How did I come up with the table? Well, I made it up. But not completely arbitrarily. For instance, BC/C (I will use that symbolism to indicate the value in the C column of the BC row) is 0.9X-0.1Y. I was thinking: if Christianity is true, and you believe and practice it, there is a 90% chance you'll go to heaven and a 10% chance you'll go to hell. On the other hand, BC/I is 0.7X-0.3Y, because Islam expressly accepts the possibility of salvation for Christians (at least as long as they're not ex-Muslims, I think), but presumably the likelihood is lower than for a Muslim. BI/C is 0.6X-0.4Y, because while there are well developed Christian theological views on which a Muslim can be saved, these views are probably not an integral part of the tradition, so the BI/C expected payoff is lower than the BC/I one. The C and I columns of the tables should also include some finite numbers summands, but those aren't going to matter. A lot of the numbers can be tweaked in various ways, and I've taken somewhat more "liberal" (in the etymological sense) numbers--thus, some might say that the payoff of NR/C is 0.1X-0.9Y, etc.

What should one do, now? Well, it all depends on the epistemic probabilities of C, I and A. Let's suppose that they are: 0.1, 0.1 and 0.8, and calculate the payoffs of the three actions.

The expected payoff of BC is EBC = 0.1 (0.9X - 0.1Y) + 0.1 (0.7X - 0.3Y) + 0.8 (-a) = 0.16X - 0.04Y - 0.8a.

The expected payoff of BI is EBI = 0.15X - 0.05Y - 0.8b.

The expected payoff of NR is ENR = 0.08X - 0.12Y + 0.8c.

Now, let's compare these. EBC - EBI = 0.01X + 0.01Y + 0.8(b-a). Since X and Y are positive infinities, and b and a are finite, EBC - EBI > 0. So, EBC > EBI. EBI - ENR = 0.07X + 0.07Y - 0.8(b+c). Again, then EBI - ENR > 0 and so EBI > ENR. Just to be sure, we can also check EBC - ENR = 0.08X + 0.08Y - 0.8(a+c) > 0 so EBC > ENR.

Therefore, our rank ordering is: EBC > EBI > ENR. It's most prudent to become Christian, less prudent to become a Muslim and less prudent yet to have no religion. There are infinities all over the place in the calculations, but we can rigorously compare them.

Oxford is beginning a large venture, to create selective bibliographies across disciplines of important topics in each discipline. Duncan Pritchard is editing the philosophy section, and I'm not sure who else is on the editorial board, but as part of my agreeing to be on it, I also agreed to do some entries. One of them is on heaven and hell, available here. The draft is very rough at this point, so any comments, including sins of omission as well as commission, are welcome!

1. If Libertarianism about the will is true then none of our decisions is causally determined by any previous physical or mental event(s) (or state(s)).

2. If none of our decisions is causally determined by any previous physical or mental event(s) (or state(s)) then there is always a possibility that even the most recalcitrant rejecter, R, of divine reconciliation may, at some time in the future, tF, freely choose to be reconciled to God.

3. Therefore if God sustains R in existence until tF, then R will be freely reconciled to God.

4. Furthermore, It is no cost to an omnipotent God to sustain R in existence until tF.

5. So then, God if God desires that everyone is freely reconciled to him, then he will sustain everyone in existence until they freely choose to be reconciled to him.

6. God does desire that everyone is freely reconciled to him.

7. Thus everyone is freely reconciled to God. (i.e, Universalism is true).

This argument for Universalism about salvation subsumes libertarian freedom as a premise. Libertarians, like Jerry Walls and Bill Craig, typically argue that Universalism conflicts with Libertarianism. They seem to think that human beings can delude themselves in such a way that they will never, ever, be freely reconciled to God, and any attempt on God's part to shatter their illusions and reconcile with them would have to violate their autonomy in order to succeed. This strikes me as odd. After all, if they truly are free in the libertarian sense, their iterated persistence in their own delusion cannot be taken as a certain datum. Surely their freedom, if it is genuine, must include the freedom to come to their senses. So it seems that only if the libertarian denies libertarian freedom can they actually assert that humans could persist forever in rejecting God.

Let me try out this proof of universalism in which perfect goodness and perfect justice seem to coincide. (Inspired by points made in discussion with Ric Otte and AP—neither is responsible for my use of the points).

1. For all x, no matter how morally evil x chose to be, it is possible that God says, after x’s death, “I commend x for having led a morally perfect life.”

2. For all x, were God to utter, after x’s death, “I commend x for having led a morally perfect life”, then x would have led a morally perfect life.

3. If God were (i) to utter, after x’s death, “I commend x for having led a morally perfect life” and (ii) to send x immediately to heaven, then it would display perfect justice and perfect goodness.

4. For all x, no matter how morally evil x chose to be, God should and does say, after x’s death, “I commend x for having led a morally perfect life” and God should and does send x immediately to heaven.

5. :. Universalism is true.

To continue the recent discussions of hell, let me ask the wise folks of PB for their collective wisdom.

I was reading a recent article by Wilko Van Holten entitled "Can the Traditional View of Hell be Defended? An Evaluation of Some Arguments for Eternal Punishment" in Anglican Theological Review--not a journal I normally read, but I figured "What the hell?" (Ok, no more bad puns in this post, I promise).

Rest below the fold:

In a new issue of Religious Studies, Gordon Knight has an interesting article on universalism and open theism that many PBers may be interested in ("Universalism for Open Theists," 42 (2006):213-223).

Here is the central thrust of his argument:

I will argue that belief in the openness of God makes a hard case even worse. Furthermore, while this problem is perhaps most vivid in the case of open theism, it also can be generalized for all theists who accept a non-Molinist account of foreknowledge and who accept a libertarian conception of freedom of the will. On the other hand, this very same commitment to liberatarian freedom also precludes non-Molinists from accepting the sort of necessary universalism recently advocated by Talbott. The solution, I will argue, lies in adopting a version of contingent universalism that is able to avoid the moral problems of the [traditional] doctrine of hell while at the same time not doing violence to the strong conception of libertarian freedom to which open theists (among others) are committed (214).

A few comments below the fold.