February 11, 2011

Sometimes It's Rational to Act Arbitrarily

In the middle sections of his 12th chapter, Sobel goes through a series of adjustments to his deductive argument from evil designed to get around various versions of the Free Will Defense and other tactics attempted by theists. For reasons mentioned earlier, I am not happy with Sobel's formal treatment of these arguments, so I'm going to reconstruct the substance of the argument somewhat differently. Consider the following:

  1. If there were a perfect being, it would take a best course of action available to it in creating the world

  2. If a perfect being took the best course of action available to it in creating the world, the result would be very different from what we observe.

  3. But the world is as we observe it to be.
    Therefore,
  4. There is no perfect being.

More formally (to remove any ambiguities), let G represent the proposition that there is a perfect being (God), B the proposition that the perfect being chooses a best course of action, and O the proposition that the world is as we observe it to be. We have:
  1. G -> B

  2. B -> ~O

  3. O

  4. Therefore,
  5. ~G

This neatly sidesteps any defenses in terms of limitations on God's power due to, e.g., free will, and also claims that the best course of action isn't creating the best world. All this is at the expense of making premise (2) easier to deny, of course, but I think (2) is still prima facie quite plausible: prior to any theoretical commitments, we are strongly tempted to endorse (2). That's enough, in my book, to make the argument pretty strong, though certainly there's still plenty the theist can say in response.

The main thing I want to discuss here is a challenge to premise (1). Note that it has been formulated as claiming that a perfect being would take a best course of action. This is intentional. Sobel thinks there might be more than one equally good world at the top of the pyramid. (For now, assume that creating the best world is the best course of action. The possible worlds are envisioned as an infinite pyramid with just one, the unique best, at the pinnacle at the end of Leibniz's Theodicy; Sobel doesn't mention this, but it's a nice image.) If there is more than one best world, he thinks that God would choose one world from among the class of best worlds. However, it might be argued (and has been argued) that there is not even a class of best worlds, any more than there is a class of largest integers. In that case, premise (1) would, it has been argued, be false: God would create some world, just any world, because any world is better than none, and no world is best.

Sobel, however, argues that even if there are no best worlds, (1) is true. A perfect being would, by definition, be perfectly rational, and it is always irrational to choose one option when you know there is a better option available to you. He sets up the following case:

Assume that a person's preferences for sums of money are ... simple. He likes money, the more the better. Suppose a choice between $1 and $2. It would be irrational for him to choose $1. Now suppose one adds infinitely many more options {$3, $4, $5,...}. Would that make his picking $1 rather than $2 rational ... ? Surely not! ... No matter how great the greatest option $n, choosing even one dollar less would be irrational for him and would remain irrational after the expansion of his choice-set to infinity ... [I]t follows that for no number k would his choosing $k from the infinite choice-set ... be rational ... This means that a rational person cannot be in a situation in which the choice-set is {$1, $2, $3,...} (pp. 471-472, internal quotation marks and citation omitted)

This is a very odd argument. It seems that Sobel's idea (though he doesn't make this very explicit) is that no matter what choice was made in this situation, it would be irrational. As a result, no being whose choices were set up in this way could be perfectly rational, and so no such being could be perfect. It follows that if the world (or the space of possible worlds) is such that if there were a perfect being it would be faced with such a choice, then there cannot be a perfect being.

This strikes me as a bizarre theory of rationality, and an even more bizarre theory of perfect rationality. It is true that in ordinary cases it is irrational to take a certain course of action when you know there is a better one available to you, but theories meant for finite cases often don't scale up to infinities very well. Besides, surely Sobel must be wrong about his money case: surely the rational course is to name some arbitrarily chosen large number of dollars. As far as I can see, the thought experiment about being offered money is the only motivation Sobel gives for his claim, and it seems to me that it is really obviously unsatisfactory. Sobel's view is almost as be as the view (endorsed by Leibniz, whom Sobel quotes in this connection) that a perfectly rational agent would fail the Buridan's Ass dilemma. Surely that can't be right.

[cross-posted at The Prosblogion]

Posted by Kenny at February 11, 2011 7:27 PM
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Comments

I haven't read any of this stuff, so I'm leaning on your interpretation of Sobel. According to your interpretation, it seems that Sobel's idea of God is a being who is under no budget constraint. He also assumes that the items which God creates for his own consumption (worlds) offer infinitely positive marginal returns. However, most items have decreasing marginal returns, such that marginal returns either level off or even become negative. In the case of worlds, decreasing marginal returns would come from the fact that certain traits of worlds may be mutually exclusive. (Here we get into the free will vs. robots retort that evangelicals like to throw around.) God can create any variety of worlds that he likes, all with differing characteristics, but he cannot create an illogical world with mutually exclusive traits. (Kind of like creating a rock that he cannot lift.) So, it seems that there could be a best possible world, given that worlds have certain mutually exclusive traits that cause decreasing marginal returns.

All this is to say that the list of all possible worlds is nothing like the list of all possible dollar values that could be in my bank account.

Here is another thought. I believe it was Augustine who argued that just because inanimate objects, plants, animals, and people are not perfect does not mean that they are not good. Evil is the absence of good, so evil represents the failure of a created thing to live up to the potential of what it was created for. (I suppose this is debatable, but I'm rolling with Augustine for now.) Nevertheless, to the extent that a creation lives up to its ideal, it is good. If something is good, then God will create it, and being created is a blessing from God to the creation itself. Now, our world may be the best possible world, who knows. But what constrains God to create only one world? How do we know we're not one of many, and how do we know God wouldn't create a variety of worlds? Perhaps we aren't the perfect human world, but only the beloved puppy dog world, or the work-horse world. Are we to deny that God exists because we are a lesser but still good world?

So, this argument is to say, do a find/replace on "the world" and replace it with "a world" and see if the arguments still make sense.

Posted by: pferree at February 17, 2011 11:06 AM

Hi Paul,

Nice to hear from you!

Sobel is here responding to theists who argue that the reason God didn't create the BPW is that there isn't a BPW: worlds increase in value infinitely. So Sobel is assuming this because his opponent proposed it as a way of getting out of an argument Sobel previously made. Now, it may be that the opponent should not have made this proposal, because there were better courses available.

Leibniz actually thought (I'm not making this up) that one of the reasons that we don't know that this isn't the BPW, despite the fact that we see lots of pain and suffering, is that there might be lots of very happy space aliens. Our suffering might be really quite trivial in comparison to the total happiness of the universe, and there might turn out to be a very good reason for the relatively little (in comparison) bit of suffering we see here on earth. This is a lot like supposing there are more universes, isn't it?

Posted by: Kenny at February 17, 2011 11:28 AM

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