Sometimes It’s Rational to Act Arbitrarily
February 11, 2011 — 22:16

Author: Kenny Pearce  Category: Problem of Evil  Tags: , , , ,   Comments: 10

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 blog.kennypearce.net]

Comments:
  • 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 ea…

    February 11, 2011 — 22:21
  • That situation does seem very strange, but I think the strangeness comes from the nature of infinity. Colloquially we talk about infinity as “the biggest number,” but it isn’t actually a number. No one can offer you “infinity dollars.” In the real world, maybe you’d be offered the choice of getting as much money as you wanted, but they wouldn’t have any arbitrarily large number of dollars right there at the time, and it would take some time to get the rest to you. Maybe the most rational thing would be to say, “I choose whatever amount you have on you right now.” Or maybe we could take into account the diminished value of future money, the opportunity cost for having to come back and get it later, and whatever existent schedule the person has for obtaining an arbitrarily large amount of money, so the rational thing would be to say, “I’ll take whatever amount you have on you right now, plus $X next Tuesday, and $Y the Tuesday after that” (or whatever the schedule was).
    This is a very verbose way of saying: it’s hard to imagine what a rational actor would do in an impossible situation. Intuition naturally fails us.
    That being said … are there really an infinite number of possible worlds? It doesn’t seem obviously true to me. If there’s a finite amount of mass/energy in the universe, there are only so many ways that can be configured. It’s a huge number of ways, but it isn’t infinite. Also, some theists describe their god as “infinite.” I’ve never really understood what that is supposed to mean, but could an infinite being be able to reach “number infinity” in a list of possible worlds ordered by goodness (if it is infinite after all)?

    February 12, 2011 — 0:11
  • Kenny Pearce

    So, there are only finitely many ways to arrange the mass/energy in the actual universe permitted by the laws of physics, structure of spacetime, etc, but presumably all of those things are contingent: God could have made a different amount of mass/energy, different laws of physics, and/or a different structure of spacetime. So it seems that there are infinitely many ways God could have made things, despite there being only finitely many ways to arrange the mass/energy of the actual universe according to the actual laws of physics.

    February 12, 2011 — 0:18
  • Ryan

    Wouldn’t the basic rationale Sobel uses work if instead the argument he used wasn’t focused on rationality so much as maximal goodness? (an oft-stated requirement for perfection)
    1) It is less good to pick an option worse than another live option.
    2) There is a better option than this world.
    3) A being created this world.
    4) This being is less good than it could be. (1-3)
    5) To be maximally good, requires that one not be less good than any other logically possible being.
    6) The being that created the world cannot be maximally good. (4 and 5)
    I am not a philosopher by training or background, so someone could probably fix this up a bit, but I think the basic logic/intuitions I use supports Sobel’s basic claim and gets past your issue of “Buridan’s Ass” by instead tying the situation to maximal goodness, as the criticism isn’t of rationality but morality.
    I dunno, does this make sense?

    February 12, 2011 — 13:40
  • Kenny Pearce

    Ryan, that’s a good point. It at least shows that, if we think that the existence of God is compossible with there being no best course of action, we can’t have a definition of God’s goodness which implies that he always chooses the best. And, of course, always choosing the best is a pretty intuitive way of defining ‘maximally (or perfectly) good.’ But maybe it would make more sense to first get a definition of ‘good’ so that it comes in degrees, and then say that ‘maximally good’ means ‘as good as it is logically possible that any being should be.’
    I think Sobel conceives of God’s goodness as meaning that he always prefers the (objectively) better over the (objectively) worse. That is, goodness is about having the right preferences. Rationality has to do with acting in a way that makes sense in terms of one’s preferences – for instance, acting in a way that is likely to lead to the satisfaction of one’s strongest preferences, at the expense of weaker preferences, rather than vice versa. So I think that for Sobel the problem is supposed to come out of rationality and goodness together.

    February 12, 2011 — 13:51
  • Clayton Littlejohn

    Hi Kenny,
    Does this help pump the intuition that Sobel is after? Suppose that at t God chooses door #2 that has $2 behind it (as God knows) over #1 that has $1 behind it. At t+1, Monte Hall says, “Alright, God, here’s the deal. You can do nothing and I’ll increase the value of what’s behind door #2 as high as you like (and is possible) or you can switch and take the $1 behind door #1, what will it be?” If God says at t+2 that he’ll now take what’s behind door #1, God is irrational.
    If God is irrational to switch, why isn’t God irrational to pick door #1 from the get go?

    February 13, 2011 — 23:29
  • Kenny Pearce

    Clayton, there’s certainly an intuition behind Sobel’s claims. They aren’t coming out of nowhere. And the point, it seems to me, is that it is very hard to come up with a theory of rationality that can say what to do in cases like this. But here’s the nub of my criticism: a theory of rationality should tell us that an ideally rational agent is one who acts in such and such a way in such and such circumstances. It shouldn’t tell us, an ideally rational agent is one who never finds himself in such and such circumstances. Being rational is not a matter of what alternatives you have available to you, it’s a matter of how you choose between them. So there is certainly a problem for the theory of rationality in cases like this, but I have trouble seeing a serious problem for theism.

    February 15, 2011 — 17:13
  • Luke Gelinas

    One thing defenders of these kind of arguments can say is that it’s rationally permissible for agents in these sort of situations to choose less than the best, but that nonetheless it’s always better to choose the better. That would permit you to choose some arbitrarily large sum of dollars, while still posing a challenge to unsurpassable rationality. It’s hard to see how theists aren’t just begging the question by insisting that a theory of rationality must accomodate unsurpassable rationality under all conditions. Why would anyone other than committed theists buy this?

    February 15, 2011 — 21:04
  • Kenny Pearce

    Luke, that’s a good point. I think you’re right. The argument does show that these sorts of conditions are incompatible with the existence of an unsurpassably rational being. And this is a very interesting result. But maybe the moral is not that we shouldn’t believe in God, but rather that we should characterize God as ideally or perfectly, rather than unsurpassably, rational.

    February 15, 2011 — 23:06
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