Monday, May 25, 2009

Counterpossible Conditionals II (Atheism Edition)

The last post was about counterpossible conditionals as applied to questions about moral rules and "ought implies can." It occurs to me that there's another obvious application of such conditionals, in arguments for atheism.

As is (for better or for worse) standard for discussions about God in analytic philosophy of religion, I'll assume that by "God" we mean an entity that combines the three properties of omnipotence, omniscience and omnibenevolence. There seem to me to be two excellent arguments against the existence of such an from the "Stone Paradox" and one from the problem of evil.

Start with the "Stone Paradox," taken from the classical formulation about stones too heavy for God to lift. (My favorite formulation of it is, of course, the Simpsons version: "Could Jesus microwave a burrito so hot that he himself could not eat it?") If you say that there are no limits to what God can do, you certainly can't turn around and say that He can't make a stone of a certain level of heaviness. If you say "but there is no such level of heaviness!", you've just abandoned the original premise that God is omnipotent....surely, an omnipotent being can make stones as heavy, burritos as hot, as He likes.

The Stone Paradox for omnipotence seems to exact structurally parallel Russell's Paradox for unrestricted comprehension in naive set theory. If the latter shows either that naive set theory is a hopelessly inconsistent theory that must be abandoned (as the orthodox story goes, although I'm sure that some readers of the blog would beg to differ with the "must be abandoned" part), then the Stone Paradox shows the same about the theory that something is omnipotent.* In both cases, ad hoc restrictions to save consistency--"well, maybe for every *logically possible* property, there's a set of things that have that property....", etc.--fall pretty flat.

The second excellent argument against the existence of God** is the argument from evil. A being that was omniscient would know about the Holocaust, one that was omnipotent would have it in His power to send bolts of lightning down onto the train tracks leading to Auschwitz, and one that was omnibenevolent would certainly want to do so. The structure of the argument looks pretty clear: If God existed, gratuitous evil wouldn't exist, but it does exist, so God doesn't.

The various traditional defenses all, it seems to me, fail pretty spectacularly. Many of them are morally repugnant on their face, some of them seem obviously inapplicable to natural evil, or rest on un-argued and non-obvious assumptions about the nature of good and evil, or on strange accounts of free will that seem to go well beyond the most wild-eyed libertarian accounts out there, or in some other way seem implausible on their face. Even the ones that seem establish that X wouldn't exist without evil and X is a good thing never come even close to clearing the bar of showing that both (a) X is more good that Auschwitz, etc., are bad, so that the trade is worth it, and (b) in order to have X, we need anything even close to *as much* suffering as in fact exists. To anyone who's ever taken an Intro to Philosophy class, the details of this argument are fairly familiar, so, if you agree with me about this, you're the one I'm talking to, and we'll move on from here.***

So, both of the major, classical, historically influential arguments from atheism mentioned here seem to be good ones.

But wait.

The formulation of the argument from evil necessarily involves a counterfactual premise..."If God existed, then such-and-such would be the case."

But earlier, didn't we establish that it's not logically possible that God could exist?****

So, if you understand counterfactuals in the Lewissian way, in terms of truth-preservation over the closest *possible* worlds in which the antecedent is true, then that conditional is completely trivial, since there are no possible worlds in which God exists. "If God existed, then everything would be exactly the way that it is now" and "if God existed, there would be a planet full of unicorns" would have precisely the same status as "if God existed, then gratuitous evil would not exist." That doesn't seem to be the case. That last conditional seems to be clearly, importantly and non-trivially true. Some one who is talked out of theism by the argument with that conditional as its first premise, far from being taken to have been irrationally suckered in by a silly argument from something trivial, should be praised for having taken a long stride in the direction of rationality.*****

If that's true, you'd better be willing to extend your logic to include a non-trivial counterpossible conditional connective, and, if you have a possible-worlds analysis of counterfactuals, you'd better be willing to entertain impossible worlds as well.

*Small prediction, BTW...someone correct me if I'm wrong here...but to the best of my knowledge, there aren't any Christian Dialetheists yet, but sooner or later, there will be. I'm sure that somewhere down the line young theist grad student interested in formal logic at Notre Dame, too honest to deny the contradictions entailed by his theology, will have a light bulb go off over his head during a phil of logic seminar, and decide to marry the teachings of Thomas Aquinas and Graham Priest.
**Remember, we're talking about the traditional omni-omni-omni God here. The average northern college town Episcopal Priest or Reform Rabbi would describe the object of their worship in a much different way. Whether any such liberal theologies are themselves plausible or not is an entirely different subject.
***If you don't agree with me, I'd be happy to follow up in the comments section, but right now, for the sake of making the logical point being built up to, I'm just gesturing at the atheistic arguments, and trying to make my case (about conditionals) to those who already accept them.
****Hey there, future Christian Dialetheists going back to read this blog post from 2009 predicting your existence! Say hi to everyone in the future for me!
*****Of course, you might be tempted to say something like the following. 'Look, given the paradoxes of omnipotence, that conditional is trivial, but it's a useful second-level-of-attack, since *if* those paradoxes could be satisfactorily solved, then the argument from evil would be an excellent objection to theism.' To which I'd have to reply, 'OK, but dude, given your assumptions, that itself was a counterpossible conditional! There's no escaping them.'

Sunday, May 17, 2009

Counterpossible Conditionals and Unbreakable Moral Rules

As we were all taught as baby philosophers, ought implies can. As we grew up, a few of us had little adolescent rebellions in which we denied this principle, but most of us kept the faith. There really does seem to be a deep absurdity involved in telling people that they should have done things that they couldn't have possibly done.

If you find this line of thought compelling, you're likely to be sympathetic to the corollary principle that we might want to call "ought implies can fail to." Norms that it's impossible to violate might seem just as irrational as norms that it's impossible to carry out. For one thing, neither can guide our actions, which might seem central to the idea of a norm. For another, if it seems unfair to blame people for things outside of their control, it might plausibly seem equally unreasonable to praise people for things outside of their control. The objects of blame in the former case have done nothing to deserve the blame, and the objects of praise in the latter case have done nothing to deserve the praise.*

In any case, in most discussions I've heard about the relationship between free will and moral responsibility, the two principles seem to be systematically run together into something like an "ought implies both can and can fail to" principle, the standard line being that it's only rational to praise or blame people for things that are matters of choice.

So there seems to be at least some reason to suppose that we should reject in principle the notion that there could be moral rules that we can't possibly break. Neil Sinhababu, however, has argued against this**, giving the example "don't kill God." Now, I'm not sure about that example. (Personally, I'm kinda sympathetic to Bakunin's claim that if God existed, it would be necessary to overthrow him.) However, nothing much hinges on this. We can substitute in the rule "don't beat people to death with round square blunt objects."

Now, OA entails ~P~A, so if we say that there is no rule against beating people to death with round square blunt objects (since there can't be unbreakable rules), it follows by Modus Tollens and Double Negation that it's permissible to beat people to death with round square blunt objects. That might seem terribly counter-intuitive. Surely (to the extent that we can imagine it***), when we imagine someone being beaten to death with a round square blunt object, we feel instinctive moral revulsion about it. Intuitively, it seems terribly wrong to say that such an action would be morally acceptable.

I'd argue that there's a good, principled way to have our cake and eat it too here. We can keep "ought implies can fail to" *and* accommodate the relevant moral intuition. A nice, simple way of doing both would be to say that, as a matter of fact, we have no such obligation, but if it *were* possible to bludgeon people to death with round square objects, then we *would* have an obligation to refrain from doing so.

The problem, of course, is that a certain type of orthodox logician would tell you that this conditional is trivial, so it's equally true that "if it were possible to bludgeon people to death with round square objects, we would have an obligation to kill as many people as possible that way." If we understand counterfactual conditionals (as Lewis did) in terms of truth-preservation across possible worlds, and if there are no possible worlds at which the antecedent is true, then the conditional is true regardless of what the consequent is.

In his article "Impossible Worlds: A Modest Approach," Daniel Nolan has a nice argument against both this Lewissian account and against more radical approaches according to which we have to abandon classical logic in order to reason about counterpossibles. On the one hand, he argues, if there are no actually existing counter-examples to, for example, Disjunctive Syllogism, there's no reason to revise our logic in order to deprive it of this bit of inferential power instead of extending it with a counterpossible conditional connective. On the other hand, we clearly *do* non-trivially reason about counterpossibles all the time. In fact, a few moments of thought should show that it would be damned hard to do philosophy at all if we couldn't do so. In interesting debates about truth, reference, metaphysics, epistemology and a lot of other things, it's surely routinely the case that if our side of the argument is right, the claims of the other side are not merely false but *necessarily* false. That said, an integral part of what it means to argue against opposing positions is that we reason about the commitments of the other theories and draw out unacceptable consequences. ("Well, if Meingongianism were true, then...") We act as if some such conditions were true, and others were false.**** Moreover, we can even, if we're so inclined, adapt Lewis' account of counterfactuals and tweak it slightly, so that counterfactual conditionals are true so long as, in the closest worlds (whether possible or impossible) at which their antecedents are true, their consequents are as well. Presumably, "possible worlds are always closer than impossible ones, all else being equal" is a plausible principle here, where "closer" means something like "similar in the contextually relevant respects." Of course, there may be tricky issues about how to cash all this out, but it doesn't seem *trickier* in the impossible cases than the possible ones.

In any case, I'd argue that the plausibility of the "ought implies can fail to" principle, combined with the intuitive force of the claim that it would be morally wrong to do certain impossible things, gives us yet another excellent reason to endorse non-trivial counterpossible conditionals.

*Of course, it could be objected that we could get around this by de-linking the notion of deserving praise from the notion of fulfilling obligations. After all, we don't normally go around go around praising each other for passively fulfilling obligations which we have no reason to expect each other to break. The following conversation, for example, would be fairly strange. Mark: "Hey, did you kill anyone on your way to the Philosophy Department today?" Ryan: "Um.....No." Mark: "Wow, man, you're so awesome. God, you're awesome!") The obvious response is that "praise" in the relevant sense means not "making a big deal of the fact that someone has done something good" but something more like "thinking that someone has done something good." The former is something we only do when people have done something good that we don't expect of them as a matter of course....we don't make a big fuss about praising people for things we would be horrified if they *didn't* do, just as we don't make a big fuss about blaming people for trivial human failures to fulfill very difficult obligations. That doesn't suffice to say that at least mild praise and blame *in the relevant sense* don't apply in both cases.
**In a talk at the University of Miami entitled "How Double-Humeans Can Make Room For Error"
***Of course, if one takes "imagining" to mean "having a detailed mental picture of how it would look," we can't imagine beating someone to death with a thousand-sided object either, but that seems "imaginable" in the relevant sense.
****It could be objected that what's going on is that for the sake of argument, we're assuming that the other side's position *was* possibly true, so as not to beg the question by starting from the position that it was impossible. Fine. This would not, however, get around Nolan's point. After all, "if Meingongianism were possibly true, then..." *is itself* a counterpossible conditional if one takes non-existent objects to be impossible.