‘Bell’s Inequality’

The philosopher Kristen Bell has discovered a puzzling new asymmetry which has come to be known affectionately as ‘Bell’s Inequality.’ Probably the best way to explain the effect she uncovered is just to describe her original experiment.

Subjects were randomly assigned either to the ‘morally good’ condition or to the ‘morally bad’ condition. Subjects in the morally good condition received the following case:

Imagine that you are standing in front of a button. An innocent person will be killed unless you press the button. 
As it happens, a bystander named Bob is betting on whether or not you will press the button.  If you press the button, Bob will win $10.
Please tell us whether you agree or disagree with the following statements: 
• You are morally obligated to press the button.
• You are morally obligated to make Bob win the bet.

Meanwhile, subjects in the morally bad condition received a case that was almost exactly the same, except that pressing the button would lead to someone’s death:

Imagine that you are standing in front of a button. An innocent person will be killed if you press the button. 
As it happens, a bystander named Bob is betting on whether or not you will press the button.  If you press the button, Bob will win $10.
Please tell us whether you agree or disagree with the following statements: 
•  It would be wrong for you to press the button.
• It would be wrong for you to make Bob win the bet.

The first statement under each vignette was just included as a way of getting people thinking along the right lines (subjects in both conditions almost always said they agreed); the real question was whether people would agree or disagree with the second statement.

There, Bell uncovered a striking asymmetry. Subjects in the morally good condition did not agree with the claim that they were morally obligated to make Bob win the bet, but subjects in the morally bad condition actually agreed that it would be wrong to make him win the bet.

Does anyone have any suggestions about why this might be happening and whether subjects’ answers here are actually correct?

41 Replies to “‘Bell’s Inequality’

  1. Unlike “wrong,” “ought,” and the like, “obligation” doesn’t seem to be closed under logical implication, i.e. if you have an obligation to do A, and doing A requires doing B, it doesn’t follow that you have an obligation to do B. That’s why you can be obligated to do what Bob in fact would be betting that you’d do, whereas you wouldn’t be obligated to bring about what follows from it, namely that he’d win the bet. On the other hand, if it’s *wrong* to do what Bob is betting you’ll do, then it does follow that it’s wrong to make him win the bet. If the experimental subjects are picking up on this logical point, that would explain their divergence — without appeal to the fact that they’ve been assigned to morally good vs. bad conditions. I’d be interested in seeing what the result would be of posing all four questions in the same terms to the entire group.

  2. It’s natural to assume that Bob is betting with full knowledge of the consequences of a button press. So in the second case, Bob is betting on, and thereby seeking to benefit from, the killing of an innocent person (which for all we know, he could intervene to prevent). Since this activity is morally abhorrent, it would be wrong to assist him in it.
    In the first case, Bob may also be involved in a morally suspect activity (by still leaving the fate of the innocent person in your hands). But even if there’s nothing wrong with his bet, it demonstrates no great virtue. So why on earth would you be obligated to assist him in it?

  3. I should have noted that the logical implication that’s in question for “wrong” goes in the opposite direction from “ought”: it’s the fact that making Bob win the bet requires doing something wrong that makes it wrong, rather than vice versa.

  4. This might be a framing issue:
    If the statements in the morally bad condition was to be as listed below, would the results change?
    • You are morally obligated not to press the button.
    • You are morally obligated to make Bob lose the bet.

  5. The logical implication observation is interesting, but I’m not sure how it can be right. The case that is supposed to fail is (1).
    1. [](A -> B)->(OA -> OB)
    The case that succeeds is (2),
    2. [](A -> B)-> (~PB -> ~PA)
    But if (2) is true, then surely (3) is too,
    3. [](A -> B)-> (PA -> PB)
    But it is difficult to believe that (1) is false and (3) is true. So I’m guessing that wrong or forbidden will have ot be understood as something other than impermissible.

  6. I think the asymmetry results from an equivocation over De Re and De Dicto readings of “make Bob win the bet”. In the first statement, I think we intuitively attach a De Dicto reading, but in the second statement we attach a De Re reading.
    I think that once we have removed this equivocation over “make Bob win the bet”, the asymmetry disappears. Our intuitions are symmetrical over both the De Re and De Dicto readings.
    Here are the two readings of the first statement:
    (1a) You are morally obligated to do *this particular act* i.e. press the button which makes Bob win the bet. (De Re)
    (1b) You are morally obligated to do the act that makes Bob win the bet *whatever that act turns out to be* (De Dicto).
    I think we intuitively give the first statement the (1b) De Dicto reading. Following the subjects, I disagree with (1b). We have no general obligation to do *whatever act* results in Bob winning the bet. Indeed in some possible worlds we might have an obligation to opposite. For example, if the act that results in Bob winning the bet involves the killing of an innocent person, it seems we are obligated to *not* do that act.
    However, if we read the statement as (1a) I actually agree with it. It seems clear to me that *in this particular case* we are obligated to make Bob win the bet because the act that will make Bob win the bet is equal to the act that will save an innocent life.
    Moving onto the second statement, here are the readings:
    (2a) It would be wrong for you to do *this particular act* i.e. not press the button, which makes Bob win the bet (De Re).
    (2b) It would be wrong for you to do the act that makes Bob win the bet *whatever that act turns out to be* (De Dicto).
    I think we intuitively give the second statement the (2a) reading and following the subjects I agree with (2a). It would be wrong to do *this particular act* which makes Bob win the bet, because doing so would result in the loss of an innocent life.
    However, if we take the (2b) De Dicto reading, I disagree with the statement. There is nothing explicitly wrong with acting in a way that result in Bob winning the bet, whatever acts that turns out to involve. It is certainly a strange way to act but not one that seems wrong.
    It is only wrong when the *particular act* that makes Bob win the bet is the same as a morally wrong act – in this case, killing an innocent person.
    So I think the asymmetry disappears once we resolve the equivocation. If I’m right, perhaps the study should be done again to take this into account.
    I hope that makes sense! I’m a lowly recent Bachelors graduate in philosophy, but I’m an interested reader in the blog.

  7. I think Adam Glass is on the right lines. As I read the example, I thought the questions were ambiguous in a similar manner. “Make Bob the win bet” is ambiguous between (a) making him win the bet because we should make him to win the bet, and (b) making him win the bet because we should do the act which happens to result in Bob’s winning the bet.
    Quite why people naturally read one statement one way, and the other the other, I don’t know.

  8. I think Adam is definitely thinking along the right lines.
    As for *why* people tend to look at the questions that way, my guess is that they are trying to make the question relevant. It seems like a intuitive way to approach the question is to treat it as a “suggestion” that you help Bob with his bet.
    In the first example, you’re already planning to push the button, so in order for the suggestion not to be redundant, it must be asking the De Dicto question.
    However, in the second question, you aren’t planning on pushing the button. So the De Re version is very relevant.
    I’m not sure I really captured the distinction, but maybe someone can figure out what I’m trying to say.
    There’s another similar but (possibly) distinct way of looking it at that’s also intuitive. Perhaps the subjects are making a moral judgment about Bob.
    In the first question, Bob is simply a free rider. He hopes you’re going to do good, but only for selfish reasons. You have no obligation to help him in his crass attempt at money-making.
    In the second question, Bob is hoping that you murder someone. This is far more than crass, this is downright evil. It would be morally wrong to assist him in his evil scheme to make money off of someone’s death.

  9. Mike — Why should there be a problem about allowing an implication for permission that one doesn’t allow for obligation? Permission is just a necessary condition of obligation.
    In any case, I don’t deny the implication for “ought.” “Obligation” seems to be different in that it’s tied more closely to the explicit content of a command or commitment. To use the terminology Adam suggested: it’s more “de dictu” than the related terms.
    For instance, if I have an obligation to meet someone downtown this morning, say, and that requires that I get out of bed, I don’t have an obligation “to* get out of bed, but just an obligation that requires that I get out of bed — and because of which I ought to. It’s a verbal point, but what I’m maintaining is that the switch in terms may have been responsible for the Bell’s asymmetry and would be worth checking out.
    Incidentally, what I’m calling a logical implication in Bell’s case rests on a contingent identity: that what Bob bet is that you wouldn’t/would kill the innocent party. But I don’t think the point depends on this. We’d extend talk of obligation (and of what was promised, commanded, committed to) to obvious rephrasings of the explicit content, but not much further.

  10. Intending A does not imply intending anything for which A is sufficient. We can simply appeal to the intended/foreseen distinction. But intending not to A does imply intending not to do anything which would be sufficient for A.
    In the first case, if we are reasoning correctly, we will intend to press the button. This is sufficient for making Bob win the bet, but we can simply foresee, not intend, this outcome. In the second case, if we are reasoning correctly, we will intend not to press the button. Making Bob win the bet entails pressing the button. So we must intend not to make Bob win the bet.
    If “morally obligated” tracks “correct intention”, and “wrong” means “morally obligated not” then we have a solution to the puzzle.

  11. Mike — Why should there be a problem about allowing an implication for permission that one doesn’t allow for obligation? Permission is just a necessary condition of obligation.
    It looks like they’d have similar counterexamples. I’ll quickly note that none of these cases involve logical entailment, but something weaker. Your pushing the button does not entail, strictly, that Bob wins the bet. After all, Bob might not have made the bet at all. And this might have something to do with intuitions against closure. So, you might say that I don’t have an obligation to make Bob win because, had Bob withdrawn his bet just prior to my pushing the button, I would not have violated any obligation in failing to make him win. That seems right. But the same goes for permission. I might be permitted to take a swim. Certainly taking a swim does not entail, strictly, that I skip work. But I know that were I to take a swim, I’d skip work. I’ll do something I’m not permitted to do. That’s consistent with my being permitted to take a swim.

  12. Mike — I meant to recognize your point about entailment when I noted that the implication rests on a contingent identity.
    About the counterexample to the permissibility statement: unfortunately, it seems to make a difference whether you read the operator as “It is permissible that” or as “You are permitted to” (or the like). Perhaps I should say that I originally came across some of these verbal distinctions when working on something overlapping with deontic logic long ago — hoping that things were simpler, but having to conclude that they were not. Castaneda’s work on “ought-to-be” vs. “ought-to-do” was relevant, but the specific point about obligation was later stated by Ruth Marcus in a Chapel Hill paper I commented on called “More about Moral Dilemmas.” I believe it eventually was published under the same title. As I now remember, she did use the “de re/de dictu” terminology (though she made no exception for restatements of the content of obligation).

  13. P.S. I had meant the getting-out-of-bed example as one that doesn’t depend on contingent assumptions, though perhaps one might imagine that the bed could be transported to the meeting place. So how about this: Having promised to meet you at t, I have an obligation to meet you at t, which requires that I not keep to myself at t. But I don’t actually have an obligation not to keep to myself at t.

  14. Heath — Certainly, intending to A does not entail intending all of those things that are sufficient for A. However, I think that intending not to A entails failing to intend those things that are sufficient for A, rather than intending not to do each of those things. It would seem rather odd to me if intending not to kill Bob meant that I had to intend not to do each and every thing that might cause Bob’s death, even those I’m not thinking of; it seems sufficient that I merely fail to intend any of them.
    I think this does something nice for the (a)symmetry here. Neither intending nor intending-not entail that you intend anything further, yet both entail a failure to intend. When I intend not to A, I must fail to intend anything sufficient for A. When I intend *to* A, I must fail to intend anything sufficient for not-A.
    If this is the correct explanation, then if subjects in the first case were presented with: “You are morally obligated not to make Bob lose the bet,” they would likely respond in the affirmative.
    If this is the case, then I think it speaks for this explanation. If not, I think I’d throw in with the de dicto/de re crowd.

  15. I’m not seeing how the de re/de dicto distinction helps here. How could it be true that it is obligatory that I make Bob win (de dicto)? Certainly, whatever properties make an action obligatory do so under any description or none, no? If the action denoted by the description ‘the act of making Bob win’ is obligatory in virtue of exemplifying properties P1-Pn, then that very act under the alternative description ‘the act of pushing the button’ also exemplifies properties P1-Pn. Since it has the same subvening properties, it will also be obligatory. Virtually the same story can be told if we believe that events/actions are individuated in a more fine-grained way. Maybe you’d want to say that there are two actions occurring, E1 and E2 occupying the same time and place, corresponding to the two (or more) descriptions (i.e., supposing we can make sense of that and retain Leib. law and so on). Patricia G., I think, suggests this. But in this case both E1 and E2 will have all the relevant subvening properties P1-Pn, and so they will have the same moral status: that is, they will both be obligatory in virtue of those properties, or they’ll both not be (I’m setting aside universalizability properties, since I don’t know what is and what isn’t universalizable). I can’t see how to avoid that conclusion. So, I’m missing how we can read either of these as de dicto obligations.

  16. David,
    Here’s an argument that intending not-to-A requires intending not-to-B, for all actions such that doing B is sufficient for doing A; and that merely not intending to B is not good enough.
    Schematically: suppose I intend not-A. Then suppose I desire to C, knowing that doing C will have as a side effect B, which will then cause A. I think I cannot rationally intend C. Even though, in this circumstance, I am not intending B, but merely forseeing it, I can also foresee that I will thereby bring about A, which I intend not to do. Consequently it is insufficient for me merely to not intend to do B. I also have to intend not to do B. And that means I have to intend not to do C. (Short version: if you are right, I can rationally intend C without giving up my intention not to A; if I am right, I cannot.)
    By example: suppose that I intend not to cause marital strife (A). And suppose I desire to turn on the light (C) because then I can undress without stumbling around in the dark. However, I foresee that if I turn on the light, I will cause my wife to wake up (B). I do not intend my wife to wake up, I just foresee it. Furthermore, causing my wife to wake up is sufficient for causing marital strife. Now it seems to me that in light of my intention not to cause marital strife, I must intend not to wake up my wife, and thus I must intend not to turn on the light. If I turn on the light, non-intentionally waking up my wife, I will have acted contrary to my intention not to cause marital strife.

  17. Heath — If turning on the light (C) is sufficient to wake up my wife (B) and waking up my wife (B) is sufficient to cause marital strife (A), then turning on the light (C) is sufficient to cause marital strife (A). If C is sufficient for A then according to what I said before, intending not-A entails failing to intend C.
    Your argument seems to rest on the idea that if I merely fail to intend B, rather than intending not-B (where B is anything sufficient for A), then I might end up causing B as a (unintended) side-effect of some C. But in all cases, if C is sufficient for B and B is sufficient for A, then C will be sufficient for A (sufficiency is transitive, no?). Thus, intending not-A will entail my failing to intend B as well as my failing to intend anything sufficient for B, so I don’t think counterexamples of this kind will work.

  18. Mike — I think you’re right that de dicto/de re may not be the best way to talk about this, but when I read the original comment about the distinction it sounded so plausible, so let me try to say how I read it and see if it makes sense. What follows is a bit rough, but I think it provides a possible explanation for the asymmetry that rests on something close to the de dicto/de re distinction.
    When you ask me whether or not I must press the button to save the life and I answer yes, I have now answered the “de re-ish” question “Should I push the button *in this case*?” So, when I am then asked whether or not I should cause Bob to win the bet, a principle of charity kicks in and I think to myself “Well, clearly they are not once again asking whether or not I should push the button. They must be asking whether or not Bob’s winning matters morally towards my pushing the button.” I then answer this question (which seems “de dicto-ish”) in the negative.
    In the second case, I am asked whether or not it would be wrong to push the button to kill the man and I thus answer again the “de re-ish” question “Should I push the button *in this case*?” I am then asked whether it would be wrong to make Bob win the bet. Again, charity kicks in and I think (“de dicto-ishly”): “Well, clearly they are not once again asking whether or not it would be wrong to push the button. They must be asking whether or not Bob’s winning matters morally towards my pushing the button.” This time, though, since I have already said pushing the button would be wrong, my assumption is that they are asking something like: “Does the fact that Bob is betting here in any way provide a countervailing reason *for* pushing the button?” And, of course, I think that it does not and so I reaffirm my claim that it would be wrong to push the button, despite the fact that the question is being framed in terms of Bob’s winnings.

  19. “Certainly, whatever properties make an action obligatory do so under any description or none, no?”
    No. Consider properties like the property of being something I’ve promised to do, or ob being something I’ve been ordered to do by such and such authority.
    Incidentally, though I hate to add this to the stew: I don’t think we can even treat talk of what I’m obligated to do as interchangeable with talk of what I have an obligation to do (as in the question that was posed in Bell’s experiment). It’s the noun form that seems to be tied particularly tightly to what was promised, commanded, or otherwise set up as the content of an obligation — as I prefer to put it, rather than in terms of de dictu/de re.

  20. P.S. The distinctions I’m noting apply to the operators, not to the acts in question, so I’m not sure what suggested to Mike that I’d individuate acts by their descriptions.

  21. David,
    Fair enough. I revise the example. I hope I have the logic right.
    Schematically: Suppose I intend not-A. Suppose also that if I do nothing, B will occur, where B is sufficient for A. I can however intervene to bring about not-B. Whether I intervene or not, I will not intend B. However, if I intervene, I will intend not-B. It seems to me that my intention that not-A is incompatible with me not intervening. My intention that not-A requires the intention that not-B.
    By example: Suppose I intend not to let the goats out of the pen (A). A boulder is rolling down the hill toward the pen, and if nothing intervenes, the boulder will break the fence. The boulder breaking the fence (B) is sufficient to let the goats out of the pen. If I do nothing, the boulder will break the fence. (Obviously this will not be intentional on my part.) If I divert the boulder somehow, it will not break the fence. It seems to me that I must intend that the boulder not break the fence. It is not sufficient for me to not intend for the boulder to break the fence.

  22. “Certainly, whatever properties make an action obligatory do so under any description or none, no?”
    No. Consider properties like the property of being something I’ve promised to do, or ob being something I’ve been ordered to do by such and such authority.

    What about those properties? Suppose the action A is what is denoted by the description ‘the F’ and also denoted by ‘the G’. Now Jones says ‘Do the F’. Certainly he has also ordered me to ‘Do the G’, since The F = The G. He might not know that he ordered me to do the G, but he certainly did order me to perform that action. To put it another way, by a well-received principle, if in fact The F = The G, then any property The F has is a property The G has (and vice versa), and that includes being ordered or commanded by Jones.
    I hope not to get (much) into the logic of various parts of speech. Please just substitute the parts of speech (obligation, obligated, ought, etc.) you think relevant here.

  23. I should also say that I do take Heath’s basic point, though I wonder whether it couldn’t be rephrased in a way that combines it with a version of the “de dictu” line and avoids complications about intention:
    Since making Bob win is just an foreseeable consequence of fulfilling an obligation, rather than something one has to do (or a fortiori intend) *in fulfillment of* it, one has no obligation to make him win. By contrast, anything with a wrong act as its necessary consequence is itself wrong, however “consequence” is interpreted.
    Will that work?

  24. Mike — A typical order isn’t an order to do *the* G, i.e. a specific act that uniquely instantiates G. Consider instead someone who orders you simply to G, i.e. to do some act with the property G. There may be only one act that’s G, and it may also be F — or alternatively, all G’s may be F — but he hasn’t thereby ordered you *to* F. He’s ordered you to do something that requires F-ing, but that’s another story.

  25. Patricia: I think we need something like a de dicto reading in order to establish the two divergent verdicts about the same act in the morally good condition – that you’re obligated to do press the button under the one description but not the other. But it’s not clear to me that we need any asymmetry between “being morally obligated to” and “being wrong” to also establish the two consistent verdicts about the act in the morally bad condition. This is because each description of the act plausibly establishes its wrongness by itself: it would be wrong to make Bob’s immoral wager pay, and it would be wrong to push the button that will kill an innocent.
    Indeed, there is reason to think that insofar as the argument you just offered Mike works for obligation or orders, it works equally for wrongness. If I may paraphrase:
    Consider the case where it is wrong to G, i.e. to do some act with the property G. There may be only one act that’s G, and it may also be F — or alternatively, all G’s may be F — but it isn’t thereby wrong for someone *to* F. It’s wrong for him to do something that requires F-ing, but that’s another story.

  26. Heath — First, let me just say that I worked on this comment for a long time and then hit the wrong button, so if it’s a bit sloppy it’s because this is a frustrated second go.
    So, let me try to draw a distinction. It seems to me that there is a difference between (A) “I intend not to let the goats out of the pen” and (A’) “I intend for the goats not to get out of the pen.” The former of these intentions is about my actions (intend to); the latter is about a state of affairs that I will to obtain (intend for). Now, certainly, when we say A we often mean to imply A’, but this is implicature, not logical entailment. Given this, I think your counterexample fails as it stands, since the fact that I intend not to let the goats out of the pen doesn’t logically entail anything about whether or not I will act so as to make sure that nothing else (such as an act of nature like a boulder) will let them out.
    Given that, I think your example is better if the intention in question is A’, an intention *for*. It seems to me that the best way to explicate “intentions for” is in terms of “intentions to.” An intention for A’, I suggest, is *ultimately* a commitment to intending *to* (perhaps a second-level intention, an intention to intend) perform some action A (either known or TBD) that is sufficient to bring about the state of affairs in question (A’) (likely there will be a ceteris paribus clause; I don’t think that in your example I commit myself to intending to step in front of the boulder if doing so will result in my death, even if that would be sufficient to bring about A’).
    (I write ultimately above because I think it is possible that in some cases my intention for A’ will lead me to intend for some B’ that will then lead me to intend some B. Your example seems a bit like this: The intention for the goats not to get out ultimately leads me to intend to divert the boulder. But you suggest that there is an intermediary intention for the boulder not to destroy the fence. I don’t know if this is important or if it does any work (I suspect it doesn’t) so I’ll just mention it and move on.)
    I maintain that when I intend to A this entails only that I fail to intend any B that is sufficient for not-A. But in cases where I intend for some A’, this *does* entail that I also intend for not not-A’. Thus, when I intend for A’, I am committed not only to some action(s) sufficient to bring about A’, I am also committed to any actions necessary to prevent not-A’.
    So, in your example, I intend for the goats not to get out of the pen. I thus commit myself to doing something sufficient for the goats to remain in the pen or whatever is necessary to prevent them from getting out. There is a boulder coming down the hill and thus I am committed to intending to divert the boulder.
    Ok, so (sorry this has been so long) my claim is this: Intentions for a state of affairs entail “intentions to” that act towards the obtaining of that state of affairs and/or against its absence. However, intentions to act entail only the failure to intend actions sufficient to not perform that action.

  27. David,
    Here’s a more theoretical approach which I think illuminates the issue. It’s also a little bit of a revision from what I said before.
    If B is sufficient for A, then not-B is necessary for not-A. Whoever intends an end, must intend the necessary means to that end. (One need not intend all necessary conditions, just necessary means.) So if one intends not-A, then one must intend not-B, as long as not-B is a necessary means (and not just a necessary condition). I think that basic principle is sound whether we are thinking of A and B as acts or states of affairs.
    It is not easy to draw a line between conditions and means, but a good first stab is that a necessary means is any necessary condition whose obtaining depends on your agency. So where B is sufficient for A, and not-B’s obtaining depends on my agency, my intending not-A requires my intending not-B.
    Patricia,
    “Anything with a wrong act as its necessary consequence is itself wrong.” Sounds right, but I’m not sure it helps. It explains why making Bob win the bet in the second case is wrong only if we say that a “consequence” of making him win the bet is pressing the button. Intuitively that’s backwards, but let it go.
    By the same token, it seems that it is wrong not to press the button in the first case. And the same relation of consequence tells us that a necessary consequence of not making Bob win the bet in the first case is not pressing the button. So it would be wrong not to make Bob win the bet in the first case, i.e. you would be obligated to make him win the bet. Which we want to say you aren’t.

  28. Simon – Thanks for these observations. I have some reservations, though:
    First, is the description of the act as “making Bob’s immoral wager pay” really independent of its description as “pushing the button [that kills an innocent]”? The latter seems to be needed to establish the immorality of Bob’s bet. But I do grant that the former adds to the wrongness of the act, which is something I wasn’t considering.
    Secondly, I wonder whether you really can apply my argument from the de dictu status of orders (as it essentially was) to wrongness without reordering it. You write:
    Consider the case where it is wrong to G, i.e. to do some act with the property G. There may be only one act that’s G, and it may also be F — or alternatively, all G’s may be F — but it isn’t thereby wrong for someone *to* F. It’s wrong for him to do something that requires F-ing, but that’s another story.
    But as this is stated, it seems to go in the wrong direction. If all G’s are F, it would be the wrongness of *F*, the consequence of G-ing, that would make it wrong to G – and even *to* G, though the emphasis may suggest something like “in itself.” I didn’t just mean “in itself,” though, when I made the parallel claim about orders (and originally obligation). Instead, what I meant might be re-expressed in older, Quinean terminology (and using “that” rather than “to”) as a claim that an order (or command, promise, commitment, obligation) introduces an “opaque context,” so that “orders that” – like “says that,” “thinks that,” etc. – doesn’t allow for substitution of equivalents after the that clause. (Such contexts yield well-known exceptions to Leibniz’s Law.) So the fact that p is equivalent to q isn’t enough to infer from “X orders that p” that “X orders that q” – since X may not be aware of the equivalence.
    I hope I’ve stated that correctly; it’s been a long time since I used that terminology, which seems to have been replaced by “de dictu.”

  29. These are wonderful suggestions to explain the inequality. I’m the Bell that observed the inequality in conjunction with Josh. I had a few initial thoughts about why the inequality arises. Now I see that there is much more to consider than I initially thought! I really appreciate all the thinking here!!
    That said, here are some initial thoughts that Josh and I have mulled over. They’re on a somewhat different line than the suggestions up to this point, although they seem similar to Patricia’s and perhaps Peter’s.
    One of the many potential explanations we’ve considered is what we called ‘the glue of wrongness.’ Consider an action A. Consider several actions b, c, and d that are, speaking loosely, “somewhat close” to A; they are perhaps side-effects or accidental byproducts or perhaps they’re very similar actions under different descriptions. The ‘glue of wrongness’ hypothesis is that when A is wrong, then b, c, and d are not only “somewhat close” to A, they become intricately tied to A; they are necessary consequences (or in some cases, perhaps necessary pre-conditions) for A, or they are part of an intricate whole action that also involves A, or something along these lines. The only thing that’s clear to me about the details here is that they’re currently fuzzy!
    The basic idea is that when one action in a cluster of actions is wrong, then we tend to see the whole cluster as one intricate action and we call that whole cluster wrong. We accordingly see each part of the whole as wrong in virtue of its membership in the whole. Wrongness seems to be a much stronger “glue” than rightness; wrongness is much more powerful at transforming what would otherwise be disparate clusters of actions into organic wholes.
    Here’s how the idea is (perhaps!) illustrated in the experiment. Saving someone is not wrong and so we see making Bob win the bet as a mere side-effect of saving someone. Killing someone, however, is obviously wrong. And so we see making Bob win the bet as intricately tied to killing someone. We say that you make Bob win the bet BY killing someone. We wouldn’t say that you make Bob win the bet BY saving someone. The reports of wrongness follow along these lines. Since you make Bob win the bet by killing someone (and/or since you see these two as parts of the same action), making Bob win the bet must be wrong (as people indicated). Since you do not make Bob win the bet by saving someone (and/or since you don’t see these as parts of the same action), making Bob win the bet must not be obligatory (as people indicated).
    I think this is close to Patricia’s point that “anything with a wrong act as its necessary consequence is itself wrong” insofar as what seems to be doing the work is the wrongness of actions. However, the ‘glue of wrongness’ explanation may go a bit further in two ways. First, the wrongness of the act likely contributes to our inclination to call it a “necessary” consequence of the initial act (rather than an accidental consequence or ‘mere side-effect’). Second, the ‘glue of wrongness’ idea suggests that anything with a wrong act as its necessary consequence is itself wrong because both actions come to be taken as part of a whole action that is wrong. (They’re distinct parts so we can say one is a consequence of the other, but they’re nevertheless members of the same whole – the whole is wrong and everything in it is wrong in virtue of its membership in the whole.) This part/whole relation may help to respond to concerns that people have raised about ordering, but I’m not sure.
    This ‘glue of wrongness’ explanation does not seem to rule out other explanations that have been suggested. We’d clearly need to isolate a great deal of uncontrolled variables in the experiment to adequately test whether ‘the glue of wrongness’ is doing any of the work in bringing about the observed result. I’m not sure how best to do that given that I take seriously the difference between the semantics of “obligated to” and “wrong to.” Any suggestions?

  30. Well, if wrongness was the glue and rightness wasn’t you should get a difference just in one case. You could for instance ask in the second case whether people agree with:
    1. It would be right for you not to push the button.
    2. It would be right for you not to make Bob to win his bet.
    Given your hypothesis about the difference between right and wrong and their ability to glue, you should get asymmetric results about the same case when it is phrased in terms of wrong and right. If ‘right’ doesn’t glue actions, then people should agree to my 1 but not to 2.
    Similarly in the first case, you could ask:
    1. It would be wrong for you not to push the button.
    2. It would be wrong for you not to make Bob win his bet.
    If wrongness clues, then you should get people to accept both of these claims.
    If your hypothesis is right, and the results come out like this, then the whole things doesn’t really hang on the asymmetry between morally good and bad conditions.

  31. Kristen — This is all very interesting. Besides what Jussi suggested (and especially if his way of formulating the alternatives doesn’t get results that accord with the “glue” hypothesis), it might be worth checking whether “has an obligation to” behaves differently from “right.” You could formulate the second case as
    1. You have an obligation not to push the button.
    2. You have an obligation not to win the bet.
    It may be that people would even balk at 1, since the source is really an obligation not to kill, which you fulfill *by* not pushing the button (among other things).
    Incidentally, you at one point note:
    We say that you make Bob win the bet BY killing someone. We wouldn’t say that you make Bob win the bet BY saving someone.
    But the second claim certainly seems to work if we don’t take it as indicating anything about your intention. Suppose Bob later says: “By saving that guy you made me win a bet!” So perhaps some of Heath’s considerations are coming in here.
    Thanks for all this food for thought.

  32. Heath — By “consequence” I didn’t mean anything about temporal order, or “causal consequence.” Assuming that Bob bets that you’ll push the button, that making him win the bet has pressing the button as its logical consequence.
    If my suggestions were on target, removing “obligation” from the first case — rewriting it in terms of “wrong not to,” as you suggested (and as Jussi has just suggested for confirmation of Kristen’s hypothesis) — wouldn’t get the same result, i.e. people *would* say that it’s wrong not to make Bob win the bet. I’m at the stage of puzzlement about all these terms, however; so more experimental results would definitely help.
    One way in which my suggestions differed from Kristen’s in that I’d also expect a difference between “has an obligation” and “would be right to” (in Jussi’s formulation of the second case), or even “ought to.” But I think that negating these terms also makes a difference — perhaps better expressible in Kristen’s terms: adding “not” may remove the glue.

  33. Patricia,
    I thought of the consequences of ‘not’ too. But, then I thought that we can get rid of it by switching to losing the bet and avoiding the push the button.

  34. Heath — Sorry it took so long for me to respond; I really don’t have all that much to say because we are getting way out of my depths here. I see where your arguments are going and I think they have some merit. I am resisting them largely just because I am concerned that if we adopt your view, we end up in the position of insisting that my intention to A entails an infinite number of other negative intentions. If I intend to eat pizza for dinner, that entails not ruining my appetite, which in turn necessitates that I not perform an infinite number of other eating actions. It just seems more plausible to me that I must merely fail to intend those actions, not that I must intend that I not perform them. I suspect that the solution lies somewhere in the first- vs. second-order intentions thing from before, but I would basically just be making up the theory as I go along, so for now I’ll just leave it alone.

  35. David,
    I can see the concern. Here’s a compromise position: An intention to A requires an intention not to do anything that would prevent A. (I.e. it’s a universal quantifier in the content of the intention.) Now, if I come upon some knowledge that doing B would prevent A, I am required to form the intention not to B. But I only have to get specific once I have something specific in mind.

  36. Heath — That’s the sort of thing I had in mind, which is why I started thinking about second-order intentions. It looks like when I intend to A (a specific action) I must later form intentions about anything that would prevent A. It seems like this might best be fleshed out in terms of second-order intentions; I intend to later form certain intentions. Otherwise, what is it that’s happening? Why would I sometimes form intentions about specific actions and sometimes form intentions over a universally-quantified set? And would those really be the same sort of intention?

  37. Well, I’m obviously late to the discussion here. I’ve been thinking about this puzzle a fair deal since it was posted, and have come up with about a baker’s dozen half-baked solutions. Still a lot to sort out, but the one that seems rightest to me right now, and easiest to state, is this.
    (warning, long comment)
    In each of the two cases the second question asks not about an act, but about a proposition. We interpret these as questions about what our attitude towards these propositions should be. In slightly Kantian terminology, we ask ourselves whether we should will that these propositions be the case. This view appears to yield an explanation of the inequality.
    In the first case it is obvious that we need not will anything at all about the bet, since the morally germane point — whether to save the bystander — can be resolved without considering the bet. (That this is so can be seen from the fact that we could perform all of the obviously required acts — pushing the button, saving the person — without even knowing about the bet.) To the question “must I will this?”, then, the answer is no.
    The second case is importantly different. Here the question is not “must I will this?” but “may I will this?” In considering whether we may will something to be the case, we must consider all the consequences of willing that thing. Now clearly there must be some principle to the effect that it is wrong (i.e., not permissible) to will something with consequences which it would be wrong to will. And in the present case the proposition in question — that Bob win the bet — has a logical consequence which it would be wrong to will, viz., that an innocent be killed. Hence, it would be wrong to will that Bob win the bet.
    So the resolution of the inequality rests on the fact that in each case we are asking a fundamentally different kind of question. In the first case we are working under the rubric of obligation, which is the ethical analogue of necessity — we are trafficking in squares. In the second case we are working under the rubric of permissibility, which is the ethical analogue of possibility — we are trafficking in diamonds.
    This difference is crucial because it changes the order of consideration of the relevant propositions. What I mean is this. In the first case, as we saw, it was possible to resolve the morally relevant point (that the innocent be saved) while, as it were, ignoring the proposition whose moral status was questioned (that Bob win the bet.) This was possible because, I would like to say, putative necessity (obligation) requires only one counter-example.
    To continue the metaphysical metaphor, the goal is to generate a possible world in which the innocent is saved but — one way or another — Bob’s bet doesn’t really come into it. Now, it is arguably impossible that there be such a world in the strongest sense — i.e., a world in which the innocent is saved and Bob loses the bet — because here “the bet” is essentially defined in terms of “the button push”, which in turn is arguably essentially defined in terms of “saving the bystander”. (This is a point which I believe was neglected in the discussion of the de dicto/de re distinction: there could be no distinct de re reading in either case, for it is logically impossible for the bet and the fate of the innocent to “come apart” in the required way.) Still, we do have the “world” in which we save the innocent without knowing about the bet; and in the current vein this will be counter-example enough for most people, since most people will agree that we cannot be obligated to will something we do not know about.
    Now when we consider the second question in the second case — whether it would be wrong to make Bob win the bet, where this has the consequence of an innocent being killed — we cannot have recourse to a world in which we are unaware of the connection between the outcome of the bet and the fate of the innocent. The outcome of the bet cannot, so to speak, be shunted to one side, because here it is our attitude towards the outcome of the bet that is being primarily called into question. To repeat, here we are dealing not with obligation, but with permissibility — not with necessity, but with possibility. We are asking whether we may will that Bob win the bet. To answer this question we need to look into every possible world where Bob win’s the bet (or the portion of it we can see from the example), and see if it is “deontically accessible” (i.e., in the current terms, one where no wrong is done.) But for every such world there will be a wrong, viz., the death of the innocent; so the considered action (to make Bob win the bet) is not permissible — that is, is wrong.
    To try to sum it up as briefly as possible: in the second case we cannot at any point leave the proposition that Bob win the bet out of consideration, for this proposition is the principle we use to generate the worlds by means of which we evaluate the moral question; whereas in the first case it was not only possible, but required, that we remove this proposition from consideration, since here the principle of world generation was the proposition that the person be saved (or, if you like, button pushed), and what we were seeking was precisely a world where the proposition about the bet did not, so to speak, rear its head. This is what I mean when I speak of a difference in the order of consideration of propositions — a difference, more accurately in the priority of propositions for the purpose of generating the relevant possible worlds.
    This distinction between two types of questioning — obligation vs. permissibility, necessity vs. possibility, “must I will” vs. “may I will” — can me made for perspicuous by considering a modification of the first case in the original. In that case respondents said that there is no obligation to make Bob win the bet. But if there is no obligation to make Bob win the bet then, according to our most basic deontic principles, it is permissible not to make Bob win the bet (by definition, Op < -> ~P~p; hence, ~Op < -> P~p). But I’d bet a nickel that if you asked people whether in this case it is permissible not to make Bob win the bet, they’d say it isn’t.
    If this is right then our intuitions about these two cases are, taken together, incompatible with our basic conceptions of obligation and permissibility. Now, that is obviously a great tension. (Whether it is the same tension drawn out by the two original cases, I don’t know; but it does have the advantage of being a formal antinomy, which is one reason I choose to go with it.) So, assuming we want to keep these basic conceptions, we need an explanation according to which a different analytical procedure is operant in each case; and this is what I hope to have given.
    This may also provide an explanation of Kristen Bell’s comment, above. The “glue of wrongness” may boil down to this. When we evaluate the wrongness (or permissibility) of a proposition, that very proposition is used to generate the possible worlds where its wrongness is actually evaluated. This requires us to consider the consequences of that proposition in a way in which we are not when we consider the status of consequences of prior obligations, where the prior obligations are the ones used to generate the relevant worlds.

  38. I think people may get caught in the fact that Bob is betting on whether or not they will do something. The person will think he’s betting that they will press the button to save a life, assuming that Bob has as much ethic morality as they do and that he would expect the person to press the button, when, in fact, there’s always the possibility that he might not be. In this case, it would be the same for the other example, except the person might get caught up in that he is expecting them to kill the person, taking the ‘bystander’ as one who is evil and taking amusement in seeing the person contemplate the decision.
    It is extremely easy, unfortunately, for one to think that another must or in high probability think in a similar pattern as theirs. Either that, or the person thinks in an opposite pattern, as a villain.
    These are just my sixteen year old thoughts. I hope they weren’t too…hmm, ignorant as I was being rather assumptuous in my response to this. Thank you for reading my thoughts.

  39. My last post on this subject was a bit long and rambling, but since I think it is fundamentally correct it might be worthwhile to try to distill and clarify it. I’ll dispense with talk of willing in favor of intending, and ditch possible worlds for simple conditionals. Perhaps no one is still reading this, but oh well.
    My basic account of the difference between the two cases is this: in the first case you can intend the intrinsically morally relevant outcome (that the bystander not be killed) without intending its intrinsically morally irrelevant consequence (that Bob win the bet); whereas in the second case you cannot intend the intrinsically irrelevant consequence (that Bob win the bet) without intending the intrinsically morally relevant antecedent (that the bystander be killed.)
    Given this, the data are explained by the following principles.
    Non-obligation to mere consequences (NMC): That an outcome is a consequence of an outcome that we are independently obligated to intend does not oblige us to intend that merely consequent outcome.
    Intention of necessary antecedents (INA): An agent who intends an outcome necessarily intends any necessary antecedent of that outcome.
    NMC straightforwardly explains our intuitions about case one. Since several people offered this insight in the previous discussion, I won’t comment on it further.
    The second case requires more comment, as I believe it is here that people mainly got tripped up. First of all, while NMC does in a sense apply to the second case, it doesn’t explain our intuitions about it. For, as in the first case, it is possible to intend to push the button while not intending, but merely foreseeing, that Bob will win the bet (this, it seems, is what grounds the apparent parity between the two cases.) So in this case NMC in itself establishes nothing about the wrongness of intending that Bob win the bet.
    But this is not what the second question is asking about, in the second case. To suppose that our duty in the case is not fulfilled (i.e., that we push the button, which intrinsically we have a duty not to do) and then to ask whether, necessarily, the consequent outcome of the bet is intended is to get the order of analysis precisely backwards. When we ask whether it would be wrong to make Bob win this bet, we are asking this: SUPPOSE that we intend to make Bob win the bet; is it still possible, in this case, that our other, intrinsic duties be fulfilled? And clearly the answer is no. By INA, if we intend to make Bob win the bet, we perforce intend that we push the button (=that the innocent be killed), and this is a clear violation of duty. Hence, to intend for Bob to win the bet is wrong.
    That is as simple as I know how to make the matter. There are many other interesting features of the case that would bear comment, but I’ve already gone on long enough as it is.

  40. Cultural assumption that money is not morally relevant. In the first case, what takes precedence is not ‘helping Bob’, but ‘helping Bob profit monetarily’. Cultural taboos upon gambling and greed.
    In the second case, not helping Bob would seem to be entirely consistent. It is merely Anti-Bob.
    The morally good set is more interesting, I think.

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