Worries about Wide-scoping

It seems the following is nowadays a popular view:

Wide scope view: sentences of the form “If p, then it ought to be the case that q” have the logical form

O(p -> q)

where O is an “ought” operator and -> denotes a material conditional.

The operator O has wide scope; it “governs” the whole conditional, not just the consequent (as in p -> Oq). Although less faithful to surface grammar, the wide-scope reading is thought to have other advantages over the more natural narrow-scope reading. But I won’t go into those advantages here. Instead I want to raise some worries about the wide scope view.

The above definition of the wide scope view is incomplete. To complete it, one would need to specify the logic of O. Here I assume that it is so-called Standard Deontic Logic. In particular, I make two assumptions:

A1. If p -> q is a theorem, then Op -> Oq is also a theorem.

A2. (Op & Oq) -> O(p & q) is a theorem.

Given these assumptions, the wide scope view has disastrous results, of which I shall note three.

1. Since ~p -> (p -> q) is a theorem, it follows by A1 that O~p -> O(p -> q) is a theorem. Thus, on the wide scope view, the following is a valid inference:

You ought not to talk during the film.

Therefore, if you talk during the film, you ought to set fire to the cinema.

But, plausibly, the premise is true and the conclusion false.

2. Since (p -> q) -> (~q -> ~p) is a theorem, it follows by A1 that O(p -> q) -> O(~q -> ~p) is theorem. Thus, on the wide scope view, the following is a valid inference:

If you save your daughter (from the fire), you ought to save your son.

Therefore, if you don’t save your son, you ought not to save your daughter.

But again, plausibly, the premise is true and the conclusion false.

3. This one is a little more complicated. Since

[(p -> q) & (q -> r)] -> (p -> r)

is a theorem, it follows by A1 that

O[(p -> q) & (q -> r)] -> O(p -> r)

is a theorem. And by A2

[O(p -> q) & O(q -> r)] -> O[(p -> q) & (q -> r)]

is a theorem. From these two it follows that

[O(p -> q) & O(q -> r)] -> O(p -> r)

is a theorem. Thus, on the wide scope view, the following is a valid inference:

If you get drunk at the party, you ought to leave.

If you leave the party, you ought to drive home.

Therefore, if you get drunk at the party, you ought to drive home.

We can imagine circumstances in which the premises are true yet the conclusion false. Suppose you’re very obnoxious when drunk; so you should leave the party if you get drunk, to avoid offending anyone. But in fact you don’t get drunk; so you should drive home if you leave, rather than walking, which would much slower and more dangerous. However, it’s not the case that you should drive home if you’re drunk.

31 Replies to “Worries about Wide-scoping

  1. Campbell,
    I am no great friend of wide-scoping but I think the wide-scoper can handle your counterexamples by pointing out that her view is not intended to apply to every conditional of the form “If p, then ought q”. Wide-scoping is invoked to explain why some conditionals of these forms don’t seem to allow modus ponens to go through. Usually, this happens when a goal-directed mental state is in the antecedent (desire, intention, wanting, etc.) and when the conditional is specifying some kind of means-end rationality. E.g. “If you want to establish a socialist utopia, you ought to kill all the capitalists.” But the wide-scoper is not committed to the claim that there are no narrow-scoping ought-conditionals.
    So here are three checks (rules of thumb) for conditionals that are candidates for wide-scoping. (1) Modus ponens seems invalid; (2) there is a goal-directed intentional state in the antecedent; (3) the conditional is paraphrasable as “In order to X, you ought to Y” where X is the object of the intentional state.
    So I think the wide-scoper would say of your examples that they were not the cases she had in mind; they are narrow-scoping.
    [Also, in your 2, there is a typo confusing p and q.]

  2. You ought not to talk during the film.
    Therefore, if you talk during the film, you ought to set fire to the cinema.

    I don’t see why this is valid. The theorem is O~p -> O(p -> q), so the valid inference it seems should be this,
    You ought not to talk during the film.
    Therefore, it ought to be that, if you talk during the film, then you set fire to the cinema.

    In order to detach an obligation to do the consequent, it is not enough that you talk in the theater; it must be obligatory that you talk in the theater. But that is trivially false in this example. That is, (1) is fine,
    1. [O(p -> q) & Op] -> Oq
    But not,
    2. [O(p -> q) & p] -> Oq
    Supposing you have some set of ideal worlds w. If OA, then it will be true throughout those ideal worlds that A. So it will be true throughout the ideal worlds that no one is talking during the film. It then follows trivially that if you talk, then you ought to set fire to the theater or kill your neighbor or mow your lawn, etc. These follow trivially since the antecedent expresses a moral impossibility. And since that is true, you will never be able to detach the consequent.
    Among the things that make the inference seem bad is that no one endorses the standard deontic truth-conditions for obligation. No one thinks that you ought to do all and only those things that occur in all morally ideal worlds. And the reason is fairly obvious: this world is pretty sub-ideal, and so doing what happens in ideal worlds can make things worse. Among the things I would never do if SDL gave the right truth-conditions for O is treat gunshot wounds. I would never treat them, since such wound never occur in ideal worlds. But not treating them makes things worse in subideal worlds.

  3. Heath,
    Good point. Let me try another example, a variation on my first example above. Consider this argument:

    You ought not to want to kill your friends.
    Therefore, if you want to kill your friends, you ought to torture kittens.

    This is invalid. So a wide-scope reading of the conclusion cannot be correct, even though it includes a “want” in the antecedent. On what grounds, then, might the wide-scoper say that wide-scoping is inappropriate in this case?
    I’m not sure whether there might be similar want-involving variations on my other two examples.
    (I fixed the typo. Thanks for pointing it out.)

  4. Mike,
    I agree that the argument is invalid. But the wide scope view, as I defined it, implies that the argument is valid. It interprets the conclusion–If you talk during the film, you ought to set fire to the theatre–as having the logical form O(p -> q).

  5. Campbell,
    Is it obvious that (A1) is an axiom?
    (1) If you sincerely apologized for setting fire to the living room, you set fire to the living room.
    (2) If you ought to have sincerely apologized for setting fire to the living room, you ought to have set fire to the living room.
    It seems (1) entails (2) if (A1) is an axiom.

  6. Campbell,
    I see. But under translation, it is not problematic at all, is it? It is only the superficial English reading that makes it look problematic. Translating the English into the logical form that you propose,
    1. You ought not to talk during the film.
    2. Therefore, if you talk during the film, you ought to set fire to the cinema.
    Translation,
    1′. O~T
    2′. /:. O(T -> F)
    What’s the problem? The English makes it look like I can detach OF just by talking in the theater. But, on closer inspection, I can’t do anything like that. No worries.
    Well, one worry. The translation you’re discussing doesn’t seem to capture what is logically important about the English.

  7. It seems to me that there is some confusion about how to translate the O operator. Should it be translated as:
    (1) “it ought to be the case that” (as Campbell originally has it),
    or:
    (2) “you/one ought”
    If we translate O as “you/one ought,” then the wide-scoping translation doesn’t seem to make sense:
    (2T) “You ought to if p, then q.”
    Whereas, if we go with (1) we get:
    (1T) “It ought to be the case that if p, then q.”
    It seems to me that if we treat O as in (2), then we won’t find the wide-scoping proposal viable, becasue, as Mike suggests, it doesn’t seem to capture the meaning at all. This seems to raise a prior question about the use of “ought” – is it primarily used to make normative assertions about states of affairs (about what ought to be the case), or as a personally directed command (that one ought to do x)? The wide-scoper, perhaps, only intends to capture the prior use of ought???

  8. Campbell,
    I take it your example is intended to be of the form

    O( p )
    So, O( ~p -> q ).

    Here’s a slightly adjusted version of your revised case, to bring out the arbitrariness of the ‘q’, and to provide a plausibly means-end conditional in the conclusion:

    You ought to not want to kill your friends.
    Therefore, if you want to kill your friends, you ought to use a penknife.

    You’re right, there’s something peculiar about any such inference. I think it’s this: the wide-scoper wanted to provide coherence conditions for means and ends. But if this argument goes through (and I don’t see why it wouldn’t) all coherence conditions are off when you want things you ought not want. That seems wrong.

  9. But if this argument goes through (and I don’t see why it wouldn’t) all coherence conditions are off when you want things you ought not want.
    I guess I still can’t see why. Suppose you want to kill your friends. There is still no chance of detaching the consequent that you ought to use a penknife to do so. After all, it also follows that it is not the case that you ought to use a penknife to kill anyone.
    The conditional in the conclusion of this argument is trivially true, given that antecedent expresses a moral impossibility. So, I’m having some trouble seeing exactly what the problem is. Are trivially true conditionals more of a problem here than they are anywhere else? Is it less worrisome that in worlds where ~(2+2 =4), I ought to kill my neighbor?

  10. Hi, Campbell. Nice set of examples. No fan of wide-scoping myself, I think your cases show that to be plausible and interesting, wide-scope views should not maintain that they are possible readings of English conditional ‘ought’ sentences like the ones that you consider – even with ‘want’ in the antecedent.
    The problem is simple. If the wide-scope readings are even possible, and we make the assumptions about the logic of the ‘ought’ that Campbell makes and which are standard in deontic logic, then there should be at least some possible reading of the sentences involved in the inferences that Campbell lists on which those inferences would be licensed. But the data appears to be not only that there are some readings on which those inferences are not good, but that there are no readings on which they are good. So the wide-scope readings are apparently not even possible, let alone mandatory.
    This is something that I’ve argued elsewhere; it might be true, for example, that:

    Wide-Scope You ought to be such that you either take the means you believe to be necessary to your end or don’t have that end

    without being true that:

    Consequent-Scope If you have the end, then you ought to take the means you believe are necessary to it

    If it is, then wide-scopers can get much of what they want, even without insisting that Wide-Scope is, in fact how to get a true reading of the claim that if you have the end, then you ought to take the means. They just have to say that it is the truth in the neighborhood, rather than the sense in which that sentence is, in fact, true.
    Of course, this undermines a certain amount of the argument for Wide-Scoping, which often turns on Wide-Scoping being “uncontroversial” or those who deny it being “confused”, on the grounds that it really is possible to get Wide-Scope readings of the appropriate conditionals. That, at any rate, is part of what I argued in The Scope of Instrumental Reason, and which I take your reasoning to support.
    Matthew asks, correctly, I think, whether wide-scope views should be understood in terms of the ‘ought’ of ‘it ought to be the case that’, which is a property of propositions, or whether it should be understood in terms of an ‘ought’ which is a relation between agents and something else. Broome is quite clear that his wide-scope view is to be formulated in terms of the relational ‘ought’. But I agree with Matthew that there are significant problems generating this reading in the first place from these sentences. In fact, in the end, I suspect that these problems are more forceful than Campbell’s; for unlike his, they don’t require substantive assumptions about the logic of the ‘ought’.

  11. Campbell — I agree with your argument about most ordinary occurences of ‘ought’ in conditionals in English.
    I thought I’d mention that your first argument is very close to the arguments that the classical deontic logicians used to support their view that these conditionals involving ‘ought’ can’t be understood either as a material conditional with ‘ought’ in the consequent, or as a material conditional embedded inside an ‘ought’, but must instead be understood as involving for a distinctive dyadic deontic operator. (See e.g. Lennart Åqvist, “Good Samaritans, Contrary-to-Duty Imperatives, and Epistemic Obligations”, Noûs 1 (1967): 361-79; and “Deontic Logic”, in Dov Gabbay, ed., Handbook of Philosophical Logic (Dordrecht: Reidel, 1984), 605–714.)
    I don’t know if John Broome has published anything about these arguments, but I know from conversation with him that his response is to call for some very severe restrictions on deontic logic. For my part, I think that there are persuasive answers to all the more recent objections that have been raised against standard deontic logic; and so I think that the right solution involves the dyadic ‘ought’ of the classical deontic logicians like Bengt Hansson, Lennart Åqvist, and David Lewis.
    Your second and third arguments are interesting — and strikingly analogous to David Lewis’s examples of how both contraposition and transitivity fail for counterfactual conditionals. Given the analogies that Lewis highlights (in Counterfactuals) between dyadic ‘ought’-statements and counterfactual conditionals, it’s not surprising that if the old-school deontic logicians are right, the same sorts of counterexamples to contraposition and transitivity can be devised for dyadic ‘ought’-statements as well.

  12. I’m not an expert on standard deontic logic and that’s why I’m wondering what is its ‘status’. Assume that the wide-scoper has an intuitive case for wide-scope reading of practical conditionals – without such a reading we would end up with strange detached oughts, bootstrapping, and so on.
    Now, if the examples above are right, the standard deontic logic together with the wide-scope interpretations of the conditionals give absurd consequences we cannot accept. Let’s assume that this really is the case. We have two choices. We could either reject the wide-scope readings or standard deontic logic.
    Now, if we reject wide-scopes, we have an idea what the bad consequences are – we might have to live with strange detached oughts and bootstrapping. So, that seems like something we would not immediately want to accept. The other choice would be to reject standard deontic logic. Here’s is what I’m ignorant about – what would be the bad or unintuitive consequences from doing that? I really just want to know.
    One reason for this is that one way to avoid Sorites is to give up some elements of classic logic. Some people do this. In this case it’s quite clear what we have to give up as a result – some ways of reasoning like the elimination of double negation, modus tollens, and so on. This seems pretty bad. What are the corresponding downsides from giving up standard deontic logic? What are we weighing?

  13. Campbell,
    It seems like your examples are objections to combining the wide-scope view (WSV) with A1 and A2. I don’t see how they’re objections to WSV in particular rather than objections to the triad.
    It also seems that we can derive absurdities similar to the ones you’ve derived from WSV without assuming WSV. All we need is A1.
    Building on the example I offered previously, it seems that I can sincerely apologize only for what I’ve done, in which case it seems this conditional is true:
    (1) If I sincerely apologized for setting fire to your living room, I set fire to your living room.
    It follows from (1) and A1 that:
    (2) If I ought to sincerely apologize for setting fire to your living room, I ought to set fire to your living room.
    Suppose I did in fact set fire to your living room. Surely I ought to apologize for that. So, it seems that the antecedent of (2) is true. So, it seems that I ought to set fire to your living room. So, what am I to apologize for? Doing my duty?
    I can’t see how you can make a compelling case against WSV assuming A1. Maybe I’m missing something obvious here, but I can’t see yet by WSV is the thing we ought to give up.

  14. Jussi – you’re ignoring the fact that Wide-Scoping independently doesn’t get us what it is supposed to get us. Just to focus on two of the most salient examples, (1) even wide-scope ‘ought’s license detachment in cases in which intuitively they should not, and (2) wide-scope ‘ought’s yield predictions of symmetry that are intuitively false.
    Keep in mind that Campbell’s argument, if we accept its auxilliary assumptions about the logic of ‘ought’, would still only show that the Wide-Scoping view cannot be correct about possible readings of English conditional ‘ought’-statements. If you think the consequent-scope reading of those sentences is false, then they’re just false. That doesn’t mean that Wide-Scope ‘ought’s couldn’t be what is true, instead. Similarly, something else could be true instead – for example, there could be consequent-scope reason statements that are true instead. Or something else. What is true instead could be different, in different cases.

  15. That’s well and good. Of course there is some controversy over (1) and (2) but you might be right. I’m still curious about what supports the auxiliary assumptions of his argument and what bullets one must bite to give them up if one wants to argue that there are possible wide-scope readings of English conditional ought-statements.

  16. Some replies.
    Clayton. By theorem I mean logical truth. So I don’t think your (1) is a theorem. There may be a theorem in the near vicinity. For example, (1′) below is a theorem.
    (1′) If you set fire to the living room and apologise for doing so, then you set fire to the living room.
    But then I’m happy to say that (2′) is a theorem.
    (2′) If you ought to set fire to the living room and apologise for doing so, then you ought to set fire to the living room.
    (Incidentally, I think you can sincerely apologise for something you didn’t do, as long as you believe that you did it.)
    Mike. Good point. But I think there might be reasons for rejecting conditionals of the relevant kind which don’t have to do with worries about detachment. Let me give another example. Suppose your friend O.J. wants to kill his ex-wife and asks you for practical advice on how best to do it. You tell him:
    (a) If you want to kill your wife, you ought to stab her with a fish.
    (For some reason you often muddle up fish and knives.) This is bad advice. Intuitively, (a) is false, but not because of concerns about detaching an obligation to stab with a fish.
    However, the wide scope view then implies that it’s permissible for O.J. to want to kill his ex-wife. On the wide scope view, (a) has the form O(k -> f). So we have ~O(k -> f). But O~k -> O(k -> f) is a theorem. So by modus tollens we may infer ~O~k. Perhaps it is permissible for O.J. to want to kill his ex-wife; but this shouldn’t follow from a piece of bad advice.
    Matthew. I was deliberately fudging the distinction between the two kinds of oughts you point out. I agree that it’s an important distinction, but I’m unsure of it’s relevance here. My examples could all be translated into “ought-that” language (e.g. “You ought not to talk during the film” would become “It ought not to be the case that you talk during the film”). Do you think that would make a difference?
    Ralph. I’m sure any similarities between my examples and those used in the deontic logic literature are not entirely coincidental. I don’t know that literature very well (e.g. I haven’t read the pieces you cite), but I am familiar with the idea of a dyadic operator and I had that in the back of my mind when I was thinking about this. I had the same thought as you about Lewis on counterfactuals, and that was indeed the inspiration for my second and third arguments. (Perhaps I should have acknowledged this in the original post, but I was trying to be concise.)
    I’m intrigued by your comments about Broome. I’ve often wondered what he thinks about deontic logic. More generally, I’ve wondered whether the current wide-verus-narrow-scope debate might benefit from some input from deontic logic.
    Jussi. I think you misrepresent the alternatives. It’s not that we have only two options: either (i) accept wide-scoping and give up some part of standard deontic logic, or (ii) accept narrow-scoping and allow dubious detachment. There are other options. We could, as Ralph suggests, ditch the material conditional altogether and instead adopt a dyadic ought operator. On this approach, we might get the best of both worlds: we can keep all of standard deontic logic without any detachment problems. Also I believe Steve Finlay has recently proposed a probabilistic analysis of the conditionals in question. I don’t know the details, but I think this would count as a fourth alternative.

  17. Campbell, how about the following variation on Clayton’s point:
    Kp -> p is a theorem of epistemic logic. Let’s instantiate: “If you know that you did something wrong, then you did something wrong.”
    But we would not want to infer OKp -> Op.
    Just because you ought to know that what you did was wrong, doesn’t imply that you ought to have done that wrong thing!

  18. Campbell,
    I was assuming that you can’t apologize for something you didn’t do. I think Richard is right that even if you don’t grant that, you can change the example ever so slightly by adding ‘knowingly apologize’ and you get your counterexample.

  19. Campbell,
    yes there might be other alternatives too. They too might have good and bad consequences. For instance, they might imply that ‘if, then’ constructions in natural language are seriously ambigous. Maybe they don’t or maybe that’s fine.
    But, that still doesn’t really tell us what price, if any, there is from rejecting parts of standard deontic logic. How uncontroversial and non-rejectable is that? I’m sure there is some price to be paid but I’m just curious about what it is. If there isn’t, then wide-scopes are still in play and to be argued against on other grounds.

  20. Richard and Clayton,
    Two replies:
    1. I meant to include only theorems of classical logic in my assumption A1, and Kp -> p is not one of those.
    2. In any case, I don’t think OKp -> Op is implausible. In Richard’s example, I deny that you ought to know that you did something wrong. If the world were as it ought to be, you would not know that you did anything wrong, because you would not have done anything wrong. Of course, we do sometimes say “He ought to know he did something wrong”. But in those cases we don’t really mean to make an unconditional ought-claim. We really mean that he ought know that he did something wrong given that he did something wrong and he knows what he did and he had a good moral upbringing etc.

  21. Campbell,
    It’s true that the factivity of knowledge isn’t an assumption of classical logic, but I can’t see how that could possibly matter. It’s a truth. It’s a truth which causes trouble for A1.
    Anyway, the example that I offered on my blog last night is a bit more carefully drawn up than the one I offered above. It captures the essence of Richard’s response.
    Consider:
    (1) Unless you’re mistaken in your beliefs, if you sincerely apologized for setting fire to the living room, you set fire to the living room.
    (2) Unless you’re mistaken in your beliefs, if you ought to have sincerely apologized for setting fire to the living room, you ought to have set fire to the living room.
    So, suppose you’re not mistaken in your beliefs. Suppose you did something you shouldn’t have done. You set fire to the living room. If we assume, as is plausible:
    (3) If you set fire to the living room, you ought to apologize.
    It follows from the fact that you’re not mistaken in your beliefs and (3) that you ought to sincerely apologize. It then follows that you ought to have set fire to the living room.
    None of this assumes the wide-scoper’s thesis. I think that’s some reason to think that the difficulties you raise stem from the ancillary assumptions that figured in your original attack on WSV rather than WSV itself.
    You say:
    In Richard’s example, I deny that you ought to know that you did something wrong. If the world were as it ought to be, you would not know that you did anything wrong, because you would not have done anything wrong.
    There seem to be two aspects to your reply.
    First, we cannot assume generally that if you’ve done something wrong you ought to know that you’ve done something wrong. There are unknowable obligations, after all, and there’s something going for ought implies can. However, there are situations in which it seems you ought to know what you’ve done. A security guard, for example, ought to know if there’s wrongdoing taking place on his watch. If there is, and we assume he’s duty bound to discover any wrongdoing, we get essentially the same problem I’ve been alluding to. [If dangerous Dave is breaking and entering as he oughtn’t to, Sam the security guard ought to know about it. He can’t discover Dave trespassing unless Dave is trespassing. So, we get: (i) Dave trespasses. Hence, (ii) Sam ought to discover that Dave is trespassing. From your assumptions it follows that (iii) Dave ought to trespass.]
    Second, you write:
    If the world were as it ought to be, you would not know that you did anything wrong, because you would not have done anything wrong
    I’m not sure what to make of this. If we can only use of the assumptions you’re making about deontic logic in reasoning about deontically perfect worlds, so much the worse for standard deontic logic. I think it was Geach who put the point best. The reason you shouldn’t go through life asking ‘What would Jesus do?’ is that by the time this question arises, the odds are good that you’ve created some mess Jesus couldn’t find himself in. If the logic you’re working with can’t make sense of the idea that there’s a right and wrong way to respond to wrongdoing, for example, the absurdity of combining these logical assumptions with WSV with these logical assumptions seems to give us no reason to give up WSV.
    Let me ask, then, a slightly different question. It seems I’ve derived the absurd conclusions you think stem from WSV without assuming WSV. How does the opponents of WSV deal with these cases?

  22. Clayton,
    I suspect that your derivation relies on a narrow-scope interpretation of premise (3). That is, (3) needs to be understood as having the form p -> Oq. But that interpretation is implausible. (Also it seems dialectically a bit awkward to assume a narrow-scope reading in order to defend wide-scoping.)

  23. Clayton,
    Another thing occurs to me. Your argument seems to be a version of the so-called Paradox of the Gentle Murderer (see e.g. the SEP entry on deontic logic). The following is plausibly a logical truth:
    (1) If Jones kills his wife gently, then Jones kills his wife.
    Thus, given A1, it is a logical truth that:
    (2) If Jones ought to kill his wife gently, then he ought to kill his wife.
    But it’s also plausible that:
    (3) If Jones kills his wife, then he ought to kill her gently.
    Now assume that Jones does kill his wife, and it seems we can derive the conclusion that he ought to have killed her. But the derivation requires a narrow-scope reading of (3).

  24. Campbell,
    The derivation does assume the narrow-scope reading of my (3). But, surely you won’t say that (3) on that reading is false. Surely you don’t think I should feel free to refrain from apologizing once I’ve set fire to your living room.
    Anyway, I can’t see what’s wrong with a wide-scoper assuming (3) in this context. First, wide-scopers assume some oughts take wide-scope. They don’t think it’s impossible for the ought to take narrow scope. Second, even if you denied that, I could assume (3) in the course of offering a reductio proof in the hopes of persuading you to reject A1.
    Anyway, there are some similarities between the examples I’ve offered and the example that figures in the Paradox of Gentle Murder. One difference between my examples and that example is that they cause trouble for A1 without having to assume a conditional like ‘If J ought to kill his wife, he ought to do it gently’. It seems that the author of the SEP article you link is of the opinion that such paradoxes are legion and require abandoning the view that [(p –> q) –> (Op –> Oq)].

  25. Clayton,
    I say that the narrow-scope translation of (3) is true only if you didn’t set fire to the living room (i.e. only if its antecedent is false). If the world were as it ought to be, you wouldn’t apologise, because you wouldn’t have anything to apologise for. So it’s not the case that it ought to be the case that you apologise. So the consequent of the narrow-scope translation of (3) is false.
    I don’t deny that if you set fire to the living room, then you ought to apologise. But, in my view, this conditional ought-statement is not correctly translated in the narrow-scope way.
    At the end of your comment you mention “the view that [(p –> q) –> (Op –> Oq)]”. This is not my view. The formula you state is not a theorem of SDL. Making it a theorem would have very bad results. For example, it would then follow that (Op & ~p) -> O~p is also a theorem. So it would be logically true that if you ought to grade the papers and you don’t grade the papers, then you ought not to grade the papers.
    As I stressed earlier, SDL does not say that the mere truth of p -> q is sufficient to infer Op -> Oq; it needs to be a logical truth.

  26. Following up on something Ralph mentioned: upon further reflection, it seems to me that Campbell’s examples show that the ought-conditionals aren’t wide-scoped over a material conditional. It doesn’t follow that they’re not wide-scoped over some stronger conditional. So these aren’t objections to wide-scoping per se, but to the disjunctive “either do this or don’t do that” interpretation of ought-conditionals. (Of course, if some wide-scoper were to defend this line, they’d have to say what wide-scoping over stronger conditional meant, and I’m not sure how that would go.)

  27. Campbell,
    As I stressed earlier, SDL does not say that the mere truth of p -> q is sufficient to infer Op -> Oq; it needs to be a logical truth.
    You’re right, I was careless in my final remark. I should have stated that we’re interested in conditionals that are theorems.
    There is something about your last reply I don’t get. You say that this is false if the antecedent is true:
    (3) If I set fire to the living room, I ought to apologize.
    That is, you say it is false if translated in the narrow-scope ought way. The thing is that I don’t see what’s wrong with the reasoning from (3) read in the way you think is false and:
    (4) I set fire to the living room.
    to:
    (C) I ought to apologize.
    Isn’t this reasoning perfectly good? I think the reasoning is good because (3) is true on a reading that permits detachment in worlds where its antecedent is true. What’s your take on it?

  28. Campbell: you write, “Since ~p -> (p -> q) is a theorem, it follows by A1 that O~p -> O(p -> q) is a theorem.”
    Now it might be that the problem is here. I take it that to get from ~p to p -> q, you can do the following transformation:
    1. ~p (premise)
    2. ~p v q (addition)
    3. p -> q (material implication)
    However, is there an “addition” rule in deontic logic; that is, does “or” work the same way? It seems to me, that if you tell someone either you ought to p or you ought to q,” you’re saying that she ought to do either one of them (and that it doesn’t matter which one). But if “deontic-addition” were a rule, then we could obviously generate counterexamples to that.

  29. Clayton, that’s a good question. I’m not sure I have good answer. And I don’t have time now to give you my half-baked answer.
    Matthew, I suggest you look at the discussion of “Ross’s Paradox” in the SEP entry. I think that might answer your question.

  30. Campbell, yes, after some googling I discovered that Ross’ Paradox is what’s bugging me here. I see how the difficulty might be dismissed, but I’m not sure what to think about that right now.

  31. This is a bit late but the participants in this discussion of deontic logic might find something useful in papers I wrote with Marvin Belzer in the 1980s and 90s. We constructed a logic with a dyadic deontic operator that doesn’t permit either deontic or factual detachment except with certain added premises. This avoids the “good Samaritan” “Chisholm’s and other paradoxes. Here are some references. The Synthese paper is the one to look at if interested.
    “Formalizing Defeasible Deontic Reasoning” with M. Belzer, in Defeasible Reasoning ed. D. Nute Kluwer 1997 p. 88-101.
    “Hector Meets 3-D” with M. Belzer, Philosophical Perspectives, ed. J. Tomberlin, 1994. P. 389-415.
    “Absolute Obligations” with M. Belzer, Philosophical Studies, (72) 1993; p. 47-70.
    “Prima Facie and Other Obligations” with Marvin Belzer, John Searle, ed. van Gulick, Basil Blackwell 1991. 359-370.
    “Help for the Good Samaritan Paradox” with Marvin Belzer, Philosophical Studies, July 1986. P.117-127.
    “Dyadic Deontic Detachment” with Marvin Belzer – Synthese, Feb. 1983. P.295-319.
    Barry
    Rutgers

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