# A Bleg for Help with Deontic Logic

I know that many deontic logicians would consider the following argument to be valid:

1. If you’re going to behead Jones, then you ought to behead him using the sharp sword.
2. You ought to behead Jones.
3. Therefore, you ought to behead Jones using the sharp sword.

I know that it's controversial just what exactly the argument's form is. So let's just keep the form in ordinary English. Thus, I take the form to be:

For any subject, S, and for any actions, A and B,…

1. If S does A, then S ought to do B.
2. S ought to do A.
3. Therefore, S ought to do B.

This is called deontic detachment (in contrast to the invalid form of factual detachment, where (2) would be 'S does A'). But it seems to me that deontic detachment doesn't just work where A and B range over only actions but also where A and B range over anything for which oughts apply (including intentions, beliefs, and desires). For instance, consider the following argument:

1. If you believe that you wouldn’t quit smoking even if you were to promise your wife that you would, then you ought to refrain from promising your wife that you’ll quit smoking.
2. You ought to believe that you wouldn’t quit smoking even if you were to promise your wife that you would.
3. Therefore, you ought to refrain from promising your wife that you’ll quit.

This seems valid to me. And the form of this argument is as follows:

For any subject, S, and for any A and B for which oughts apply…

1. If S As, then S ought to B.
2. S ought to A.
3. Therefore, S ought to B.

So I have two questions. First, can anyone think of any counterexamples to the form directly above? Second, does anyone know of any literature in which it is claimed that deontic detachment works not only for instances ranging over actions but also for instances ranging over combinations of things for which oughts apply?

Any suggestions about what to read as well as any suggestions about whether I should continue to consider such an argument form to be valid would be greatly appreciated.

## 46 Replies to “A Bleg for Help with Deontic Logic”

1. Daniel Elstein says:

Interesting question! Suggested counterexample scenario – S is a member of a team contesting a quiz show; there is a penalty for buzzing with an incorrect answer.
i. If S knows the answer, then S ought to buzz.
ii. S ought to know the answer.
iii. Therefore, S ought to buzz.
What’s going on here is that (thinking consequentially for the moment) the payoff from S B-ing is high when S As, but low when ¬(S As), even when S ought to A. In such cases, deontic detachment can fail. Is the counterexample convincing?

2. John Broome has some potential counterexamples to your first argument schema (and thus to the more general one as well) in chapter 5 of his book manuscript about reasoning (I think it’s now called Rationality through Reasoning). The cases are supposed to be counterexamples to certain transmission principles, but they work just as well here. Here’s one of his cases:
1. If you exercise regularly, then you ought to eat heartily.
2. You ought to to exercise regularly.
3. Therefore, you ought to eat heartily.
Broome’s intuition is that 3 is only true if you actually exercise regularly. In other words, he doesn’t think you are doing something you ought to do if you eat heartily but don’t exercise regularly. I’m not sure what I think about this case, but I’m somewhat sympathetic to Broome’s views about it.

3. Jussi Suikkanen says:

It seems like there are good semantic reasons not to think of the inference form valid. The first premise seems to be saying that in the deontically acceptable worlds which are accessible from the world in which S As S also Bs. The second premise says what happens in the deontically acceptable worlds that are accessible from our world – S As in these worlds.
The conclusion then claims that it follows the previous that S Bs also in all the deontically acceptable worlds that are accessible from our world. But, that doesn’t follow. Our world could be one in which S does not A and the first premise doesn’t say anything about whether S Bs in the deontically accessible worlds from that kind of worlds (as Daniel’s and Errol’s examples illustrate). So, there’s a shift in the context about which sets of deontically acceptable worlds we are talking about between the premises and that makes the inference invalid.
Another way to think of the inference is Matt Bedke’s. He would say that the first premise should be understood in the following way:
S ought to B on the presupposition that he As.
The second premise says that S ought to A.
It doesn’t follow from these that S ought to B because the
second premise does not guarantee that the presupposition
of the first premise is fulfilled.

4. Hi Douglas, thanks for the interesting question! I like Daniel’s (quiz) counterexample. One possible defense against it, I suppose, is to claim that they involve equivocation of different senses of (or contexts for) ‘ought’, making the truth of the conditional statement seem plausible in one sense, and that of the detached antecedent statement plausible in another sense. E.g., the first (conditional) statement may seem plausible in an all-things-considered sense, and the second (detached antecedent) statement may seem plausible only given epistemic norms governing our mental states. If your own example is intended as a counterexample, it might similarly involve equivocation or shifting of context. Maybe a similar response might work for Errol’s, but I’m not sure about that.
I think an elaborate counterexample can be drawn from Humberstone (1992), “Direction of Fit” in MIND, Vol.101, No.401, esp. in p.75, 77 where he talks about the problem of contraposing material conditionals in light of the asymmetry implicit in different directions of fit. This needs some spelling out. (I have no formal training in modal/deontic logic, so what follows may be confused!)
First, we should get clearer about the logical form of the argument on which deontic detachment comes out valid. Because it is not obvious (to me at least) why, when the argument is dressed in plain ordinary language, deontic detachment comes out valid and not some other alternative pattern of inference.
So here’s my guess as to the standard way in which deontic detachment comes out valid. The components of the standard account (it seems to me) are:
(1) wide-scope reading of the ‘ought’ in the conditional statement,
(2) reading that ‘ought’ as a monadic operator, with the material conditional as its argument, &
(3) the distribution axiom (K): O(p -> q) -> (Op -> Oq).
On the standard account, we can see why deontic detachment comes out valid; why we can validly infer Oq from O(p -> q) and Op. I don’t mean to suggest that this is the only way it can come out valid.
Humberstone’s contraposition argument can be seen as either an objection to (1) or (2). He sees it as an objection against (2). The argument is this. Beliefs and desires are governed by normative standards characterizing their different directions of fit. If something is not the case, then one ought not to believe it. And if one desires something, then one ought to realize it. These can be symbolized as:
Thetic direction of fit: O(~p -> ~Bp)
Telic direction of fit: O(Dp -> p)
But if we have material conditionals within the parentheses, then it seems we can contrapose them. And if we can contrapose them, then the asymmetry in the different directions of fit of beliefs and desires will be lost. So, if we want to save the asymmetry, we should give up either deontic detachment or the standard account of it.
I think similar objections are made in the literature on narrow-scope vs. wide-scope debate on the normativity of reasons and rational requirements. Those in favor of narrow-scope (like Schroeder) appeal to the asymmetry in the transmission of reasons.
Sorry for the long comment! 😀

5. Oh, I see that I’ve repeated Jussi’s points, it took me a long time to compose my comment so I didn’t get to read it.

6. Doug Portmore says:

Thanks everyone for the helpful comments. I think that perhaps one way to resist these counterexamples is to index obligations to time. In that case, we may revise the argument form as follows:
For any subject, S, and for any A and B for which obligations apply…
1. If S will A at t’, then S is obligated at t to B at t’.
2. S is obligated at t to A at t’.
3. Therefore, S is obligated at t to B at t’.
So the Daniel’s putative counterexample might go like this:
i. If S will know the answer at t2, then S is obligated at t1 to buzz in at t2.
ii. S is obligated at t1 to know the answer at t2.
iii. Therefore, S is obligated at t1 to buzz in at t2.
And Errol’s putative counterexample might go like this:
1. If you will start exercising regularly at t2, then you are obligated at t1 to start eating heartily at t2.
2. You are obligated at t1 to start exercising regularly at t2.
3. Therefore, you are obligated at t1 to start eating heartily at t2.
So although I certainly see the force of Errol’s and Daniel’s counterexamples, I think that there may be some time-indexed form of deontic detachment that is valid. And when we take Errol’s and Daniel’s counterexamples and add the relevant time-indexing, they seem to lose their force as counterexamples.
And as far as Jussi’s worry (which Boram says is also his worry — although I’m still digesting all that Boram said), I read things a bit differently. What’s wrong with the following reading? In all normatively ideal worlds accessible at t, A occurs at t’. And if in all the normatively ideal worlds accessible at t in which A occurs at t’ B also occurs at t’, then in all normatively ideal worlds accessible at t B occurs at t’.
I know that I’m being a bit of a moving target here. I gave one argument form and people gave good counterexamples to it, and now I’m suggesting another argument form. So I apologize for not being clear on the form initially. But I’m still at the very early stages of thinking about this stuff.

7. Daniel Elstein says:

Thinking about this more, it may help to think of ranking the relevant worlds. The potential counterexample cases are ones where the (A & B) worlds are most preferable; but of the imperfect (¬A) outcomes the (¬A & ¬B) worlds are preferable to the (¬A & B) worlds. So the question, as Jussi points out, is whether, when we evaluate the conclusion, the A-worlds are accessible or not.
I don’t find the Broome counterexample convincing because I think that the A-worlds (the exercising worlds) must be counted as accessible when evaluating the conclusion, since they are counted as accessible when evaluating the second premise. That is, the argument only appears invalid if we illicitly switch contexts.
My quiz example was meant to avoid this problem – I don’t think there’s any context shifting involved in holding the premises true and the conclusion false. Of course I agree with Boram that there are different senses of “ought” at work. It’s because the accessibility relations of the two senses of ought differ that we get the counterexample. Different “ought”s can have different accessibility relations in the same context. But I don’t see this as a problem. If I understand Doug’s challenge, we’re allowed arguments which mix different senses of ought, and that was what I was going for. If the sense of “ought” has to stay the same I don’t think we get genuine counterexamples, only ones where the context shifts illicitly.

8. Daniel,
I don’t want to allow the mixing of different senses of ought if by different senses of ought you have in mind the all-in sense versus the prima facie sense or the objective sense versus the subjective sense. I do want to allow that we can mix what we ought to believe with what we ought to do.
Do you think that following is invalid?
i. If S will know the answer at t2, then S is obligated at t1 to buzz in at t2.
ii. S is obligated at t1 to know the answer at t2.
iii. Therefore, S is obligated at t1 to buzz in at t2.

9. Daniel Elstein says:

Sorry Doug, posted before I saw your response. I think “S ought at t1 to know … at t2” is funny because it can be true even if there is nothing S can do at t1 to make sure she knows at t2. It may be that S already missed her chance (which was at t0) to know the relevant thing. For example, there are various things that I ought to know about Kant when in the middle of giving a lecture on Kant, but this doesn’t mean that I am at that time in a position to know; I was in a position to know at some earlier time, but it’s now too late. In this sense I think “ought to know” is subject to a weaker “ought” implies “can” principle than “ought to do”: my obligation to do something doesn’t outlast my ability to do it, but my obligation to know something can outlast my ability to get to know it.
Given that, I think my counterexample still works so long as t1 is set at a time when it is too late for S to get to know the answer before t2, though at some earlier time t0 S was in a position to know.

10. Hi Daniel,
There are at least two very different sorts of cases:
Case 1: Imagine that at t1 S knows both that P and that Q if P, but that S, at t1, still hasn’t put two and two together and inferred Q. I would want to say, then, that S is obligated at t1 to come to know that Q at t2, assuming that S has at t1 the capacity to recognize and respond appropriately to the reasons that he has for believing that Q (those reasons being that he knows both Q and Q if P).
What you seem to have in mind is something like the following very different sort of case.
Case 2: Imagine that if S had paid attention in history class at t0, S would now know at t1 both that P and that Q if P and thus would then now have reasons to believe that Q. But imagine that since S didn’t pay attention in history class S has, at t1, no reason at all to believe that Q and will not have any reasons to believe that Q at anytime prior to t2. In that case, I want to deny that S is obligated at t1 to come to know that Q at t2.
So, in Case 1, I want to accept (i)-(iii). And, in Case 2, I want to deny both (ii) and (iii). In Case 2, you seem to want to accept (i) and (ii) but deny (iii). Do I have that right? Why should I find it plausible to think that, in Case 2, S is obligated at t1 to know that Q at t2? The only sense of ought in which this makes sense to make this sort of claim is the evaluative sense of ought, the sense in which there ought to be world peace. But the sense of ought in (iii) is the normative sense, not merely the evaluative sense. And in the normative sense, I don’t think that it makes sense to say that, in Case 2, S ought at t1 to come to know Q at t2.

11. Daniel Elstein says:

Hi Doug, we may just have a clash of intuitions here! I think in your Case 2, S is obligated at t1 to know (at t1) that P and that Q if P, and so is also obligated to come to know (at t2) that Q.
I don’t think this sense of ought is evaluative rather than normative. What I think is going on instead is that “ought to know” is normative but backward-looking. What I ought to know at t1 depends on how I ought to have exercised my cognitive faculties etc. at earlier times – that is, it depends on my earlier epistemic abilities. This distinguishes it from merely evaluative oughts, which don’t depend on our abilities at all. My view is that the actual usage of “ought to know” has this backward-looking, but still normative, element. The thought, “I ought to know this but I don’t” isn’t purely evaluative but its normativity is backward-looking – it connotes criticism of one’s past behaviour.
Maybe it helps to make the intuition clear to imagine yourself in the quiz situation. You hear the question, and you deliberate about whether to buzz. You think, “if (right now!) I know the answer, then I ought (in an instant) to buzz. And I ought (right now) to know the answer (right now). But I don’t know the answer. So I have no reason to buzz.” I don’t think there’s any funny business here with the time indexes. It’s just that “I ought to know the answer, but I don’t” is normatively backward-looking so that it can be true when thought even when it is too late to come to know.

12. Hi Daniel,
I take your point. I’ll need to think about it more. I agree that the quiz contestant will criticize herself for not knowing the answer in Case 2 (assuming that she ought to have paid attention in history class), but I don’t think that it follows that she has some obligation now (at t1) that she’s not fulfilling. It could be instead that she had an obligation at t0 to know that Q at t2. She failed to fulfill that past obligation and is therefore criticizable. To me, it’s like the case in which I promised someone yesterday that I would bring to work today the book that I generally keep at home. If I show up to work without the book, I will (and he will) criticize me, for I had an obligation yesterday when I was still able to retrieve the book from home to do so. But now that I’m at work and have forgotten to bring it with me and so can’t now retrieve it (assume that this is so), I don’t now have an obligation to produce the book that I cannot produce. Similarly, I don’t think that I can be obligated at t to come to knowledge that I can’t as of t come by. For instance, I can’t be obligated now to know how many people were in the bagel shop yesterday when I didn’t go into the bagel shop and count how many people were in the bagel shop yesterday. You want to say that I can so long as I was yesterday obligated to go into the bagel shop and count. I’m not so sure, but I see where you’re coming from. It’s seems to me, though, that there is some pressure for you to explain why although are practical obligations can change as a result of our becoming unable to do something, our epistemic obligations can’t change as a result of our becoming unable to come to know something.

13. Hi Doug,
Interesting post! In your original case, you give the form as involving two independent actions, A and B. But, I’m not sure that this is the appropriate way to understand the form of the original case of beheading Jones. It looks to me to be the following:
If you ought to A, then you ought to A by B-ing.
You ought to A.
Therefore, you ought to A by B-ing.
If this is the correct form, then notice that the counterexamples given by Broome (and posted above by Errol) don’t seem to apply (at least, not to the argument form I’ve just given). The original argument starts to look to me more like a means-end relation, and so I think that what is going on is simply the case of a hypothetical imperative: given that I have some particular end, it is rational (or, I am rationally obligated) to take up effective means to that end. The argument proceeds by giving a specific hypothetical imperative, and then in the second premise saying that one ought to hold the end contained in the hypothetical imperative. The conclusion is that one ought to take up the means to that end contained in the hypothetical imperative.

14. Hi Pete,
That’s a fair point. My original example was a poor illustration of the form that I had in mind. Here’s a better one.
If you kill Smith, then you ought to kill Jones (because Jones will just go on a murderous rampage if you kill Smith and leave him alive).
You ought to kill Smith.
Therefore, you ought to kill Jones.

15. David Sobel says:

Doug,
I was not tempted to think that time indexing solved the problem. Both the quiz show case and Broome’s case seemed compelling counterexamples to me. Generally if I am obligated to X but know I will not X, then there can be cases where although if I do X, I ought to do Y, the fact that I know I will not X keeps it from being the case that I ought to Y. If I know that I am obligated to X and that I will not X at t1, then that can keep it from being true that just because if I X I ought to Y, it follows that just because I ought to X, I ought to Y. It seems to me at least that you have to add that I do not know I will not X. Likely that is not enough, however.

16. Hi David,

17. So here’s how I would reason:
Let t1 be now, let t2 be later today, and let t3 be tomorrow.
1. If Phil is going to administer Drug C at t3, then Phil is obligated at t1 to administer Drug C at t2.
2. Phil is obligated at t1 to administer Drug C at t3.
3. Therefore, Phil is obligated at t1 to administer Drug C at t2.

18. It might be better to imagine all of the following: (1) that if Phil administers Drug C both today and tomorrow, Pat will be cured, (2) that if Phil administers Drug C on one day but not the other, Pat will die, and (3) that if Phil does anything else Pat will stay alive but remain incurable and suffer from her ailment.

19. David Sobel says:

I don’t think what I wrote commits me to that conclusion. Take a case where if I do not X, then Y-ing would be disastrous. If I know that I will not X, then it seems implausible to say that just because I ought to X, it follows that I ought to Y. In your case there is no harm, by the relevant standard, of Y-ing whether one X’s or not. That is a possible case, but not mandated by the premises.

20. I’m letting X be administering Drug C tomorrow and letting Y be administering Drug C today. Given my latest stipulations, this is case where if Phil is not going to do X, then his doing Y would be disastrous: Pat will die. Phil knows that he will not do X, for he has no intention now of doing X. But it still seems to me that he ought to do Y. He doesn’t get out of an obligation to do Y simply by intending not follow up with X.

21. David Sobel says:

Doug,
I am not fighting that example (taking no stand on it), just wondering to what extent that example, even if correct, can vindicate the more general claim.

22. Hi David,
I’m not trying to vindicate the validity of the argument form by appealing to one particular instance of that form. I’m trying to see whether any conclusive counterexamples to the form can be given. You said that you thought that the Broome counterexample was conclusive. What exactly, though, was the Broome counterexample to the time-indexed form? Is it just this:
1. If you will start exercising regularly at t2, then you are obligated at t1 to start eating heartily at t2.
2. You are obligated at t1 to start exercising regularly at t2.
3. Therefore, you are obligated at t1 to start eating heartily at t2.
Is it that you think that (1) and (2) can be true even though (3) is false? I don’t share that intuition.
But, in any case, my example concerned this quote which I’m not exactly sure how to interpret: “Generally if I am obligated to X but know I will not X, then there can be cases where although if I do X, I ought to do Y, the fact that I know I will not X keeps it from being the case that I ought to Y.” But I’m skeptical that there are cases where although if I do X at t3, then I ought at t1 to do Y at t2, the fact that I know that I will not do X at t3 keeps it from being the case that I ought to do Y at t2 even though I ought to do X at t3. Do you have a case in mind?

23. David Sobel says:

You are not fighting the addition that the agent can know that they will not do X. If we know this, then surely it is easy to rig cases where failure to do X and yet doing Y will be terrible. And in such cases it seems to me we ought not to Y, given that we know we will not X. That feels to me like it just follows from the factive nature of knowledge and the thought that I ought not do what will produce terrible results if I can help it.

24. You say that, in “cases where the failure to do X and yet doing Y will be terrible, …it seems to [you] we ought not to Y, given that we know we will not X.” But isn’t my example of Phil a counterexample to this? In that case, it will be terrible (Pat will die) if Phil fails to administer Drug C tomorrow and yet administers Drug C today, but it is not the case that Phil ought not to administer Drug C today given that he knows that he will not administer Drug C tomorrow.
In may be a fact that Phil will not X at t3 given that Phil is a bad person with evil intentions at t1, but this fact doesn’t get Phil off the hook for an obligation at t1 to do Y at t2 when whether Phil will X at t3 depends on whether or not Phil intend at t1 to do X at t3.
Now there may be other cases where Phil will not X at t3 no matter what Phil’s actions, intentions, and other attitudes are at t1. In that case, the fact that Phil will not X at t3 does get him off the hook for an obligation at t1 to do Y at t2. But it also gets him off the hook for an obligation at t1 to do X at t3, or so it seems to me. So I don’t see any conclusive counterexample here.
Why don’t you give me a concrete instance of the time-indexed form that you think is a conclusive counterexample to it. Then it will be easier to see where, if anywhere, our disagreement lies. Perhaps, the counterexample will convince me. But these abstract cases involving X and Y are not as persuasive as a concrete case might be.

25. David Sobel says:

1) If I have permanently quit smoking by t2, then I ought to take this pill at t1.
2) I ought to have permanently quit smoking by t2.
3) I ought to take the pill at t1.
4) If I take the pill I will die if I ever voluntarily smoke again after t2. I get 5 dollars for taking the pill.
5) I know that although I ought to quit smoking at t2, I will not do so.
At t1 I know all of 1-5. It seems to me that 1 and 2 can be coherently be seen to be true yet 3 false.

26. Hi David,
I don’t see how that’s an instance of this form:
For any subject, S, and for any A and B for which obligations apply…
1. If S will A at t’, then S is obligated at t to B at t’.
2. S is obligated at t to A at t’.
3. Therefore, S is obligated at t to B at t’.
But let me try to fit into the above form:
I) If I will permanently quit smoking at t2, then I ought at t1 to take the pill at t2.
II) I ought at t1 to permanently quit smoking at t2.
III) I ought at t1 to take the pill at t2.
Now, I have to ask: Is there any way for me to ensure at t1 that I will permanently quit smoking at t2? For instance, is it the case that were I to intend at t1 to permanently quit smoking at t2, I would?
Here are my responses for each of the two possible answers:
On the one hand, if I’m not capable at t1 of seeing to it that I permanently quit smoking at t2, then I would deny (II). The whole point of indexing obligations to times is to accommodate the fact that my options can change over time and that my obligations at a particular time are constrained by what my options are at that time. So if my quitting smoking at t2 is not am option for me at t1, then I am not obligated at t1 to quit smoking at t2.
On the other hand, if I am capable at t1 of seeing to it that I permanently quit smoking at t2 (by, say, intending at t1 to permanently quit smoking at t2), then I would insist that (III) is true. You can’t avoid an obligation at t1 to do x at t2 in virtue of your failing to intend to do what must be conjoined with x to ensure that your doing x has good as opposed to disastrous consequences.
So it seems to me that you must deny one of the two following claims that I endorse: (a) an agent’s obligations at a particular time are constrained by what her options are at that time (where, roughly speaking, S has an option at t to do x at t’ only if S could ensure that S does x at t’ by having a certain set of attitudes at t) or (b) you can’t avoid an obligation at t1 to do x at t2 in virtue of your failing to have at t1 the attitudes that you ought to have at t1–the attitudes that if you did have would ensure that your doing x at t2 would have good as opposed to disastrous consequences.
Am I right, then, in thinking that we disagree in that I accept both (a) and (b) and that you deny (a) and/or (b)? If so, which of (a) and (b) do you deny?

27. David Sobel says:

I may agree with all that and would want to reject b. While I do not deny that b has some good intuitive appeal in some cases it seems to me too insensitive to how big the bad will be if I get the bad combo and how small the good will be if I get the best combo. It also seems too insensitive to the differences between someone who is strong willed and knows it and someone who aspires to do the thing they ought to do but has learned of themselves that they frequently fail to do so. I see some such cases not as one’s where the agent gets to cancel their own obligations just by not feeling like doing what they ought to do, but rather cases where people take reasonable precautions against disastrous outcomes when they know of themselves that their sincere efforts to do what they ought are likely to fail (but not because they literally cannot do the action). I do see the fear that a principle that sensibly makes room for the latter sort of case may allow people to weasel out of their obligations inappropriately just by not wanting to do what they are obligated to do.

28. Hi Doug,
I haven’t had time to read all the comments carefully, but let me report that adding the time-indexes doesn’t alter my reaction to Broome’s case. The core intuition is that you aren’t doing something you ought to do by eating heartily unless you exercise regularly. So suppose you start eating heartily at t2 but don’t start exercising regularly at t2. In that case, you say that you do something you were obligated to do at t1–viz. eat heartily. That seems wrong, though.

29. Hi David,
Fair enough. We may just disagree about the plausibility of (b). But one thing that I would like to point out is that I’m not sure that this is fair criticism: “It (i.e., b) also seems too insensitive to the differences between someone who is strong willed and knows it and someone who aspires to do the thing they ought to do but has learned of themselves that they frequently fail to do so.”
If you want to talk about the subjective ought, then it seems right to say that one cannot get out of a subjective obligation at t1 to do x at t2 by not having the attitudes that S subjectively ought at t1 to have at t1. But this is compatible with S’s subjective obligations being sensitive to S’s awareness of the fact that generally she doesn’t follow through on her intentions. And, in that case, it may be subjectively permissible at t for S to refrain from intending to act in a certain way given her justified belief that such an intention would be ineffective. And this may be true even if she’s mistaken about this — that is, even if her intention would be effective despite all her evidence to the contrary. So (b), when interpreting all the oughts as subjective, is quite sensitive in the way that you want it to be.
Now, if we’re instead talking about objective obligations, then I think that we should say instead that what we’re objectively obligated at t1 to do at t2 doesn’t depend on whether we believe or even justifiably believe that we can effectively intend now to follow up as we should. Rather, it depends on whether we could in fact effectively intend to follow up as we should. If our intention to do something good would be effective, then we objectively ought to have that intention even if we are unaware of this fact.
So I think that (b) is plausible whether you want to talk about objective or subjective obligations so long as we’re consistent in using the same sense (objective or subjective) sense of ought throughout the principle. Likewise, I think that the deontic detachment is valid so long as we interpret the oughts consistently throughout.
So I think that you should reject (b) given your insensitivity worry only if you think that objective obligations should be sensitive to the agent’s informational state, which includes such things as the fact that she has learned of herself that she frequently fails to follow up appropriately.

30. Hi Errol,
I agree with this: “you aren’t doing something you ought to do by eating heartily unless you exercise regularly.” I just don’t see how this supports your position.
You also say, “Suppose you start eating heartily at t2 but don’t start exercising regularly at t2. In that case, you say that you do something you were obligated to do at t1–viz. eat heartily. That seems wrong, though.”
I’m not so sure. I think that what’s clear is that I do something wrong. And I can account for this, for I certainly want to say that I am obligated at both t1 and t2 to refrain from starting to eat heartily at t2 while not starting to exercise regularly at t2.
What seems to be driving your intuition is the thought that whether I am (or was) obligated at t1 to eat heartily at t2 depends on whether I am going to (or did) start exercising regularly at t2. But I think that this is a tricky question and that you should not be so quick to trust how things seem to you. And this is where the discussion with Sobel would be relevant.

31. Hi Errol,
I retract the first paragraph in the comment directly above.

32. Doug, I am puzzling over what you write in reply to Daniel: “I do want to allow that we can mix what we ought to believe with what we ought to do.”
Take the special kind of case where what one ought to do = deciding to believe in something. This is where the general norms governing what one ought to do can come into conflict with the general norms governing what one ought to believe. There are cases where: one ought practically or pragmatically believe what’s happens to be the best thing to believe in, but one ought epistemically to not believe it if it’s false. And if they can come into conflict in such special cases, then the norms governing actions and the norms governing beliefs must generally speaking be different. If different norms, then different accessibility relations; and hence equivocation in the sets of normative worlds used to evaluate the statements in “mixed” inferences. There is shift from one domain of discourse to another.
Or perhaps you could deny that there is irresolvable conflict between epistemic and practical norms. You could suggest that epistemic pros and practical cons can be weighed against one another according to some single overall ranking that assigns relative weights to norms. But what is the ordering source for this ranking? Is it epistemic or practical or some other source?
I’ve read through about a 3rd of the way down the comments. Fascinating discussion! The impression I get is that maybe the debate has shifted from logical considerations to substantive normative issues about the choice of accessibility relations and distance metrics (or modal bases and ordering sources as linguists might say) to include in the domain of discourse. If so, then it’s strange that the logical issues cannot be separated from substantive issues. Dunno, maybe my impression is wrong, I will have to read on and see. (p.s. I see there are big confusions in my earlier comments, I blame the sugar-fueled excitement from coffee and donuts.)

33. I found an article that neatly addresses all the worries I raise in my last comment(!): Lou Goble (2000), “Multiplex Semantics for Deontic Logic”. Easily downloadable by anyone on Google Scholar.

34. Hi Boram,
“There are cases where: one ought practically or pragmatically believe what’s happens to be the best thing to believe in, but one ought epistemically to not believe it if it’s false.”
I think that there are practical reasons (reasons for action) for doing what will cause you to believe what it would be good for you to believe, and I think that there are epistemic reasons (reasons to believe) what is true or what there is evidence to believe, but I don’t think that there are practical reasons (reasons for action) to believe something. That’s a category mistake. Now maybe, although I don’t think that this so, there are both pragmatic and evidential epistemic reasons. That is, maybe the fact that it would be good for you to believe that P is a reason for you to believe that P while the fact that the evidence supports ~P is a reason against your believing that P. But I don’t see how this would be a problem for me.

35. Oh, and I’ll check out that article. Thanks for the tip.

36. Hi Doug and everyone else,
I had wanted to get into this yesterday, but I’d try to post and someone else would post and I’d have to try again. So, apologies for the length, I had some free time on my hands and thought I’d try defending the virtues of Doug’s original argument in spite of where my intuitions would take me.
I wanted to see if I could help defend Doug’s deontic detachment:
1. If S does A, then S ought to do B.
2. S ought to do A.
3. Therefore, S ought to do B.
It seems like there’s a very easy proof that this is valid. Assume that 1 is a material conditional where the deontic operator takes narrow-scope. Either S A’s in w1 or doesn’t. If the former, 3 is true. If the latter, 1 and 3 are both false. So, there’s no reading on which 1 and 2 are true on which 3 is false. (Doug says that factual detachment is invalid. I don’t think that’s right, not unless we read the deontic operator as taking wide-scope and have a factual premise rather than 2 as it is written. The problem with factual detachment if we read 1 as stated (i.e., where the deontic operator takes narrow scope) the truth we express in talking about conditional obligation is probably never captured in terms of a material conditional.)
[Boram suggests that Doug’s argument might be valid if we read it as having a material conditional with a wide-scope operator. It’s valid on that reading (I think), but for reasons touched on below, I don’t think the wide-scope account could be the whole story.]
So, maybe my defense of deontic detachment doesn’t work because it’s just assumed that we’re not dealing with a material conditional. The conditional that we use to express conditional obligation is probably some other sort of conditional. Here’s an analysis of conditional and unconditional obligation lifted from Zimmerman’s 1996 book (simplified because there’s nothing about “can” in these analyses):
(Unconditional Obligation) OA is true in w1 iff some A world accessible to w1 is superior to each ~A world accessible to w1.
(Conditional Obligation) A >> OB is true in w1 iff some A-world accessible to w1 in which B is superior to every A-world accessible to w1 in which ~B.
Our argument:
1. A >> OB
2. OA
C. OB
There’s four kinds of worlds accessible to w1:
{A, B}, {A, ~B}, {~A, B}, {~A, ~B}
If 2 is true, we know that the following holds: either {A, B} or {A, ~B} is superior to both {~A, ~B} and {~A, B}.
If 1 is true, we know that the following holds: {A, B} is superior to {A, ~B}.
If it’s not true that OB, there’s some accessible ~B world that’s at least as good as some accessible B world. That can’t be satisfied given what we’ve established since we’ve established that {A, B} is better than any of the other possible combinations. So, OB holds. There’s a B-world that’s superior to each ~B world since 1 and 2 entail that {A, B} is better than the other three combinations.
Now, there might be problems with the analyses of conditional and unconditional obligation, but if we assume that the analyses are correct, I think this vindicates Doug’s argument. I’m still trying to puzzle out the quiz example from the top of the thread. I don’t see what’s wrong with saying the following. I’m there with my hand above the buzzer and I say to myself, “I really should know the answer to this!” It certainly seems plausible to also say to myself, “I really should buzz in and win the prize because I really should know the answer to this. Damn! I don’t know it, so I guess I really shouldn’t hit the buzzer.” This looks like a case where we want to introduce the notion of subsidiary obligation, the obligations that arise when you don’t manage to meet your primary obligation. It’s the thing that’s best to do once you’ve messed up and the best is no longer available. So, your primary obligation is to know and buzz. Your subsidiary obligation if you fail to know is to refrain from buzzing.
(One problem with the wide-scope approach to this kind of case is that it seems incomplete. O~p entails O~(p & q) as well as O~(p & r). So O~p entails O(p → q) and O(p → r). So, let’s let ‘p’ be ‘I don’t know the answer’, let ‘q’ be ‘I don’t hit the buzzer’ and ‘r’ be ‘I don’t step out of the way of the next bus that comes at me’. We can get from ‘I oughtn’t fail to know the next answer’ to ‘I ought to see to it that if I fail to know the answer, I fail to hit the buzzer’ and ‘I ought to see to it that if I fail to know the answer, I fail to step out of the way of the next bus that comes at me’. I take it that this second conditional doesn’t really capture what we’re after when we offer the wide-scope treatment to these cases. The right account will entail that lots of these conditionals are true, but they don’t seem to tell us what’s going on in these cases.)
I do think that some of the examples (e.g., Broome’s example Lord introduced) have a real intuitive pull, but it’s the same sort of intuition that seems to pull me towards actualism. One of Ralph’s posts seemed to me to contain a pretty compelling objection to actualism.

37. Hi Clayton, if I may interject (sorry). I agree that, “If 1 is true, we know that the following holds: {A, B} is superior to {A, ~B}.” But 1 says nothing about whether {~A, B} is superior to {~A, ~B} or not.
Daniel’s counterexample describes the following case:
1. A >> OB
2. OA
3. ~A >> ~OB
4. ~A
In which case it seems invalid to draw the conclusion that OB? So, I’m not sure about your proposed validation of deontic detachment, but I agree with what you say about factual detachment.

38. Jussi Suikkanen says:

Clayton,
a couple of questions. Firstly, why is 1 false if S doesn’t A and the conditional is a material one. Aren’t material conditionals true when the antecedent is false?
Also, I grant you that the second argument, when formalised in that way, is valid. However, Doug asked about the argument in natural language. It is not clear that the accessibility relations you give capture the argument when it is presented like that. It does seem like, in natural language, the antecedent changes the context about which worlds are accessible.

39. Doug; A quick question about your response to David S. Suppose that you can ensure that you will quit smoking just by wholeheartedly intending to do it at t1 (which is totally within your power), but the intention is not transparent to you (so you can’t tell by introspection that you’re wholeheartedly intending), and even though it is totally within your power to intend wholeheartedly, you have strong evidence that the vast majority of people who are relevantly similar never form the proper intention to quit in those circumstances (even though it was completely within their powers). Do you still think that you ought to take the pill at t1? I must say that I am playing Devil’s advocate here. I found all those counterexamples to deontic K dubious, but I am not sure time indexing can allay the concerns of those pulled by these intuitions.

40. Daniel Elstein says:

Hi Clayton, I tend to agree with what you say, though I have similar worries to Jussi. It seems to me that if the two “oughts” have the same accessibility relation the argument is clearly valid, but if they don’t all bets are off. And this is discussed lots upthread. So my take is that we aren’t dealing with a dispute about logic here – the logical situation is clear enough to all disputants. The question about the accessibility relations isn’t purely technical.
Take what you say about subsidiary obligations. You’re surely right that the primary obligation is to know and buzz, and the subsidiary obligation is to refrain from buzzing when you fail to know. But the relevant question is whether the obligation to know can still be in place when that subsidiary obligation is active. One thing that’s tempting to say is that this can’t happen, because the subsidiary obligation is only active when no “know” worlds are accessible, but when no “know” worlds are accessible there can’t be an obligation to know (that follows from the Unconditional Obligation clause). The point I was arguing with Doug is that there isn’t a single accessibility relation here, because the accessibility relation for each “ought” depends on what kind of “ought implies can” principle applies to it. I say that “ought to know” is less constrained by ability than “ought to do”, which is to say that there are worlds accessible with respect to the epistemic ought that aren’t accessible with respect to the practical ought. That explains why it seems so plausible that “I ought to know at t1” and “I ought not to buzz, given that I fail to know at t1” can both be true at t1 when I don’t know.
Notice that this is far less plausible with the Broome example: we’re not going to have “I ought to exercise regularly at t1” and “I ought not to eat heartily, given that I fail exercise regularly at t1” both being true at t1 when I don’t exercise regularly. It’s obvious that because at t1 I can no longer make it the case that exercise regularly at t1, I am no longer under the obligation to do so. Here ought implies can, unlike with “ought to know”.

41. Hi Sergio,
Good question. So there are two possible versions of Dave’s putative counterexample:
The Objective-Ought Version:
I) If I will permanently quit smoking at t2, then I objectively ought at t1 to take the pill at t2.
II) I objectively ought at t1 to permanently quit smoking at t2.
III) I objectively ought at t1 to take the pill at t2.
The Subjective-Ought Version:
I’) If I will permanently quit smoking at t2, then I subjectively ought at t1 to take the pill at t2.
II’) I subjectively ought at t1 to permanently quit smoking at t2.
III’) I subjectively ought at t1 to take the pill at t2.
The case that you’re imagining is one in which my evidence strongly suggests that I can’t effectively intend at t1 to quit smoking (which, in turn, suggests that my quitting smoking is not an option at t1), but in fact I can (and, thus, my quitting smoking is in fact an option at t1). In that case, I want to accept (I)-(III), but deny (I’) and (III’). I think that (I’) is false. What’s true instead is something like (I*) if I believe at t1 that I will permanently quit smoking at t2, then I subjectively ought at t1 to take the pill at t2.

42. Hey Jussi,
Oops. That was a slip. I was very tired when I tried to work out the details of this.
Hey Boram,
I can’t imagine you’d have to apologize for your interjection to me given that I swooped in way late to interject and skated over lots of details. (So, I apologize for my interjecting!)
Alright, you wrote:
“I agree that, “If 1 is true, we know that the following holds: {A, B} is superior to {A, ~B}.” But 1 says nothing about whether {~A, B} is superior to {~A, ~B} or not.”
That’s right, but I was assuming that in evaluating the validity of the argument we should hold all of the premises true and that that requires assessing what’s accessible to w1 given 1 and 2 together. Maybe that’s a mistake, but I think it looks pretty good. Maybe whether it’s good or not depends upon how this assumption affects the examples. So, let’s turn to your reconstruction of Daniel’s example:
1. A >> OB
2. OA
3. ~A >> ~OB
4. ~A
Given 1-4, can we validly deduce OB? I think so. Given 1, 2, and 4, we can validly deduce OB as above. So, what does ~A >> ~OB give us? One suggestion is that we introduce something like levels of obligation where your primary obligation is to do what’s best, your various subsidiary obligations are to hit what’s next best and so on once you’ve failed to do what’s best. If we suppose that ~A >> ~OB holds in w1, I take it that we’re assuming that when ranking the worlds accessible to w1 and limiting our attention to the worlds in which S doesn’t A, the worlds where S also doesn’t B are better than those in which S B’s.
If 2 is true, we know that the following holds: from the perspective of w1, either {A, B} or {A, ~B} is superior to both {~A, ~B} and {~A, B}.
If 1 is true, we know that the following holds: from the perspective of w1, {A, B} is superior to {A, ~B}
With 3 added, here’s what we learn: from the perspective of w1, it’s not the case that {~A, B} is superior to {~A, ~B}.
So, 3 gives us no reason to think we cannot validly infer OB is true in w1 because it doesn’t give us any reason to think that there’s a ~B-world accessible to w1 that is at least as good as a B-world.
Hi Daniel,
I think I agree with your point. I wasn’t clear on what the issue in the thread was exactly because there were some disagreements that seemed to be pitched at the level of the logic. Your example brings in lots of extra interesting issues I’m still not sure how to deal with.
You wrote, “Take what you say about subsidiary obligations. You’re surely right that the primary obligation is to know and buzz, and the subsidiary obligation is to refrain from buzzing when you fail to know. But the relevant question is whether the obligation to know can still be in place when that subsidiary obligation is active. One thing that’s tempting to say is that this can’t happen, because the subsidiary obligation is only active when no “know” worlds are accessible, but when no “know” worlds are accessible there can’t be an obligation to know (that follows from the Unconditional Obligation clause).”
I think that in approaching your example, I suppressed the feature that I now suspect most interested you about the example, which is has to do with whether the accessibility relations for “ought to know” and “ought to do” are the same. Sorry, I didn’t think I could get a handle on the example until I worked out the prior issue about primary/subsidiary obligations and conditional/unconditional obligations. Now that that’s clear, I think I’m more skeptical that we can construct valid arguments with Doug’s form if we extend from actions to all things that can be your obligation (e.g., knowing, believing, etc…). Given some standard assumptions about, say, what makes it the case that you ought to believe (e.g., relations between beliefs and the evidence you happen to have on hand) and what makes it the case that you ought to do (e.g., further relations having to do with the actual or expected value of outcomes), I wouldn’t bet my life on this:
1. If you believe you ought to go to Larissa, you ought to hire a chariot.
2. You ought to believe you ought to go to Larissa.
C. You ought to hire a chariot.
Suppose your enemies have fed you tons of misleading evidence that going to Larissa will bring about the best of all states of affairs. It turns out that it won’t. You’ll meet your demise in Larissa if you go. If having sufficient evidence to believe p is consistent with ~p but entails that you ought to believe p, let’s stipulate that 2 is true but you oughtn’t go to Larissa. Let’s also add that beliefs about what you ought to do move you to act, so your belief puts you in peril if formed.
Suppose further that you are friends with all the chariot drivers and you know that they are both factually informed and practically wise. I think that makes it plausible that in the worlds where you are taken in by the evidence, you ought to hire a chariot. (They’ll save you!) If we add further, however, that you actually do fail to meet the standards of epistemic normativity and fail to believe that you ought to go to Larissa, there’s no reason to hire the chariot and some reason not to. You might be friends with the driver, but he doesn’t work for free. That money could be better put elsewhere. So, in the accessible worlds where you form the belief you ought to form, 1 is true. In the accessible worlds, you ought (in the relevant sense for the belief). In the accessible worlds, however, there are better worlds where you don’t hire a chariot that are at least as good as the worlds where you do. So, false conclusion.
[Maybe the example doesn’t work because we’re supposed to insert subscripts like epistemic and practical to the Os. Alright, but then so long as we’re sticking with Os that can be made true by practical reasons (exclusively or in combination), I don’t think premise 2 in my example could be true given this stipulation and the argument is trivially valid by virtue of having a necessarily false premise.]

43. Doug Portmore says:

Hi Clayton,
It seems to me that, in your discussion of the chariot example that you gave, you were equivocating between objective and subjective senses of both ‘ought’ and ‘reason’. Objective obligations and reasons are a function of what the facts are, whereas subjective obligations and reasons are a function of what the subject takes (or subjectively should take) the reason-constituting facts to be. Thus, having sufficient subjective reason to believe p is consistent with ~p, but having sufficient objective reason to believe p is not consistent with ~p. After all, the fact that ~p is a decisive reason to believe ~p. And the fact that you’ll meet your demise in Larissa constitutes a decisive objective reason for you to refrain from going to there, but if you believe (and subjectively ought to believe) that going to Larissa will bring about the best state of affairs, then I would think that you have decisive subjective reason to go and are, thus, subjectively obligated to go (and, given what you say, to also hire a chariot).
So, of course, the argument isn’t valid if you equivocate between objective and subjective senses of ought, but is there any reason to think that it’s invalid if you don’t equivocate?

44. Hi Doug,
Yes, I thought that one response would be to distinguish between objective and subjective senses of “ought”, but I offered the example for two reasons. The first is that I’m more convinced by the line pushed by Thomson and Zimmerman that there’s just what you ought (really) to do. Perhaps it’s an open question whether what you ought (really) to do depends upon the facts about the situation, the facts about you, or some combination, but saying that “ought” is true by virtue of objective things or subjective things is not to introduce different senses of “ought”.
The second is that I think there’s a significant number of people working in epistemology who think “So and so ought to believe…” will only be true in virtue of epistemic reasons and that it’s not some mere subjective sense in which epistemic obligations depend upon a subject’s evidence. Look, if you and I are aware of all the facts and they include facts like it seems to so and so that p and the further fact that it seems that way because so and so is hallucinating, doesn’t it seem totally counterintuitive to say that the subject ought to believe ~p simply because it’s true that ~p? So, I don’t think many people would say, “the fact that ~p is a decisive reason to believe ~p”. I’ve said that the fact that ~p is a decisive reason not to believe p and almost everyone I know who knows I say that thinks that that’s just nuts.
[[Fwiw, I don’t endorse the argument I offered above for a number of reasons. For one, I think it’s rarely the case that someone has an unconditional obligation to believe something as I think our epistemic obligations are typically negative. But, I know (from more referee reports than I can count) that a significant number of people working in epistemology think it’s just obvious that it can be that you ought to believe p even if it’s not true that p (e.g., when the evidence indicates p) and that even if p is a proposition about what you ought to do, it doesn’t follow from the fact that you ought to believe, say, that you ought to A that you ought to A. Again, these aren’t my views, but they are views that I think many people accept.]]

45. Clayton, thanks for your patient response and explanation. I keep forgetting that I should hold all the premises true in evaluating the validity of the argument. So I agree when you say “that requires assessing what’s accessible to w1 given 1 and 2 together.” Now that I see it, your explanation is very neat.
That said, (and building on Jussi’s comment) I’m not sure that the semantics you give for conditional obligation is one for a non-deontic conditional with a deontic consequent (narrow scope ought), as opposed to a deontic conditional (wide scope ought), or a dyadic deontic operator taken as primitive. It could be that, given your (and Zimmerman’s) semantics for unconditional and unconditional obligation, and depending on the details of your semantics for “>>”, conditional obligation may just turn out to be a special case of unconditional obligation? (In which case, the semantics you provide for “A >> OB” might actually be for O(A>>B).)
Here’s another worry, which suggests to me that you may have to choose either deontic or factual detachment but not both. Let’s take our 1~4 from earlier:
1. A >> OB
2. OA
C. OB
3. ~A >> ~OB
4. ~A
D. ~OB
We get conclusion C via deontic detachment from 1 and 2 (as per your explanation), and conclusion D via factual detachment from 3 and 4 (assuming that the elim rule for “>>” allows modus ponens). So, contradiction, and to avoid it, it seems either deontic or factual detachment must be given up.
There are other issues in other comments that I’d like very much to discuss (shifting of context in evaluating the argument, etc.), but it’s too difficult for me to think about right now.

46. Thinking about your response more carefully, I see that you may avoid the contradiction (OB & ~OB) by noting that there’s shift in context (one where the primary obligation is available and one where it’s not).
Anyway, thanks for the discussion, I will have to think more about shifts or equivocation in evaluative contexts, and references to relevant literature will be appreciated.