Friday, August 12, 2011

Remarks on the logic of commanding and permitting


If I command you to do something, I thereby permit you to do it. But suppose I command you to do A or B or both. Then it seems that not only do I permit the disjunction, but I also permit each disjunct.

It is, I think, necessary that if I command you to do something, I also permit you to do it. Working out why exactly would be interesting.

But I do not think it is necessary that if I command you to do A or B or both, then I permit you to do A and I permit you to do B. Imagine a case where you are under all sorts of orders that I have no authority to override and which I do not know all of, but I know that you're not both prohibited from doing A and from doing B. I might then say: "Do A or B or both. Of course, stay within the scope of your other orders." If one of your other orders is never to do B, you can't say that my disjunctive command permitted you to do B. If this is right, then it's not part of the fundamental logic of commanding and permitting that by commanding a disjunction one permits the disjuncts.

Interesting question. Is it ever morally licit to issue the command to do A or B or both, when B is morally illicit? It is, I take it, always wrong to command or permit something wrong (I distinguish permission proper from waiving punishment). If commanding a disjunction always involves permitting the disjuncts, it follows that one may not licitly command a disjunction when one of the disjuncts in it is wrong. But if it is possible to command the disjunction without permitting each disjunct, then it may be licit to command a disjunction one disjunct of which is wrong, though not a disjunction both disjuncts of which are wrong. We can imagine a situation where very bad things will happen (to you and to your subordinates) if you refuse to issue an order you were commanded to issue, and the order is to do A or B or both, and B is morally wrong. In that case, it may be licit to say: "I command you to do A or B or both. And I forbid you from doing B." You've fulfilled your order to the letter and haven't commanded or permitted anything wrong. Still, in ordinary contexts, commanding A or B or both carries the implicated (and still real) permission of doing A and of doing B and of doing both.


Suppose now I command you to do both A and B. Interestingly, while it does follow that I permit you to do both A and B, it does not follow that I permit you to do A. I may only be permitting you to do A if you're going to do B as well. So commands are not closed under logical entailment. For if they were, then in commanding A and B, I would be commanding A, and hence also permitting A.


Heath White said...


I think all you need here are the observation that to command is to impose an obligation (or something like a prima facie obligation--whatever one comes up with, hold constant across what follows) and a bit of deontic logic, mainly that if you are obliged to do X then you are permitted to do X. For deontic logic we can, as a rough and ready measure, use normal modal logic.

So to command a disjunction is to oblige one to make a disjunction true; but since O(AvB) does not entail P(A)&P(B) it doesn't permit each disjunct.

Likewise, I think you need to say about conjunctive commands that O(A&B) entails O(A)& O(B), which entails P(A) & P(B), but it does not entail P(A) & P(~B).

Alexander R Pruss said...


The claim that if you're obliged then you're permitted entails the controversial claim that there are no real dilemmas. Otherwise, you might be obliged to A and obliged to refrain from Aing, and permitted to do neither.

By the way, as to your parenthesis in the first sentence, I think the relevant modality is not obligation, but obligation(x).

For suppose I have some authority over you and command you to do something that obviously negatively impacts both me and Mark Murphy in such a way as to render the action impermissible when not permitted by those affected. My commanding you issues a permission vis-a-vis the negative impact on me, but does not issue a permission vis-a-vis the negative impact on Mark. To be permitted to do the action simpliciter, you or I need to ask Mark's permission.

So we need to distinguish: obliged(Alex), permitted(Alex), obliged(Mark) and permitted(Mark). When I issue the command to A in this case, you come to be obliged(Alex) to do it, and permitted(Alex), but neither obliged(Mark) nor permitted(Mark). And unless you come to be permitted(Mark), you are not permitted simpliciter. Interestingly, in this case, however, my command is not null and void in the way a command to do something impermissible is normally null and void, since the command gives you reason to seek Mark's permission, if it's the sort of thing that it's permissible to seek permission about (there may be some things where we have no right to ask, but if the other volunteers then we can accept that).

These deontic modalities "permitted(x)" and "obliged(x)" are interesting. I think we can paraphrase "obliged(x)" as "owe to x". I don't know of a good paraphrase of "permitted(x)". The obvious thing is "permitted by x". But that's not quite right. For suppose I have appropriate authority over Mark. Then you can come to be permitted(Mark) by virtue of my giving you permission (think of parental consent to children's medical procedures). Maybe we should just take "permitted(x)" to be "not obliged(x) not".