Deontic logic: meta-imperatives?

(This is a reflection on Jorg Hansen’s “Imperative logic and its problems”)

I am not sure whether there is reasoning from imperatives to imperatives, but there does seem to be reasoning from imperatives to ‘ought’ statements. Say, Tim is a soldier and his captain has ordered him to stand guard. Then Tim ought to stand guard. Or, I have promised to meet you for lunch. Then I ought to meet you for lunch. My promise has had the same effect as the captain’s order: in my situation I am now subject to an imperative (!Meet him for lunch!), which is in force (not defeated or in any other way deprived of force), so I ought to see to it that it is satisfied (that I meet you for lunch).

This reasoning from a premise that a certain imperative is in force to a conclusion stating that something ought to be (or be done) appears to be central to the subject of deontic logic, the subject of normative reasoning. It seems so basic that it must perhaps be accepted as logically necessary, or as necessary by virtue of the meanings of the terms involved. I don’t mean to dispute that (though I have no idea what sort of necessity it is). But I do see some complexities and some questions I feel I need to face.

As preliminary, let’s take an old example. Suppose two imperatives are in force: !Honor your parents! and !Do not honor your father! Does valid reasoning from the existence of these two imperatives lead to the conclusion that I ought to honor my mother?

Perhaps so, but in that case it must be non-monotonic reasoning. For if there were an additional imperative in force, !Do not honor your mother!, I would be in a situation of moral conflict, and it is not clear what I ought to do. Prima facie, yes, I ought to honor my mother, and also my father, and also not honor them … But all things considered? There may be no answer, or there may be an answer that draws on additional features of my situation, not mentioned so far.

Let’s go back to soldier Tim and his captain. The example seemed straightforward because we naturally read it as describing a situation in which there was only one imperative in force. Actually, there were also many standing orders, and perhaps an order by the lieutenant, and promises Tim had made, and so forth. Should the principle if you are subject to an (undefeated) imperative to do X you ought to do X be extrapolated to if you are subject to many (undefeated) imperatives you ought to satisfy them all ? The move from each to all seems inescapable here, though we know that in other contexts it may be invalid.

In the case of a moral conflict, you can’t satisfy them all. It may still be true for each of those imperatives that you ought to comply, but it cannot be true that you must comply with all, since that is impossible.

So if we cannot reason from each to all in this case, how should we reason? I know what I want to say, I just don’t know whether it is something I can justify. What I want to say is:

[IMP] if you are subject to many (undefeated) imperatives, satisfy a maximally consistent set of those imperatives!

(In the case of a moral conflict, merely satisfying this does not necessarily lead to a unique thing you ought to do. I realize that, but it seems to me step one.)

But what is the status of [IMP]? Is it an imperative to which we are all subject? What gives it force (if it is in fact in force)? Is it a meta-imperative, or perhaps we should say, a higher-order imperative that governs reasoning from imperatives? if so, what could bring a meta-imperative into force? I’m going to have to think about this.

Is [IMP] defeasible?

Is [IMP], just as any other imperative, defeasible? An authority might explicitly issue a permission:

[PERM] if you cannot do all that, just do any or none, just as you like!

Actually, I don’t think that this is an instance of defeasibility, for [PERM] is not a higher-order imperative. For suppose that [PERM] is added to a set [S] of imperatives. Then this addition will not subtract from the family of maximally consistent sets of imperatives in force, though it will add some. And the calculation of what ought to be need not be seen as any different: for [PERM] is (or can be expressed as) an ordinary imperative, not a meta- or higher-order imperative.

Example: Imperatives 1, 2, 3 are to do A, B, C, which are not jointly satisfiable, but any two of which are compatible. Hence there are three maximally consistent sets. Now add imperative 4: !if you have any difficulty, just do one or none! If the agent does not know of any difficulty, nothing changes in what she ought to do, for the addition is a conditional imperative. But if such knowledge is added, then there are four possibilities for action, of which three are maximally consistent (satisfying 4 alone by not doing any of 1, 2, 3, is not maximal).

So, unless there are theoretical considerations (whether for or against, or for ways of qualifying it) that have not occurred to me, I would say that [IMP] is at least not a defeasible imperative.

Two points in favor of [IMP]

Meanwhile I note that [IMP] settles the examples about honoring your parents in the right way. If !Honor your parents! and !Do not honor your father! are the only imperatives in force, they form a maximally consistent set (the only one) and so you should satisfy both, which you can only do by honoring your mother (only). If however !Honor your parents! and !Do not honor your father! and !Do not honor your mother! are all in force then there are three maximally consistent subsets, and the only thing you ought not to do is to honor both your father and your mother. Which, as Bertrand Russell would have said, is just the conclusion that would have been reached by common sense.

Another way to check our intuitions is to imagine how someone might be called to account, and what would count as a good defense. So imagine that I live in a communal house, and through some unforeseen circumstances I end up, 40 minutes beforehand, facing three household chores to complete before dinner. Each would take 20 minutes: washing the lunch dishes, cleaning the dining room, managing the dishes that are already cooking. Impossible! At dinner I am called to account.

Scenario 1. “I did none of the three. My excuse is that it was impossible for me to do all that I ought to have done.”

This is fairly clearly unacceptable.

Scenario 2. “I did one of the three: I cleaned the dining room. My excuse is that it was impossible for me to do all that I ought to have done.”

The obvious retort is that I had time to do two of the tasks, and ought to have done so.

Scenario 3. “I did two of the three: I washed the dishes and cleaned the dining room. My excuse is that it was impossible for me to do all that I ought to have done.”

There may be resistance to this, on the basis that the third task, managing the cooking, was the most important. But the retort will not be that I did fewer or less of what I ought to have done. Except that we have a pointer here to the need for a value ranking of the admissible alternative, this tale of an accounting supports the intuitive appeal of [IMP]. We ought to do the most of what we ought to do, if we cannot do all that we ought to do.

Anecdotes and intuitive appeal are all very well — I still wonder if there are theoretical ways to support meta-imperatives, or higher-order imperatives, whatever we should call them, like [IMP]?

REFERENCES

Jorg Hansen “Imperative logic and its problems”. Pp. 137-191 in D. Gabbay et al. Eds. Handbook of Deontic Logic and Normative Systems. College Publications 2013.