Wednesday, July 17, 2019

Distributive promises

Suppose I promise my class to grade all the weekly homework within three days. In week four, I fail and am late with grading. If the content of my promise was simply the proposition

  1. that I grade all the homework within three days,

then after week four, then no matter how speedy I am with grading the homework, proposition (1) is just plain false. And this means that my promise no longer generates any reason for me to grade the homework in weeks five and onward within three days, which seems wrong. I should, instead, apologize for failing in week four, and work even harder in the succeeding weeks.

I think this is because the promise was distributive. It wasn’t a promise to make proposition (1) true. It was a promise that for each week of homework generated a separate promissory reason to grade that week’s homework within three days.

The normative force of the promise is rather like making a separate promise for each week of class:

  1. I promise that in the first week, I will grade the homework in three days. I promise that in the second week, I will grade the homework in three days. … I promise that in the 15th week, I will grade the homework in three days.

But other cases of distributive promises aren’t as neatly handled. Suppose I promise my class:

  1. If you come to office hours, I will try to answer any question you might have about logic.

Again, this is distributive. If I refuse to answer a question out of laziness, it doesn’t let me off the hook with regard to the next question. But if I analyze this as a sequence of separate promises, then that sequence has to be infinite:

  1. I promise that if you ask me q1 at t1, I will try to answer. And if you ask me q2 at t1, I will try to answer. … And if you ask me q1 at t2, I will try to answer. …

where the list goes through all the possible questions about logic and all the possible times that fall within office hours. Have I really made an infinite number of promises? This seems implausible. Moreover, normally, we think that one cannot make a promise without knowing that one has done so. But I might not know that q8 is a question about logic or that t3 is a time within office hours (in fact, I might not even know that t3 exists—I might think that there are no intervals finer grained than a Planck time, but there might be).

Or I could make a promise to God regarding my treatment of all future as-yet-unconceived persons who have some property. Again, this is distributive: failure in one case does not excuse me from trying in other cases. But if analyzed as a collection of promises about actual future persons, we get the weirdness that what I have promised depends on what I will do. So it would have to be a collection of promises about possible future persons. And it’s not clear that this makes sense except given some controversial metaphysical assumptions, such as the existence of haecceities.

So, I think distributive promises don’t reduce to non-distributive ones.

Maybe, though, one can try to handle the cases with some sort of a doctrine of approximate truth. Perhaps when I promise a proposition, if I am no longer in a position to make the proposition true, I am required to make it as approximately true as I can? I think this kind of a principle will lead to counterintuitive results. For suppose that there is some benefit to you from having p be exactly true, while close approximations to p are harmful to you, while some way of making p very false is much better for you. Then I shouldn’t strive for a close approximation to p. (Think of cases of medicinal dosage, perhaps.)


SMatthewStolte said...

Maybe it would help if we could say that promise-breaking comes in degrees. As long as the promise could still be broken to a greater degree than it already has been, it still carries force. Usually, if you say, “I promise to have the first paper graded within three days,” the fact that it is day four and you haven’t finished grading doesn’t mean that the promise is no longer a reason to finish as soon as possible. But at some point, the promise is perfectly broken. If you discover that you made this promise about a small assignment 25 years ago and still haven’t finished grading it, doing it now would be pointless.

Heath White said...

Can't we just appeal to logical form? There is a difference in quantifier structure between

(a) For all questions about logic Q, I promise to try to answer Q
(b) I promise to try to answer: all questions about logic.

I think we hear (a) rather than (b) because it makes more sense (Gricean considerations). But I can imagine cases where the first structure made more sense and then we would assume that one. Suppose the Army Corps of Engineers promises to do their best to keep every part of the structure protecting New Orleans from flooding intact. If they simply can't fix one large breach, it does not make sense to keep working on other breaches. They should turn their attention to, say, evacuating the city.

Alexander R Pruss said...


Good point. But it's going to be highly contextual as to what counts as a greater or lesser degree of satisfaction.


This sounds right, but it emphasizes my point: The distributive promise isn't a promise of a single proposition, or a set of promises of single propositions, but logically a quite different beast.

And the logic of this sort of quantification is rather odd. Normally, where a universal quantifier goes, an existential one can go. And if the sentence with the universal quantifier makes unambiguous sense, so does the one with the existential one.

Now, (a) is a sensible performative. But consider:

(a*) For some question about logic Q, I promise to try to answer Q.

This makes no sense as a performative (it makes sense as a plain assertion of the fact that one has made a particular promise), just as it would make no sense for the dean at graduation to declare: "I hereby confer on some of you the degree of Master of Arts."

So whatever is going on here isn't just simple logical embedding of the sort we learn about in logic. I guess compositionality is rather more complex when one is embedding speech acts rather than formulas. For instance, while "If it's raining today, I promise to visit you" makes sense as a performative, "If I promise to visit you, it's raining today" doesn't seem to. And while "I promise to visit or call you" makes sense (ordinary simple promise), "I promise to visit you or I promise to call you" does not.

By the way, it turns there is some interesting-looking literature on embeddings of illocutionary acts that is relevant but I don't have the energy to figure it out:

Alexander R Pruss said...


Let me build on your quantifier suggestion, and try to solve the complexities in my previous response.

Take a sentence P that embeds "I promise that I will". Replace every instance of "I promise that I will" with "I am obligated to" to get a sentence P*.

Hypothesis: The normative force of P is that I am obligated to phi in any circumstances C coherent with P* and such that P* entails that I am obligated to phi in C.

(For greater precision, replace "obligated" throughout with "promissorily obligated".)

Let's try this on some cases.

P1. For all questions Q, I promise that I will answer Q.
P1*. For all questions Q, I am obligated to answer Q.

Well, P1* entails that if Q1 is a question, then I am obligated to answer Q1. Hence, when saying P1 succeeds, I am obligated to answer all questions.

P2. I promise to visit you or I promise to call you.
P2*. I am obligated to visit you or I am obligated to call you.

Now take any circumstances C coherent with P2*. There is no phi such that P2* entails that I am obligated to phi in C.

It is tempting to think that P2* entails that I am obligated to visit or call you. But here I will take the Mark Murphy line that we don't want to multiply obligations unnecessarily, and in particular an obligation to alpha does not entail an obligation to alpha-or-beta.

Note that not all the obligations are the ones that are actually described in P*. Consider:

P3. For all homework H, I promise that I will grade H within three days.
P3*. For all homework H, I am obligated to grade H within three days.

Let C be these circumstances: it's Monday and this week I won't have any time for grading. Then because of the general obligation to see to it that I am able to fulfill all my obligations, P3* entails that I am obligated to assign no homework in C. This isn't one of the obligations described in P3*, but it is an entailment of P3*. (This may be another way in which the distributive promise P3 is not just a large set of individual promises.)

Finally, maybe we can say that P was successfully uttered provided that P's being uttered non-aberrantly brought it about that P* is true.

Heath White said...

A few thoughts.

First, I don't think performatives can be embedded, properly speaking. So I don't think

P2. I promise to visit you or I promise to call you

makes any sense. (What would have made sense is "I promise to visit or call you.") For the same reason, you can't put a performative in the antecedent of a conditional.

I do think you can put a performative in the consequent of a conditional. ("If it's raining, I promise to visit you.")

I also think you can use them with existential quantifiers. ("Ask me any question about logic you like. I may not answer all of them, but I promise to answer at least some.") What makes "I hereby confer on some of you the Bachelor of Arts degree" weird is that ordinarily there is nothing else specifying who gets the degree. But if he clarifies, like "I hereby confer on some of you--the ones with a passing GPA--the BofA degree" then I think the appearance of weirdness vanishes.

I think the "hypothesis" above is sound, as far as I can make out.

Now, why would I say performatives can't be embedded, but then say that they can function in quantified contexts and the consequents of conditionals? Well, the quantified contexts are well-understood as making claims about possible worlds (circumstances): In all/some of *these* circumstances, I am obligating myself to do such-and-such. If I understand the advanced thought about conditionals these days, they are similar. In the [antecedent-world] circumstances, I am obligating myself to do [the consequent]. This is logically different from, say, the embedding in a disjunction.

Alexander R Pruss said...


"Ask me any question[s] about logic you like. I may not answer all of them, but I promise to answer at least some."

I think this is not a case of existential quantification into the scope of a quantifier. I would analyze this as:

"For all qs, if the qs are questions about logic that you ask, then I promise that there exists at least one r among the qs such that I answer r."

I.e., the existential quantifier is in the scope of the "I promise that", and there is a universal quantifier (over pluralities) with wide scope.

Laws that are insufficiently determinate are invalid. Thus, I assume, one cannot have a law that prohibits people from selling "a lot of" alcohol to one customer. I wonder if we have a similar thing with performatives: A performative that fails to sufficiently specify (perhaps with a lot of help from the context) its normative effect is invalid. Thus, "I hereby confer on some of you the degree of Master of Arts" is invalid, but there is no difficulty in "I hereby confer on those of you who did not fake your dissertation data the degree of Doctor of Philosophy" (and would mean the university does not need to withdraw the degree if it turns out that someone's dissertation data was fake, but simply issue a clarificatory announcement that that person never graduated).

Some vagueness is OK, though, and more vagueness is OK in day-to-day performatives than in laws. There is nothing wrong with an accountability partner promising: "I won't let you drink a lot tonight."