Thursday, May 21, 2009

An odd puzzle about eternal life

Suppose I am going to live forever. I promise you that I will one day sing Yankee Doodle to you. But I never do. It seems like in the world where this happens, I do something wrong, namely broken my promise to you (if it is acceptable to break promises with good reason, then in all of my examples add the proviso that there is no good reason). But when do I break the promise or do this wrong? At any given time t, I am in compliance with the promise (i.e., my actions are compatible with the fulfillment of the promise).

I can run the same puzzle on a finite interval. Suppose I have the superpower of singing Yankee Doodle at any exact given time I wish, and I promise you that before noon I will start to sing Yankee Doodle. But I don't. I've done something wrong. But when? At any time before noon, I am still in compliance with the promise, so I haven't done anything wrong yet. At noon, it's too late to comply, so I have an excuse for not starting to sing at noon—it wouldn't be the fulfillment of the promise. So when have I done wrong?

There are a couple of moves one could make in response:

  1. We can say that the above paradoxes tell us something about the nature of time or action, such as that it is impossible for one to have an infinite number of choices.
  2. We can deny the principle that if you do wrong, you do wrong at some time. Denying this principle may push one towards four-dimensionalism, though perhaps the denial is less radical in the case of omissions than of commissions.
  3. We could conclude that certain kinds of open-ended promises are invalid. We could try to say that it is a necessary condition on the validity of a promise that the promise could (in a contextually relevant sense of "could") give one a reason to act on pain of violating it. Thus, I cannot validly promise you that the weather will be nice tomorrow, because the weather is not up to me, so I cannot (in the ordinary sense) get a reason to act on pain of violating the promise. In the Yankee Doodle cases, while I have a reason to sing Yankee Doodle at many different times, at no time do I have, or can have, a reason to sing Yankee Doodle on pain of violating the promise (because there is always more time). So the promise is not valid. This is an ad hoc restriction on promising: it is of the very nature of promises to give rise to reasons to do something on pain of violation of the promise.
I think (3) is probably the best way out.


Heath White said...

(3) comes as an unhappy surprise to me, since I frequently make open-ended promises like, "I will take the trash out before I go to bed" or "We will go get ice cream some time this weekend."

Mike Almeida said...


This is an interesting puzzle. In the infinite case, the problem is purely epistemological. It is not that there is no time at which it is proper to punish the person. It's that we don't know what that time is. So long as we assume that the proposition 'S will keep the promise' has a truth-value, we can punish S iff. it's false. We just can't easily know that it's false. The finite case seems easier to solve. You can punish for having failed to keep the promise during the interval, though not for failing now (post interval) to keep the promise.

Alexander R Pruss said...


Hey, it should be a happy surprise. For if the promises are invalid, then you're not bound by them, and shouldn't that be happy news?

Seriously, in real-life cases, one can roughly identify a time at which one has a reason on pain of promise violation. There is a minimum length L of time it would take you to get ice cream (it's rather larger than 2d/c where d is the distance from your house to where the ice cream is sold, and c is the speed of light). Thus, if you've promised to get the ice cream this weekend from the grocery store, and the grocery store is open 24-hours a day, you have a reason on pain of promise violation at L units of time before midnight on Saturday (it's wrong to do non-emergency grocery shopping on Sunday).

The taking out the garbage promise does give you a reason not to go to bed before you've taken out the garbage, a reason you have on pain of promise-violation. So it's not so much a reason to take out the trash, as a reason not to go to bed. Of course, combined with a prudential reason to go to bed, you will be rationally well served by taking out the trash. Still, this is counterintuitive, I agree.

Alexander R Pruss said...


But, I think, one can only punish for an action that involved a wicked act of will. But when did the wicked act of will occur?

Huume said...

Has anyone ever told you that you are brilliant?
My goodness. I will be around here more often. You are natures hidden secret.

Chong Choe said...

Dr. Pruss,

Both (2) and (3) seem drastic to me. As to (2), I think, if a wrong occurs, it occurs at some time (even if the exact time is unknown).

The wrong occurs in the finite interval case when the time expires—at noon. It is too late to comply, but that doesn’t save the promisor from having broken his promise. Impossibility is no excuse because the promisor could have started to sing at any time before noon.

The infinite interval case is more complicated (I say “complicated,” because in my mind it takes extra steps to explain). I think we still can say, if the wrong occurs, it occurs at some time. The only thing is, the wrong has not occurred and may never occur.

At this point, we may be tempted to resort to something like (3), but I don’t think that’s necessary. So long as the promisor is willing to make an open-ended promise and the promisee is willing to accept it, I don’t see why the promise would be invalid simply because the promisor has no reason to perform on pain of violating the promise.

Maybe the less drastic alternative is to say that open-ended promises essentially are conditional promises—i.e., performance at the will of the promisor. In the infinite interval case, you promise to sing Yankee Doodle, but really you are promising to sing Yankee Doodle if you want to. (Such promises may be considered one-sided, but I think where the stakes are low, it really doesn’t matter.) You say, “you never do,” and so you’ve done something wrong, but I don’t think so. Because you have eternity to make good on your promise, it may be more accurate to say, “you haven’t done so yet.”

If you never intend to sing Yankee Doodle, well, that’s another matter…

Anonymous said...

Let's consider Russels picture of an author (was it Tristram Shady) who writes about every event that happened
in his life (the formulation here could be more elegant).

It takes him 1 year to write about the first day.
It takes him another year to write about the second day.
And so on.

Let's say the author would ask God "Lord, please keep me alive forever. I swear that I will write about every day of my life."
What does God say and what are the consequences?

It could be used as an argument in favor of the possibility of an actual infinite. God knows everything the author will write. So God knows infinitely many books.