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Paradoxes and promises

Imagine that, on a Tuesday night, shortly before going to bed one night, your roommate says “I promise to only utter truths tomorrow.” The next day, your roommate spends the entire day uttering unproblematic truths like:

  1. 1 + 1 = 2.
  2. The grass is green.
  3. The sky is blue.

She continues on, in this vein, until going to bed. As she is about to fall asleep (and we assume she goes to bed before midnight), she proudly pronounces:

I kept my promise.

The question is this: Has she?

Your roommate’s pronouncement has a similar logical form to the truth-teller:

This sentence is true.

Unlike the Liar paradox:

This sentence is false.

which is true if false, and false if true, the truth-teller is true if true, and false if false. So it is indeterminate between the two truth-value assignments – it could be either one, and no inconsistency, incoherence, or any other sort of problem arises either way.

Likewise, your roommate’s pronouncement is, logically speaking, indeterminate. If we assume that is true, then in fact every one of her pronouncements on Wednesday was true, and hence she kept her promise. If, however, we assume it is false, then in fact it is not the case that each of her pronouncements on Wednesday was true, and so she failed to keep her promise.

But there seems (in my mind, at least) to be a strong intuitive push to attribute truth to your roommate’s assertion. In other words, it would be totally perverse to respond to your roommate’s assertion along the lines of:

Well – perhaps not. Maybe you are lying right now!

But why is this? After all, nothing in the logic of the situation seems to privilege an assignment of truth to your roommate’s assertion over an assignment of falsity.

It is worth examining how other, superficially similar situations work. First, note that if your roommate had, on Tuesday, promised to only tell truths on Wednesday, and then said true things throughout the course of the day on Wednesday, and then, just before falling asleep, finished off the day with:

I didn’t keep my promise.

then we have a paradox. If the last sentence is true, then every sentence uttered by your roommate is true, so she kept her promise, so the last sentence must be false. But if the last sentence is false, then your roommate did not utter only truths on Wednesday, so she didn’t keep her promise, so the last sentence must be true.

Similarly, if you roommate, on Tuesday, promised to only utter falsehoods on Wednesdsay, and then on Wednesday said only false things like:

  1. 1 + 1 = 3.
  2. Grass is blue.
  3. The sky is green.

during the day and finished up the day with:

I kept my promise.

then we, again, have a paradox.

The final case, however, is the most interesting. Imagine that your roommate, on Tuesday night, promised to only state falsehoods on Wednesday, and then made only false claims during the next day, and finished up the day with:

I didn’t keep my promise.

Here there is no paradox. If the final claim is true, then she didn’t keep her promise, because at least one of her assertions (in fact, this last one) is not false. If the claim is false, however, then she did keep her promise, but is lying to us about it.

So this fourth case, like the one we started with, is indeterminate: there seems to be nothing in the logic of the situation that privileges either assignment – truth or falsity – to the final claim made by your roommate.

But what is interesting in this case is that (again, at least in my mind) there is no intuitive ‘push’ to assign truth to your roommate’s claim, rather than falsity. This makes it rather different from the first case. The question is why it is so different.

The answer, I think, lies in looking at more than the logic of the sentences in question. In particular, it lies in noticing that, when we are communicating linguistically, we are implicitly agreeing to live up to certain expectations, and interpreters construct their understandings of our utterances (and their truth values) in part in virtue of these same expectations.

The first such default expectation on the part of interpreters is that we will tell the truth (at least most of the time). Thus, listeners are justified in adopting something like the following principle, when interpreting our utterances.

Truth-telling Principle:

All else being equal, I should attempt to interpret speakers as if they are telling the truth.

Of course, things are not always equal. But the upshot of this principle is this: when confronted with an apparently sincere utterance that has two interpretations, where on one interpretation the utterance is true, and on the other interpretation the utterance is false, and where there are no other reasons to prefer one of these understandings of the utterance over the other, listeners should opt for the interpretation that makes the assertion true, since this accords with the expectation that speakers generally tell the truth.

The second expectation is that we will keep our promises (again, at least most of the time), and hence we have a second principle:

Promise-keeping Principle:

All else being equal, I should attempt to interpret speakers as if they are keeping their promises.

Again, things are not always equal. But the upshot of this principle is this: when confronted with an apparently sincere utterance that has two interpretations, where on one interpretation the speaker is keeping a promise, and on the other interpretation the speaker is failing to keep that same promise, and where there are no other reasons to prefer one of these understandings of the utterance over the other, listeners should opt for the interpretation where the speaker is keeping her promise, since this accords with the expectation that speakers generally tell keep their promises.

We can now easily explain the intuitive difference between the first and fourth case described above. In the first case we have two choices: either your roommate is telling the truth (and hence also keeping her promise), or your roommate is lying (and hence failing to keep her promise). Both of the two principles described above weigh in favor of the first option, however, so we are strongly motivated to assign truth to your roommate’s utterance.

In the second case, however, things don’t work out so uniformly. Again, we have two choices: either your roommate is telling the truth and hence failing to keep her promise, or your roommate is lying and hence keeping her promise. What we called the Truth-telling Principle weighs in favor of the first option, but Promise-keeping Principle weighs in favor of the second option. The two principles conflict, and hence we remain undecided between the two options, with no intuitive preference for one over the other.

Image credit: “Truth”, by Daveblog. CC BY 2.0 via Flickr.

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