Friday 22 January 2016

Variant of the Liar Paradox

Each day, except on Wednesdays, when children have the afternoon off, my son's teacher checks in class which kids stay on school for lunch and whether they signed up for a hot meal or not. By now, he pretty much knows the lunch habits of his pupils and so this morning, when arriving at Maitée on his list, he said, "Okay, I know Maitée is going to say now she's going to eat sandwiches", at which point Maitée simply replied with "Yes." My son was quick to point out to his teacher that this was a paradox. Reporting this to me at lunchtime today, he also said the teacher looked in his direction right after his exchange with Maitée, since the teacher also knows by now that my son is a paradox enthusiast.

The paradox can probably be resolved
A. with the help of simple pragmatic theory, which makes a distinction between (i) what is said (literally) and (ii) what is meant by an utterance,
B. and by pointing out that the verb say can be used vaguely to refer either to verbatim statements or to what one means by a linguistic utterance. (That's why, if I ask you whether you'll come over to my place tonight and you just say "Yes", I can say to you tomorrow, in case you didn't show up, "But you said you'd come over," even if you didn't really say "I'll come over.")

Update (29/06/2018):
My son was perhaps a bit too eager to think there was a paradox involved. Maybe the reply "yes" is just ambiguous, i.e., between "Yes, Sir, you're right to assume that I'm going to say I'll have a sandwich lunch" and "Yes, Sir, I'll have a sandwich lunch". Still, what's vaguely (or, who knows, truly) paradoxical here is that when the "yes" is taken to mean the former, the reply actually defeats itself, in the sense that agreeing with the teacher that he has just made a correct prediction is not the same thing as explicitly agreeing with the implicit question "Are you going to eat sandwiches?". So, Maitée's reply should have been: "Yes (you're right), yes (I'm going to eat sandwiches)". With just a single "yes", agreeing with the teacher's full claim corresponding to the entire sentence, the teacher's prediction is both correct and false.

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