Three logicians walk into a church

Rector: Would any of you like to fill out a visitor's card?

Logician 1: I don't know

Logician 2: I don't know.

Logician 3: No.

Comments (14)

Help me get it.

Jim,

A logician could only answer "I don't know," if he or she personally did not want to fill one out.

The third one knows that neither of his or her colleagues wants to, knows that he or she does not want to, and is able to answer for the group.

Peace,

Bill

If even one of the logicians wishes to fill out a card, then the answer to the question "Would any of you like to..." would be "yes". So if Logician 1 wished to fill out a card, he could answer "yes". He doesn't wish to fill out a card, but he doesn't know if L2 or L3 wants to fill one out. If either one does, the answer to the question would be "yes". At this point, he has to reply that he doesn't know what the answer to the question should be.

L2 has the same problem. She knows she doesn't want to fill out a card, and she knows L1 doesn't want to (or he would have answered "yes"). She still doesn't know if L3 wants to fill out a card, so she has to reply that she doesn't know what the answer to the question should be.

Lucky L3! L3 knows that neither of his companions wants to fill out a card, because neither answered "yes". He also knows that he doesn't want to fill out a card. So he concludes that none of the three wishes to fill out a card, and he can safely, and logically reply "no".

Allison de Kanel

In other words, it has to do with the logic of quantifiers.

The question, to a logician, would be parsed:

"Is it the case or not that there is one of you who wishes to fill out the card."

For the first two, the only possible answer is "yes" or "I don't know." Only the third has enough information to answer "no," though he or she could also answer yes.

And what does the Rector know?

That none of them wants to fill out a card. Or that is is not the case that some one or more of them wants to fill out a card. And that asking questions of logicians is always a bad idea.
(retired logician bur still practicing)

Harry - Haven't you assumed that the Rector follows logic, and also that the Rector knows the three are logicians?

Hmmm. yes. I was already going to modify what I said by noting that the Rector doesn't *know* that questioning logicians is a bad idea, since he has only anecdotal, low-sample, uncontrolled evidence. So, not following logic and not knowing that his people are logic followers, he can at best decide that one man definitely doesn't want a card and that the other two are strange, since they don't seem to know their own wants in the matter. That is, he takes the question as being, in fact, three questions, one to each logician (a metaquantifier, if you will) and so treats each answer separately as for the speaker only.

Now... which one of the logicians is wearing a blue hat?

Must be a slow news day at the Cafe! Rector should worry about how the will evaluate his question at that German site.

@Michael, slow news day, but I thought that this conversation was a blast.

I though this post was very funny, but it loses some of its humor when it has to be explained.

Always a problem for logicians. whose jokes have not only to be explained, but proven. Think of poor Kurt Goedel; the best joke in three thousand years of mathematics and the punch line gets lost in the pages of proof. Theologians are always stepping on god's jokes, too.

Dear Lionel - sorry some of us are so stupid about logic that we need it explained. Thanks to those who helped your lesser beings!

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