Date: Jul 27, 2013 6:16 AM Author: quasi Subject: Re: Maximisation problem pepstein wrote:

>quasi wrote:

>>pepstein5 wrote:

>> >Peter Percival wrote:

>> >> Paul wrote:

>> >> >

>> >> >Let n be a fixed integer > 1. n logicians walk into a bar.

>> >> >The barwoman says "Do all of you want a beer?" The first

>> >> >logician says "I don't know." The second logician says

>> >> >"I don't know." ... The n-1st logician says "I don't know."

>> >> >The nth logician says "Yes please."

>> >>

>> >> That doesn't answer the question correctly.

>> >

>> >Please could you state your objection? Everyone is narrowly

>> >focusing on the yes/no question: "Do all of the n logicians

>> >want a beer?"

>>

>> It's not exactly a yes/no question since some of the answers

>> have been "I don't know".

>>

>> >Everyone saying "I don't know" clearly wants a beer because,

>> >if they didn't want a beer, they would know that not everyone

>> >wants a beer and would answer "no" instead of "I don't know."

>>

>> The joke has the implicit assumption that each logician would

>> answer yes or no if asked individually as whether or not

>> they want a beer. With that assumption

I'm no longer so sure of my claim below about infinitely many

levels of recursion.

>>together with infinitely many levels of recursion about that

>>assumption, the logic of the joke works.

>>

>> To eliminate that issue, the joke could be stated as follows.

>>

>> BEGIN JOKE

>>

>> Let n be a fixed integer > 1. n logicians walk into a bar.

>> The barwoman says "Do all of you want a beer?"

>>

>> Assume that

>>

>> (A1) Each logician either wants a beer or doesn't want a beer.

>>

>> (A2) Each logician knows that each of the others either wants

>>

>> a beer or doesn't want a beer.

>>

>> (A3) Each logician knows that each logician knows that ...

>>

>> and so on, for infinitely many levels.

A1 and A2 seem necessary, but I don't now see any need for

further levels. I don't know what I was thinking.

>>

>> (B1) Also assume that each logician will answer either

>> "Yes","No", or "I don't know", and will only answer

>> "I don't know" if they can't deduce the preferences of

>> the others.

>>

>> (B2) Each logician knows that each logician will answer

>> either "Yes","No", or "I don't know", and will only answer

>> "I don't know" if they can't deduce the preferences of the

>> others.

Once again, as far as I can see, B1 and B2 are needed, but I

don't see a need for further levels. Then again, right now I'm

very tired, so maybe I'm not thinking it through all the way.

>> (B3) Each logician knows that each logician knows that

>> each logician will answer ...

>>

>> and so on, for infinitely many levels.

>>

>> With those assumptions,

>>

>> The first logician says "I don't know." The second logician

>> says "I don't know." ... The n-1st logician says "I don't

>> know." The nth logician says "Yes please".

>>

>> END JOKE

>>

>> Of course, the joke should be left as it is, so as not to

>> ruin it. The goal is humor, not precision.

>

>quasi,

>

>I agree with everything in your posting.

I think you agreed too quickly.

I now think the stuff about infinitely many levels is nonsense.

>Would you be so kind as to answer the question I opened the

>thread with? Which value of n do you think makes the joke work

>best?

I like n = 3 best.

n = 2 wraps up too quickly, with no suspense.

n = 4 or higher is too long-winded.

Leaving n unknown is too abstract, suggesting more conceptual

depth than is actually there.

quasi