Brain Fried Logicians

Logic Level 2

Sometimes, when logicians have been awake for more than 24 hours, they start being fuzzy and may not know the answer to a question that they normally would.

One day, after a Logicthon, 3 logicians were asked: Did anyone sleep in the past 24 hours?

  1. The first logician says I don't know .
  2. The second logician says I don't know .
  3. The third logician says I don't know .

What is the minimum number of logicians that have been awake for more than 24 hours?

Assumption: A logician is someone who usually is rational, perceptive and truthful, unless otherwise stated.

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Chung Kevin by Chung Kevin , 46, Australia

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1 solution

If any of the logicians slept the previous day, they would be able to reason correctly. And they would know that they've slept, and that the answer to Did anyone sleep in the past 24 hours? would be true.

However, since none of them could answer the question, none of them slept.

Moral: Early to bed and early to rise, makes a man healthy, wealthy and wise.

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Also , observe that if the logicians would reason correctly and when they would be asked "have slept in the last 24 hours ?" they would reply "I don't know" they could deduce that because they reply like that they didn't slept and would eventually come to the conclusion that "No , because I said I don't know and would have known otherwise".

This is an interesting exercise if this thing which , in order to obtain a technical understanding of things can be denoted as "reflexive" or auto-referential reasoning is taken into account making that there is a difference between the condition "not reason right" and the condition "not remember" (but still reason right or not) that would change the answer.

A A - 4 years, 11 months ago

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I am afraid I do not understand.

Agnishom Chattopadhyay - 4 years, 11 months ago

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What I tried to say is this : if the logicians would analyze their reply to the question (meaning , they would come to their output and reflect on it) and still reason correctly they would find that because they don't know if they slept or not they must have not slept but may have been a little mixed with technicalities.

I pointed out by this , that the problem is interesting if this "reflexive" or auto-referential characteristic of their reasoning which can be defined as being able to reason about your own output and therefore a II order thinking , anyway taken into account.

A A - 4 years, 11 months ago

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