Logic Question: Mathematician's Life Depends on Next Statement to Cannibals

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SUMMARY

The logic question presented involves a mathematician who must make a statement to determine his fate at the hands of cannibals. The key resolution is that the mathematician states, "You will hang me," creating a paradox that prevents the cannibals from executing either option without violating their own rules. This paradox highlights the complexities of truth and belief, as the cannibals' interpretation of the statement directly influences the outcome. Ultimately, the discussion reveals that the mathematician's survival hinges on the cannibals' perception of truth.

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Philosophers, mathematicians, logic enthusiasts, and anyone interested in the interplay between language, truth, and belief systems will benefit from this discussion.

almoo
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Honestly, I have no clue how to answer this question. A professor sent this out in a email, but I don't have a class with her so I don't think its homework. Care to throw some ideas? Is it really simple...? Apparently its a logic question, but it seems illogical to me.


"A mathematician is stranded on an island and is captured by a group of cannibals. They tell him that he gets to choose his way to die. The cannibals will shoot him if the next statement he says is true, and they will hang him if the next statement he says is false. The mathematician makes a statement and the cannibals have to let him go. What did the mathematician say?"
 
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I guess something like, "this statement is false", which is a sort of paradox, so because it can be neither true nor false, they release him.
 
It's called a http://mathworld.wolfram.com/LiarsParadox.html" .

CS
 
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almoo said:
"A mathematician is stranded on an island and is captured by a group of cannibals. They tell him that he gets to choose his way to die. The cannibals will shoot him if the next statement he says is true, and they will hang him if the next statement he says is false. The mathematician makes a statement and the cannibals have to let him go. What did the mathematician say?"

The mathematician just said:
"You will hang me."
 
Rogerio said:
The mathematician just said:
"You will hang me."

So they shot him as he hung.
 
Well, the question is who decides what is truthfull, the cannibals or the mathematician? (-:
 
He could also decide not to talk, and then nothing happens.
 
loop quantum gravity said:
He could also decide not to talk, and then nothing happens.

The riddle states that he makes a statement and then they let him go.

CS
 
As Rogerio says, he says "you will hang me". If the cannibals believe that is true, then they must shoot him which makes his statement false and so they must hang him. If the cannibals believe that is false, they must hang him which makes it true so they must shoot him. Either way violates what they said.
 
  • #10
Thanks guys. I think i can follow what Rogerio said. Makes sense to me.
 
  • #11
If he tells them look ,every Sunday i play football, what will the cannibals do??
 
  • #12
poutsos.A said:
If he tells them look ,every Sunday i play football, what will the cannibals do??

This answer doesn't help him...
If the cannibals believe him, they whill shoot him.
And if they don't, they will hang him.
 
  • #13
Anyway, he will stop to play football.
So, I guess the cannibals will hang him.
 
  • #14
Does his life depend on what the cannibals believe or not??or whether the statement is true or false??
 
  • #15
poutsos.A said:
Does his life depend on what the cannibals believe or not??or whether the statement is true or false??

If the statement is true, then the cannibals will shoot him.
But what specifically would be driving the cannibals? A magical force? A lie detector?
How can they know? Maybe they are very sensitive, and they can "feel" that?
Well, I prefer to think that the cannibals themselves decide whether the statement is true or not.
 
  • #16
Anyway, his life (or death) depends on what the cannibals believe.
 
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