A native, either a knight or a liar, once pointed to a man sitting below a tree and told me "If asked, that man would say I'm not the same type as he is."
What can you deduce about the native or the man?
It is given that the native is a
knight or
liar, but it is not given that the man sitting below a tree is limited to one of the categories of
knight or
liar.
If the native were a
knight, then the treeshaded stranger would give an answer congruent to "I'm not the same type as he (
the knight) is". Thus, the treeshaded man could not be a
knight, yet this does not make the treeshaded stranger a
liar. He could be a
knave,
normal, or some other type.
Given the native was a
liar, if the treeshaded man were a
knight the treeshaded man would have answered the question with an answer congruent to "I'm not the same type as he (
the liar) is". This answer would have the native, a
liar, making a true statement  a contradiction, thus the treeshaded man could not be a
knight.
Given the native was a
liar, if the treeshaded man were a
liar the treeshaded man would answered the question (assuming he would have answered) with an answer NOT congruent to "I'm not the same type as he (
the liar) is", i.e., "I'm the same type as he (
the liar) is". Such a statement could not have been made by a
liar, as it would be a true statement  a contradiction, thus the treeshaded man could not be a
liar (who provided an answer similar to that given).
In conclusion, nothing new is known of the native. He is either a
knight or a
liar.
What is known is that the treeshaded man is not a knight and likely not a
liar, yet he could be
knave,
normal, or some other type.

Posted by Dej Mar
on 20110911 00:02:41 