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6 Truth and Lies
Basic Concepts Paradox
Consider the phrase, “I am lying.”
If this were true, I would be lying. Therefore, it is logically incorrect. If this
was not true, the fact that I am lying would be a lie. This is also logically
incorrect. Phrases that contradict themselves, like the one above, are called
paradoxes. The paradox above is the famous liar paradox stated by
Eubuleus.
Example Peter met three natives on an island. One native is from the honest
tribe and tells only the truth. The other two natives are from the
dishonest tribe and tell only lies. Read the following conversation
and determine who is from the honest tribe.
Peter: Is the girl from the honest tribe?
Boy: Yes, she is from the honest tribe.
Old Man: No, she is not from the honest tribe.
Peter: Then which tribe are the boy and the old man from?
Girl: The boy and the old man are from the same tribe.
Class Notes
If the boy is from the honest tribe, his statement is (true, false). Then, both the boy and
the girl are from the (honest, dishonest) tribe, which is logically (correct, incorrect).
If the old man is from the honest tribe, his statement is (true, false). Then, the boy’ s
statement becomes (true, false), meaning that the girl is from the (honest, dishonest) tribe.
The girl’s statement becomes a lie, which is logically (correct, incorrect), if the old man is
from the honest tribe.
Therefore, the is from the honest tribe.
50 NUMINO Challenge C2
Basic Concepts Paradox
Consider the phrase, “I am lying.”
If this were true, I would be lying. Therefore, it is logically incorrect. If this
was not true, the fact that I am lying would be a lie. This is also logically
incorrect. Phrases that contradict themselves, like the one above, are called
paradoxes. The paradox above is the famous liar paradox stated by
Eubuleus.
Example Peter met three natives on an island. One native is from the honest
tribe and tells only the truth. The other two natives are from the
dishonest tribe and tell only lies. Read the following conversation
and determine who is from the honest tribe.
Peter: Is the girl from the honest tribe?
Boy: Yes, she is from the honest tribe.
Old Man: No, she is not from the honest tribe.
Peter: Then which tribe are the boy and the old man from?
Girl: The boy and the old man are from the same tribe.
Class Notes
If the boy is from the honest tribe, his statement is (true, false). Then, both the boy and
the girl are from the (honest, dishonest) tribe, which is logically (correct, incorrect).
If the old man is from the honest tribe, his statement is (true, false). Then, the boy’ s
statement becomes (true, false), meaning that the girl is from the (honest, dishonest) tribe.
The girl’s statement becomes a lie, which is logically (correct, incorrect), if the old man is
from the honest tribe.
Therefore, the is from the honest tribe.
50 NUMINO Challenge C2
