Angels and Daemons
Logic
Level
3
I arrived on an island where each inhabitant is either Angel or Daemon (but not both). Angels always say the truth and Daemons always lie. Who can say the following statement?
"If I'm an Angel, then I'm a Daemon"
Angel
Both
Daemon
Neither
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1 solution
Let's suppose that an Angel says that statement. Thus, the antecedent of the conditional is true, and, by Modus Ponens, the consequence is true; that is, the Angel is a Daemon. As this is contradiction, an Angel cannot say the statement.
Now, let's suppose that a Daemon says that statement. Therefore, the antecedent of the conditional is false, and hence, recalling the conditional definition, the statement is true, either the consequence is true or false (although we know is true as the Daemon is, actually, a Daemon). As the Daemons always lie, we have reached a contradiction, because when a Daemon says the statement, he's saying the truth.
As each inhabitant on the island is either an Angel or a Daemon, no one can say the statement.
It is curious that we can set up an imaginary situation in which we define each element and get really strange situations, as the described above, where an statement is "forbidden". Indeed, each of us is an element of a situation... as we are defined as humans, which statements can we not say? We cannot think about that, because when we think about some of these statements, we're descovering them, thus, we can say statement. It will always be an enigma as we'll always be humans.