Question
A Monster steals a Child from a Father. The Father pleads to the Monster for the return of the child.
The Monster promises that Father that he will return the child if the Father can guess what he is going to do.
Then, the Father guesses, “You are not returning the child to me.”
What would be the Monster’s response to the Father’s guess?
My approach is as follows
Let $p =$ monster intends to return the child
Case 1: $p $ is true
$p \implies \lnot p$
Case 2: $\lnot p$ is true
$\lnot p \implies p$
Combining the above two cases
$p \implies \lnot p \implies p \implies ... $
Which is clearly a contradiction, hence this question has no solution.
I disagree.
The Monster does not say that he will return the child if and only if the father guesses what the monster is going to do.
If the Monster would have said that, then yes, the Monster would indeed be in a pickle: he would be lying no matter what he does.
But instead, the Monster only says that he will return the child if the father guesses what he is going to to.
So, given the father's guess, can the Monster not return the child? No, Assuming he does not return the child, thre father guessed correctly, and so the Monster will return the child. As you say: $\neg p \rightarrow p$
OK, but if the Monster does return the child, does that mean the Monster does not return the child? No. In that case, it is true that the father did not guess correctly, but nothing else follows from that, because the Monster did not say that if the father did not guess correct, he would keep the child. So, we do not have $p \rightarrow \neg p$
And so, there is really no contradiction here, and the Monster is forced the return the child.