Consider the following paradox:
On Silicy everyone lies all the time, and if you are not from Silicy, you speak the truth all the times. Call the proposition "I am from Silicy" $p$.
Then $p$ is not true, because then he is from Silicy, thus lies.
But $p$ cannot be false either because then he is not from Silicy, which means he always speaks true, which contradicts that $p$ is false.
Can someone explain to me where I go wrong here? My knowledge of logic is very limited: I know truth tables, the logical symbols and some tautologies such as de Morgan's laws, and that is pretty much it.