1)Can we write a paradox in propositional logic?
2)I'm trying to solve the following problem : Let $\epsilon$ be a set of evaluations and $\gamma$ = {$\psi \in Form$ | $ e \models \psi $ for each evaluation in $\epsilon$ } ( $Form = $ the set of all formulae). We suppose there are at least 2 elements in $\epsilon$. Show that there exists a formula $\phi$ so that $\phi \notin \gamma$ and $\neg\phi \notin \gamma $ .
I was thinking that a paradox might be the answer? If not can someone show me a solution? I would greatly appreciate your help!