Is the liar paradox a defect in our language or a genuine limit of truth?

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How does modal logic separate necessity from apriority? Why do counterfactuals with false antecedents resist a truth value? Why does defining free will by necessary and sufficient conditions keep generating counterexamples? Why is the existential quantifier so hard to render in ordinary speech? Who is on each side of the dispute over whether reasons can be causes? What is the difference between a noema and the object it seems to present? Why does the problem of universals keep returning in new vocabulary? What does possible-worlds semantics actually explain about necessity? What is the difference between logical consequence and derivability in a proof system? Why is the absurd a collision between our need for meaning and a silent universe?