During a conversation with a friend, they said something confusing to me (I can't remember what exactly). I questioned them further, asking them to clarify a potential conflict, to which they responded: "Paradoxes are real."

Context aside, this statement has stuck in my head for months now. When I think of the word "paradox," I think of impossibilities. I.E. time travel can't be possible because killing my grandfather would result in a paradox. If God is defined by being omniscient, omnipotent, and omnibeneveolent, then the Problem of Evil shows the paradox disproving a God of that definition... Etcetera... Even paradoxes like "This sentence is a lie," seem to fall on an abstract language more than 'reality' in the material sense. So are paradoxes really real or some illusion of the abstract/conceptual?

Oh, and sometimes I'll listen to Žižek lecture, and he'll often use the word paradox to describe something counterintuitive; "X group is paradoxically repulsed and infatuated with Y." But this usage of the word seemingly just refers to complexity, not inherent contradiction. Dichotomized yet in harmony, what have you. I'm not really asking about this variant of "paradox."

I don't know, this is making my head hurt. Help me think this out, and thanks in advance!