We (the undivided divinity operating within us) have dreamt the world. We have dreamt it as firm, mysterious, visible, ubiquitous in space and durable in time; but in its architecture we have allowed tenuous and eternal crevices of unreason which tell us it is false.Thus Borges has memorably summarized his brief discussion of the appearance in philosophy of paradoxes flowing from the idea of infinity. (A formulation suggestively posed just after another quote from Novalis to the same effect, but formulated in terms of magic instead of dreams, thus replacing one form of mystified unreality with another one.)
'Unrealities', as Borges uses the term (in the essay, though not in the passage I quoted), seem to be exclusively paradoxes, which are however assumed to reflect something in the nature of the universe. Mere fiction, say, or ordinary dreams would not count as unrealities in Borges' use of the term, as they would in mine. He finds examples for his unrealities in Zeno's paradoxes of motion and Kant's antinomies of reason. (The former he traces through a mostly arbitrary selection of philosophical works.) Given the "hallucinatory nature of the world", which remains in Borges' essay a mere claim rather than a motivated view, the function of such paradoxes (those "tenuous and eternal crevices of unreason") is to remind us of the falseness of the world. They are part of the original plan: the illusion might be perfect, so that we can't see through it; but anticipating that success, we have put some signposts for our dreaming selves into it which tell us that this dream world is false.
But it remains to be clarified in what relationship a 'false' world and a 'true' world would stand. (Note that the pair of terms, reality vs. unreality, is already used up for the reality of the dream world vs. the paradoxes built into it.) Would a world that didn't contain those 'unrealities', in Borges' sense of the term, be so perfect that it couldn't be distinguished from a 'true' world then? Would that mean that it were a 'true' world? Or would it still be 'false' because of its origin as dreamt? Moreover, is there yet another world, that of the dreamer who "has dreamt the world"? And if so, is that containing world now a 'true' world, or yet another dreamt one? And if the latter, how could we avoid the infinite regress that Borges himself has found in all those philosophical texts? Wouldn't he have to diagnose that regress first and foremost in the idealist philosophies to which he refers so admiringly?
For all its bibliographical interest, there isn't much to be gained from Borges' essay. What, then, remains to be drawn from it? At least, there is a memorable (and beautiful) quote: right at the end.
 Jorge Luis Borges, "Avatars of the Tortoise", in: Labyrinths. New York: New Directions 1964, 202–208, 208.