Jorge Luis Borges and infinity that exists

Abstract This article examines Borges' “The Library of Babel” (1941) and “The Aleph” (1945) as literary constructions that radically reconfigure the concept of infinity—not as a metaphysical abstraction, but as a finite, combinatorial structure whose effects are epistemologically and aesthetically infinite. Drawing from mathematics, philosophy, and poetics, the article argues that Borges' stories function as conceptual laboratories, simulating infinity through recursive formal constraints. In “The Library of Babel,” Borges constructs an apparently infinite universe using a strictly finite set of characters and structural rules, producing a combinatorial totality that overwhelms cognition through redundancy rather than expansion. In contrast, “The Aleph” collapses infinity into a point of simultaneity, dramatizing the impossibility of representing totality within temporal and linguistic constraints. Engaging with theories from Georg Cantor, David Hilbert, and David Deutsch, the article explores how Borges' fictions operationalize the infinite within the limits of human perception and representation. Literature, in Borges' vision, does not merely reflect infinity but enacts it, revealing a poetics of recursion, saturation, and structural paradox. In this light, Borges' work emerges as both an aesthetic and cognitive model of infinity, wherein fiction becomes a mode of thinking that renders the ungraspable momentarily thinkable.