This story recounts the events of Borges discovering the chronicles of a world which was invented by a secret society, and which slowly penetrates the real world. Fantastical in nature, it can be viewed as an allegorical critique of religion. This is particularly apparent in the imaginary metaphysical realm of Tlön.
Borges first learns about Uqbar in 1935 from his friend, Bioy Casares, who, during a discussion about first-person novels with unreliable narrators, quotes a saying he remembers from a heresiarch of Uqbar: "Mirrors and copulation are abominable, for they multiply the number of mankind" (68). Casares believed that Uqbar, along with the quotation, was catalogued in The Anglo-American Cyclopaedia, but Borges finds no such entry in his copy. The following day, Bioy brings him a copy containing the entry on Uqbar, with the actual quotation Casares had paraphrased: "For one of those gnostics, the visible universe was an illusion or, more precisely, a sophism. Mirrors and fatherhood are hateful because they multiply and proclaim it" (69). The article is in an alphabetically-incorrect volume of the cyclopaedia, and the geography of the region surrounding Uqbar is unrecognizable to Borges and Casares, suggesting the country was imaginary. The article also notably says that the literature of Uqbar, as opposed to discussing reality, refers to two imaginary realms: Tlön and Mle'khnas.
In the next section, Borges recalls an encounter with a close friend of his father, Southern Railway Line engineer Herbert Ashe. Ashe had told him about the duodecimal number system (that is, a system of numbers operating with base 12), and about how he had been commissioned to transpose a duodecimal system into a sexagesimal system (one with base 60). Later, a few months after Ashe's death, Borges discovered a manuscript which had been left for Ashe in a bar, titled Orbis Tertius ("third orb," in Latin), which was the eleventh volume of an encyclopedia surveying the imaginary planet of Tlön. This discovery took place in 1937.
In the remainder of the second section, Borges describes the world of Tlön in vivid detail. Language is split between the northern and southern hemispheres. There are no nouns in the language; in the north, modified verb constructions are emphasized instead to show the subject of sentences, and in the south, compound adjectives show subject. People of Tlön understand reality as progressive time, rather than spatially-localized objects. This worldview allows them to effectively conceive of many more subjects than the nouns of Indo-European languages cover (73).
The culture of Tlön, Borges says, is entirely based in psychology, because the world itself it understood as a series of mental processes lacking temporal duration (73-4). This nullifies the idea of science because correlation and causation depend upon the linkage of events or states across time, which is incoherent with the Tlönian perception of the universe. However, this allows for a huge proliferation of metaphysical systems of thoughts, all with the goal of being as fantastical as possible - since any real form of explanation is literally incoherent due to no notions of spatial relations across time.
The lack of spatial relations across time lead to a distorted conception of identity, as evidenced through two examples: the first is a rejection of materialism on the grounds that materialist proofs involving finding things one had once lost depend on inexplicably presupposing that a found thing is the same thing as what one has lost; the second is the concept of hrönir. Hrönir are imperfect copies of objects which are formed when an object is lost. Experiments in hrönir lead to them being mass-produced by people being shown pictures of what they were to discover, and subsequently unearthing objects from the past or future, thereby making time itself malleable. Hrönir degenerate periodically, and are contrasted with ur, which are produced by suggestion or hope and are peerlessly pure.
The postscript to the story is dated from 1947, and reviews the inception and subsequent impact of Tlön. It explains that Tlön, Uqbar, and Orbis Tertius were the brainchild of a secret society of experts from a wide array of disciplines (including Herbert Ashe), funded by millionaire Ezra Buckley, who convinced the society in 1824 to expand their aim from inventing a country to inventing a world. Borges notes several "intrusions" of Tlön into the real world, the most notable being the 1942 discovery of a Tlönian artifact in the hand of a dying man in the Cuchilla Negra: a small metal cone of unknown material which was inexplicably heavy (80). Borges believes that the secret society, propagated through time, orchestrated the discovery of various Tlönian artifacts and documents, causing reality to eventually be subsumed by Tlön. When Borges' account ends in 1947, Tlön "has disintegrated this world. Spellbound by Tlön's rigor, humanity has forgotten, and continues to forget, that it is the rigor of chess masters, not of angels" (81). Every domain of human knowledge has been rewritten to accommodate the truths of Tlön, and Borges expects the process to only continue in the future.
This story may be viewed as an allegory for religion - particularly, institutionalized religion. The Tlönian practice of inventing fantastical metaphysical structures reflects the human construction of religious doctrine which is not accessible to science. The imposition of meaning and modification of the past and future through excavation of artifacts also resembles religious artifacts.
It is important to recognize that this story is not necessarily atheistic or even agnostic in nature. The critique which Borges makes is about the human construction of metaphysical structures and beliefs which mimic or pose as divinity, when they are in fact man-made. This is the thrust of what is meant by his statement that the rigor of Tlön is "the rigor of chess masters, not of angels" (81).
The reference to chess masters puts one in mind of the labyrinth motif which recurs throughout Borges' The Garden of Forking Paths collection. Chess is similar to a labyrinth in that the structure of a game is often as unclear and convoluted to the uninitiated as the path of a labyrinth; thus, a chess master can effectively construct the equivalent of a labyrinth around his opponent, who would inevitably lose. In this way, Borges describes the "illusion of the inevitable" (i.e., the false doctrines of Tlön) as a labyrinth imposed on unwitting people by an intelligent secret society.
This perspective provides us with more clarity on Borges' line of argumentation. In later stories from this collection, Borges offers descriptions of the fabric of time and the universe itself as labyrinthine (see The Garden of Forking Paths and The Library of Babel). The infinity associated with time and the universe are closely linked to notions of the divine; thus, that which is man-made and imposes a labyrinth upon people in a metaphysical manner also imitates divinity. This is made clear by the title of the encyclopedia about Tlön, Orbis Tertius: the "third orb" is Earth, the third planet from the sun, meaning that the encyclopedia is implying Tlön's validity in reality.