The aim of Badiou’s book THE IMMANENCE OF TRUTHS is to provide a fully worked out critique of and alternative to contemporary relativism. The line of argument is to convince us that we live in L, the « constructible universe » of set theory (a universe that is « finite » because constructed out of assemblages of already known predicates), without being aware that this is the case, to guide us progressively from L to V (the class of all sets – the universe containing the large non-constructible infinities), and to elevate us to the « Absolute » (the philosophical name for V), and finally to take us down again into the finitude of L equipped with perceptions drawn from V, thus permitting us to « re-index » the world according to absoluteness and no longer in terms of relativity.
This conceptual path may seem daunting, but it is well worth the effort. It is conjoined with a more accessible a « poetic » path comparable to Dante’s DIVINE COMEDY, centred on the four movements of descent into the hell (Inferno) of our market-dominated finitude (of the commodity defined as the « waste product » cut off from infinity), of purgation of our finite-oriented ideological presuppositions (Purgatorio), and of ascension to Paradise, the paradise of the Absolute, or « Cantor’s paradise » of multiple infinites, (Paradiso), and finally the re-descent into the finitude of the work (of art, science, love or politics) no longer closed off inside pre-programmed ideological schemas but opened to the Absolute and « touched » by the infinite.
Many works (including Dante’s) deal with the ascent to the Absolute but remain silent on the return (or what I propose call the « Ritorno »), Badiou devotes the last quarter of his 600 page book to the return to finitude and its practices re-fashioned by the traversal of the Absolute. A true masterpiece.
For a full review, see: https://terenceblake.wordpress.com/2018/10/06/my-path-through-badious-the-immanence-of-truths-full-english-text/