Saturday, December 24, 2016

BADIOU ON INFINITY AND THE GOOD LIFE: “mathematical rudiments and poetic breakthroughs” (Agent Swarm blog post)

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BADIOU ON INFINITY AND THE GOOD LIFE: "mathematical rudiments and poetic breakthroughs"

In my recent series of posts I have been presenting an entry into Badiou's system by way of his readings of various poets. For the moment I have translated and summarised from his discussion of poems by Arthur Rimbaud, René Char, and Victor Hugo, and next I will be moving on to Mallarmé.

Badiou's philosophy has been amply discussed in terms of the mathematical condition and of the political condition, but a more existential entry is possible. Badiou himself has placed increasing emphasis on the question of "what is it to live?", on the problem of the good life, true life, and happiness.

However, Badiou maintains that although this is a genuine and important philosophical question, it cannot be answered at the purely speculative level as it involves the category of "life", which is an empirical category. Poetry has the advantage of transposing life into language.

According to Badiou, poetry, like mathematics, is particularly suited to the critique of the dominant ideology of the finitude of human life. This ideology of finitude is the source of the multiple obstacles and repressions to the life of immanence, which is necessarily a life of immanence to truths conceived as infinite processes immanent to a determinate world.

After discussing Victor Hugo's poem "Words on the Dunes" and extracting the concept of infinity as point Badiou passes to a discussion of ω, the first infinite ordinal , which is the order type of the natural numbers, that can also be identified with the entire set of natural numbers. There is no immediate predecessor to ω, i.e. the meaning of ω – 1 is undefined, but ω has an infinity of successors.

Badiou concludes this discussion of "mathematical rudiments" by extracting a typology of infinities: the infinite as point, as place, as horizon, and as repetition. He then returns to poetry to "explore the labyrinth of the different forms taken by the couple finite/infinite".

The role of poetry and of the "poetic breakthroughs" it accomplishes (but I would argue this characterisation applies also to science fiction) is to provide figurations, between the speculative and the empirical, of the noetic life and its incorporation in or exclusion from the truths of science, art, politics and love.

Badiou concludes at the end of the first year of his seminar on the immanence of truths:

"The principal obstacle encountered…, the nucleus of the repressive practices that constrain us to be ignorant of the replies to the question "what is it to live?", is the multiform ideology of the finitude of life. Which is natural, as every process of truth is virtually infinite…We have thus explored the labyrinth of the different forms taken by the couple finite/infinite, making use of, in order to do this, mathematical rudiments and poetic breakthroughs".