This is my summary of Badiou's “The (Re)turn of Philosophy Itself” found in his Manifesto for Philosophy. As you will see, there are many similarities as well as divergences with American pragmatism, of which I had earlier hinted.
This essay is laid out in a series of thesis/propositions. But we will not engage all of them, only the once pertinent to Badiou’s understanding of truth and philosophy.
Thesis 1: Philosophy today is paralyzed by its relation to its own history.
Thesis 2: Philosophy must break, from within itself, with historicism. This break with history is to assume a definition of philosophy which will judge the history of philosophy, rather than the other way around.
These 3: A definition of philosophy exists. But this definition must distinguish itself from modern sophistry. “Who are the modern sophists? The modern sophists are those that, in the footsteps of the great Wittgenstein, maintain that thought is held to the following alternative: either effects of discourse, language games, or the silent indication, the pure ‘showing’ of something subtracted from the clutches of language. Those for whom the fundamental opposition is not between truth and error or wondering, but between speech and silence, between what can be said and what is impossible to say…The modern sophist attempts to replace the idea of truth with the idea of rule.” (117).
So, Thesis 4a: Every definition of philosophy must distinguish it from sophistry.
Thesis 4b: The category of truth is the central category, be it under another name, of any possible philosophy.
Now this (re)turn of philosophy to the category of truth flows through Plato. Why? Well, for all those claiming the End of Metaphysics, they point out that Plato was the down fall, the “moment of the launching of metaphysics” (121). For Badiou, both continental philosophy following Heideggar and analytic philosophy following Carnap proclaim the end of metaphysics, the end of Plato, the emblem of metaphysics. But, Badiou wants to announce the end of the “End of metaphysics” and announce the return of philosophy, of truth, and therefore of Plato. Badiou, in other writing proclaims a return to a “Plato of the multiple”, the multiple of set theory.
So, continuing on from thesis 4b, Badiou sketches the category of truth, in another list.
1) “Prior to philosophy, a ‘prior to’ that is not temporal, there are truths. These truths are heterogeneous, and proceed within the real independently of philosophy” (123). These truths are the sites of/for philosophy. There are four sites (for Badiou’s Plato): Mathematics, Art, Love, Politics.
2) “Philosophy is a construction of thinking wherein the fact that there are truths is proclaimed against sophistry. But this central proclamation supposes a strictly philosophical category, the Truth.” There is a relationship between the multiple truths and the Truth, such that we can maintain the “plural state of things (there are heterogeneous truths) and the unity of thought”(123).
3) “The philosophical category of Truth is by itself void. It operates but presents nothing. Philosophy is not a production of truth, but an operation from truths”(124) When Badiou speaks of the void, he is not talking of some vague, existentialist notion of angst, nor of the beyond being of God, but of the mathematical void of set theory, the null/void set from which all other sets are built. Badiou points out that this is the fundamental crossing of philosophy and mathematics (ontology = mathematics), and that while Truth is an operational void, it is not the void of being. The Truth is a logical void, not ontological (but to illuminate this will get us a bit off track). So,
4) “What is the structure of this operation?” (124). The structure of this operation borrows from the discourse of philosophy’s two longstanding opponents: the sophist (dialectical reasoning, endless definitions, proofs and refutations) and the poet (metaphor, images, myths, and narrative). The Truth is the un-known of sophists fictive knowledge, and the un-utterable of fictive art (125). Truth is a set of tongs or pincers, one side being the being argumentative proofs (sophistry) and the other being subjective potency (art).
5) “The pincers of Truth, which link and sublimate, have a duty to seize truths”(126). Philosophical Truth seizes truths, captures them for thought.
This seizing of Truth by the thought of philosophy can also be thought of as “subtractive”, based in the thought of the void. Philosophy subtracts thought from the maze of sense, from the hold of presentation, for the Truth is never merely presented, it has no immediate presentation. This seizing effect of philosophy (seizing the truths of life for thought) is “first and foremost a rupture with the narrative and with commentary about the narrative…Philosophy separates itself from religion because it separates itself from hermeneutics” (127).
Now, in the above, Badiou has outlined the ‘structure’ of the operation of Truth, but not what he calls a “truth procedure” or the “procedure of truth.” This will have to wait for another time. From here Badiou examines some consequences of (mis)understanding this conception of Truth.
One misunderstand is to confuse the condition of Truth (which are the truths of mathematics, art, politics, and love) with the operation (which is empty, formal) of Truth. We can’t think of particular truths as identical to the operation of Truth. Philosophy is not identical with art (Nietzsche/Heideggar), politics (Plato/Marx), love (Pascal/Kierkegaard), or science (Husserl/Carnap) (129). The Truth is never found in the being of these situations (art, mathematics, politics, love); Truth is not!
For Badiou, to claim that Truth is, to substantialize Truth, is to give up on truths, the multiplicity of life, and reinstate the One, the God of metaphysics. Badiou is for the metaphysic of the multiple, the “Plato of the multiple” but not the “Plato of the One” beyond being. Badiou does not want anything to do with the beyond being, the sacralization of eternity or infinite, because eternity/infinity can both be happily understood via set theory, one of the conditions (truths, ‘mathematics’) of philosophy. And for Badiou, via Derriad, Levinas and Ricoeur, sophistry leaves the door way too wide open for religion to enter back in.
Badiou ends the essay with this helpful summary:
“Asserting the end of philosophy and the irrelevance of Truth is strictly a sophistic appraise of the century (speaking of the disaster of the 20th century toward which much continental philosophy is directed)…Language games, deconstruction, feeble thinking, irremediable heterogeneity, differends and differences, the ruin of Reason, the promotion of the fragment and discourse in shreds: all of these argue in favor of a sophistic live of thinking and place philosophy at an impasse.”
Against this reign of sophistry, Badiou ends with,
Thesis 5a: Philosophy is possible.
Thesis 5b: Philosophy is necessary.
On this return of Truth, the return of philosophy, the seizing of truths, Badiou claims that while Truth is not, it is becoming, and this becoming is the work of philosophy, such that Badiou can affirm with Marx, the “point is to change the world.”