I found this to be not only an interesting work on Wittgenstein, but one of the most enjoyable pieces by Alain Badiou that I've had the opportunity to read. What impressed me most was the philosophical precision with which Badiou interrogated Wittgenstein's "Tractatus."
As Bruono Bosteel's introduction explains, Badiou has recently attempted to define two traditions that he feels serve a foundations for philosophy precisely by attacking the philosophical tradition: sophistry and anti-philosophy. Those who Badiou labels modern sophists, such as Derrida, replace the philosophical distinction between truth and error with the distinction between speech and silence. For sophists, the problem of though is not to uncover truth, but simply to persuade the other that what is being said is believable, that what is being said can be said in a meaningful fashion. Language functions for the sophists the same way the Church (God) did for medieval thinkers and the subject did for the philosophers of the Enlightenment- it is that which cannot be transcended and which therefore provides the philosopher (sophist-in-disguise) who sides with it an absolute foundation for their thought. Sophistry attacks philosophy's sense of purpose, but it actually serves as a necessary compliment to philosophy. For, without the sophistic challenge to truth which philosophy must overcome, philosophy could delude itself into imagining itself the producer of truth, imagine that it makes a thought true just by thinking it. For Badiou, philosophy can only discover and enunciate new truths that emerge from political, scientific and artistic revolutions- which he calls Radical Events. Ironically, without the sophistic challenge philosophy runs the risk of devolving into sophistry.
Anti-philosophy, on the other hand, appeals to notions of the unsayable- to truths that are so intense and transcendent that they cannot be conveyed- they can only be felt, lived. Anti-philosophy thus resists both philosophy, which Badiou defines precisely as the articulation of newly unleashed truths, and sophistry, which insists that nothing exists outside of the the articulateable. Anti-philosophy also provides philosophy with necessary support, exactly because the great anti-philosophers succeed in suggesting the inexpressible. The anti-philosopher feeds off of the uncertainly created by Radical Events. At times, the work of an anti-philosopher can itself be a radical event. And it is during such events that philosophy again becomes necessary. Badiou offers Nietzsche as the paradigmatic example of an anti-philosopher. He also considers the Wittgenstein of the "Tractatus" to be an anti-philosopher, but the later Wittgenstein to be a mere sophist. This is because the "Tractatus" clings to a notion of the "mystical"- a state of being that can be felt, but not known.
Badiou begins his interrogation of the "Tractatus" by noting the profoundly religious ambitions of its author. For Wittgenstein, happiness can be achieved only by living according to sense. That is to say, one must strive for certainty in expression. Wittgenstein's demands on thought are so stringent that they feel more like those of a master architect than a philosopher. For this reason, Badiou characterized the "Tractatus" as an "archiaesthetic" work. It seeks to show even what cannot be shown b showing what can be shown so comprehensively and, at once, precisely. That which is revealed through its inexpressibility in the archiaesthetic work is, for Wittgenstein, the Mystical, God. What is at stake in the archiaesthetic act, the quest for clarity, is a life lived according to sense- which is to say happiness, or non-sense, which is to say negation of the divine, a life not worth living.
Philosophy, for Wittgenstein, is the most depraved form of non-sense. It seeks to pass itself off as sense! The metaphysical tradition, at least sense Plato, has sought to convey the ungraspable through expression- i.e. idealism. The call and response of skepticism and metaphysics dare to ask "how is it that something is known?" and then attempt to answer the question. Both are unacceptable for Wittgenstein because the initial question is non-sensicle. The question is, for Wittgenstein, an assault on the Divine. In contrast to this tradition, Wittgentsein seeks to create a work where language sows its own limit, answering all answerable questions, and therefor points us to the unknowable, the Divine, so that we may live ethically.
It is interesting to note that the only way to live or think valiantly is to remain silent about what can not be expressed. The unexpressible is the ethically paramount. This implies that, for Wittgenstein, what can be expressed is of little or no ethical substance. Wittgenstein writes that, "of what one can speak, one can speak clearly." But how is this so? If someone addresses me in a very clear articulate way does this guarantee that I have been spoken to "clearly?" Could not the speaker be lying or simply be mis-informed? For Wittgenstein, it does not matter. The only important thing in to live according to sense, and if a statement is sensible, it does not matter if it is factually true or not, nor, it seems, would the repercussions of a non-truth in the world. The world, the expressible, is not the site of ethics. In and of itself, the expressible is without value.
Badiou characterizes this aspect of Wittgenstein's thought as an "ontology of the virtual"- that which is not true, is not of the world, is granted sense. In this, Badiou feels, the "Tractatus" instigates the "Linguistic Turn" in philosophy. And with his ontology, Wittgenstein throws his lot in with all anti-philosophers and sophists- the deposition of the binary "true/false" in favor of "sense/non-sense."
At this point, Badiou begins his assault on the "Tractatus", his defense of philosophy. There is real drama in the ensuing duel.
Badiou's criticisms focus on two points. First, Wittgenstein's understanding of the "sensible" pre-supposes a very conservative, even close-minded, outlook on the world. Secondly, for Wittgenstein's denunciation of metaphysics to hold water, much that would generally be considered forms of thought must be exiled from the category.
Wittgenstein's rejection of "non-sense" is so severe that it give an artificially simplistic idea of the "sensible" or, to put it in more Badiouian terms, the "possible". This implies that what is possible is fully knowable at any one point in history, which Badiou asserts is not a tenable position. The phrase "worker's state" was non-sensicle before the Paris Commune because its signified had not yet been proven possible. But "worker's state" became sensible and its sense changed drastically in the aftermath of the October Revolution. What is sensible corresponds to what is possible and what is possible is constantly being expanded and/or altered by political, scientific, and technological upheavals, i.e. Radical Events.
Badiou also points out that Wittgenstein's use of "sense/ non-sense" is problematic in that it labels all of philosophy as "non-sense" when for millenia readers have found sense in it. This is particularly problematic for Wittgenstein who claims that skepticism is absurd because it asks one to render doubtful what one has already understood as valid.
However, Wittgenstein's is a philosophy (or anti-philosophy) of knowledge, not of history. But the political and technological are far from being the only subjects that Wittgenstein must insist are irrelevant. The mathematical concept of infinity states that what "can be" (and thus what is potentially sensible) cannot be quantified and therefor cannot be measured. Thus, one could never rule out the possibility that there could be "sense" to "non-sense". Badiou states that such mathematical concepts prove that being can be articulated without being experienced, and thus that there is validity to idealism. Wittgenstein's only recourse is to insist that math is not thought, but merely an observation- 2+2=4 (or "simple proposition") proven to be correct, rather than a conjecture about what can be known ("thought").
Badiou then moves in for the kill. Wittgenstein's concept of sense relies on the irrefutability of the understood. Objects have names and the acceptance of these names is an operation of non-thought which is foundational to thought. So naming can never be thought. How then, Badiou asks, does the poem function? Is not poetry simply the act of naming in a new way, at times even the act of announcing something new to be named (an artistic Event)?
If poetry is naming in a new way, and Badiou asks us to accept that it is, then Wittgenstein must say that the poetic, which is to say the aesthetic, is non-thought. How then can the Tractatus, the archi-aesthetic work which seeks to reveal the unexpressible through the perfect, comprehensive expression of the expressible, qualify as thought? If the name is the foundation of the understood, and if new names (and name-ables) can come into being then the understood is elastic, and language can convey a being of which it has no objective experience. Metaphysics is valid.
The entire book is Badiou's attempt to solve a profound philosophical problem- to refute a great anti-philosophical work. The "Tractatus" is a great, beautiful crisis- an Event. It requires that new truths be named- which is to say new philosophical systems formed. For Badiou, the new truth that the Event that is Wittgenstein and the Linguistic Turn leave behind, what the crisis uncovers, is Badiou's own philosophy.