To frame our discussion of Paul Livingston’s paper on “Derrida and Formal Logic: Formalising the Undecidable,” (Derrida Today 3.2 : 221-239), I want to sketch the framework of Paul’s recent book, The Politics of Logic: Badiou, Wittgenstein, and the Consequences of Formalism (Routledge, 2012; hereafter PL) in which the Derrida paper is Chapter 4. (Paul touched on some of the aspects of his book in this wide-ranging New APPS interview from September 2011.)
Livingston begins with Wittgenstein’s claim in the Philosophical Investigations that “the given” is “forms of life.” He moves below the conventionalist (anthropological) and naturalist (biological) interpretations of this saying to the ontological level revealed in the genitive “of”: how can a form be a form of life? How can form inform matter? (PL, 4)
Let’s pull back a little now and consider the title, Politics of Logic. Livingston is after how formal structures of sets (the various ways of relating the one and the many) illuminate not just the (conceptual or logical) relation of objects and predicates or properties but also the (political) relation of states or communities to their members: how they include them in a whole and also how the excluded can lead to their rupture or transformation (PL, 5-6).
We can now understand the subtitle. What Livingston means by the contemporary “consequences of formalism” are the ways formalist advances make possible not just information technologies but also the very bureaucratic / administrative forms of government and social organization which they subtend. So we have to investigate two grounds: 1) how any kind of collective life can be reflected in formal structures and 2) how our collective life is being transformed by these information technologies and political rationalities (PL, 4).
The immediate context for our interest in Paul’s work on Derrida and formal logic was a discussion of how the term “clarity” functions in reinforcing the analytic-continental divide (link to Gutting thread). A staunch advocate of overcoming the divide, Livingston shows us a way to look back at 20th century philosophy to see a “unified field of investigation”, as if the split had never occurred (PL, xiii). He does this by calling attention to the “formalization of formalism” as it occurs in the critical reflective practices of both analytic metalogic and in continental post-structuralism (PL, 7).
The “aleatory point” in Livingston’s narrative of overcoming the analytic / continental divide, if I can put it that way in borrowing a technical term from Deleuze’s Logic of Sense, is Alain Badiou. A “continental” thinker who makes the “analytic” move of grounding his thought in set theory, a Platonist who opposes the mathematical to the post-structuralist linguistic, Badiou seems both here and there, everywhere and nowhere, unplaceable on the map drawn with the usual co-ordinates. However, the interest in Badiou for Livingston lies not just this being out-of-place -- nor even in the way Badiou’s work thematizes the “out-of-place” -- but in a particular decision of Badiou’s that enables Livingston to draw his own, new, map (PL, 57-60).
This map has four positions whose variables are the relation to totality, consistency, truth, and language.
The first is good old-fashioned onto-theology, which sees totality as complete and consistent, and grounded in an element external to -- or identical with -- that totality, even if the properties of the grounding element, and its relation to the totality, remain ungraspable by our finite cognition, so that truth exceeds language.
The second is the “constructivist,” a position that attempts to delimit the totality from a stable point outside the totality, and thereby requires a hierarchy of distinct metalanguages that seek to solve the paradoxes of self-reference revealed by Russell; here language captures truth as long as the limits of that language are properly defined.
The third is the “generic” position occupied by Badiou, who grasps the self-referential bull by the horns and chooses consistency over totality, sacrificing totality for the irreducibly multiple. Rather than work at the margins or limits of language, Badiou does this in mathematics, which expresses a truth beyond or before language.
The fourth position, overlooked by Badiou, is the “paradoxico-critical,” and is occupied, among others, by Derrida (Livingston also names here Lacan, Agamben, Deleuze and the late Wittgenstein). Livingston’s insight is that the partisans of the “paradoxico-critical” orientation operate on the same ground as that of Badiou. Like him they have passed through the trials of self-reference, and like him they decline the option of the hierarchy of metalanguages.*
But they differ from him in two ways: first, unlike Badiou, they choose totality over consistency, and second, they do not flee language for mathematics, but use formal reasoning to consider the “paradoxical topology” (PL, 33) of operating at the limits of language: what happens when you try to name in language the limits and structures of language? How is it that language can “figure” itself in a display of its own structure? (PL, 56) As a result of taking this position, these thinkers end up affirming a totality that is “constitutively rent by the paradoxes of in-closure at its boundaries” (PL, 56). (“In-closure” refers to the work of Graham Priest, whose work in Beyond the Limits of Thought is employed by Livingston throughout PL; in this symposium, Jeff Bell and Jon Cogburn will consider the relation of Priest’s treatment of Derrida to that of Livingston.)
I have downplayed the political aspects of Livingston’s work in this introduction, but I hope I have provided something of a context for our symposium on his “Derrida and Formal Logic” paper.
* Badiou’s position is more complex than a simple “declining” of metalanguages. After the “event” and forcing, the situation is expressed in a transformed language; in this progression there is thus a certain similarity, Livingston argues, with the constructivist hierarchy of metalanguages. However, this transformed language of the situation does not come from a point that totally encompasses the previous language, as does a true metalanguage.