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Paul Livingston responds to the New APPS symposium on "Derrida and Formal Logic"

Here is Paul Livingston's response to the posts and comments on our New APPS symposium on his paper, "Derrida and Formal Logic."

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“Derrida and Formal Logic” – Response

First I would like to thank the New APPS bloggers for hosting this symposium and those who have contributed to the discussion so far.  I believe it is deeply important for this kind of discussion to take place, especially in view of the divisions that still persist between “analytic” and “continental” philosophy in the U.S., and I thank the contributors for their willingness to talk constructively across this damaging divide. 

The scope of the analogy

I’ll begin by responding to a few of the points and questions raised in Catarina Dutilh Novaes’ post, “Diagonalization and différance: A mismatch of scope”, since of the original symposium posts this is the most critical of my general strategy in the paper.  There, I argued for the existence of analogies on several points between structures involved in producing Gödel’s results and those involved in deconstructive readings. 

New APPS symposium on Paul Livingston, "Derrida and Formal Logic"

Link to pre-print of Paul Livingston, "Derrida and Formal Logic"

Context of Livingston's Derrida work in his Politics of Logic

Précis of Livingston's "Derrida and Formal Logic" paper

Jeffrey Bell, The Prince of Darkness Reads Derrida

Catarina Dutilh Novaes, Diagonalization and Différance: A Mismatch of Scope

Jon Cogburn, Livingston on Semantic Doubling

John Protevi, Logics of Deconstruction

UPDATE, 12 March: Paul Livingston, Response to symposium posts and comments

Logics of deconstruction: undecidable, quasi-transcendental, aporia

Jeff mentions my hesitation as to whether Derrida’s work could be formalized. Is there a method of deconstruction so that you can identify a three step procedure of diagnose, overturn, re-inscribe? My hesitation was in how to formalize the third step, which I characterized as the move to a general economy, or to a quasi-transcendental. So I hedged my bets by saying the identification of the three-step procedure was only possible for “pedagogical purposes.”

 Now partially this was just to head off the polemical trap EM Edwards was laying, well laid out by John Drabinski at 89 on the Gutting thread. I’ve dealt with the EM Edwards of the world long enough to know when it’s no longer a pedagogical situation but a polemical one, and I wasn’t about to get into that. And partially my hesitation was because it had been so long since I had worked on Derrida that I was unsure of what to say. So I mentioned that a cautious way of dealing with deconstruction is to deny it is a method and to say it produces "singular effects."

After some time with Paul Livingston’s work, and a refresher course on Derrida – and a refresher course on my own work on Derrida, such is the effect of time – I would say that my hesitation in calling deconstruction a “method” or calling it a “textual practice producing singular effects” is precisely one of the undecidables Livingston talks about, a meta-undecidable if you will.

Livingston on Semantic Doubling

In what follows I first sketch Livinston's three part journey, where he moves Derrida from Gödel to Priest. This journey intrinsically involves looking at views that engage in what Quentin Meillassoux calls "semantic doubling." In my sketch I give examples of doubling from Averroes, Berkeley, and religious Wittgetnsteinians.

To make clearer Priest's master argument I show how something like it was instanced by early critics of Kant (from whom Priest got his initial inspiration). Then I consider three other instances of semantic doubling: (1) Carnap's pragmatism, (2) Robert Kraut's "robust deflationism," and (3) Lee Braver's interpretation of Heidegger, which is a clear instance of what Meillassoux calls "correlationism." In each case, Livinston's three steps is an important part of shedding light on the positions in question.

This is a blog post, not a paper, so my citational habits are shoddy, and the arguments trade in cartoons to some extent (but as my friend Roy Cook has argued, cartoons have an important role in philosophy).

1. LIVINGSTON ON SEMANTIC DOUBLING; WITH EXAMPLES FROM AVERROES, BERKELEY, KANT, AND RELIGIOUS WITTGENSTEINIANS AS WELL AS THE UR-CRITIQUE FROM SCHOLZE

One of the really nice things about this chapter is Livingston's discussion of how an axiomatized system’s Gödel sentence only really means “I am not provable” from a perspective outside of the system. Inside of the system it is just an incredibly long sentence of number theory.

Diagonalization and Différance: a mismatch of scope

(This post is part of the NewAPPS symposium on Paul Livingston's 'Derrida and Formal Logic: Formalizing the Undecidable')

Paul Livingston’s paper presents a comparative analysis of Gödel’s incompleteness results, Priest on diagonalization, and Derrida on différance. One of the goals seems to be to show that there are significant analogies between these different concepts, which would be at odds with the fact that Derrida’s ideas encounter great hostility among most philosophers in the analytic tradition. In particular, Derrida’s différance and the concept/technique of diagonalization are presented as being each other’s counterpart (a view earlier defended by Graham Priest in Beyond the Limits of Thought).

But crucially, while différance is presented as cropping up in any discourse whatsoever, for a particular language/formal system to have the kind of imcompleteness identified by Gödel specifically with respect to arithmetic, certain conditions must hold of the system. So a fundamental disanalogy between what could be described as the ‘Gödel phenomenon’ (incompleteness arising from diagonalization and the formulation of a so-called Gödel sentence) and Derrida’s différance concerns the scope of each of them: the latter is presented as a perfectly general phenomenon, while the former is provably restricted to a specific (albeit significant) class of languages/formal systems. Although Livingston does not fail to mention that a system must have certain expressive characteristics for the Gödel phenomenon to emerge, it seems to me that he downplays this aspect in order to establish the comparison between différance and diagonalization. (There is much more that I could say on Livingstone’s thought-provoking piece, but for reasons of space I will focus on this particular aspect.)

The Prince of Darkness reads Derrida

In the midst of the numerous comments to Eric’s post on the supposed differences of clarity between analytic and continental philosophy, Reinhard Muskens asked (#110) whether or not “deconstrucion dialectics can be formalized in some way,” to which John Protevi answered that yes, for pedagogical purposes one can discern a three step methodology consistently at work (or play?) in Derrida’s analyses of texts, but as one actually grapples with the texts the deconstructive reading produces “singular effects” (#111) whereby the “formulaic deconstructive dialectic pretty much vanishes” and where it is difficult to discern the “three step approach easily” (#121).

The distinction John is working with here between an abstract methodological rule or dialectic and a material to which this rule is applied, is precisely the distinction that Derrida’s work challenges, though John knows this and was bringing this distinction in for purposes of clarifying Derrida’s project. This is not to say that formalization is ruled out as inappropriate or irrelevant to the project of deconstruction; rather, Derrida is attempting, if you will, to employ a logic of singular effects, or what Deleuze will call, in similar fashion and for similar reasons, a logic of sense. To keep this to an appropriate length for a blog post, I’ll confine myself to two main points about what this logic of sense entails, drawing from two important attempts to formalize Derrida’s project—Graham Priest’s and Paul Livingston’s.

Précis of Livingston's "Derrida and Formal Logic"

“Derrida and Formal Logic”: précis

Livingston sets out to explore the “analogy” between results in metalogic and Derrida’s terms such as différance and “undecidable.” Livingston is following up on two leads. First, Derrida’s suggestion in 1970 in his paper on Mallarmé (“The Double Session” in Dissemination) of an analogy between his term “undecidable” and the same term in Gödel’s incompleteness theorems, and second, Graham Priest’s suggestion in Beyond the Limits of Thought of différance as an instance of diagonalization and “in-closure.”

Context of Livingston's Derrida work: Politics of Logic

To frame our discussion of Paul Livingston’s paper on “Derrida and Formal Logic: Formalising the Undecidable,” (Derrida Today 3.2 [2010]: 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.)