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.
- The abstract needs to be accounted for rather than presupposed.
In earlier posts (here for example) I’ve written about Husserl’s recognition of Hume as the first to identify what Husserl calls the “constitutional” problem, which is the problem of accounting for the identities that are accepted as a given within the natural attitude, identities that are, according to Husserlian phenomenology, the result of the syntheses of a pure transcendental ego. Kant did not go far enough in this regard for while he recognized the important role the subject plays with respect to the syntheses that result in the objects of experience, he nonetheless held on to the identity of the “pure concepts” of the understanding. As Husserl put it in his Formal and Transcendental Logic, Kant “asked no transcendental questions about formal logic.” Husserl asked these questions and thus set out, with his method of eidetic variation for instance, to develop a transcendental logic rather than a formal logic.
Derrida’s philosophy – and Deleuze’s I would argue – needs to be understood in light of this Husserlian tradition. As a result, one will not find, nor should one expect to find in light of Husserl’s arguments, Derrida embracing a formalization of deconstruction that would single out abstract rules and principles that serve to determine and guide the proper practices of Derridean deconstruction. Moreover, much as Deleuze argues in the preface to the 1987 English language edition of Dialogues that he is a pluralist and by that he means he is one for whom the abstract “must itself be explained” (p. vii); similarly for Derrida he will not presuppose abstract conceptual rules or principles but will “deconstruct” them in order to show what they themselves presuppose.
It is at this point where Graham Priest’s understanding of Derrida’s project becomes relevant. According to Priest, Derrida is attempting to think the limits of thought itself, or the limits of abstract, conceptual thought. This attempt inevitably leads, Priest argues, to a generalized version of Russell’s Paradox, or what he calls the Inclosure Schema, since this very effort to think the limits of thought necessarily involves a thought that is beyond or transcends these limits (Priest draws much from Hegel on this point).
Priest lays out the Inclosure Schema in his Beyond the Limits of Thought (BLT) and even more succinctly in his 1994 essay, “The Structure of the Paradoxes of Self-Reference.” Priest formulates the Inclosure Schema as follows:
1) Ω = {y: φ(y)} exists
2) If x is a subset of Ω such that ψ(x): δ(x) ∉ x
δ(x) ∈ Ω
Ω is the class of all things, y, that have the property φ, and x is a subset of Ω that is definable, conceivable, etc., in terms of ψ (Priest does this so as to show that his schema can account not only for set-theory paradoxes such as those of Russell, Burali-Forti, and Mirimanoff, but also the semantic paradoxes of Konig, Berry, and Richard); and δ(x) is a particular function, most notably the diagonalization function which Livingston details nicely in his essay, though for Priest it is not exclusive to this function.
A consequence of this function is that when applied to x it results in a set that both belongs to the class Ω (Inclosure) but not to x itself (Transcendence), and then when we apply the function to Ω itself we end up with a contradiction whereby it does and does not belong to itself. If Ω is the totality of what can be thought then the effort to think the limits of this totality, the limits of what can be thought, through δ(x), the result is a thought that both belongs to the totality of what can be thought (δ(x) ∈ Ω) and yet it is precisely what cannot be thought (δ(x) ∉ Ω).
To take the case of Derrida, Ω is the class of linguistic expressions φ(y), and x is a subset of linguistic expressions, a particular text, defined by the property ψ such that this text is conditioned by, and hence only meaningful as a result of, the binary opposition presence/absence, or by iterability as we will see below, and δ(x) is, as Priest puts it, “some statement that concerns the notion undecidable in terms of such an opposition” (BLT 222). Whether this statement δ(x) be among the numerous terms in Derrida’s writing, hymen, supplément, and parergon (just to give the ones Priest lists), it is a term whose meaning cannot be determinately decided relative to the particular text, x, (therefore we have Transcendence) and yet as a linguistic expression it belongs to Ω (and so we have Inclosure). It cannot be determinately decided, to give yet another example, whether pharmakon means poison or cure within Plato’s Phaedrus, and hence the binary opposition that defines such texts remains undecided with respect to this particular linguistic expression.
The contradiction and paradox of this process becomes most evident when, as mentioned above, the function δ(x) operates on or self-refers to the class or totality as a whole, and this is precisely what gives rise to the Liar’s paradox as well as the paradoxes listed earlier. Now to those who would deny the existence of such sets (Meinongians for instance), or argue that their existence is not well founded in terms of Zermelo-Fraenkel set theory, Priest argues that his Inclosure Schema, and Livingston follows Priest on this point, applies to beings (to satisfy Meinongians) as well as to sets that are well founded within ZF set theory. Moreover, in his arguments for paraconsistent logics, Priest attempts to show that the contradictions that paradoxes such as that of the Liar lead to are not indicative of something being wrong with the self-referring statement but rather that “the contradictions in question are actually true” (BLT 205).
It may seem counter to common sense to claim that certain contradictions are true. It would certainly be anathema to most logicians to even consider admitting a true contradiction, which is perhaps why the nickname the Logician’s Liberation League has given to Priest is the prince of darkness (h/t to Catarina's post on Priest for this). If we allow for a true contradiction, the traditional argument goes, then everything can be proven to be true. In developiong his paraconsistent logic, Priest is very careful to accept that while certain contradictions are indeed true it is nonetheless necessary to show “how it is possible to quarantine the contradictions into points of singularity” (BLT 205). In other words, with paraconsistent logic Priest develops a logic of singularity, a logic that embraces contradiction (or a logic of sense and the paradoxes of becoming as Deleuze understands this) alongside traditional formal logic. It is this logic of singularity that surfaces in the work of Derrida’s project of deconstruction (as well as in the projects of Kant, Wittgenstein, Quine, and others), and it is this logic that Priest formalizes, as Livingston shows in his essay. And it is this logic, I would argue, that is presupposed by, and enables us to account for, the emergence of abstract, formal concepts. This brings me to my next point.
2. The problem of Cratylus.
One of the problems of taking Hume’s constitutional problem seriously is that one appears to deny oneself the very leverage one seems to need in order to account for the successful syntheses of the objects of knowledge and experience. How do we account for the identity of that which is determinately known, experienced, or meant if a determinate, identifiable condition for the possibility of such successful syntheses must itself be accounted for?
Priest discusses this problem as Cratylus’s view of the flux of meaning, from Theaetetus 181b-183c, whereby determinate meanings are impossible because they are always becoming other and in flux and thus they never maintain sufficient stability to give us the confidence that we are saying the same thing from one moment to the next, to ourselves or to others.
As unenviable as this position may be to defend, Derrida, Priest argues, has it even worse than Cratylus for while Cratylus allows that “meanings do not change in the short term,” thus enabling determinate meanings, “this reply is not open to Derrida” (BLT 219). This is a consequence, Priest claims, of Derrida’s conception of iterability, by which is meant the fact that the marks of writing are themselves repeatable and in relation to other marks, and they are repeatable – iterable – even in the absence of any intended addressee. It is the iterability of the marks of writing (or repetition as Deleuze discusses this) that accounts for the fact, to use Priest’s example, that the lines from Shelley’s poem Ozymandias – “My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair” – were originally intended and likely understood to demonstrate the magnificence of Ozymandias but today simply illustrate “the vanity of pretension” (216).
A consequence of iterability for Priest is the revenge of Cratylus, since the “meaning of any statement,” Priest argues,
is constituted by the chain of interconnections (differences and deferrals) between itself and other statements. Any time that someone makes a remark…this extends the chain and, therefore, changes the meaning. And the more one says (for example, by way of exegesis or clarification!) the worse the situation gets, since the more meaning changes.” (219)
Livingston reads Derrida much more positively (or more charitably) on this point. While Priest reads Derrida’s conception of iterability as leading Derrida hopelessly into a morass of indefensible positions even worse than those espoused by Cratylus, Livingston stresses the importance for Derrida of the “excess of the syntactic over the semantic” for properly understanding the conditions of interpretability of syntax that allows for both the possibility of applying the diagonalization argument that leads to a Derridean incompleteness argument and it entails important ethical implications for Derrida. In particular, Livingston’s reading is more in line with the original Humean problematic that largely motivated Husserl’s project – and Derrida’s too I would argue.
With this in mind, the Cratylus problem is indeed a problem, but one I think Derrida is aware of, especially if we keep in mind that Derrida is calling upon an ethics of reading. For Derrida there are misreadings of texts – one can get it wrong, as Derrida claimed Searle did of his own writings – but there is no predetermining rule that tells us how to go about getting it right. Such rules are nonetheless necessary – Derrida admits guardrails to interpretation are needed – but they are to be constituted in the context of reading and grappling with the texts themselves.
It is this necessary constitution of the rules and guardrails that is a consequence of the logic of singularity discussed above. Such singularities cannot be addressed by the ordinary conceptual apparatus – hence the need for them to be quarantined as Priest argued. There are two (and probably more) ways in which one can undestand the relationship between the quarantined paradox and the workings of our everyday conceptual apparatus - or common sense. We can resign ourselves to quietism where everything (the non-quarantined) is to be left as it is (this is how Priest reads Wittgenstein for example) and we thus left with simply accepting and describing the common forms of life as they present themselves. I happen to think this is not what Wittgenstein would have us do, but that will have to wait for another time.
On the other hand, we can see the relationship between the paradoxical singularity and the field of common sense as a source of problems and a prompt for creating concepts, for drawing connections and planes of consistency whereby one can establish a basis upon which to offer constructive, fruitful criticisms of alternative positions. This is precisely how Priest describes the task of philosophy in his more recent essay, "What is Philosophy?" Rather than point to anomalies and recalcitrant data points, Priest argues that one's criticisms are at their "most powerful only when [they have] the backing of some rival theory," and "Not only is developing an alternative view the best way of giving one's criticisms force, the articulation of an alternative view is itself a way of uncovering problems, and therefore criticisms, that might never have come to light otherwise."
What philosophers can do then is to create concepts, but they do so in a context where there is no predetermining totality or set of rules and axioms that is sufficient to guide the process. This is a consequence of the logic of singularity and Derrida, I argue, and Deleuze even more explicitly, opts for this approach of creating concepts (and Eric and I have stressed this in a number of posts [here and here for example]).
Another consequence of the logic of singularity is that it entails important ethical implications, which Derrida famously explored in his later writings (to the displaced dismay of many). One of the many strengths of Livingston's essay is that he gives due weight to this aspect of Derrida's work and shows how it follows from Derrida's own emphasis upon the "undecidable," or from the logic of singularity.
I close, then, with a relevant quote from Livingston:
…far from suggesting hesitation or indifference, what he calls the ‘undecidable’ is, for him [Derrida], an essential precondition for the possibility of responsibility: for if we have only to decide what is already in some sense decided by the system in which we operate, there is no responsibility in our decision.
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