There’s a fascinating post over at M-Phi, asking whether Godel’s use of numbers to code formal relations of derivability in his proof of the incompleteness of arithmetic can be generalized to logical systems which don’t “contain” arithmetic. Not coincidentally, it includes a link to an interesting paper by Paul Livingstone on Derrida, Priest and Godel which looks at the role of syntax in marking the undecidable elements of texts in deconstruction. New APPS will be hosting a symposium on the paper next week.
Derrida’s reading of Stéphane Mallarmé’s poem Mimique is central to Livingstone’s discussion, but as an aid for those who are not familiar with either, I’ve posted a brief commentary on it from my dusty PhD thesis (It was entitled: The Metaphysics of the Deconstructive Text, if you have to know!).
Rodolphe Gasché compares Derrida’s philosophical project with Husserl’s program for a logical grammar. Logical grammar, in its Husserlian sense, is only derivatively concerned with the structure of language. Syntactic distinctions between linguistic elements are of interest to logical grammar to the extent that they are indicative of the a priori laws governing the composition of intentional contents in cognitive or expressive acts. For example, in Logical Investigation IV Husserl distinguishes between complete, or ‘categorematic’, expressions which express a complete propositional content or a singular presentation, and non-independent, or ‘syncategorematic’, expressions whose senses contribute systematically to independent meanings but which do not express thoughts or refer to objects. Examples of syncategoremata are: ‘but’, ‘between’, ‘The sister of…’, ‘…implies…’. Among the a priori laws that Husserl has in mind would be that a syncategoreme cannot concatenated with a definite article.
The parallel between Husserl and Derrida, according to Gasché, consists in a common concern with formal or, in Derrida’s case, quasi-formal structures which account for the articulation of elements into discursive wholes. For Derrida, as for Gasché, Husserl’s project is limited by being oriented by semantics: in particular, the values of truth or reference. Thus sentences that are necessarily false, such as ‘The circle is square’, are meaningful, but, according to Derrida, are presumed meaningful because their grammatical form ‘tolerates the possibility of relation with [an] object’. Derrida’s project, according to Gasché, extends formality beyond the domain of semantics or logic, to structures which resist either phenomenological or semantic interpretation. He illustrates the quasi-syntactical character of différance, trace and the other infrastructures with reference to Derrida’s reading of part of Mallarmé’s prose poem, Mimique, in ‘The Double Session’:
La scène n’illustre que l’idée, pas une action effective, dans un hymen (d’où procède le Rêve), vicieux mais sacré, entre le désir et l’accomplissement, la perpétration et son souvenir: ici devançant, là remémorant, au futur, au passé, sous une apparence fausse de présent...
Though hymen contributes to the imagistic content of the poem, Derrida suggests that its structural role is as a syntactic place holder which resists onto-grammatical categorization. Although formally a noun – and thus a categoreme in Husserlian terms – Derrida argues that the role of hymen in the poem is largely independent of its meaning but is, rather, determined by its relation to entre, ‘between’: ‘Through the “hymen” one can remark only what the place of the word entre already marks and would mark even if the world “hymen” were not there. If we replaced “hymen” by “marriage” or “crime”, “identity” or “difference”, etc. the effect would be the same, the only loss being a certain economic condensation or accumulation’. The putatively independent hymen is thus textually dependent upon the nominally syncategorematic entre, an element whose ‘signification’ is itself dependent upon its placement. In addition to its grammatical equivocation, hymen is also a ‘between’ of temporal phases of action and cognition (entre le désir et l’accomplissement, la perpétration et son souvenir: ici devançant, là remémorant, au futur, au passé) without being temporally situated (sous une apparence fausse de présent). The indeterminacy of this locus (which, for Derrida, cannot without violence be interpreted as ‘eternal’) can nonetheless be articulated with respect to more or less stable lexical values (devançant, re-mémorant, futur, passé, présent, etc.).
Mimique thus demonstrates, in microcosm, the process by which language extracts a surplus of meaning without being informed by a prior relation to some domain of objects. This is the sense in which, for Gasché, Derrida’s investigations can be considered as a generalization of Husserl’s project:
The system of these infrastructures as one of syntactically re-marked syncategoremata is a system that escapes all phenomenologization as such; it constantly disappears and withdraws from all possible presentation. In privileging the syntactical in the sense in which I have been developing it – suspended from semantic subject matters of whatever sort – the general system spells out the prelogical conditions of logic, thus reinscribing logic, together with its implications of presence and evident meaning, into a series of linguistic functions of which the logical is only one among others. 
D Dissemination, Barbara Johnson (trans.),
(1972; London: Athlone Press, 1981).
SP Speech and Phenomena, David Allison (trans.),
(Evanston Ill.: Northwestern University Press, 1973).
TM Rodolphe Gashe, The Tain of the Mirror: Derrida and the Philosophy of Reflection
(London: Harvard University Press, 1986).
 Edmund Husserl, Logical Investigations, IV, pp. 501-503.
 SP, p. 99.
 TM, pp. 248-249.
 Cited in D, p. xx.
 Ibid., p. 221.
 TM, p. 250.
There’s an instructive debate going on between Graham Harman at Object Oriented Philosophy (henceforth OOO) and Levi Bryant over at Larval Subjects (henceforth LS) about whether Derrida’s work is serviceable for realism. OOO is emphatic: not only is Derrida not a ‘plug and play’ realist, his work has no realist application at all. Unlike Heidegger – whose account of withdrawal can be given a realist spin in Object-Oriented circles – Derrida’s position is not amenable to realist use or even to creative abuse. Here’s OOO:
I think it’s simply madness to call Derrida a realist. His entire argument makes sense only by identifying realism with onto-theology and hence with parousia/presence. He reads the concept of substance as the foot soldier of onto-theology. His critique of the proper is a very frank critique of realism. His theory of the trace is another anti-realist maneuver, not a realist one since that would open the door, in his view, to the “transcendental signified.”
There’s obvious textual support for OOO’s position. Derrida does claim in Of Grammatology that infrastructures like trace and différance provide a condition of possibility for presence and ‘onto-theological’ thinking without being presences or grounding entities themselves. Indeed, for Derrida, they provide the invisible underside or ‘tain’ of all thought, reflection or representation.
The term Différance, like its cognate infrastructural markers ‘trace’ and ‘supplement’ and ‘iterability’, is an economical allusion to structures of negation, co-involvement and co-implication within general textuality. Textuality, for Derrida, should not be identified with language. A text, according to Derrida, is any structure that can be characterized by such operations and relationships. For example, any text will have to consist of elements that are minimally repeatable: ‘A sign which would take place but “once” would not be a sign: a purely idiomatic sign would not be a sign’ (SP, 50) Language is the paradigm of this, but Derrida argues that even the neural memory trace within Freud’s prototype theory of neural networks has to be reactivatable to do its job – though each reactivation alters the relative amenability to stimulation that differentiates it from other memory traces (WD). Derrida’s analysis of the neural trace in ‘Freud and the Scene of Writing’ meanwhile refers to his earlier analysis of Husserl’s account of temporal awareness. Again, this requires any ‘now’ to be implicated with a retained past while potentiating a not yet determinate, novel future. Thus as Derrida claims in ‘Signature Event Context’ structures like spacing, trace and iterability are invariants. They extend to all representation, to all experience (LI 10).
Derrida’s claim about general textuality may all seem like an excessively subtle way of saying that meaning and content cannot be instantiated in formless pap. However, the infrastructural account has the virtue of extreme generality. It is something very much like a textual ontology – even if JD never conceded this.
Enter LS who makes the central point that iterability (one of the textual infrastructures) requires that entities cannot be dissolved into their relations. Since he is an object-oriented philosopher he frames this as a claim about objects: ‘For Derrida, it seems, any object can be severed from its relations to other objects.’ This is important because Derrida is usually cast as an arch-holist. But it is obvious to anyone who reads him carefully that this is not the case. LS is alluding, of course, to passages such as following one from ‘Signature Event Context’:
Every sign, linguistic or nonlinguistic, spoken or written (in the usual sense of this opposition), in a small or large unit, can be cited, put between quotation marks: in so doing it can break with every given context, engendering an infinity of new contexts in a manner that is absolutely illimitable . . . This citationality, this duplication or duplicity, this iterability of the mark is neither an accident nor an anomaly, it is that (normal/abnormal) without which a mark could not even have a function called ‘normal’ (LI, p. 12).
So while Derrida may not be a realist, it is clear that he cannot be a holist. No text is exhausted by its passing affiliations. This also means that Derrida cannot be a relativist since relativism requires relativization to some constraining super-context. Iterability says, in effect, that there is no super-context: all contexts are fragile and open. ‘Mass’ may play a different role in Newton to the role it plays in Einstein (for whom there is both relativistic and proper mass) but this does not mean that the two terms are just their respective theoretical roles. Can this point be generalized to get us something like realism? Well, we need to ask: ‘Realism with respect to what?’ Both LS and OOO use the idiom of things or objects. So if LS is right and iterability requires that things be reusable from context to context and Derrida is committed to iterability, then Derrida is committed to things. Ergo, he’s a realist about objects. But OOO is probably right to insist that Derrida’s no thing fan.
However, it may be that Derrida has ontological commitments to things other than things. An iteration like my quotation/mention of ‘if’ in this sentence is an event. For texts (in the general sense) to work there need to be events that are both differentiated and repeatable. What makes this further ‘if’ a token of the same type as this ‘if’ is not its instantiation of a common signifying essence but its iterability. So Derrida is committed to events and he’s committed to relations of repetition between event instances. This means that he’s committed to repeatable events, of course. But there are different models of repetition. Here’s Nelson Goodman: ‘
Repetition as well as identification is relative to organization. A world may be unmanageably heterogeneous or unbearably monotonous according to how events are sorted into kinds (WWW, 9).
THIS is relativism: repetition is relative to organizing scheme. But it’s clear that Derridean repetition cannot be scheme-relative in this sense because that would limit iteration to super-contexts and iteration is ‘absolutely illimitable’. So, as I argued long ago in RQRR, we have to say that Derridean repetition is real repetition. Since repetition occurs to events, these must be structurally repeatable. Derridean events are repeatable particulars, however, not abstract events of the kind posited by Ronald Chisholm. So Derrida is a) not a relativist and b) he is ontologically committed to repeatable particular events and their repetitions. So Derrida is a realist with regard to events and their repetition. However, these occurrences are realized they occur independently of organizing schemes or concepts. They are mind-independent, then, insofar as their occurrence does not depend on the constitutive activity of subjects and language users.
LI Limited Inc., Samuel Weber and Jeffrey Mehlman (trans.),
(1977; Evanston Ill.: Northwestern University Press, 1988).
OG Of Grammatology, Gayatri Chakravorty Spivak (trans.),
(London: Johns Hopkins University Press, 1976).
SP Speech and Phenomena, David Allison (trans.),
(Evanston Ill.: Northwestern University Press, 1973).
WD Writing and Difference, Alan Bass (trans.),
(1967; London: Routledge and Kegan Paul, 1978).
WWW Nelson Goodman, Ways of World Making (Indianapolis: Hacket, 1978).
RQRR, David Roden, ‘Radical Quotation and Real Repetition’, Ratio (new series) XVII 2 June 2004, 191-206.