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).