Derrida and Formal Logic: Formalising the Undecidable

Derrida’s key concepts or pseudo-concepts of différance, the trace, and the undecidable suggest analogies to some of the most significant results of formal, symbolic logic and metalogic. As early as 1970, Derrida himself pointed out an analogy between his use of ‘undecidable’ and Gödel’s incompleteness theorems, which demonstrate the existence, in any sufficiently complex and consistent system, of propositions which cannot be proven or disproven (i.e., decided) within that system itself. More recently, Graham Priest has interpreted différance as an instance of the general metalogical procedure of diagonalisation. In this essay, I consider the extent to which Derrida’s key terms and the essential operations of deconstruction can be formalised. I argue that, if formalisation is indeed the technique of writing par excellence, then the formalisation of deconstructive concepts tends to show how the auto-deconstruction of total systems arises from the problematic possibility of writing itself. For instance, since diagonalisation permits the ‘arithmetisation of syntax’whereby a formal system is able to formulate claims about its own logico-grammatical properties, we can understand its potential to inscribe the undecidable within the systematicity of language as simply one instance of the potential of writing, in figuring itself, to render inscrutable the trace of its own origin.