“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.”
A crucial presupposition of Livingston’s argument is that Gödel’s results are usefully analogous to operations on the structure of natural languages, even if they were developed in a reflection on formal systems, stricto sensu. In the Introduction to Politics of Logic Livingston argues, following Davidson, that any language, “formal” or “natural,” in order to be learnable and usable, must take the form of a finite set of symbols capable of infinite iteration (PL, 35). In this move to an underlying and shared structural level, Livingston deconstructs the opposition between natural and formal languages and thereby defangs the criticism that Derrida has illegitimately extended Gödel.
Livingston wants to see to what extent Derrida’s key terms, or more precisely, the practice of deconstruction whence they come, can be formalized; if they can, then the target of deconstruction is formalization as such, or, in Derrida’s terms, “writing.” (In the terms of Livingston’s The Politics of Logic, Derrida exemplifies the “paradixico-critical” position that “draws out the critical consequences of language’s inherent reflexivity” [PL, 111].)
In particular, Livingston claims a structural analogy between deconstruction and diagonalization, in that both are ways in which a system “encodes” its own structural logic at a specific point; this self-referential point is “undecidable” in terms of the system – you cannot pin it down as true or false, inside or outside, meaningful or meaningless. The undecidable term operates by means of an “essential crossing” of semantics and syntax; the term names the operation of writing; that is, it means the operation of the production of meaning.
A second key point is thus that Derrida’s “undecidable” terms do not trade on semantic ambiguity; they do not contain, thanks to the historical path of a language, speculative riches as does Hegel’s “Aufhebung.”
A final point is that deconstruction produces an ethics of the undecidable, an ethics of the aporetic structure in which the condition of possibility of pure decision is at the same time its condition of impossibility. This ethical aporia is a “consequence of formalism,” for a decision cannot be the result of a formal procedure, a deduction from the facts of the case, but neither can it be arbitrary, bearing no relation to the facts of the case. Contrary to readings that claim Derrida demands a relation to a singular “other” wholly outside a system of meaning, Livingston instead claims ethics is precisely living and acting in the aporia, so that “responsible decision as such is conditioned by the complex topology on in-closure” (ms, p 13; PL, 129).