The Letter, Issue 39, Autumn 2008, Pages 71 - 89
IN PRAISE OF INCOMPLETENESS
Patricia McCarthy
In Todd Haynes 2007 movie on the life of Bob Dylan I’m Not There, one of the many Dylan semblances states ‘I’m not there but the song goes on As parletres, we are subject to lalangue, expressed equally as, we are subject to the phallic function (p. Lacan’s unwavering stance is that the phallic
function calls the shots and how it is ‘variabilised’ decides our existence and our sexuality. We exist as semblances which doesn’t allow a complementarity or ratio between a couple - man and woman being the exemplars. Making the phallic function its keystone, Lacan built his
formulae of sexuation - a version of Aristotle’s logical square - with the mathematical bricks of function and variable as fashioned by Frege (1848- 1925). Hisformulae show the limitation ofa logic, cf. Aristotle’s, that masks rather than handles thefault or faille that structures us. Beginning with a detailed examination of the relationship between function and variable, this commentary recasts the concept of the Primal Father, the at-least-one who is not subject to the phallic function as a necessary inexistent, by revisiting the paradigmatic case of Little Hans. It concludes with a comment on the
fault in knowledge systems - recognised by Peirce and Godel in science and mathematics and by Lacan in his not all - as ultimately residing in S(Ø).
I’m going to start by telling you what I have not been able to achieve in this paper. When our reading group began to meet last September, I thought, a little over-ambitiously, I might get to tackle Aristotle’s Prior Analytics, study the text - in English, I might add! - and work through his proofs of inconclusiveness and the indeterminacy of the particular. Inconclusiveness and indeterminacy, these terms suggest that something is not whole and complete. They suggest equivocation, and this, Jacques Brunschwig in his article The Particular Proposition and the Proofs of Inconclusiveness according to Aristotle[1] argues, was sacrificed, not only by Aristotle in favour of a logic that might not be equivocal, but by those who, in the succeeding centuries, translated, interpreted and revised his work. And the fact of this sacrifice, why might it be of importance to us? For Lacan, it is quite simply symptomatic of the attempt in logical systems to maintain that there is a consistency at the heart of language and of knowledge. And he is going to go a whole lot further than that and claim