The (im)possibility of rhetoric: The relation of rhetoric and geometry in Aristotle and Lacan

Aristotle and Lacan's work on rhetoric will be helpful in the promotion of rhetorical and interdisciplinary work in the academy, since no matter what degree of insight might be attributed to them, their formalizations of rhetoric are themselves "interdisciplinary." What is more, theirs is an interdisciplinary study with very particular structural consistencies (the imperative and the interrogative)--consistences which Lacan and Aristotle make evident only in terms of the relation of geometry and rhetoric.;In his conception of rhetoric as a dunamis (faculty, potentiality), Aristotle understood that rhetoric was not psychology, philosophy, ethics, nor any other science, but that rhetoric consisted of what dropped out of the symbolization of each of those genres of inquiry. And, what is even more insightful, Aristotle assigned a particular construction (a particular space) to rhetoric as an "unrealizable." Relating it quite specifically to his discussion of the ontological status of geometrical constructions, Aristotle assigned rhetoric the place of an imperative ("Let rhetoric be a dunamis") which demands we "negotiate" (render as both continuous and discontinuous) the active and passive principles of our world.;Lacan, likewise, conceived of rhetoric as an "unrealizable," but as a question--or better yet the mark of a question indicating the persistence of a gap between an utterance and its enunciation. Rhetoric is formalized as an adunamis by Lacan--the trajectory of an impossibility or impotence operating within his four discourse structures. The relation of rhetoric and geometry appears, here, in the form of a vector analysis with which Lacan makes possible not only the formalization of those rhetorical trajectories ("A Jakobson") but, as well, his particular formalization of metaphor and metonymy ("The Agency of the Letter").