Star Trek's 'I, Mudd': liar's paradox and the Cartesian subject as rhetorical form

This has always been one of my favorite scenes from the original Star Trek series starring William Shatner as Captain Kirk and Leonard Nimoy as Spock. It's the liar's paradox scene from the "I, Mudd" episode. I am currently contemplating that this scene illustrates not simply the operating of a logical paradox but also how faulty rhetoric supplies disruptive content to a subject that defines itself as rational, resulting in fragmentation and paralysis of the subject under the Cartesian model of subjectivity.