If knowledge is socially constructed, then students' discursive attachments should be eminently malleable. Students' radical openness to change, however, is not the defining characteristic of a university classroom. Instead, learners appear to desire coherence of knowledge over revelations of contingency, and pedagogical acts that disrupt existing formations are as likely to produce reactionary responses as revolutionary reorganizations of the self. In this article Chris McMillan argues that neither the constructivist nor the social constructionist readings of critical pedagogy are able to account for this fixity of knowledge. In response he contends that Slavoj Žižek's Lacanian-inspired theory of subjectivity and of the Real can effectively respond to the limitations of these approaches by insisting upon the pedagogical value of the lack within subjectivity. A Žižekian conception of subjectivity is able to respond to this lacuna by positing the negativity of the subject as the agent of transformation and to produce a "pedagogy of the impossible" that evokes the moments of impossibility within discourse embodied by the subject "qua" the Lacanian Real.