Alain Badiou and Barbara Cassin, close collaborators and friends, seem to stand at opposite ends in their philosophical choices. While Badiou adamantly stands up for philosophy against the ever new kinds of sophistry, Cassin’s career is largely devoted to ‘rehabilitating’ the sophistry which she sees as a structural effect of philosophy, so that philosophy, in its epic battle against sophistry, was combatting its own shadow. The paper tries to investigate how these different choices are based in two strands of Lacan’s theory. Lacan in his later teaching proposed two new concepts, lalangue and matheme, with on the one hand the capacity of language for homonymy and punning, and on the other the stringency of formalization and the letter. Both depart from his earlier theory of conceptualizing language and the symbolic, but seemingly in opposite ways. While Cassin makes a clear choice of lalangue and its jouissance, seeing in matheme a philosophical residue, an off-spring of philosophical obsession with logic and formalization, Badiou on the other hand takes matheme as his central issue. They both seem to take one part of Lacan’s later teaching and play it against the other. The paper argues that there is no choice to be made between the two and scrutinizes the underlying assumptions of this apparent alternative. It proposes a ‘speculative identity’ of these two entities which seem to have no common measure, and considers the ways in which they are both involved with the real.