In the Seminar Crucial Problems for Psychoanalysis Lacan suggests that the logical conditions for the subsistence of the subject are indicated in Plato’s Sophist. Lacan argues that the same conditions are necessary for there to be a signifier orientated with respect to another signifier as for there to be a subject. This amounts to saying that the subject is the effect of signifiers. This article sketches the conditions Lacan indicates as necessary for the operation of signifiers. This amounts to an account of the conditions for a logic. The article deals mostly with the implications of the discussion of being and not-being in Plato’s Sophist. A new status for not-being is established in the face of arguments proposed by the sophist and seemingly supported by Parmenides. Before the Sophist being and not-being were thought as contraries. Not-being by this account is problematic and ultimately unspeakable. Therefore, Parmenides could prohibit research into not-being. Plato’s dialogue situates not-being in the logical realm and suggests a relation between being and not-being which is marked by otherness and introduces a function of negation which allows what is not present to be presented. Lacan refers to the Sophist because something of the logical status of the subject, in so far as it is the effect of the operation of signifiers (in other words, the logic of the signifier), “overlaps” with the status of not-being established in Plato’s text.