ABSTRACT
This chapter argues that just like G. Frege's functional analysis of predication freed him from the limitations of Aristotelian logic. Allowed him to extend the use of the particular, Lacan's logic of the not-all extends Frege's use of the particular in the direction of what we will call the singular of the singular or the singular within the single case. In other words the idea is to distinguish between a simple and a complex singularity or a partial and a total singularity. The category of the simple singular in the case of femininity represents castration: "There does not exist a woman not subject to castration." In the case of femininity Lacan says that "there does not exist" rather than all women are subject to castration. Aristotle mentions singular propositions but they are not part of his logic. Frege's logic allows for the same logic to be used for a particular subject or object of a sentence.
