The mirror operator

The paper explores the Lacanian metaphor of the mirror as a logical operator. While the mirror-stage has often been discussed regarding its imaginary relevance, the mirror as a logical operator has not yet been discussed. To mark a first approach to this, the paper discusses the formulas Lacan offers in his Seminar X, "Anxiety," as an example for the use of this operator. The formulas show a great deal of complexity that binds several elements of Lacanian thought together. Within Lacanian theory, they show a distinct relationship to the specularised and non-specularised images of the Möbius strip, as well as to the cross-cap, and they offer a deeper insight into the widely used metaphor of the mirror. These formulas also offer a wider insight into how 'mirroring' can be understood formally in non-Lacanian psychoanalysis. The mirror operator as a logical tool enables analysts to conceive of how an indeterminate element is part of our identity and how this structures angst.