'Logic of the fantasy': the expression recurs throughout the Seminar as a leitmotif, yet not a single lesson is devoted to it; not even a briefly sustained development. Does this mean that the logic of the fantasy is here playing the role of some new-fangled mirage? No it doesn't, not if we can take on board how this logic is the very site at which Lacan's comments converge, which is what I have sought to indicate by entitling the final chapter 'The axiom of the fantasy'.It begins with him audaciously blending the mathematical Klein group and the Cartesian cogito, modified in such a way as to offer up the alternative, 'Either I am not, or I am not thinking'. On this basis, Lacan summarises the course of an analysis in four phases.A further mathematico-psychoanalytic blend: the sexual act is illuminated by the light of the Golden number. What ensues is that 'there is no sexual act', this being the first trace of what was to become a pons asinorum: 'there is no sexual relating'.The reader will also come across the invention of a 'value of jouissance', inspired by Marx, and will be surprised to see the big Other, the 'locus of speech', being newly defined as 'the body', the primordial locus of writing.A good many other gripping insights and constructions await this reader, if he is minded to follow the meandering, the stalling and the about-turns, along with advances and flashes of brilliance, an obstinate and profoundly honest thinking that, whenever it comes up against a stumbling block, never skirts around it but endeavours to turn it into a cornerstone.Jacques-Alain Miller