“The Parisian nonsense machine [Althusser, Lacan, Deleuze] was used to mount a ballistic assault on the bourgeois culture, throwing dense blocks of impenetrable Newspeak over the battlements into the public square of the beseiged city. The effect was to destroy the conversation in which civil society depends. All delicate ideas concerning law, constitution and the roots of civil order, all the ways in which human beings argue over rights and duties, honor their opponents and seek for compromise, were flattened by mathemes, ‘deterritorialized’ and buried beneath the debris of the great Event. This was the turning point in a battle that has now been raging for a century – the battle to take possession of the culture, by defining the intellectual life as an exclusively left-wing preserve.”

— Roger Scruton, Fools, Frauds and Firebrands.

The aim of analysis is to generate knowledge about the unknown. So, the paradoxical position of Lacan concerning truth is that there is no knowledge of truth, but finally there is a psychoanalytic knowledge concerning this absence of knowledge; that is the great paradox of the unconscious.

The key of this enigma – because it is an enigma – has for Lacan a name, a strange name, a Greek name which is the ‘matheme’.

What is a matheme? To understand this name, we must return to the act, to the fundamental analytic act.

For Lacan, a subject can have an experience of its proper real only in the form of an act. There is, if you want, no abstract knowledge of the real. The real is a revelation in the form of an act. And this act is like a cut in language and also a cut in the ordinary representation of the word; representation which is imaginary.

So, the act suddenly isolates the real from its normal connection to imaginary and to symbolic order. It’s very important, this point.

The act generally speaking is not only in the field of psychoanalytic cure. The very essence of the act is to separate the real from symbolic context and imaginary context. It is when something of the real is pure. And you face the real not in the mediation of symbolic presentation or imaginary re-presentation, but directly. You face the real, but when you face the real, always in the form of an act and not in the form of a knowledge or in the form of an abstract language.

It’s why that sort of presentation –sudden presentation of the real – it is why the real appears always not as a continuity but as a point.

The real of a subject is always a point of real, of a real point. So, we have the question finally in all that: Where is the knowledge? And where is the truth of the knowledge, of the knowledge of the unknown? (…to speak as Lacan)

Is there a knowledge of the result of this sudden apparition of a real point? Is there somewhere a connection between knowledge, generally speaking, and the real point? Or have we a sort of mystique of the real which is an experience, but without any knowledge?

The answer of Lacan is that there can exist a knowledge of the real, in some sense, at the price of a rigorous formalization. Because formalization – by the strict use of some letters – reproduces the operation of the real and the separation of the real from its common imaginary presentation.

With formalization – with small letters, without any imaginary context – we can touch the experience of the real and we can have a transmission of that sort of experience; and that is precisely a ‘matheme’. A matheme is the formalization of a local form of apparition of a real point.

—  Alain Badiou, Is Lacan An Anti-Philosopher? [youtube]