Lacan does something really interesting in his 11th seminar. He claims that the impossible is not the contrary of the possible. He never admits what the contrary (or, if you like, the negation) of the possible is called. For our purposes, we could claim that the negation of the possible is the “not-possible” or the “non-possible”. But Lacan really just leaves this concept to one side. If, then, the impossible, as the place of the real, is not the negation of the possible, then what exactly is it? It seems to me that it is much rather the negation of the negation of the possible. Clearly, when we describe the “negation of the negation” we are not returning to the possible. The negation of negation is not a return to affirmation. The negation of the negation of the possible is the impossible. And this, the impossible, is what admits something new. Lacan is very clear on this point. This, of course, raises all kinds of interesting questions about the place of the new within Lacan’s thinking. The full quotation follows:
The function of the impossible is not to be approached without prudence, like any function that is presented in a negative form. I would simply like to suggest to you that the best way of approaching these notions is not to take them by negation. This method would bring us here to the question of the possible, and the impossible is not necessarily the contrary of the possible, or, since the opposite of the possible is certainly the real, we would be lead to define the real as the impossible.
Personally, I see nothing against this, especially as, in Freud, it is in this form that the real, namely, the obstacle to the pleasure principle, appears. The real is the impact with the obstacle; it is the fact that things do not turn out all right straight away, as the hand that is held out to external objects wishes. But I think this is quite illusory and limited view of Freud’s on this point. The real is distinguished, as I said last time, by its separation from the field of the pleasure principle, by its desexualization, by the fact that its economy, later, admits something new, which is precisely the impossible.