“There is no truth that, in passing through awareness, does not lie. But one runs after it all the same,”^[1] is a phrase by Jacques Lacan, from the preface to the English language edition of seminar XI, The Four Fundamental Concepts of Psychoanalysis, written in 1976. Formulated via the logical device of double negation, this sentence corresponds with one of the formulas of sexuation, on the feminine side: ​“There exists no x that is not under the phallic function,” or in other words ​“there is no one who is not castrated.” Once more: double negation.

Instead of stating the proposition in a positive form (every x is y), Lacan adopts a different formulation (there is no x that is not y), in order, not to support the universal and to present it as merely possible, [but] not necessary.^[2] Lacan could have said that every x falls under the phallic function, but he rather chose to phrase it using the device double negation. At first glance, there seems to be no difference in meaning between the two formulations, but this is deceptive. Double negation makes it possible to extricate from the universal in favour of something open, not whole. Feminine sexuality, in containing a double negation, opens onto the contradictory logic of the impossible real.^[3] Thus, women dwell closer to the real of the drives because they are not defined as being wholly in the symbolic order of the group(s).^[4]

By means of double negation, we approach the edge of what can be said about x, the limit; this limit is the boundary of language. Double negation touches the edge of what can be said in language; it reaches the limit of what can be expressed, approaching the place where one can say no more, where language begins to fail – the real. And it is no coincidence that Lacan defined this same real as something that never ceases not to be written^[5] and as the lack of the lack^[6] – both being forms of double negation.

Double negation positions woman in the ​“pas tout” – not whole, beyond the phallic function. Hence, their proximity to the impossible real. And, in the same way, double negation leaves truth itself as incomplete, not encompassed by the universal. In this sense, ​“no truth that […] does not lie”^[7] does not merely mean that every truth lies, but that truth is not whole – that she remains open, not final, perhaps even extending toward the infinite – yet with a proximity to the impossible real, without being identical to or equated with it.

1. Lacan, J., The Seminar of Jacques Lacan, Book XI: The Four Fundamental Concepts of Psychoanalysis, ed. J.-A. Miller, trans. A. Sheridan, New York: Norton & Company, 1978, p, vii. ↑
2. Ragland, E., The Logic of Sexuation, Albany: State University of New York Press, 2004, p.61. ↑
3. Ibid. ↑
4. Ragland, E., The Logic of Sexuation, op. cit., p,86. ↑
5. Lacan, J., The Seminar of Jacques Lacan, Book XX: Encore: On Feminine Sexuality, the Limits of Love and Knowledge, ed. J.-A. Miller, trans. B. Fink, New York: Norton, 1998, p. 59. ↑
6. Lacan, J., The Seminar of Jacques Lacan, Book XI: op. cit., p, ix. ↑
7. Ibid, p, vii. ↑