Full details at Seminar IX The Identification (1961-1962) : from 15th November 1961 : Jacques Lacan, see this site /4 Jacques Lacan (19611115). There are excursions into the Chinese language in this session.

English translations :

– Translated by Cormac Gallagher

From original tapes – Chapter 4 – Wednesday 6th December 1961 : p28-37
Published by www.LacaninIreland.com /Translations/Seminars
– Translated by Ben Hooson

Translated from transcriptions of the original tapes and Michel Roussan’s text, by Ben Hooson, December 2022, p39-53. Available at www.LacanianWorksExchange.net /Lacan

In French

Transcribed from original tape-recordings, Séminaire- Jacques Lacan – 9 : L’identification, at http://staferla.free.fr/S9/S9.htm

Citation

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-Clinic and Topology – The Flaw in the Universe, The Clinic of the Borromean Knot : 1st January 1993 : Pierre Skriabine, see this site /5 Authors A-Z (Skriabine or Index of Authors’ texts)
p81of Part 1- Flaw in Universe, Skriabine : If it comes to complete the Other in this way, it also renders it inconsistent.

Incomplete or inconsistent, the Other only exists as barred.

And let us note with Lacan that each time the question of nomination is posed, each time, for example, that one tries to designate a signifier with itself, to write d = d, this signifier will come to the logical place of the point of inconsistency: there is no tautology.
“A signifier,” says Lacan in L’identification (6 December 196l), “can be defined in no other way than through its not being what the other signifiers are. From the fact that it can only be defined precisely by virtue of not being all the other signifiers, there arises another dimension: it is equally true that the signifier could not be itself.” In other words, one cannot write a = a. Lacan adds that “the signifier is essentially different from itself; nothing of the subject could identify itself with it without excluding itself from it.”

Session of 6th December 1961, P44 of Ben Hooson’s translation : I don’t want to go further with this, which is really a way of disposing of false tautologies that are simply the ongoing, permanent use of the language, because the only reason I am talking about it is to make clear to you that it’s not what I mean.

If I say that tautology isn’t possible, it’s not because the first “a” and the second “a” mean different things. The point is that it is inscribed in the very status of “a” that “a” cannot be
“a”.
That was how I ended my discourse the last time, when I drew attention to the place in Saussure where it is stated that “a” as signifier cannot be defined in any way except as not being what the other signifiers are. From this fact, that it cannot be defined except precisely as not being all the other signifiers, there depends this dimension whereby it’s equally true that it cannot be itself.
It’s not enough to make the point in this opaque fashion, precisely because it surprises and upsets the belief that this is the real support of identity. [15] You must be made to sense it.[15] i.e. the belief that “a = a” is an evident truth and is the essence of identity.

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-A Vision of the Streaming (ruissellement – trickling down) of the One : 1st March 2021 : Éric Laurent, see this site /5 Authors A-Z (Laurent)
P51-52 Laurent, It is throughout his Seminar on identification that Lacan turns the trait of the One into an isolated sign. He takes a diversion into prehistory and to the notches on the bones, carved by Magdalenian hunters. He contrasts the trait with the things in the world that it comes to mark. “The relationship of the sign to the thing must be effaced. This One of the Magdalenian bone, it would be a shrewd man indeed who could tell us what it was the sign of […] This One as such, in as much as it marks pure difference, is what we will refer to in order to (designate) the diverse ways of effacing […] from which the signifier comes into the world.”[18]

Of course, in “Identification”, Lacan speaks of the signifier and not of the letter, but the process of isolating the One from the signifier, separated from all signification allows us to better understand this way of effacing to the second power, where the bar comes to mark the effacement of signification in order to only designate the trace of the experience of jouissance, there where the subject gets effaced.

[18] Lacan, l., The Seminar, Book IX, Identification, lesson of 6 December 1961, unpublished

Seminar IX 6th December1961 : p51-52 of Ben Hooson’s translation,

From pIV 36 of Cormac Gallagher’s translation, www.LacaninIreland.com , : The first definition that one can give of a someone is: someone who is accessible to a sign. It is the most elementary form, if one can express oneself in that way of subjectivity; there is no object at all here yet, there is something different: the sign, which represents this something for someone. A signifier is distinguished from a sign first of all in this which is what I tried to get you to sense: the fact is that signifiers only manifest at first the presence of difference as such and nothing else. The first thing therefore that it implies is that the relationship of the sign to the thing should be effaced:

sign_____ [OR sign/someone]

someone

something S, these ones of the Magdalenian bone, it would be a very clever man could tell you what they were the sign of. And someone we, thank God, are advanced enough since Magdalenian 4 [Ben Hooson gives ‘Fourth Magdalenian’] for you to perceive the following – which for you has the same sort no doubt of naive obviousness, allow me to tell you that “A is A”, namely that, as you were taught in school, you cannot add up oranges and apples, pears with carrots and so on, is a complete error; this only begins to be true when one starts from a definition of addition which supposes, I assure you, a number of axioms which would be enough to cover this whole section of the blackboard.

pIV 36 : … it is a question of 1 very exactly in what one calls the element of sets. This is not sufficiently remarked on in the text to which I allude for a celebrated reason: it is because precisely this reflection on what a 1 is, is not well elaborated even by those who in the most modern mathematical theory nevertheless make of it the clearest, the most manifest usage.

This 1 as such, in so far as it marks pure difference, it is to it that we are going to refer to put to the test, at our next meeting the relationship of the subject to the signifier. It will first of all be necessary for us to distinguish the signifier from the sign and for us to show in what sense the step taken is that of the effaced thing: the different “effaçons” if you will allow me to use this formula, in which the signifier comes to birth, will give us precisely the major modes of the manifestation of the subject.