This explores the possibility that Lacan was starting to use his neologism ‘dit-mansion’, transcribed as dimension, in his Seminar IV. The Agency of the Letter (9th May 1957) was given at the same time as the last sessions of Seminar IV. [See ‘Dit-Mansion’ for ‘Dimension’ in ‘Agency/Instance/ Insistence of the Letter’ : 3rd February 2025 : Julia Evans on this site /5 Authors A-Z (Evans)]

There are 51 occurences of ‘dimension’ in the transcription given at http://staferla.free.fr /Séminaire IV. The one possible use of dit-mansion, so far found, is given below. The EC Collective translation team found this passage very difficult to translated, so gave up on making the meaning easily accessible. As the translation of the complete Seminar IV is continued, further examples of dit-mansion may emerge.

20th March 1957 p8-9 of EC Collective’s translation, www.LacanianWorksExchange.net /Lacan (19561121)

These things seem to cause in [chez] some minds a certain number of very large resistances.

Nevertheless, it seemed to me that it was a more single track [voie] in order to make sense of a [une] certain dimension, that of recommending for example the reading…

perhaps from commenting on it

…from Mr Frege[23], Mathematician of this century who devoted himself to this science, in appearance the most simple of simples, that is arithmetic, and who believed they had to make some considerable detours…

Because that the more one thing is near to simplicity, [the] more it is difficult to grasp

…but undoubtedly some detours, all convincing, in order to demonstrate that there is not one [aucune] deduction possible of the 3, starting from experience alone. This [ceci], of course, leads us within a series of philosophical or mathematical speculations on which [desquelles] I have not believed [I] ought to make you undergo the proof. This [ceci] is nevertheless very important, because if not one [aucune] deduction from experience…

Contrary to this [ce] that Mr Jung might believe in …can only give us access to the number 3, it is certain that the distinction from the symbolic order by ratio [par rapport] to the real order enters within the real like a ploughshare[24] [soc] and introduces there [y] an original dimension. This [cette] dit-mansion/dimension, that we other analysts work on, and as long as we work over [sur] this [ce] register of the word [parole], we ought to take account of its originality. It is this [ceci] which is at issue within [dans] the occasion [occasion].

To be honest, I am afraid to tire you, and I am going to do something else to you, I am going to tell you a more intuitive idea that came to me, and this-here [celle-ci] is less certain within [dans] its assertion.

Footnote 23 : Frege’s theory – this was downloaded from the internet and appears not to be now available.

Frege’s theory of sets was to take extensionality plus the axiom scheme of comprehension,

Axiom Scheme of Comprehension: ∀[𝑎-] ∃𝑥 ∀𝑧(𝑧 ∈ 𝑥 ↔ 𝜙(𝑧,[𝑎-])) for all first order 𝜙 (𝑧,[𝑎-])

This makes a very natural theory exactly in accordance with our idea that sets should correspond to (first order) properties. Frege spent many years of his life developing his theory as a mathematical-cum-philosophical theory of property, and as a basis for the idea of number. For Frege, a number is the property of a set describing the size of that set, and a set might have 6 elements if it has the property of having size 6, and hence is a member of the set 6. This is an elegant idea to get the counting numbers off the ground. Unfortunately, Russell proved Frege’s theory inconsistent.

Any model of Frege’s theory would have to have an element 𝑅 such that ∀𝑧 (𝑧 ∈ 𝑅 ↔ 𝑧 ∉ 𝑧). But then 𝑅 ∈ 𝑅↔𝑅 ∉ 𝑅 which is contradictory. From

https://web.mat.bham.ac.uk/R.W.Kaye/logic/settheory .

Footnote 24, 24 The sharp blade of a plough (https://dictionary.cambridge.org/dictionary/english/ploughshare )

Related texts

‘Dit-Mansion’ for ‘Dimension’ in ‘Agency/Instance/ Insistence of the Letter’ : 3rd February 2025 : Julia Evans on this site /5 Authors A-Z (Evans)

The Agency (Insistence or Instance) of the Letter in the Unconscious or Reason since Freud : 9th May 1957 (Sorbonne, Paris) : Jacques Lacan, see this site /4 Jacques Lacan (19570509 or Index of Jacques Lacan’s texts)

Session of Seminar IV The signifier in the real in Seminar IV The Relation from Object (La relation d’objet) & Freudian Structures (1956-1957) : from 21st November 1956 : Jacques Lacan at this site /4 Jacques Lacan (19561121 or 19570320)