I just finished Absolute Recoil. My diagnosis:
— You’ve got the exchange abstraction. Nothing much to worry about. Very common in these ages of the world [Weltalter]. You just need some relativity as such: take one each morning after breakfast.

Long answer: The book elaborates a variety of absolutes relative to one another and relative to themselves (‘self-relating negativity’, ‘absolute recoil’) but it does not investigate relativity as relativity as the oppositional determination of absoluteness.

A dialectic is needed between relativity and absoluteness like the dialectic of necessity and contingency formulated in Less Than Nothing.

Do I have a solution? I’d written a mathematical formulation a few years ago:

It has some implications for the book’s resolution:

“den is less than nothing”.
— Yes. It is the unicity ‘less than zero’ that I indicate by a dot:
0′ = ·

“objet a is more than one, but less than two: 1 + a.”
— No. Objet a is ‘less than one’ (‘to be or not to be’), where the outer dot (‘not to be’) embodies the shadowy double:
1′ = · {·}

“In short, the objet a is den processed through the One.”
— Here we have the exchange abstraction. There’s the input, the blackbox and the output: ‘Technology.’ (*)

“[sinthome is] the Two, a couple (yin-yang, masculine-feminine, the two classes in society), plus the One of Y a d’l’Un which makes the sexual (or class) relationship impossible and possible at the same time as its constitutive obstacle (chimney sweep, Jew, rabble): 2 + a.”
— No. What is expressed here is a dilemma (‘this one or that one’), which is ‘less than two’, where the outer dot (‘none of them’) embodies the dilemma:
2′ = · {·} { · {·} }

Note that there could be 3 or more elements, and the outer dot (‘none of the above’) would still embody the antagonism:
3′ = · {·} { · {·} } { · {·} { · {·} } }

In this light, I have an answer to this Freudian question: Why did he make up the story of the three prisoner women? I think it was a passage a l’acte to mark the absence of relativity as relativity in the book, to mark the abstaining from relativity as such.

(*): See Alfred Sohn-Rethel 1951 Intellectual Labour and Manual Labour (which was cited in The Sublime Object of Ideology). In fact I have a paper on necessity, contingency and Sohn-Rethel, but I have submitted it to a conference just a few days ago — OK, I’ve got the exchange abstraction too, well, I’m working on it.


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