In an excellent passage from Parallax View , Žižek defines “freedom” as “recognized/assumed necessity”. How does this definition of freedom relate to class identification?
One way to distinguish bourgeois identification from working class identification is to look at the character of their recognized/assumed necessities: The fundamental necessity of life is, for a bourgeois, the surplus-value added to capital; but for a worker, it is the need to sell his/her labor-power. One can also distinguish the Marxist notion of proletariat identification from working class identification: Proletariat identification recognizes/assumes a “political” necessity, e.g. to “organize as the ruling class and eventually abolish itself as a class”. This notion of proletariat is the paradox of a social class that aims to both rule the society and abolish itself. Defined and distinguished in this way, one can clearly see the contradiction between the proletariat and the working class: A ruling class would no longer need to sell its labor-power, and the working class cannot be “abolished” as a form of identification. An alternative is to define the proletariat in terms of the revolutionary party.
To see the role of the symbolic order in these identifications, let us redefine the Lacanian-Žižekian notions of alienation and separation in these terms.
In alienation, the recognized/assumed necessity comes from an existing symbolic order where it was previously inscribed. Therefore, alienation is a relative freedom that depends on a big Other. For example, in bourgeois alienation, surplus-value is inscribed in the notion of “profit”. In working class alienation, the need to sell one’s labor-power is inscribed in the notion of a “job”. In proletarian alienation, the need to rule and abolish itself may be inscribed in a particularly Marxist notion of “history”. In class alienation in general, the class of identification is previously inscribed in the existing symbolic order.
In separation, the recognized/assumed necessity does not come from a previous inscription: the act of recognition/assumption results in a new inscription of necessity. In other words, separation creates the necessity that it recognizes/assumes. Therefore, separation is an absolute freedom, a founding gesture that clears the space to re-ground the symbolic order. In this sense, separation is properly political. For example, in bourgeois separation, surplus-value acts as an abstraction that “melts all that is solid into air” (Marx). In working class separation, one’s labor-power is an abstraction that generates a “right of distress” (a notion of Hegel that Žižek emphasizes). In proletarian separation, one becomes the embodiment of the Party: “Who is the Party? We are the Party. You and I and he – all of us” (Brecht). Thus in separation, there is no prior class of identification. Instead, there is a free act of identification that may or may not generate a class of its own.
The relative freedom involved in alienation depends on a previous chain of signifiers (S2), whereas the absolute freedom involved in separation is a free act that basically clears the space by identifying with the objet petit a, which may or may not be followed by a Master-Signifier (S1) that initiates a new chain of signifiers.
To emphasize the distinction “alienation versus separation”, I’ll introduce a term from computer science, and talk about “class versus cluster” .
In computer science, “classification” is the task of labeling new data based on previously labeled data. It’s called a “supervised method” due to its dependence on prior labels. Its logic is analogous to “alienation” which depends on the prior existence of a symbolic order. On the other hand, “clustering” is the task of labeling data without any prior labels. It’s called an “unsupervised method” due to this independence, and its logic is analogous to “separation” which is the act that re-grounds the symbolic order. Based on this analogy, it makes sense to talk about “class alienation” and “cluster separation”.
A “cluster” is a proto-class, it’s something signified that may or may not become a symbolically inscribed class of objects. A cluster is basically an objet petit a that grounds the founding act of a Master-Signifier. To give a familiar example from Žižek, consider the use of the word “solidarity” as a Master-Signifier. When this special word “solidarity” is used politically to found a new symbolic order, it signifies a collection of “solidary” activities that did not constitute a classified whole prior to this signifying act. Thus when it’s used as a Master-Signifier, the word “solidarity” does not initially signify a class of activities, but a cluster of activities, which may or may not generate and establish a symbolically inscribed class of activities. If the signified cluster of activities is only a temporary phenomenon, then the “solidarity” will soon disappear and become a memory remembered as part of a political history, even if it plays a critical role as a vanishing mediator. If the signified cluster of activities can establish itself as a permanent class of activities, then the word “solidarity” will become a proper Master-Signifier and initiate a new chain of signifiers.
In bourgeois cluster separation, “all that is solid melts into air” because of the insistent emergence of several clusters of activities associated with the social efficiency of surplus-value. The emergent bourgeois clusters of activities may establish themselves as permanent classes of activities insofar as they take part in the self-generating loop of capital and surplus-value. Such sedimentation leads to bourgeois class alienation that relies on notions like “profit”, “growth” etc. Occasionally, bourgeois cluster separation brings about great historical events, but it may or may not lead to a Master-Signifier, it may disappear as a vanishing mediator.
In workers’ cluster separation, masses of subjects are reduced to their labor-power, which is at the same time included and excluded by bourgeois alienation. There is surely a “working class” of people that are alienated in their “jobs”, but these jobs are always threatened, fragile and insecure, which is why it makes sense to talk also about “working clusters” which can never be established as classes under the bourgeois symbolic order. This permanent exclusion of “working clusters” generates the “right of distress” (Hegel) that bestows upon the workers in the bourgeois society a special status that is the logical basis of the notion of the proletariat. Workers may also bring about great historical events as Master-Signifiers and vanishing mediators.
In proletarian cluster separation, the proletarian subject embodies the Party and enacts clusters of historical activity. If the proletarian subject perceives oneself as a mere instrument of “history” (big Other), it is more fitting to call his/her status, proletarian class alienation. For example, that “proletariat will be a ruling class that abolishes itself” is the assumption of a prior historical necessity, and should be termed proletarian class alienation. In the absolute freedom of cluster separation, the recognized/assumed necessity is created by the very act of this recognition/assumption, so the proletarian perceives himself/herself as a free agent that decides what will have been history. The proletarian’s historical intervention consists of clusters of activity that may or may not be established as permanent classes of activities. The proletarian’s clusters of historical activity may as well be temporary, they may re-ground the symbolic order and then be forgotten as vanishing mediators. In proletarian cluster separation, the Party depends on “you”, not the other way around. What is right is decided by a “we” of a Party that includes “you”. In Brecht’s words, “We may be wrong and you may be right; therefore you must stay with us!”
 Parallax View, page 206. Read here: https://vanishingmediator.blogspot.com/2011/06/loop-of-freedom.html
 This is like “symbolic class versus paradoxical class” in Jean-Claude Milner’s Indistinct Names. Milner also calls the paradoxical class, a “cluster”.