An (Ostensibly) Ridiculous New Contradiction

Those of you whom are not familiar with Levi Bryant’s fascinating reinterpretation of Lacan’s formulae of sexuation should take a moment to read it. I find myself compelled by Bryant’s arguments. However, I’ve also found that that all of this stuff needs to be rethought from the ground up (so to speak). Today I want to approach the ridiculous by proposing a new chart on sexuation.

If all human animals are in some relation to the phallic function then perhaps their respective masculine and feminine formulae should be newly arranged to account for this fact. That is, the human animal as it is defined by psychoanalysis could be regarded as but one type of thing among many other things in the world. To maintain some degree of clarity and focus, I resolve to discuss this new form of “sexuation” (a word which I intend to be synonymous with “relation”) only from the standpoint of the top row of the traditional Lacanian formulae for masculine and feminine sexuation. To recapitulate, the traditional formulae appears below. For clarity, I have assigned the colour green to the formulae of masculine sexuation and the colour red to the formulae of feminine sexuation.

Masculine

Feminine

x Φx

x ~Φx

~Φx

~∃x ~Φx

Recall that Lacan achieved the matheme for the analyst’s discourse simply by rotating the elements of the hysteric’s discourse clockwise. I would like to do something similar for the formulae of sexuation. To be sure, nothing inherently justifies this exercise. It is much rather an opportunity afforded to me by recent developments in speculative philosophy. For now, I simply note the new formulae as follows.

One

Two

~∃x ~Φx

Φx

~∀Φx

x ~Φx

One should immediately notice that the masculine and feminine formulae have been displaced. The new formulae introduces a new interpretation. For example, the formulae associated with column “One” permits the following interpretation:there does not exist a human animal that is not submitted to the phallic function and every human animal is submitted to the phallic function. On the other hand, the formulae associated with column “Two” permits another interpretation: not every human animal is submitted to the phallic function and there exists a human animal which is not submitted to the phallic function.

In column “One” we should notice that there are two ways of suggesting that human animals are submitted to castration. In the case of the top formula, we suggest that human animals are submitted to castration simply by adding a bar above the entire formula. Thus, we achieve our proposition by means of a total negation of both an existential quantifier and the phallic function: there does not exist any human animal which is not submitted to castration. In the case of the bottom formula, we suggest that human animals are submitted to castration simply by removing the bar above the entire formula. Thus, we achieve our proposition by means of a total affirmation of a universal quantifier: it is true that every human animal is submitted to castration.

In column “Two” we should notice that there are two ways of suggesting that human animals are (affirmation) and are not (negation) submitted to castration. In the case of the top formula, we suggest that not every human animal is submitted to castration simply by adding a partial bar for negation above the universal quantifier. Thus, we achieve our proposition by means of a partial negation of a universal quantifier. In the case of the bottom formula, we suggest that there does exist at least one human animal which is not submitted to castration simply by adding a bar for negation above the phallic function itself. Thus, we achieve both of our propositions by using a partial negation on the side of the universal quantifier for the top formula and a partial negation on the side of the phallic function for the other formula.

The problem is that our thinking has hitherto remained trapped within the relation that the human animal has to the phallic function. We should thereby begin to wonder how the ding itself relates to the phallus as signifying function. For this reason, I have adjusted the formulae once again by adding some black ink for the new ding relation. Moreover, I have changed the columns from “One” and “Two” to a more logical naming scheme. Moreover, I have added a new row to the chart. I thus have everything I need to produce the new table of “sexuation” below.

Things Subjects

Subjects ¬ (Things)

~∃x ~Φx

~∀ΦD

———————

D ~ΦD

Φx

~∃D ~ΦD

~∀Φx

———————

x ~Φx

ΦD

I want to take a moment to point out what makes the black ink truly a new contradiction. Recall that the new contradiction for the sexuation of human animals consists of an entire negation of the existential quantifier and an entire affirmation of the universal quantifier. These appear in the red and green ink within the left hand column. The same contradiction exists for the new formulae of the ding in the right-hand column (the black ink). We have also used our partial negations in a contradictory way – note the partial contradiction of the traditional formulae for the human animal in the right-hand column (the red and green formulae) and the partial contradiction of the new formulae for the ding in the left-hand column (the black ink). Of course, contradiction was an essential component of the traditional Lacanian understanding of sexuation. Lacan’s original formulae assumed a contradiction between upper and lower formulae for each sex, but it also assumed a contradiction between the sexes themselves. This was of particular importance for our research question about hysteria precisely because the hysterical relation was implicated in feminine sexuation.

Now that we have some understanding of the contradictions. I want to begin to decipher the formulae themselves. In contradistinction to the traditional formulae of sexuation, let us suppose that ~D ~ΦD & ~Φx is one formula for the sexuation of Things and that it is to be inscribed in the top portion of the right column of the new chart on sexuation. It reads: there does not exist a Ding which is not submitted to the phallic function and not every x is submitted to the phallic function. Beneath it, we shall inscribe x ~Φx & ∀ΦD. In this case, we claim that there exists an x which is not submitted to the phallic function and every Ding is submitted to the phallic function. Moreover, let us suppose the following inscription in the top portion of the left column: ~x ~Φx & ~ΦD. It reads: there does not exist an x which is not submitted to the phallic function and not every Ding is submitted to the phallic function. Beneath it, we shall inscribe ∃D ~ΦD & ∀Φx. In this case, we claim that there exists a Ding which is not submitted to the phallic function and every x is submitted to the phallic function.

For the sake of clarity and organization, I note the respective interpretations of these new formulae as follows.

t[$]

there does not exist an x which is not submitted to the phallic function and not every D is submitted to the phallic function

———————

there exists a D which is not submitted to the phallic function and every x is submitted to the phallic function

$[a]

there does not exist a D which is not submitted to the phallic function and not every x is submitted to the phallic function

———————

there exists an x which is not submitted to the phallic function and every D is submitted to the phallic function

In the left hand column one should take notice that it is precisely when the human animal (as an x) is submitted to the phallic function (or when not every human animal is not submitted to the phallic function) that we can speak of each and every ding as not being submitted to the phallic function. I have demonstrated in a previous blog that this is consistent with Lacan’s own line of thinking about the ding vis-a-vis the human animal. In the right hand column one should take notice that it is precisely when the human animal is not entirely submitted to the phallic function (or when there is an x; i.e., a god or a primal father) that the ding is castrated and turned into an objet petit a. In other words, we no longer begin with a god-figure, as psychoanalysis does, but with things. It is this focus on things that makes the new approach, which I call non-psychoanalysis, a little different from psychoanalysis.

I’ve now provided two naming schemes. In the left-hand column we can speak about the Thing and the Subject (i.e., Things ∧ Subjects). Another admittedly more formulaic way of writing this is t[$] inasmuch as we presume that the t stands for our Thing (or, rather, Ding) function and that the Subject is bracketed by the Thing. In the right-hand column we can speak about the Subject and not the Thing (i.e., Subjects ¬ (Things)). Another admittedly more formulaic way of writing this is: $[a]. As we have discovered, the ding ceases to exist from the perspective of the human animal. In this case the a, as objet petit a, is bracketed by the subject precisely because we no longer have a Ding. The objet petit a is its substitute. I have also demonstrated that the objet petit a, unlike the Ding, is a uniquely human object cause of desire. In the left column we can understand the “sexuation” of subjects as a function of Things and in the right we can understand the “sexuation” of the objet petit a in the capacity of the human animal

All of this simply opens up the possibility to think before the decisional structure of psychoanalysis by dislodging the subject from its place of primacy and making Things the centre of analysis. Fundamentally, this is an exercise in bracketing. Levi Bryant, borrowing from George Spencer-Brown’s Laws of Form (1969), distinguishes between the marked space of distinction and the unmarked space of distinction. Bryant claims that the unmarked space of distinction is something like a blind-spot from the standpoint of the marked space. For example, if we summarize the new contradiction as one between t[$] and $[a] then we are really changing our decisional structure entirely, bracketing the Subject. For example, t[$] is actually similar to writing t[$[a]] because a Subject is, in this understanding, already a Thing. In any case, whatever finds itself within square brackets indicates that which is within the unmarked space of distinction – either the $ is bracketed or the a is bracketed. We know that objects have traditionally been placed within the unmarked space of distinction (in opposition to subjects) in much of philosophy – they were continuously placed into the shadow of $. This philosophical practice has best been understood as the strategy of correlationism. Quentin Meillassoux describes correlationism as the underlying philosophical belief that we can only ever have access to an object by way of its relationship to the thinking human animal. According to correlationist thinking we can never discuss the object itself, outside of this relationship. In contradistinction, Bryant proposes that begin from the place of the Thing by placing it in the marked space of distinction as follows:

marked

The old way placed the Subject within the marked space and things/objects within the unmarked. The new way swaps the places of these two terms. The marked space wraps around the unmarked space and the unmarked space assumes itself as the blind-spot for thinking from the point of departure of the marked space. The old way placed the subject in the privileged marked space of distinction and put things into its blind-spot as objet petit a. The new way, as proposed by Bryant, places Things in the privileged marked space of distinction and places Subjects into the unmarked space. The most difficult question today – and I believe that Badiou was the first to make this claim – is not “what are things?” but “what is a subject?” If we begin from the place of the Thing then the real difficulty is to begin to understand what a Subject is vis-a-vis the Thing. This new form of bracketing is such that, borrowing the phraseology of Levi Bryant, “subjects and culture are not excluded, but rather are treated as particular types of [Things].” Here, we should note that t[$] is to be read as follows: the Subject or human animal is placed in the unmarked space of distinction and the ding-function is placed in the marked space of distinction. This sets up the contradiction of $[a] such that objet petit a is placed in the unmarked space of distinction and the human animal is placed in the marked space of distinction. It is the former contradiction which makes possible the latter.

The difficulty is that psychoanalysis begins with the subject as the centre of its world. For psychoanalysts, things in the world are entirely reduced to what they are for the subject’s unconscious desires and conscious speech. The world is always structured by the transferences. Things are related somehow to the symbolic processes of human life and therefore lose their status as real autonomous things. To be sure, there are convincing reasons during analysis to assume that the analyst and the analysand do not have direct access to real things. Psychoanalysis requires of itself a rigorous investigation into the nature of unconscious resistances. Transference is thus important to analysis precisely because it reveals the place from which the analyst must begin to locate the analyst’s unconscious desire. If we begin with real things rather than symbolic subjects then we seem to presume ourselves to be rid of the problem of the transference. However, if we supplement this trend by taking as our point of departure things in the real, rather than the subject of the symbolic, then our entire philosophical system begins to shift. This shift is more like a displacement rather than a rejection of the previous model. The transferences still exist but in a different register. Traditional psychoanalysis begins with the symbolic and then finds what is real within this order. Contemporary non-psychoanalysts seem to want to begin from the real and then find what it is that is symbolic within this order. This radical departure opens up the possibility that there are, in fact, two outsides or two orders of the real.

Lacanians have long been aware that the real has been inconsistently developed. For example, Lorenzo Chiesa has claimed that Lacan was blatantly contradictory in his deployment of the concept. He wrote: “Lacan associates [sic] the Real with both (1) objects as they are given to us in everyday reality; and (2) a rather vague notion of undifferentiated matter as it is in itself before the advent of the Symbolic […] the term ‘Real’ is also understood in a third sense as a non-symbolized Symbolic which should be located within language.” Thus we have the object for the subject in the first case and the object outside of the subject in the second case. Bruce Fink, a foremost translator of Lacan’s work, has written something that appears to me to be strikingly similar to Chiesa’s argument: “[there are] two different levels of the real: (1) a real before the letter, that is, a pre-symbolic real, which, in the final analysis is but our own hypothesis, and (2) a real after the letter which is characterized by impasses and impossibilities due to relations among the elements of the symbolic order itself, that is, which is generated by the symbolic.” Fink provided a simple diagram to demonstrate this point:

Real 1 –> Symbolic –> Real 2

Interestingly, Fink never ended up discussing the first order real again. It seems that his mentioning of it was nothing more than an academic exercise in systematization. However, perhaps, Fink was on to something: as Chiesa later argued, maybe the concept of the real was not deployed inconsistently. Perhaps the real was thought to have always returned to its place precisely because the symbolic was in all actuality inherent to it rather than vice-versa. In other words, perhaps the symbolic was a part of the real rather than the real being a part of the symbolic. Certainly, if we begin with the presupposition that the real exists first of all within the symbolic then it would appear inconsistent to claim that the real also exists outside of the symbolic. However, if we begin with the claim that the real exists outside of the symbolic and if we only subsequently maintain that the symbolic exists with its own version of the real within itself, then we could suppose that this real amounts to something like the piece of the first outside real from which the Symbolic was truly unable to escape. Thus, the symbolic is perhaps within the ding of the first-order real entirely, much like a monad. The subject vis-a-vis the second-order real thereby exists like the poverty stricken proletarian whom hasn’t escaped his placed of birth – even the symbolic returns to the real.

As it turns out, there is, in fact, only one version of the real and, moreover, only one object of the real: das Ding. However, the change of perspective that psychoanalysis offered by way of its decision to bracket this first-order real also necessarily changed the radical immanence of things in the real into the radical semblance of objet petit a. From the perspective of the human animal, and from the perspective of much of traditional Lacanian thought, the real only ever exists in the second-order. Moreover, as we change our perspective on the place of the real we also by necessity change the object of our analysis: we are either dealing with das Ding or we are dealing with objet petit a. Perhaps, therefore, it is time to allow psychoanalysis to return home to non-psychoanalysis, its place of birth.

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5 thoughts on “An (Ostensibly) Ridiculous New Contradiction

  1. Pingback: A Note on Copjec’s Ontology | dingpolitik

  2. Pingback: Hypertranscription: Alain Badiou, Localizing the Void | dingpolitik

  3. Pingback: Zizek Versus Badiou: Is Lacan an Anti-Philosopher? | dingpolitik

  4. I stumbled upon a PDF that exhaustively goes through the upper portion of the table, explaining each symbol, each formula and their relation to each other, then incorporates both Lacan’s discourse theory iand his topological figures (sphere, torus, moebius strip and crosscap) into the table. Can’t say I understand much, but it looks worthwhile. Seems Lacan derived things from Aristotle and ripped-off some French logician to arrive at this formulae. Typical story with Lacan!

    http://www.academia.edu/5984726/Sexuated_Topology_and_the_Suspension_of_Meaning_A_Non-Hermeneutical_Phenomenological_Approach_to_Textual_Analysis

  5. Pingback: Alain Badiou: Two Names for Infinity | dingpolitik

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