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Hysterical fantasy:  ◇ A Obsessional fantasy:  ◇ φ (a’ a’’ a’’’ …) In the first, we see described the hysteric’s strategy of covering her own intrinsic lack (-φ) by way of an identification with what one believes the Other desires a. When this identification fails, as of course it always will for the Emmelines of the world, this is not so much because “Charles” does not match up to her illusion of him—although this is typically regarded as the source of the hysteric’s constitutive disappointment in the Master. Rather, as A continually reminds us, Emmeline fundamentally does not know Charles. Thus how could she know what to match him against? Hence when Emmeline becomes convinced that “Charles” is not “Charles,” we must conclude that her conviction derives not from any change in Charles’s real or imagined characteristics, but rather because at some level he has failed to recognize her. A explains how Emmeline “does not seek the alteration in the fact that Charles has become a spendthrift or possibly something even worse, but in that he has not confided everything to her, as he was accustomed to do” (Either, 268). It is this change in his relation to her, rather than his failure to match up to her ideal, that convinces the hysteric that “Charles” “is not the same anymore” (Either, 267). Read this way, Kierkegaard thus offers an intriguing new slant no the hysteric’s eternal question to the Master, “what [or who] am I?”6 For here we see that the hysteric knows very well who she is—the question is whether the Master also knows, and when it becomes apparent he does not, she re-embarks on her quest for a new One, a Master who truly knows and recognizes who she is.

A different objective drives the obsessional fantasy, which in this case is not propelled by the subject’s lack. The obsessional, famously, does not feel he lacks anything. It is, on the contrary, precisely because he feels he satisfies the Other all too well that he is led in his fantasy to emphasize the lack in the Other (). Accordingly, the obsessional’s entire fantasmatic scenario is designed to keep the Other in a state of desire, which he employs as a defense against the threat of being entirely swallowed up by the (m)Other.

Thus, like Charles, the obsessional becomes an expert in mystification. The obsessional generates a proliferating series of substitutive objects—the traditional obsessional behaviours or “disguises” that are to keep the Other (in 272 Penumbra Charles’ case, his uncle and Emmeline) occupied while preserving his real identity (as a married man) beyond the Other’s reach. These “disguises” are what is expressed in the formula as the little a-apostrophes, semblances of the semblance that the obsessional, as the Other’s a, attempts to hide behind.

Naturally what the obsessional fails to realize, however, is that, like Charles, it is he who is the most taken in by his disguises. As A puts it, Charles “believes it is he who contrives intrigues, he who mystifies, and yet the spectator sees that the mystification was in operation before Charles appears” (Either, 259).

Imagining that he is the puppet master generating illusion, the obsessional in fact “give[s] the whole thing away” (Either, 260).

One might ask what is the point of these “fantasies”? As is well-known, the fantasy’s psychic function is to mitigate an original trauma Freud termed an “internal” arousal, renamed by Lacan as jouissance. The various fantasies achieve this by providing this incomprehensible arousal or jouissance with some kind of interim representation. This provisional representation acts to reduce and siphon off the anxiety the subject experiences in its confrontation with what it cannot comprehend—the Other’s desire7—by supplying some kind of form to the nothing, the original “object” of anxiety. One can thus regard the different fantasies—hysteric, obsessional and perverse—as different ways of “dramatizing” this nothing.8 Like comedy, with which they therefore share an intrinsic kinship, the fantasies put the nothing or “void,” on stage.

The fantasy’s generic “equation”  ◇ a can accordingly be put in mathematical terms in the following way:

∅ ~ ({∅} = 1) = 0 This expresses how the void or unpresentable point of being, ∅, is made ‘equivalent’ to the empty set {∅}, which can serve as the first provisional representational placeholder for the void, and accordingly be counted ‘as’ One in the ordinal counting system. The ordinal count gives this void a name, the empty set or zero, which forms the first and original One from which all subsequent addition springs. The number 2 is accordingly derived from the empty set +1, while the number 3 is derived from the empty set +1 +1, and so on.

In the algebra of the fantasies, the ultimate result of this ‘equation’ is “inertia”—the ideal state of the subject prior to the eruption of jouissance. The empty set, counted here as the first positive One, balances the pure negative (or minus “One”) of the void, returning the subject’s psychic state to zero.

Expressed in words, we get:

Void, equated to the empty set, which can then be counted ‘as’ One, gives the result “inertia” or zero.

If we now populate this generic formula for fantasy with the specific values of the hysteric’s fantasy, we obtain the following:

∅ ~ ({ ◇ A} = 1) = 0 Signifier and Letter in Kierkegaard and Lacan In this formula, the generic empty set {∅} has been filled in with the specifics of how the hysteric “stages” the appearance of the “nothing” or void. The equation depicts how the hysterical subject positions herself in the fantasy as vertically split between her phallic castration (minus phi) and the object a which, as we saw, represents her identification with what she believes the Other (A) wants from her.9 Like the generic version of the equation, the hysterical fantasy also aims to “count” to One (whose ultimate result, as for all the fantasies, is a return to inertia, or zero). However, we quickly see how the hysteric encounters a difficulty in performing her “addition.” The problem lies with the a, the semblance of the Other’s desire with which the hysteric attempts to cover over her imaginary lack (-φ). It is this a that ensures her count will always, like Achilles, either over- or undershoot its mark.

In Lacan’s teaching, the cause of this permanent over- or under-shooting is found in the fact that the field of representation where the fantasy is “staged” is not flat but is topologically distorted by the a insofar as it belongs to another register than the symbolic “count.” Created in the original nominal act of “making equivalence” that enabled the void to be bracketed as the empty set and counted ‘as’ the first One, the a is that part of the void or Real that was never completely taken up by the provisional presentation (which psychoanalysis calls the phallic signifier). As a result, the a guarantees that every fantasmatic “equation’s” staging of the impossible sexual relation through the exigencies of a subject-object relation will always be inflected with something of the original traumatic jouissance that the fantasies were intended to palliate. This little sliver of jouissance that slipped into the symbolic through the back door during the original catastrophic equating of the void (“castration”) ensures that the fantasy of a complete or intact One (i.e. an utterly seamless fusion of the subject and object) will never be attained. For it is this a that drives the subject’s unconscious repetition. The a is the source of the continual failure that causes every count to One to always have to begin again. It is for this reason, then, that any “mathematical” equation that contains the a will always come up lacking in its final result in a very precise way.10 As we saw, the One-result of the hysterical fantasy will always necessarily be missing a little bit since the presence of the a ensures the Other (A) will never be completely satisfied with her. Despite all the “narcissistic coatings” as Lacan puts it, that subsequently come to envelop and surround it, the a never fully covers over the minus phi of the hysteric’s castration, and the resultant One of the hysterical fantasy always falls short.11 A similar, albeit opposite, thing happens with the obsessional. Although his desiring formula also aims to count to One, the obsessional’s One-result will always be a little bit in surfeit, again because it is produced by an object a that carries along with it something of the same impossible void. In the obsessional’s formula, this surplus is indicated by the little distinguishing supra symbols that mark the substitute a objects with which he showers the Other 274 Penumbra in the fantasy (a’, a’’, a’’’ … etc.). These marks give themselves away as the

semblances of the a that they are:

∅ ~ ({ ◇ φ (a’ a’’ a’’’ …)} = 1) = 0 The question is why the obsessional’s One-result will always be a tiny bit more than One, while the hysteric’s always a little less? It stems from the neurotic structures’ original affective response to the traumatic arousal of jouissance. In “Heredity and the Aetiology of the Neuroses,” Freud locates at the basis of hysteria an original experience of unpleasure, “an event of passive sexuality” that was “submitted to with indifference or with a small degree of annoyance or fright.”12 Accordingly, as a “representative” (Vorstellung) of this original experience, the a hauls something of this unpleasure along with it into the hysterical desiring fantasy, ensuring that her One-result will always be inflected with a tiny little lacking sign or “minus.” For the obsessional, on the other hand, it concerns an event which originally, Freud says, “has given pleasure.” The obsessional’s a will thus ensure that his One-result always suffers from a tiny little surfeit, expressing how the obsessional’s “disguises” are just that tiny bit too successful in deceiving the Other. At some point, the Other will inevitably take him too literally and mistake the semblance for the real thing. In this way, the Other will sabotage his fantasy that he can endlessly keep substituting new objects for himself ad infinitum.

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