# The cross-dressing of logic.

Lacan's account of sexual difference in his Seminar XX, Encore, has become something of a commonplace in recent work on sex and gender in a wide array of fields in the Humanities from philosophy and feminism to cultural studies and queer theory. (1) It is often cited and hotly debated, but it has rarely been approached through a direct examination of the logical formulae in which he articulates his theory. In what follows I explain Lacan's account of sexuation by showing how it distorts the formulae of the predicate calculus to achieve a precise effect. In contrast with the few commentators who attempt to explain Lacan's position, (2) I argue that Lacan's appeal to logic can be made sense of in its own terms. Rather than introducing some new or alternative logic, I demonstrate that Lacan is consciously distorting and mimicking the structure of the predicate calculus in an attempt to suggest what it fails to comprehend. After a brief review of what these formulae mean in their original context, I show how Lacan subverts their original sense in a manner that suggests that the goal of analysis is a feminine jouissance, understood as a jouissance that is attained by inverting the lack in the other back into the body. I conclude with a short explanation of Lacan's claim that metaphysics has systematically misunderstood feminine jouissance as the jouissance of God.

I. The Argument-function Schema of the Predicate Calculus
```Diagram A: Translation & Definition of the Four Formulae of
Sexuation

Paternal function

1. 3x(-[PHI]x)
There is one not subject to [PHI]x

Man

2. [for all] x (F)
All are subject to [PHI]x

Feminine Jouissance

3. (-[there exists]x)(-[PHI]x)

Not one is not subject to [PHI]x

Woman

4. (-[for all]x)[PHI]x

Not all are subject to [PHI]x

```

The reversed E and the inverted A are called existential and universal quantifiers, and they are employed in the predicate calculus to define the scope of predication in a given propositional statement. In such statements some subject 'x', is asserted to possess a specific predicate (in Lacan' s usage this is the predicate of being subject to the phallic function, represented by [PHI]). But as one can see, the subject 'x' appears twice. First as quantified (to indicate the possible range of values x might possess) and then again, to indicate its attachment to a predicate.

Let us consider an example: [there exists]x Fx. One reads this as "there is at least one x such that x has the attribute F." In other words, the meaning of x, specifies a certain quantified range of individuals (in this case "at least one" rather than "all") which is subject to the predicate-function F. Thus we can already see that Lacan's usage of thisargument function schema primarily means that, the quantified range of individuals in x is subject to the function [PHI]. Hence, within "the universe of discourse" of speaking beings (which is the range of possible values for x), some quantified class of individuals ('at least one' or 'all') is, or is not, subject to the function [R], the phallic function. In other words, some quantified class of individuals is or is not subject to the function of castration. (3)

I have taken the liberty of rephrasing Lacan's four formulae into a more standard notation. Thus I have rendered the negations, which Lacan portrays with horizontal bars over the quantifiers and the predicates of his formulae as a minus sign, or dash, preceding each part of the formula, which Lacan's horizontal bar negates. I have also enclosed the negated portion of the statement in parentheses, in order better to indicate the way Lacan's original formulation applies the scope of the negation. The advantage to this approach is that it makes Lacan's travesty of the syntactical rules of the predicate calculus even more apparent than his original notation. Normally, the rules of syntax demand that any negation standing outside a formula apply to the whole formula. Lacan, however, seems to want to negate each portion of the formula. One can see this clearly in the case of the two feminine formulae" on the right, e.g., (-[there exists]x)(-[PHI]x) and (-[for all]x)[PHI]x. But these "formulae" no longer fit within the parameters of the predicate calculus (Loparic, 241). In fact, they are completely idiosyncratic, because Lacan wants to use the negation as if it only applied to the symbol beneath it, although this clearly violates the established rules of syntax. As Andrea Loparic writes, "one symbol of quantification does not constitute a formula all by itself; so, there is no grammatical construction which can put the bar only above this symbol (and not above the rest of the symbols where it appears, and of which it is a part)." (4)

This unusual restriction of the negation permits us to specify the sense in which Lacan is reading these formulae, for even as we find Lacan abandoning conventional logical syntax, we can still trace the manner of his variation from the norm in a way that is highly instructive. Because the negation of either an existential or universal quantifier which is itself followed by a negation is identical to its opposite, it might at first appear that the diagonal opposites in Lacan's schema mean almost the same thing. In other words, because 'there is not one which is not' is convertible into 'all' [i.e., -[there exists]x - < = > [for all]x], and 'not all x are not' is convertible into 'there is at least one' [i.e., -[for all]x - < = > [there exists]x], it might appear that 1 is inter-derivable with 4, and 2 is inter-derivable with 3. [e.g., it might appear that [there exists]x(-[PHI]x) < = > (-[for all]x)[PHI]x and [for all]x ([PHI]x) < = > (-[there exists]x)(-[PHI]x)]. If we could remove Lacan's restriction of the scope of the negation, and apply the negations to the formulae as a whole, then 2 and 3, [for all]x ([PHI]x) < = > (-[there exists]x)(-[PHI]x), would be indeed be inter-derivable. But Lacan's idiosyncratic use of this notation is specifically designed to exclude the possibility of such a symmetrical and commensurable relation between the sexes.

So why is Lacan using this notation if it has no proper meaning within the predicate calculus? On the most general level, what he seems to be trying to suggest is that the way our relation to the symbolic order is assumed in the event of castration is something so fundamental for our understanding of sexual difference, that it is on par with the basic notation and rules of deductive logic. So, just as the rules of logic can yield certain results without reference to the particular meanings to which they apply, so too, the structural positions available to speaking beings can be seen as the result of the determinate rules governing sexual difference without reference to biology. On this view the castration complex is a kind of roll of the dice which functions according to rules which are as determinative of sexual identity as the rules of logic are determinative of truth and falsehood. Thus Lacan's account provides a way of understanding how sexual difference turns--not around biology, but rather--around the decisive way in which one is subjected to the economy of imaginary identification. This means there can be no genuine sexual relation, Lacan insists, because one can no more mediate between these two possibilities than one can find a middle ground between the binary oppositions of the true and the false in formal logic. I

The crux of the problem is Lacan's claim that this system of logical rules is decidedly phallic, for this permits him to demonstrate that by favoring the masculine, the logical/phallic order fails to capture the essence of the feminine position, which the phallic order can only designate as a "supplementary" jouissance which falls outside it. But as there is no "outside" of the law, woman can only appear within it as doubled. Thus, the diagram below the formulae presents woman as having a dual relation to both the phallus ([PHI]) and to the signifier of the lack in the Other, S([empty set]). What this means is that this peculiar, supplementary, and feminine jouissance is nothing more than a relation to the lack in the law, implying that woman somehow perceives the Other as lacking in a way that man does not.

In the time that remains, I will try to show how Lacan is consciously distorting the notation of the predicate calculus in an attempt to suggest what lies beyond the phallic order by articulating the antinomy that woman is both subject and not subject to the phallic order. What I propose is that the only way to reconcile this antinomy with the rest of Lacanian theory is to interpret it as calling for the evagination or the turning of the phallic order back in upon itself, like the Minister's evagination of the purloined letter in Poe's tale. Thus, I am claiming that Lacan's antinomial formulation of feminine jouissance does not simply suggest woman's openness to the lack in the law, but goes further to suggest a positive characterization of her jouissance of that lack by implying that this jouissance is attained through evaginating the symbolic back in upon the body in order to effect a bodily jouissance of the lack that the law imposes. In other words, what I am suggesting is that this antinomy does not imply the existence of some alternate feminine reality beyond the phallic order as some feminists would have it, but rather, that it only designates the existence of a lack which some women (or rather some speaking beings who desire like women) are able to enjoy. In addition, I am also suggesting that leading the analys and to an acceptance of this lack is the analyst's primary concern.
```Figure 1: Lacan's Attempt to suggest feminine jouissance through
the evagination of (-[there exists]x)(-[PHI]x)

(1) Paternal Function
as the uncastrated which is necessary
to uphold the phallic law.

[ILLUSTRATION OMITTED]

(2) The bar of castration in 1 defines
man as "all" subject to the phallic
function. The necessity of the
paternal function makes him possible
as altogether subject to it.

(3) Feminine jouissance, or a jouissance
accessible through the
real of the body, portrayed as the
evagination of the signifier (-[there exists]x)
(-[PHI]x), as a way of suggesting the
lack ignored by the phallic order
because of the visual/imaginary
bias implicit in even the purest
symbolic expression.

(4) Woman is "not all" defined by
castration. Thus her relation to it
is contingent, making it possible
for her to have a double relation
to the phallic order, in which she
can both be and not be in it at
the same time. Insofar as she is
castrated she has a relation to the
phallus. Insofar as castration fails
to address her essence she has
real, or a jouissance of lack, which
man does not possess.
```

II. The Formulae of Sexuation (5)

To portray how Lacan's formulae of sexuation exhibit such an antinomy, let us examine each of Lacan's formulae in turn. The two formulae on the left signify male desire, and the two on the right represent his attempt to symbolize female desire. The first formula, [there exists]x(-[PHI]x), says that "there is at least one who is not subject to the phallic function." We can think of this one who is not subject to the phallic function as the father of primal horde in Totem and Tabu. It is the father's possession of all the women that marks all the sons as subject to the threat of castration if they try to enjoy the women for themselves. This uncastrated Father who is not subject to the phallic law is the limit case, which defines all the rest as subject to the paternal law. Accordingly, the second formulae, [for all]x ([PHI]x), says, "all are subject to the phallic function" which, as we have just seen, means that all male speaking beings are wholly subject to the bar of castration wielded by the paternal law described in the first formula.

On the right side, on the top (e.g., #3, in diagram A), we find a formula that is quite strange, (-[there exists]x)(-[PHI]x), which reads: "there is not one that is not subject to the phallic function." The symmetry of the diagram (which shows the two male formulae on the left, where the top one defines the one below it) creates the expectation that the same relation holds on the right hand side of the diagram, but this is not the case, for as we shall soon see what is at issue in Lacan's account is a complete lack of complementarity between these two kinds of desire. If Lacan's table were in standard logical notation the second and third formulae would mean the same thing. In other words, "there is not one that is not subject to the phallic function" would mean the same as "all are subject to the phallic function," for as everyone knows, a double negation constitutes an affirmation. But given Lacan's idiosyncratic restriction of the quantifier, which separates the negation of the quantifier from negation of the function, one cannot transform the double negation of "there is not one that is not subject to the phallic function" into the positive affirmation that "all are subject to the phallic function." On Lacan's peculiar distortion of the predicate calculus, there is no logical commensurability or complementarity between the masculine and the feminine sides of the diagram. As a result the logical clarity and exclusivity of the masculine side is contrasted with the logically equivocal and undecidable character of Lacan's formula for feminine jouissance: "there is not one which is not subject to the phallic function," (-[there exists]x)(-[PHI]x). As one can easily see, this formula can be read in two opposing senses. On the one hand this formula may appear to claim that there is a feminine experience outside the law, for the way the negation remains bound to the quantifier renders the privative "not one" as something positive, indicating the existence of a "not one" which is exempt from the law. And yet on the other hand, the formula can also be read as claiming that there is no feminine experience outside the law, because there is not one individual that is exempt from the law.

This ambiguity amounts to an antinomy, which states that feminine jouissance is at once wholly inside and wholly outside the phallic order. (6) Now what I propose is that the only way to reconcile these contradictory claims, without lapsing into metaphysics, is to read feminine jouissance as a jouissance of lack, which is unrepresentable as such within the phallic order. Thus, when Lacan writes that there is "not one that is not subject to the phallic function" he means to indicate that feminine jouissance is a jouissance of the lack in the phallic law, and not some otherworldly enjoyment of an imaginary feminine reality beyond the phallic order. The point is that this other jouissance does not fall into neat logical categories because it is nothing that can be positively represented within the phallic order. As a result, it is not necessary that every woman experience it; rather, it is an experience to which women are contingently open. This is why Lacan cancels the definite article, and says that "the woman does not exist," for feminine jouissance is a contingent non-universalizable experience that cannot be predicated of all women. Some experience it, others do not. This is what he is trying to indicate with the fourth formula, (-[for all]x)[PHI]x, "not all are subject to the phallic function." What this formula indicates is woman's contingent openness to the jouissance of lack described in the preceding formula.

III. The Schema below the formulae

With this interpretation of the formulae, we can now see that the lower two formulae represent the modes of desire open to masculine and feminine subjects, while the upper two formulae indicate the jouissance which characterizes each gender. This reveals that the desire of man, who is "all" subject to the phallic function, is as an illusion. He wants to be the uncastrated father, but this position is permanently foreclosed to him. This is why Lacan will say that it is not possible for a man ever really to enjoy a woman. As "not all" subject to the phallic order, woman, in contrast, can desire on both sides. She can desire (and be desired) phallicly, but she might also have access to in a peculiarly feminine mode of desire that is not accounted for by the phallic order.

As I have already suggested, Lacan is not trying to designate a positive feminine experience, which corresponds to phallic jouissance; rather, he is trying to bring lack as such into view in order to suggest the possibility of a jouissance of our inability to enjoy the positive image of plenitude imagined by phallic desire. (7) Thus, Lacan's formulae and the Schema directly below them suggest that this lack can be positively characterized both as the lack in the Other and the lack to which the Other subjects us in castration. This lack is precisely what phallic desire wants to disavow and cannot recognize.

Diagram B: Woman's Dual Relation to the Phallic Order (8)

[ILLUSTRATION OMITTED]

In the Schema below the formulae of sexuation, we see that men are portrayed as barred subjects that are completely defined by their subjection to the phallic function. This means that they only desire in one way, by projecting a fantasy, or an objet petit a, onto the object of their desire, which is usually incarnated by a woman. Thus, they have a unitary relation to the phallic order inasmuch as their desire is completely defined by it. The result is that male desire altogether fails to recognize woman's jouissance.

Women in contrast, have a dual relation to the phallic order. To the extent that women are in the phallic order, they can desire the way men do by projecting their objet petit a. Thus, they can both desire their own objet a, and they can strive to incarnate the objet a for a man. But beyond participating in the phallic order as either subjects or objects of phallic desire, woman may also have a relation to the signifier of the lack in the Other, S([empty set]). What this means is that to the extent that woman is not altogether subject to the phallic function of castration, she may have a contingent opening to a jouissance of the real lack which the law imposes on the subject but which escapes phallic symbolization. On this view, feminine jouissance is not an insight into the real as some sort of alternative feminine plenitude beyond the phallic law, but much rather, an integrated acceptance of the real limitation of being split by the law. It is an acceptance of castration--a jouissance of the lack it imposes--which is not possible for masculine desire because it remains wholly defined in terms of its subjection to the phallic law, and can neither perceive the law's limits, or the lack it imposes.

What this suggests is that feminine jouissance is a non-thetic awareness of the being of the lack by which the subject is constituted. This is why Lacan can say most women do not know anything about this jouissance. It is also the reason why Lacan can ironically refer to his Ecrits as on par with the writings of the mystics. What Lacan is suggesting is that, like mysticism, psychoanalysis is also a hysterizing discourse that speaks from an ek-static experience that is beyond the grasp of the phallic law. The difference is that psychoanalysis is aware of what it has experienced, so that it is capable of grasping both the law's function and its limits. This means that Lacan is claiming that psychoanalysis constitutes an improvement on mysticism to the extent that psychoanalytic theory possesses the conceptual tools to articulate this ek-static experience as feminine jouissance of the symbolic, or the barred Other, rather than as an experience of the unbarred Other, or God [e.g., as S([empty set]) rather than S(O)]. Thus, Lacan's articulation of woman's "supplementary" relation to the signifier of the lack in the Other, S([empty set]), is not just an empty theoretical articulation, but rather, an attempt to name the way psychoanalytic practice turns around this relation to S([empty set]), and seeks to transmit its understanding of the function of this lack in analysis. This means that Lacan's account of feminine jouissance is less about orgasm than it is about enjoying the being of signifiance and embracing the lack by which you are constituted. But it also means that Lacan's theoretical articulation of sexual difference is closely connected to the question of the goal of analysis. For after all, is not the most favorable outcome of analysis one in which the analys and learns to enjoy his lack? What I am saying is that Lacan's account of sexual difference implies both that psychoanalysis speaks from the place of feminine jouissance, and that its goal is to help others reach that place as well.

IV. The Confusion of Woman and God in the Metaphysical Tradition

If feminine jouissance grasps and enjoys this lack, then phallic desire refuses to acknowledge it, and remains constitutionally incapable of grasping it as such. Rather than acknowledging this lack, the phallic order has instead transposed it into the idea of divine plenitude, or the idea of an unbarred other, or of an uncastrated heavenly father who stands outside the phallic order and who brought it into being. This is why Lacan will say that the metaphysical tradition has confused woman with God, for as a result of its inability to symbolize the mystery of woman's lack (for how after all can you represent absence as such from within the symbolic order?) and its inability to grasp the mystery of her ability to bear, it has confused the petit a of male desire for woman with the metaphysical desire for an ultimate ground of explanation (e.g., for an unbarred grand Autre, or big Other).

This confusion, or meconnaissance, occurs on two levels: there is a displacement of man's desire for woman as his objet a onto the desire to know an ultimate metaphysical ground of explanation (here one objet a metonymically slides into the other so that man passes from the desire for woman to the desire for God along the axis of contiguity). But the metaphysical tradition, Lacan suggests, arose from a more basic confusion, namely, through a condensation which substitutes woman's presumed enjoyment of a mysterious plenitude for God's presumed enjoyment of an absolute knowledge of his own creation. Here the mistaken notion of woman's enjoyment of a plenitude beyond the phallic order is substituted for the idea of the divine enjoyment of an absolute knowledge of the whole of creation along the axis of substitution.

Because the phallic order can only represent feminine jouissance as a mysterious plenitude, rather than as an enjoyment of a lack (i.e., as it cannot grasp this lack as such from within the symbolic order of substitution), man has substituted woman's lack of subjection to the phallic function (and the corresponding fantasy of her supposed enjoyment of a plenitude beyond it), for the idea of God. It is as a result of this confusion that Lacan can say that the ethical and metaphysical tradition aims at effecting the jouissance of God.

Lacan's position in this analysis is essentially that of the materialist critique of religion in modern philosophy. Because man is unable to accept the idea of a meaningless universe, he paves over this lack with the idea of God, thereby substituting the notion of God's jouissance of his creation for woman's jouissance of a capacity to bear that man imagines as a mysterious plenitude of the eternal feminine, and an enjoyment of the real beyond the symbolic. What men fail to grasp is that woman's capacity to bear is just another instance of our common subjection to the more primordial lack of sexuation and death. (9) Thus, the phallic order confuses woman with God because it fails to grasp that the lack of the signifier is taken up within in "a real, earlier lack situated at the advent of living being" in its relation to sexuation and death. It is to this more primordial lack which Lacan's diagram refers when it indicates woman's extrasymbolic relation to S([empty set]), the signifier of the lack in the Other.

On this view, those feminists who read Lacan's notion of feminine jouissance politically, or who support some notion of feminine generativity as participating in some primordial fullness beyond the phallic order, are subject to the same meconnaissance as phallocentrism, for like the metaphysical tradition, they too fail to grasp Lacan's articulation of the meaning of feminine jouissance as a jouissance of the lack imposed by the law. This lack is nothing positive; rather, it is simply the lack constituted by our subjection to castration, understood as both the symbolic lack of the signifier and the real lack of our subjection to sexuation and death. Thus, feminine jouissance is not an enjoyment of an imagined lack of subjection to the law, but rather an enjoyment and an implicit recognition of our subjection to the lack in the Other. As such, it is more an insight into the limits of the phallic law, and an integrated acceptance of the absolute limitation constituted by the lack which the phallic law conceals, than it is something which can be reified and thus brought into the phallic order as something positive, upon which either feminists--or church fathers, for that matter--might establish a platform for social change. This is why Lacan can say that most women do not even know anything about it. Their lack of awareness of their jouissance indicates its contingent and ephemeral character. By positing the ek-sistence, or standing forth, of feminine jouissance beyond the phallic order Lacan is in effect claiming that the hysterizing discourse of psychoanalytic theory can name feminine jouissance because it itself emerges out of such a jouissance of the lack by which the subject is constituted.

Erich Freiberger

Jacksonville University

United States of America

Works Cited

Copjec, Joan, "The Euthanasia of Reason" in: Supposing the Subject. New York: Verso, 1994.

Dor, Joel. Introduction a Lecture de Lacan , vol. II. Paris: Denoel, 1992.

Fink, Bruce. "There is no such Thing as a Sexual Relationship: Existence and Formulae of Sexuation." Newsletter of the Freudian Field, 5.1.2, (1991):59-85.

--. The Lacanian Subject: Between Language and Jouissance. Princeton: University Press, 1995.

Lacan, Jaques. The Four Fundamental Concepts of Psychoanalysis (SeminarXI). Ed. Jacques-Allain Miller, tr. Alan Sheridan. New York: W.W. Norton, 1978.

--. The Seminar of Jacques Lacan: On Feminine Sexuality, the Limits of Love and Knowledge (Encore), (Vol. BookXX). Tr. Bruce Fink. New York: W.W. Norton, 1999.

--. "God and the Jouissance of the Woman" and "A Love Letter" in: Feminine Sexuality, tr. Jaqueline Rose, ed. Juliet Mitchell. New York: W.W. Norton, 1982.

Lee, Jonathan Scott. Jacques Lacan. Boston: Twayne Publishing, 1990.

Loparic, Andrea. "les negations et les univers du discours." Lacan avec les philosophes. Paris: Albin, 1991.

Plato, The Collected Dialogues. Ed. Cairns and Hamilton. Princeton: university Press, 2005.

(1) Two earlier versions of this paper were presented under the title "The Travesty of Logic in Lacan's Account of Sexual Difference" at the Society for Phenomenological and Existential Philosophy, at Georgetown University and at the International Conference on Sexuation sponsored by Nomos and the South Florida Lacan Group at Columbia University Teacher's College.

(2) Viz., Bruce Fink "There is no Such Thing as a Sexual Relationship: Existence and Formulae of Sexuation" in Newsletter of the Freudian Field, 5.1-2, (1991): 59-85, and The Lacanian Subject: Between Language and jouissance (Princeton: University Press, 1995), and Jonathan Scott Lee Jacques Lacan (Boston: Twayne Publishing, 1990). Joel Dor's Introduction a la Lecture de Lacan, vol. II. (Paris: Denoel, 1992), is an exception and provides an excellent and careful introduction to the formulae, but because Dor reads Lacan as articulating a new logic rather than as distorting the conventions of existing logic (233), he does not try to assess the significance of Lacan's deviation from standard notation. Cf. also Joan Copjec's "The Euthanasia of Reason" in Supposing the Subject (New York: Verso, 1994). Copjec's remarkable article casts these formulae in terms of Kant's antinomies, arguing that the masculine and feminine sides of Lacan's formulae represent the dynamical and mathematical antinomies respectively. Although I also use the term 'antinomy,' my reading of the antinomial nature of Lacan's formulae is somewhat different from Copjec's. Where I examine the formulae on the basis of their deviation from the rules of the Predicate Calculus, to discover an an antinomy in the formula (-[there exists]x)(-[PHI]x), Copjec's is more concerned with interpreting the formulae as symbolic expressions of Kant's antinomies. In spite of this difference of emphasis, my approach is ultimately consistent with her claim that "sexual difference cannot be deconstructed," (23), even if it does not concern itself with her thesis that Lacan is explicitly appropriating Kant's first Critique. Indeed, my only reservation about her article concerns the severity of her thesis that Lacan has appropriated Kant. For, persuasive as she is, this thesis goes too far on purely Kantian grounds. For if one grants the Critique is true, it would be quite astonishing if the antinomial character of reason could reveal itself nowhere else.

(3) To the extent that no one completely escapes the bar of castration a pure feminine jouissance does not exist beyond the law, but designates, rather, a supplementary jouissance to which woman may have access--not as something separate from her subjection to the phallic order, but rather, precisely because of it. This is a jouissance of her lack of the phallus, and not a jouissance which would derive from a supposed lack of subjection to the phallic order, as if she had an openness to something outside it.

(4) Loparic, 241, translation mine. Loparic's focus on Lacan's violation of the established rules of syntax becomes the source of her interest in developing a logical calculus in which quantifiers can be negated by themselves. But brilliant as it is, I cannot see how this helps us attain a better understanding of what Lacan is up to; for in the end his violation of syntax aims at articulating an experience in the real which lies beyond the limits of the symbolic. Apart from this my only quibble with Loparic is that her translation of this as Ox as "x is a O" (240) seems to obscure the point that what is at issue here is a subjection to the castration wielded by the paternal function.

(5) The ensuing discussion will refer to the English translation of Lacan's two lectures "God and the Jouissance of the Woman," and "A love Letter" in Feminine Sexuality, tr. Jacqueline Rose, ed. Juliet Mitchell and Jacqueline Rose (New York: W.W. Norton, 1982) 137-161.

(6) This double reading of (-[there exists]x)(-[PHI]x) which renders it both as something positive referring beyond the phallic, and something negative which makes all women subject to the phallic order is what Fink has in mind when he says that ex-sistence is not exclusive of existence. Lacan's play on the word existence appears to be drawn from Heidegger's use of the word ekstasis in Being and Time. By appealing to Aristotle's use of the word enstasis in the Rhetoric and the Topics (Feminine Sexuality, 141), Lacan appears to be trying to suggest a contrast between in-sistence within the phallic order as the realm of logical opposition, and a possible ek-sistence (147), or standing forth beyond it in feminine jouissance. Thus, to say that the feminine jouissance named here does not exist means it does not exist in the phallic order. This does not, however, exclude its ek-sistence--or standing out--into the real. The trouble is Fink doesn't clearly distinguish between (-[there exists]x)(-[PHI]x) as feminine jouissance and (-[for all]x)[PHI]x as the source of a possible openness to it. So he claims that (-[for all]x)[PHI]x ex-sists as well, which I think is a mistake. This latter formula names the contingent, non-universalizable condition of women who exist (or in-sist) in the phallic just as [for all]x[PHI]x names the universalizable condition of men who exist. The point is that as existing in the phallic the way women are marked by castration means they have a contingent access to something that escapes the phallic order. As (-[for all]x)[PHI]x woman might ex-sist, i.e., she might stand forth beyond it, but then again she might not.

(7) In other words, he is suggesting that it is possible to experience a jouissance of our subjection to the law instead of concealing the inexorable fact of our symbolic castration beneath the guise of phallic substitution. But how to say this through symbolic substitution is a notoriously difficult problem which is at least as old as Parmenides injunction against naming non-being. What I am suggesting is that like the Eleatic Stranger in Plato's Sophist, Lacan is committing the "parricide" of saying "not-being is." But unlike the Eleatic Stranger, Lacan recognizes that to name the lack and bring it into the phallic order is to fail to grasp its character qua lack. This is why he tries to bring the lack into view through a travesty of logical form which subverts the structure of logic by articulating an antinomy which is at once within and without the phallic order. His formula for feminine jouissance is an attempt to suggest psychoanalysis' non-thetic awareness of the limits of the law in a way that cannot be fully articulated within the symbolic formulations of the predicate calculus, which as the most univalent and precise formalization of the phallic order, represents the phallic order par excellence.

(8) This is the second part of the diagram that begins Lacan's lecture "A Love Letter" (Feminine Sexuality, 149).

(9) Lacan, The Four Fundamental Concepts of Psycho-analysis, 204-205.

The full quote reads as follows:
```   Sexuality is represented in the psyche by a relation of the subject
that is deduced from something other than sexuality itself.
Sexuality is established in the field of the subject by a way that
is that of lack.

Two lacks overlap here. The first emerges from the central defect
around which the dialectic of the advent of the subject to his own
being in the relation to the Other turns--by the fact that the
subject depends on the signifier and that the signifier is first
and of all in the field of the Other. This lack takes up the other
lack, which is the real, earlier lack, to be situated at the advent
of the living being, that is to say, at sexed reproduction.

The real lack is what the living being loses, that part of himself
qua living being, in reproducing himself through the way of sex.
This lack is real because it relates to something real, namely,
that the living being, by being subject to sex, has fallen under
the blow of individual death.
```
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