SEXUATED TOPOLOGY AND THE
SUSPENSION OF MEANING

A NON-HERMENEUTICAL PHENOMENOLOGICAL
APPROACH TO TEXTUAL ANALYSIS

WILLIAM J. URBAN

6.3 Additional Interpretive Consequences of the Minimal-Maximal Distinction

The third chapter of Le Gaufey's work recommends itself for more deeply specifying the relationships which adhere between the propositions in the Lacanian logical square. Ostensibly the chapter is an attack on the cherished clinical practice of the vignette in psychoanalysis, to which he counters by arguing for a clinical practice that might instead be modeled on the logic of the maximal particular. But this effort is so favorably peppered with insights into how the particular undermines the universal that they easily form their own separate theme and so permit the text to be more broadly applicable. Thus this work could easily be adapted to counter the 'cookie-cutter' approach to textual analysis which begins with a universal framework and subsequently cuts out textual material into readily digestible morsels or failing that, otherwise submits the uncooperative text to the Procrustean bed of a well-constructed theory. More pertinently and to prepare better for Chapter 7 below, insofar as hermeneutics has established itself as a universal field since Schleiermacher (and with important renewals of its universality coming from different directions by the likes of Dilthey, Heidegger, Bultmann and Gadamer), for a project interested in suspending this supposed universal field, the insights of Le Gaufey prove invaluable. This is especially the case given that his thematic aims towards demonstrating the overall non-relationship which adheres between the two sides of the bipartite structure of the Lacanian logical square in such a way that one can additionally recognize how the crucial accent falls on the left deixis whenever it is a question of parting company with the common notion of the universal on the right.

To say that the Lacanian logical square inscribes a non-relationship is at once to say that its two sides cannot be reduced to a binary, even one in its most primitive form. Yet the analysis in the previous section might suggest otherwise. For clearly the right deixis supports the existence of an essence, which develops a symbolic value of the element , which contrasts with the left deixis where it is affirmed that there is no essence for those elements which do exist and therefore cannot be so symbolically mapped out. It thus seems the logical square inscribes the most elemental binary whereby the right deixis bears a symbolic mark while the left deixis does not. This can be seen in the very writing of the propositions. On the right there is at least one sticking out from all the others,628 and its exceptional status presents itself with the mark of a bar over the phallic function , while on the left the absence of this mark is denoted by negating the existential quantifier . But can the logical square be reduced to the oppositional couple of presence/absence of a distinctive mark? To answer in the affirmative is to conceive the relationship between the two sides as one of complementary difference whereby absence simply responds to presence and vice versa. Yet the writing of the two propositions indicates that the actual relationship is thoroughly asymmetrical since what is at stake is a relationship of quality which founds absolutely separate terms. Consider that one can deny the presence of the given mark of to arrive at its absence . But there is no certainty that this vector can be reversed, for by denying its absence one might return to the same mark but it is also possible that another mark will appear or perhaps none at all. The same mark would be returned to if the relationship were a matter of simple difference where what is not in one deixis is in the other. But being absent in one in no way obligates its presence in the other, for the absence of the mark in the left deixis provides no reference point as would its presence in the right.629 Those elements without a place in the latter must be content to find themselves without complement in the strange space of the former. Again the difficulty is conceiving of the equivalencies to be had between the two sides (as seen in Figure 6.2 above) without generating from this equilibrium a symmetry whereby the mark present on the right grounding the All and the absence of the mark on the left requiring the Not-all share an already circumscribed space.

If there are two global choices regarding how to read the Lacanian logical square, one which naturally slips into positioning all four propositions into a common space and one which endeavors to resist this tendency, it is important to realize how these are not choices made somehow independent of the logical square but are already inscribed into the two sides by the writing of the propositions themselves.630 As is often the case with Lacan, the subject should not move so quickly so as to overlook his own subjectivity in the matter being examined and the topic of the logical square is no exception. For the notion that this square operates in a single space is only had through a strict reading of it from the right deixis which forgoes supplementing with a reading from the other deixis; the inclusion of the latter would reveal a true spatial asymmetry to the logical square. If this is the case it would be clear how the space of the One to the right is troubled by the space of the Other to the left, 'that no heteros encloses the allos; that no alter subsumes the alius' and that the right and left sides are not aliquot parts but instead aliquant.631 To begin gaining an appreciation of this, it is advisable to rearticulate the four propositions of the logical square as a maximal particular choice to limit the range of the universal notion.

It was seen in the previous two sections how classical logicians followed Aristotle in setting aside the maximal understanding of the particular so as to better provide for logical consistency and how Lacan, through Brunschwig's analysis, directly confronts the ambiguity that nevertheless remains. This ambiguity can be expressed at the level of the two universals, which are related as contraries in the classical logical square. The two different understandings of contrariety determine the two different approaches to the particular (minimal and maximal), which at once map onto the two ways of conceiving the spatiality of the logical square. On the one hand the two universals can be seen as marking the extreme points of a common space so that the relation between them is one of continuity; standing in contrast, they oppose (without entirely excluding) each other so that they might be said to be reciprocally complementary. On the other hand they manifest themselves in terms which cannot unite and so must be said to occupy mutually exclusive spaces which are minimally separated; contrariety is defined here by incompatibility rather than by contrast. These two senses of contrariety are admittedly difficult to distinguish but the defective nature of the perfectly ordered logical square this distinction is designed to illustrate becomes more transparent by approaching the problematic through the level of the particular. Now, what differences are there between the particular affirmative and the particular negative despite being equivalencies in the Lacanian logical square? As equivalent the former lends the partitive term 'some' and from the latter the restrictive 'not-all' so that together either of the propositions reads as 'some, but not-all.' This is to read in the maximal sense that takes the partitive as a restrictive and such a reading thoroughly corresponds to the 'natural ear,' which hears the particular 'Some of Gadamer is Heideggerian' as a statement excluding the universal statement 'All of Gadamer is Heideggerian.' In contrast, the classical logician drops the restrictive so that the propositions would read as 'some, because not all' (recall that through subalternation 'some' is implied by All). In this case 'Some of Gadamer' is taken against the way it is naturally heard by considering it only a partial instantiation of 'All of Gadamer.' Here it becomes possible to see how the logical square has no perfect order. Recall that both the classical and Lacanian versions of this square are identical in having grouped each particular to its universal according to quality (affirmatives to the right and negatives to the left) and also hold that a relation of contradiction runs diagonally between each universal and its opposite particular according to quality. The problem is that the single word 'some' is utilized for both the existential particular affirmative and the restrictive particular negative. A choice must be made, and for their part Aristotle and classical logicians privileged the 'some' of the particular affirmative, which denies the 'nothing' of the universal negative without restriction, whereby leaving the field free to the dictates of the All since their choice of the minimal particular has it that 'some, because not all.' This choice places the restrictive particular negative into a secondary slot since its equivocation is only removed by adding the restrictive 'some, but not-all' of the maximal reading which for them has been ruled out.

So despite its apparent symmetry the classical Aristotelian logical square nevertheless leans to the right deixis, favoring the particular affirmative for its agreement with the universal affirmative and for the ontological weight it carries through its contradiction with the universal negative. Thoroughly remaining within the limits of the classical framework (though inverting its values as has been seen), Lacan instead leans to the left deixis by giving priority to the Not-all of the particular negative .632 This move acknowledges the difficulty discussed above in conceiving the particular affirmative as the negation of the universal negative and allows it to enter into contradiction with the universal affirmative in a manner which removes the need to conceive the particular as an exception to the rule of the universal; instead, the particular affirmative stands in contradiction to the universal affirmative through the prior affirmation of the Not-all which denies the universal affirmative and thus leaves to it the space of the right deixis. This privileging of the restrictive aspect of the particular negative which restrains both the universal affirmative and universal negative again better accords to the way the ear naturally hears the particular proposition and moreover, empties the universal of any ontology remaining from its Aristotelian heritage. For with the classical logicians, the universal quantifier does possess some existence through its existential subaltern which stands in agreement with it. But with the Lacanian logical square, while is as predicable as it is with the classicals it is now to be considered strictly a symbolic element without any assured existence. The symbolic status of the universal is even more pronounced with the universal negative, which allows for predication in the absence of a subject. And the validity of the two particular existentials no longer stems from being partial instantiations of a universal truth which claims to govern the logical square within a single space. Seen as working in tandem, they both directly object to such universality by a common disagreement: for those that say no () and those that say yes () reject the equivalent universal suppositions that all say yes () and that there is none to say no () and thus also the single spatiality of the logical square.

By evacuating any assured existence from the universal so that only its symbolic dimension remains, the logical arrangement of the Lacanian square creates a new epistemological situation for textual interpretation.633 Consider an academic text which sets out to demonstrate that 'Gadamer is Heideggerian.' This is called its 'thesis' and as per standard academic practice this is usually declared openly at the beginning of the text. Such an intention effectively operates as an articulated universal statement which delimits the common space within which the text subsists. As the text proceeds, particular passages will be pointed out and perhaps explicitly cited as demonstrative of the thesis. In this sense the academic text appears as the locus of a deictics charged with drawing links between the theoretical knowledge embodied by the thesis where the parts making up its subject are only rationally described and the opaque presence of the actual passages selected by the author. The ideal is for a significant passage not so selected to nevertheless find its place in the epistemological edifice, yet too often it is the case that the reader simply defers to the authority of the author's good name and believes his thesis stands or fails on the passages actually selected. Moreover, the thematics of classic texts are often authoritatively established by their first commentators and considerable time must pass before radical deviations from these norms become tolerable. Thus the assessments of Gadamer by Betti, Hirsch, Habermas, Palmer and Ricoeur establish an interpretive horizon within which the following generations of commentators are obligated to remain. In large part they are content to expand on the common narrative but forego any seriously attempt to escape from its grasp.

This style of textual interpretation is not the prerogative of a method of textual analysis which would instead follow the inner relations of the Lacanian logical square. To begin to see this, the standard operating procedure of the interpretive text seeking to impart its thesis upon the reader must be more closely examined. What is at stake here concerns the basic operation by which particular elements of primary texts are used to impress upon the reader the truth of the interpretive hypothesis. As already stated, the interpreter may refer to primary textual material through direct citation and in such a case it becomes quite clear how the reference stands to the secondary text in much the same fashion as the vignette does for the psychoanalytic case study. After providing a brief etymological analysis of the word itself whose history from the medieval period onward indicates 'the difference of workmanship in these vignettes that ornament, decorate, garland, enhance, embellish, adorn remarks that one fears lack some flesh,' Le Gaufey notes how 'it is remarkable that they all accomplish the same task, which moreover justifies their appellation: to illustrate, by a demonstrative example, some statement that is too arid and because of this is qualified as "theoretical."'634 On a very basic perceptual level, is not the citation an adornment to the interpreter's text and one made especially obvious not only by its frame of quotation marks but when length demands that it stand apart from the surrounding text with its own distinct set of margins, line spacing and font size or when made to stand in even greater isolation at the masthead of a chapter? More importantly and as already noted, these citations read in isolation are often nonsensical, but as embedded within the surrounding text (their context), they become completely understandable and ideally serve to illustrate the intended thesis. Yet when some passages of Gadamer are referenced, this is not simply an invitation to enter into interpretive debate. For what is at stake is not whether the author is correct to have selected these particular passages to illustrate the thesis 'Gadamer is Heideggerian.' Indeed it may very well be generally acknowledged that the particular passages referenced satisfactorily fall into the abstract category of 'being Heideggerian.' But what the foregoing analyses of the minimal and the maximal particular underscore is the collection of hypotheses accompanying even this noncontroversial case by which a particular is straightforwardly subsumed under a universal.

To produce a thesis is effectively to produce a concept or notion which holds that a certain number of elements correspond to its definition. The notion is a basic component of (scientific) knowledge, providing the elements under its purview a link to other notions and their associated elements and thus opens up new avenues with which to potentially expand the epistemological field. Defined this way it is clear how the notion is similar to the universal as both subsume in a common space elements according to a similar feature. This allows the plurality of elements to be treated as a unity since each element bears the same mark and so is valid for all, which in turn makes of the universal notion the bearer of a truth liable to enter into relations with other similar unities. The universal 'Gadamer is Heideggerian' may very well supply the correct notion for reading a particular passage by Gadamer. But note how the universal implies the reading of the particular in this case. Opposed to this minimal reading is the maximal, which is just as legitimate and logically rigorous despite its objection to the universal of the same (and different) quality. This reading resists a certain rationalist approach which reduces using the notion to subsume positive occurrences to instead consider its contradictory relationship to every existence. Rejecting subalternation and embracing active refusal, the maximal reading of the particular recognizes that the mark a particular element presents which allows it to be subsumed under a universal notion is not of the same nature as the mark present in the universal notion. With the minimal particular such a prospect is absurd, since by definition the particular is only subsumed under the universal notion to the extent that the mark is identical in both. But with the maximal particular, affirming that elements exist which do not fall under the notion ('There exist some passages of Gadamer that are not Heideggerian' in the face of 'All of Gadamer is Heideggerian') gives precedence instead to existence. This, however, does not so much attack the notional order itself as 'offer it on the contrary a possibility of consisting otherwise than as the map of a country that is already there' and thus one which comes complete with a navigable set of organized signs.635 In sum, the two readings of the particular are radically opposed perspectives on how knowledge operates with respect to the phenomena it structures. Yet they stop short of being diametrically opposed because while the minimal reading is recognizable within the horizon of the maximal (though it is rejected), such recognition does not hold in the reverse. This may help dispel the impression that there is a simple technical choice to be made between the two readings. For we can hardly do without the minimal reading which acknowledges how the notional architecture expresses the structured order of the world. Yet the phenomenologist reminds us that we daily experience how this architecture nevertheless misses the wealth of the world so that we are forced to conclude that the notion is wholly blind to the brute fact of existence. Far from reconciling these two readings, they should be further distinguished along their divergent paths to better assess the consequences for textual analysis.

With respect to the minimal reading, if the predominant rationale for utilizing particular textual evidence is to illustrate a larger thesis, a certain false rigor is lent to the overall project. For even when the intent is critique, such evidence is never used in so radical a manner that it would seriously jeopardize its critical stance; if it did, the minimal reading of the particular would simply call for a change at the theoretical level to resynchronize it with the evidence presented and so ensure that the critical thesis achieves the highest possible reality coefficient. This latter possibility, whereby the textual evidence necessitates adjustments to the notional architecture, is actually a secondary movement under the minimal reading. As seen in foregoing discussions, in theory it is possible to begin the inner movement of the hermeneutical circle with the particular. But this happens precisely only in theory, for it is always already the case that the notion organizes the experience of particular existences even when one 'starts' with the latter level. In this sense the minimal reading does not take the notion in its simple symbolic dimension but rather views it as an accurate reflection of reality. Here it is fair to associate, as Le Gaufey has done, the notion with the Platonic Idea according to which existence is but its shadow.636 Certainly academic standards dictate that the judgment of a text proceed according to whether its use of referenced textual material from primary sources is in line with its intended thesis. This paradigm, firmly entrenched in academia for some time now, quite simply judges a work of interpretation a success if it demonstrates through textual evidence what it says it will demonstrate. Here it becomes clear that cited textual material is much more than a mere adornment for an interpretation. Through its recourse to authoritative texts, both primary and historically significant secondary ones, the interpretation gains a certain legitimacy. Moreover, along with this greater legitimacy comes an assurance that these references index the essential core of the matter, thus reflecting the interpreter's treatment of the reference as a sign which indexes the real. In this sense references act as anchoring points for the entire interpretive venture, lending it both credence and an authoritative weight. So an interpretation, making ample references to passages where Gadamer utilizes Heideggerian phraseology, effectively says to the reader 'See, it's really like I purport it to be: Gadamer is Heideggerian!' The reader leaves with the distinct impression that the entire opus of Gadamer so reflects this thesis that, as per the law of large numbers, even a randomly selected set of references would suffice to demonstrate it. Thus the minimal approach to interpretation severely restricts the relation one can strike with the text, for the victor seems to be thoroughly determined in advance, it being ruled out that a passage might be presented that would contradict the thesis. The suspicion here that the 'deck has been stacked' thus already works against its own aims, but the minimal approach suffers another setback in the other direction. To this 'too much' stands a 'too little' whereby the thesis cannot be made to account for the wealth of details which begin to mount as the number of references increase. On this point the strategy of the minimal approach might be captured by the motto 'less is more' so as to counter the suspicion that the interpretive effort is grossly inadequate to the task at hand.

These problems with the minimal approach to textual interpretation become much more severe when the lessons of the maximal particular are reintroduced back into the discussion. The terms above were intentionally kept as simple as possible to ease the discussion and to better distinguish the two approaches. To this end it should already be suspected how the potential suspension of meaning in textual analysis as reflected in the asymmetrical space of the Lacanian logical square is only obtained by starting from the maximal particular which invalidates the universal affirmative. This right away problematizes the use of textual material for the sole purpose of illustrating the veracity of theoretical statements such as an interpretive thesis. If an existent textual passage does inadvertently confirm the universal notion, it is at the cost of the loss of the emergence of the Not-all as a particular which maintains a minimal separation between its existence and essence. So utilizing the maximal particular reflects a far greater mistrust of theory than the one held by the more minimal-minded hermeneutical phenomenological approach; this is the case despite the latter's well-vocalized call to move away from theory toward the immediacy of meaningful experience. In contrast to the maximal, it is the minimal approach of the classical logical square which quite rigidly points to reality in its attempt to seamlessly connect its knowledge to such experiences without a gap. Here lies the conception of an all encompassing common space, much like what is had in the right deixis of the Lacanian logical square in contrast to the reading by the left which purports instead an asymmetrical spatiality. This discontinuity between the two logical squares, which in large part is reflected within the Lacanian version itself, must be maintained if interpretive theory in its maximal setting is to be understood.

With respect to the Lacanian logical square, the affirmation of existence at the level of the two particulars each contradicts the two universals. What must be better appreciated is the precise status of the universal without considering (its relation to) the actual existence of the particular, and this can be approached by recognizing how the existent constitutes an exception to the universal only in the qualitative, not quantitative, sense. To think in terms of the latter would make of the particular affirmative a rarity and this is simply not warranted, for the universal affirmative does not imply any existence. In other words, it is not the case that we are dealing with an existing minority qua detracting exception to the existing majority subsumed under a common law. Le Gaufey discusses the graph of the hyperbolic function once again (cf. Figure 6.3) to demonstrate this point.637 The reservations noted above concerning his criticism of Lacan's invoking of this function aside, Le Gaufey is correct to note how the graph is misleading as it reverses the expected existential weightings of the two propositions in the right deixis. That is, the particular affirmative is what should carry such weight, yet in the graph this is the zero of the ordinate axis; while the curve representing the universal affirmative has determinate values for all its points when these values should not be so easily implied.638 In light of these failings and to resist the temptation to quantitatively treat the universal and the particular on the same existential footing, it is worthwhile to follow one or two of Le Gaufey's alternative recommendations on how to conceive the dislocation of the universal from existence. One enlightening way comes by considering the valid elemental inference from traditional propositional calculus called modus ponens [Latin, 'mode of placing']. Often called a hypothetical syllogism, the first of its three lines begins with a hypothetical proposition usually written in the form 'If p then q ' where p is held to be in the position of the antecedent and q in the position of the consequent. But precisely as a hypothetical, nothing else follows until a subject affirms the antecedent p , at which point the proposition unfolds its truth and allows for the concluding line 'therefore q ' to be written. The point here is that if the existence of p is not affirmed, the implication remains inert.639 It does express a certain knowledge at the level of the conditional relations between the two terms or elements, but without the actualization of the antecedent this knowledge remains unrealized.

This same epistemological status can be seen in Frege's revolutionary move to predicate logic, which Lacan follows as discussed in Section 6.2 above. Recall that with Frege the function takes logical precedence as it presents an empty place for an object-term which might later come to fill it. But it is important to understand that it must be so filled for the function to take on its value and give birth to a meaning. To reach an understanding of the universal as such, the task here is to ask what the mode of subsistence is of the Fregean function prior to its being filled by an object-term. Just like with the inference of modus ponens, the answer is that until the function is so endowed by an object-term it possesses a not-yet-full existence. Le Gaufey cites W. V. Quine to provide a poetic sense to this precarious status, referring to 'functions waiting for their objects as "semi-twilight entities."'640 We can move a step further in this analysis to also enquire after the status of the object-term apart from the function. Certainly it has existence but not yet an essence, as essence is only granted to it when it comes to fill the empty place in the function. Here is yet another way to understand how existence takes precedence over its essence. Moreover, affirming the existent object-term and thus submitting it under the semi-twilight function also brings to mind Husserl's moderate Platonic notion of the ideality of meaning whose creation is similarly had through the meeting of two. In a comparable fashion, for Husserl a subjective meaning-intentional act is needed to instantiate the possible universal into a fully existent particularity complete with a meaning and with what Frege would call a truth-value. To this series of traditional logic, Frege, Quine and Husserl, one may add the Lacanian notion of the symbolic which similarly provides a way to conceive the status of the universal sans the particular. As the internally fractured treasure-trove of signifiers, the symbolic prescribes a knowledge of inferences, conditional relations and rules of validation in a way which also grants to this epistemological realm a certain independence. In this sense it enjoys a sovereignty from both the register of the real and the imaginary order of meaning.

It now becomes clearer that the maximal reading allows for universal notions to go their own way and interact with one another in a relatively independent fashion from the reality of existing objects. They can thus be read, as the foregoing has shown, without the need to precipitate one's own subjectivity so as to offer them an existential grounding. For the lifeless meaning they convey at the denotative level momentarily suffices in its promise of full expressive sense to come once subjectivization occurs by an affirmation of a p or the performance of a meaning-intentional act. At this level the notion qua spoken word is a pure declaring about something outside itself which nevertheless escapes its designation. Here is the basis of life philosophy's romantic complaint about the limits of representation. But what this theoretical disposition itself misses is how that which refuses to be subsumed under a universal notion has to do with the Not-all particular. It is towards this understanding the maximal particular invites its reader. Already the right deixis clearly separates out the exception of the particular affirmative as that which contests the universal affirmative . But this is to consider it qualitatively as the manifested existence which gives form to the function. In contrast, with the minimal particular affirmative the function takes precedence over the existence of this form since it blends in with its universal model. Thus the universalized mark of 'being Heideggerian' takes a position of ascendency over the existence of the passages in which they are found when it comes to minimally affirming 'Some of Gadamer is Heideggerian.' But with the maximal particular affirmative this ranking is reversed since the affirmation of existence finds its way to the foreground without the need to justify itself by bearing the universalized mark. Yet nothing can be said about this exception. Consider the affirmation of existing passages of Gadamer which form an exception to the universal claim 'All of Gadamer is Heideggerian.' Because it negates the function 'being Heideggerian,' it is only permissible to affirm this exception in the form of the proposition 'Some of Gadamer is not Heideggerian' and nothing more.

The decision by Lacan to clearly distinguish existence from the function has its historical roots again with Frege and this can be appreciated by clarifying and expanding the discussion originally had in Section 6.2 above. There it was seen how the function '( ) is Heideggerian' takes on its value when an object-term like 'Gadamer' comes to occupy its empty place. Now, the discussion in the present chapter has consistently treated 'Gadamer' not as a proper name designating the actual existence of a singular man who once went by that name; rather, 'Gadamer' has effectively been treated as equivalent to 'the texts of Gadamer.'641 But the presentation moved too fast by overlooking how Frege's first move was precisely to make this distinction. In doing so, his solution effectively lead to a conception which eliminates the singular from consideration. Taking the second of the two designations above, the universal affirmative can be written as 'All the texts of Gadamer are Heideggerian.' What Frege does is treat this as a complex proposition involving two functions, '( ) is a text of Gadamer' and '( ) is Heideggerian,' between which a certain relation is stated to have been obtained: whatever truthfully satisfies the former also satisfies the latter. If this is represented as 'For all , if is a text of Gadamer, then is Heideggerian,' the two propositions can be regarded as ' is a text of Gadamer' and ' is Heideggerian' and further linked together by a propositional connective and bound by the universal quantifier . This reasoning can similarly be applied with respect to the singular designation which considers Gadamer as a man, as in the proposition 'Gadamer was Jauss' teacher.' But the affirmation of such a proposition confuses in the name 'Gadamer' a conviction about his existence and the fact that he was Jauss' teacher. This duality is what concerns Frege and thus what comes to pass is the distinction of the factum brutum of existence from the predicates which might be attributed to it. In order to help conceive of this existential a priori without further consideration, the proposition could be placed into a form like 'There exists an such that is Gadamer and such that this was Jauss' teacher' which would formally be written with the existential quantifier . With Lacan's division of the right deixis into two propositions, one written with the universal quantifier and one with the existential quantifier, this distinction becomes clearly expressed. For the work of the maximal particular affirmative distinguishes the existent (with its propositional connectives to the symbolic mark and the function) from their negation. In this way the existent is posited separately from the symbolic determinations that it supports, yet finds itself submitted to their determination. This is similar to how the asymptotes support the hyperbolic function through a point where its calculation is undefined; yet nevertheless this precise point is what determines the graphical position of the asymptotes. In a maximal reading, textual references in an interpretation would be treated asymptotically, in contrast to the more forced minimal reading which fails almost in principle. For if the qua textual reference is only so summoned because of the relevant symbolic marks it displays, it is nothing more than the shadow cast by the notion whose affirmation it defends. Such an existent would no longer find itself in the position of an ambiguous outlier; rather, it would be entirely determined as a well-defined point on the graph of a function whose domain is continuous. Between the 'done deal' of the minimal particular and the romantic bemoaning (or celebration) of the failure of every representation of reality stands the maximal particular interpretative strategy. But what exactly does such an interpretation look like?

As will be appreciated from the foregoing, this strategy cannot be directly 'illustrated,' as it would then readily slip into the minimal order of the particular. That in some sense it can only be approached through what it is not is indeed readily seen in the very writing of the particular proposition at the level of its quality, for it negates the function affirmed in its universal. Thus it is quite appropriate that Le Gaufey would have us study a case from classical Freudian psychoanalysis only as a first approximation to the maximal approach: in the end he rules it as indirectly endorsing the minimal approach of the clinical vignette and so it is accordingly rejected.642 But as it does provide a case where Freud takes up the challenge of evidence that directly contradicts one of his theories, it does bear brief examination if only to underscore the falsity of the notion that a maximal approach seeks only to realign the theoretical to better account for the existence of contradictory evidence. In simple terms and without entering into the specific details of the case, Freud theorized paranoia to have a homosexual foundation, and this implied that the persecutor must be of the same sex as the persecuted paranoiac. All cases which Freud came across confirmed this theoretical notion but one: he became acquainted with a female patient whose persecutor was a man. The existence of this exception for Freud takes precedence over his theory and he accordingly investigates further. What he eventually finds is that the true persecutor is in fact a woman. So this case only appeared to form an exception, for in the end it was compatible with his thesis on paranoia. The lesson here seems to be the same lesson imparted by an aspect of hermeneutical phenomenology which teaches that harmony is found if one simply digs deep enough beneath the apparent opposition. In terms of Freudian dream analysis, this lesson amounts to the recognition of how the manifest face of the text hides another latent text beneath it. But as seen in Section 5.1 above, Freud does not halt his interpretation after the manifest content yields up its latent content but further inquires after this very displacement, endeavoring to account for the structured passage from the latent to the manifest which indexes the real and also allows for adjustments to the theory predicting the manifest content.643 In the present case he does follow that passage and makes appropriate adjustments to his theory. So as Le Gaufey points out, the temptation is to read this case as do his usual critics who accuse him of harboring theories so sophisticated that they can always be maneuvered out from any contradiction. Yet we do well to note that the universal affirmation of the theory was initially put into question not only through contradictory manifest content, but through the subordinate (and, unfortunately, subalternate) role Freud assigns to the latent content found 'beneath' it, for he treats that latent content as only a stage in deciphering the text. This alone makes Freud's technique superior to the strict minimal approach that deals only with non-contradictory textual evidence confirming the thesis. However, at least with respect to the present case Freud does not deal with an existent fact resistant to all theoretical explanations which on that basis alone would be able to negate the theory. Such an exceptional point is what makes plain with its writing in its opposition to .

Yet on this basis alone one cannot conclude that every existence eludes the set of notions which frame it. Believing otherwise might lead to interpretive practices which simply point out those textual passages that remain resistant to the commonly accepted understanding of the primary source material. What stops such a simplistic demonstration of the failing of the universal notion is that does not stand alone in its contradictory opposition. In fact, without factoring in the contribution played by the two propositions in the left deixis of the logical square of the maximal particular, it becomes rather difficult to make full sense of the contradiction inherent in the right. For his part Le Gaufey takes up the contradiction in the right deixis through the traditional 'liar paradox' Lacan himself raised on the November 11, 1961 session of his ninth seminar. Le Gaufey's discussion644 presents a way to conceive of this contradiction that aids in understanding the discussion first had in Section 6.2 above with respect to the elemental universal affirmative 'All men are mortal.' But it is interesting that while his discussion begins by strictly making use of the two propositions in the right deixis, there is an eventual turn to those of the left in order to better reveal the true status of the exception. Again this must be read as a move which demonstrates how the left deixis takes logical priority over the right.

Often simply conveyed by the statement 'I am now speaking falsely,'645 the liar paradox has been known since antiquity and has traditionally been attributed to Epimenides the Cretan in the form 'All Cretans are liars.' If Epimenides affirms that all Cretans are liars, what are we to make of his assertion given the fact that he himself is a Cretan? It seems this is precisely the dilemma inscribed by the two propositions in the right deixis. The universal affirmative 'All Cretans are liars' () is a theoretical statement purporting a truth about a generic All of Cretans () stated by Epimenides (), who does not claim to escape from either the All to which he belongs or from the law () he states is true and according to which he is also a liar. In so stating, his full intention is to tell the truth in this respect. Yet in doing so he positions himself in direct contradiction to this universal as soon as he states it (). While it suffices for many to simply mention these paradoxes, treating them little better than amusements in logic, the advantage of Lacan's formulae is that it allows for a better understanding of the mechanism which structures them. This concerns a certain redoubling at the level of quality in propositions which generate such a paradox over-against what is had in classical logic. With respect to the latter it has been seen that a logical proposition claims to be either true or false according to whether its subject bears the predicate or not and since Frege this has been called its truth-value. Here truth is taken as strictly subsisting at the level of the entire statement regardless of whether one affirms, say, the Heideggerian-like quality of All or Some passages by Gadamer or whether one denies that they bear this mark. That is, all four propositional cases have a truth-value: in the first two cases the truth-value is true and in the second two cases it is false. But it has also been seen that while Lacan's version of the logical square maintains a classical structure, his interests have lead him to thoroughly subvert it. In the terms of the present discussion this subversion is understood as an endeavor to inscribe the paradox which results when the question of truth itself takes up the position of predicate in the classical framework. This is the situation of Epimenides who, by telling us that 'All Cretans are liars,' in effect also claims 'At least one Cretan (Epimenides) is not a liar (is truthful).' The paradox results because truth is doubled, for a mode of relationship of Cretans to the truth is affirmed in an assertion which itself also bears a truth-value. If the predicate were instead 'tall,' no such paradox would result if Epimenides were in fact short and had said 'All Cretans are tall.' In such a case he would constitute an exception by simple contradiction which would not at all trouble the formation of the set of Cretans composed of those who bear the predicate and those who do not. But with truth split between its position of truth-value subsisting at the level of the statement ('S is P') and its position of predicate ('S is truthful') in the very same statement, it seems a choice must be made between the two poles. In which position should one consider the truth of a statement? Classical logicians have opted to consider truth only as truth-value. They of course recognize the paradox that results by also positioning truth in the position of predicate yet only seem to invoke this paradox as an interesting logical exercise. Faced with this same choice, Lacan's answer is a resounding 'Yes, please!' which acknowledges how the choice itself must be chosen. It is this choice that is inscribed into the writing of his logical square.

But exactly where in the logical square this inscription ultimately lies is rather vague. If anything it appears that suddenly what is at stake concerns the a priori logic inscribed in the left deixis despite the fact that the analysis of this paradox was initiated in the right. That this analysis effected a movement from right to left is confirmed by Le Gaufey's own conclusion that this paradox is 'the paradox formally presented by the structure of Russell's paradox,'646 which was located in discussions above as subsisting in the left deixis. To see this, consider that if Epimenides tells the truth, his exclusion from the universal proposition makes it false ( and are contradictories), and so he is telling a falsehood when he is being truthful; but if he tells a falsehood, he rejoins the lying Cretans which makes the universal proposition true and so he is telling the truth when he is lying.647 In a word, by telling the truth, he lies and by lying he tells the truth. The source of the difficultly lies with how truth designates the nature of the link between subject (or argument) and predicate (or function), just as in the case of the paradoxical 'set of all sets that are not members of themselves' where 'membership' is taken as a noun designating the link between sets and their elements. In most cases no issues arise. Sets that are not members of themselves certainly exist648 and it is perfectly acceptable to utter how 'All Cretans are liars' when one is not in fact a Cretan. But fold the properties of membership and truth back onto themselves and paradoxes result.649 Through its ultimate recourse to the left deixis where no set can be determined, this analysis thus unmasks the ultimately phantasmatical dimension of the particular affirmative to the right. This proposition alone simply cannot form an acceptable exception by refusing to submit to the function in question, for All are so submitted.

To reemphasize, the proper (maximal) understanding of the particular affirmative is arrived at by taking into consideration those propositions subsisting in the more radical deixis of the left. It should therefore not be conceived as a singular exception (there is no meta-language), nor quantitatively as if it forms a minority to a majority of elements in the universal affirmative which it contradicts. Rather, it should be thought of as arriving on the scene of the logical square through its contradiction to the universal negative , whose writing has been shown to inscribe a 'nothing,' an absence of any predicable subject. The particular affirmative thus affirms what exists with respect to the predicate (or function) without bearing its mark (or satisfying it). What the logical paradox of Epimenides shows is not a rare aberration (as classical logic would consider it) but the much more common regime every speaking being finds himself within whenever he lends his voice to the establishment of an All to which he is a member but whose completeness he prevents by this very declaration – although he will not do so without simultaneously arranging for himself the exceptional point of a meta-language to occupy sub rosa and to which we must judge from the left as ultimately phantasmatic. If this phantasmatical dimension to the declaration of the All is taken into account, it is better appreciated how the status of that entity collectivizing elements into an All carries no existential weight, subsisting as it does more on the side of the signifier than on any ontologized thing (contrary to what the hermeneutical phenomenologist would have us believe). The paradox of Epimenides also underscores the ambiguity of the term 'membership' in the formation of a set. Using the universal quantifier necessitates a set populated with elements said to be members of this set. But if it is affirmed that (at least) one exists which does not satisfy the function and thus forms an exception to the All of the universal, an ambiguity immediately arises as to whether it ceases to be a member of this All or not. Classical logic cannot tolerate such an ambiguity and on this point Lacan seems to concur, constructing his maximal logical square in such a fashion so that either the universals are true or the particulars are true while the contradictory relation linking them appear to assure that they cannot be true at the same time. However, a proper reading of the particular and the universal as inscribed in the right deixis reveals that the very ambiguity in question is actually preserved there in such a way that the contradiction between them does not strictly imply that the truth of one level annihilates the truth of the other. Rather, since the particular affirmative establishes the universal affirmative precisely through its objection to it (providing it as it does with the existent that declares it), the possibility is raised that these two propositions in the right deixis can be simultaneously true despite their contradictory relation.650 Such an inscription clearly departs from classical logic.

A fuller picture emerges by looking to the top proposition of the left deixis where the exception in the right finds itself denied, at once shutting down any lingering aspirations to be the One. The very writing of the universal negative exposes the charade of a meta-language, affirming as it does through its use of a double negative that there does not exist any which does not satisfy the function. Coupling this with the bottom proposition of the particular negative , the paradoxical result is that the elements which do satisfy the function nevertheless do not collectivize into any All set. Based as it is on this All, the universality of the notion takes its first hit from the right (as it is founded on the existence of exceptions), but is then delivered a fatal blow from the left (insofar as there is no exception and what does exist cannot form into an All). Pitting the All against the Not-all, the latter emerges as the clear victor. It could be said that the Lacanian logical square is the square of the Not-all in the sense that the exigencies of this left-leaning proposition have guided the writing of each of the other propositions to optimize the attack directed against any universal notion that would presume to possess existential weight. In its most consequential reading the notion is thoroughly split. However, this does not imply that the universal notion is thereby rendered entirely ineffectual, for its symbolic status does carry a certain interpretive weight by readily consigning elements to its sphere – indeed interpretation could not proceed without this initial send-off by its minimal particular reading. But the move to an interpretation based on the maximal particular that would break free of the hermeneutical circle would recognize that what ultimately effectuates such interpretive weight is the Not-all which thoroughly resists being subsumed under any universal thesis. Maintaining itself instead as an existence without essence, it is the Not-all which proves itself decisive in the interpretive endeavor by raising the possibility that meaning can be suspended. This claim is a central thesis of Chapter 7 below.

To help prepare for that discussion, some concluding remarks would be welcomed regarding the different global stances assumed by the minimal and maximal logical squares towards the interpretive endeavor. In hermeneutical terms, what assures that the two sides of the classical Aristotelian logical square are harmonized is meaning. The interpretive process begins by gaining entry into the hermeneutical circle by assuming a universal thesis such as 'Gadamer is Heideggerian.' Particular passages of Gadamer are then read and found to either affirm or deny this thesis. If affirmed, the meaning of Gadamer is firmly established: he is Heideggerian and this meaning encompasses both sides of the square. Or more accurately the left deixis effectively collapses into the right, for if Gadamer is not 'not Heideggerian,' the left deixis is removed from consideration. The hegemony of meaning is not tapered in the slightest if the particular passages are found instead to deny the universal thesis. In fact it is arguably strengthened in this case. For judging Gadamer to be 'not Heideggerian' equally unites the two sides although this time under the authority of the left deixis. But since this judgment comes in the form of a negation, it amounts to an abrupt 'No' which plays the part of a scansion that precipitates concluding moments in the mind of every reader. If Gadamer is not Heideggerian, then what is he? How should his work be positively characterized? Opening infinite avenues for future exploration, this meaning-to-come for the present moment nevertheless stabilizes any inherent tension in the minimal logical square by removing all affirmative stances to be had in the right deixis to favor instead the left. The analysis here that only a single deixis is put into play during any single turn of the hermeneutical circle, so that this circle could be said to nourish itself across both sides, confirms the findings above that the minimal logical square operates within a singular, symmetrical and unified space.

With the asymmetrical space of the maximal particular logical square, this harmonization through meaning thoroughly breaks down. For each side is not to be treated as one pole of a binary couple so that the choice of one simply equates with the negation of the other. This is not to say that meaning does not subsist in this square altogether but rather that it seems to be confined to just one of its sides, that of the right. But already the hermeneutical circle is problematized in the right deixis in that it is no longer clear which level, the universal or the particular, initiates its circular movement. Keeping to the discussion of Epimenides above, one could issue an existential challenge to the always already status of the universal notion by arguing that such a notion must always be articulated with respect to a particular existence. In this case the voice which a particular passage of Gadamer lends to the interpretive proceedings becomes the necessary condition for the declaration of any universal thesis such as 'Gadamer is Heideggerian.' But in so doing this textual passage withdraws itself so as not to be swept up in this universal. As seen above, the particular declaration supports this universal by its own defection at this level. This would produce the essence of the being of the text while simultaneously maintaining its objection by its very existence. The castrating 'No' isolated to the left deixis of the classical square thus has a presence in the right deixis of the Lacanian square, but in the latter case the negation does produce a determinate meaning at the level of the universal. This donation of the meaning of Gadamer as Heideggerian might be brought about by a lengthy citation from one of his texts. Its special handling (indicated by changes to font size, line spacing, etc...) assures its exceptional status with respect to the interpreting text and more importantly, to Gadamer's own body of work, will not be missed. What often follows such citations are lines like 'This means that...' or 'What Gadamer is saying...' that immediately engage in explication, as if the cited passage cannot entirely be trusted on its own to demonstrate the thesis in question. In terms of the right deixis the worry here is unwarranted. For it is precisely through its withdrawal, at its very point of exclusion from the thesis it is intended to demonstrate, that the existence of this passage is best poised to declare it in its symbolic-virtual dimension and affirm the notion that 'Gadamer is Heideggerian.'

Yet in terms of the left deixis the worry that such a particular passage might disappoint is justifiable. Not only at the level of its content where elements can always be found contradicting the interpreter's official explication which might call for critical rebuttal; indeed at this level the hermeneutical task is endless and expansion to the secondary literature is assured. Rather, at a much more consequential level the left deixis of the maximal square fatally attacks the right at the very level of its existential exceptionality and thereby undermines the grounding of the universal thesis. For in the left deixis those existing elements which satisfy nevertheless do not form any thesis and so do not generate any exception. The contradiction here is even more troubling than the contradiction to be had in the right deixis: it is affirmed in the left that there is no exception yet those elements present cannot form a thesis; each one to the left is not an exceptional One as on the right. The Not-all affirms each existence through the use of a negated universal quantifier so as to display its restrictive aspect and here is why cited passages may incite concern that they are either in default with respect to the unity of the thesis or else appear overly eager in excessively displaying their thematic markings. This wavering between a too little and a too much prevents such passages from being identical to themselves. A minimally consistent self-identity is needed to integrate elements into a thematic unity, but the Not-all disturbs this unity from within and so prevents the collectivization of particular textual passages under a unified meaning.

This dissonance should not be seen as a weakness of the left deixis in contrast to the symbolic unity to be had in the right but rather as its undeniable strength which grants to it its logical priority. To the initial difficulties which the right introduces into the smooth operation of the hermeneutical circle, the left complements by further introducing the Not-all which thoroughly disturbs the unity and cohesiveness of the hermeneutical field. Insofar as it is the Not-all which ultimately suspends this field, the left deixis could be said to complete the work started by the right. In this way no unified field of meaning traverses the maximal logical square and its two sides could in no way enter into a relationship. That this square inscribes a non-unified hermeneutical field is underscored by the fact that the same is utilized in the writing of the propositions on both its sides. Had an been used to the right and a to the left so as to designate two different spaces or two aspects of the same space, one would be justified in entertaining the notion that the two sides enter into some relation. But the use of the same , everywhere valid, calls on the reader to endeavor to think the one and same space as self-undermining. Consider that from one perspective the is taken as excepted from the All-space that it presupposes and within which it is a member, and from another perspective this same is taken as existing without being a member of some All. Again if this denotes a particular textual passage of Gadamer of interest to the interpreter, both these functionings must be considered. First, this passage could be conceived as harboring an essential meaning for All of Gadamer's work while the second functioning of this very same passage refuses to authorize any such essence but would instead be based entirely on an existence which remains resistant to any meaningful unity whatsoever. Together they establish and then immediately undermine the set of signifiers of a text along with whatever meaning they carry. However, it should be cautioned that the terminology of 'perspective' is perhaps rather misleading. The danger is to read this as a binary, as if there were determinate -right and -left perspectives. What must be kept in mind is how it is the same textual passage that is being examined from both these 'perspectives' and that a proper interpretation must consider both at once: as a text which ultimately bears no relation to itself due to the nonsensical Not-all preventing a set of common terms from coming to subsume the putting into relation of the 'two' perspectives under a unified meaning. It can hardly be stressed enough that no relationship is possible since at the level of essences one is lacking and the existences from either perspective are incommensurable to the other.

The logical priority of the left deixis over the right in the maximal logical square cannot only be expressed by the different argument forms of the same element but also in terms of the phallic function , for it too makes an appearance in each of the propositions. Given that the phallic signifier is exceptional to the field of signifiers, it is legitimate to approach this rather enigmatic function which bears its name as involving the status of the exception in the logical square. Yet as the link between signifiers and jouissance is also involved, the phallic function can fruitfully be taken as equivalent to the function of castration, which states that a certain jouissance must be given up by every user of signifiers. It not only serves to distinguish and disconnect the two irreducible functionings of the element , but its use in each proposition allows for the two sides of the logical square to be read has having inscribed the two different relationships that can be struck with this function. Accordingly, in the right deixis this function is affirmed by the One excepted from it while making itself the nucleus of the movement of signifiers which fails to deliver the promised jouissance; while in the Other deixis this impossibility is supplemented by an experience of dissatisfaction preventing closure through meaningful unity. Interpreting with the One holds out promise that the elusive meaning of a textual passage can eventually be corned and be made to corral the infinite slide of signifiers. But as far as the Other is concerned no such relation could be struck and here lies the sobering truth of the One which might exclude itself so as to uphold a meaningful unity. This truth equally holds for anyone wishing to be excluded from the Lacanian logical square itself so as to find there a meaning. But as its two sides stand in thorough non-relation, ultimately only its suspension will be found there.

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