Lacan and Modality

By the time of his 19th seminar, Lacan started to associate the four places of discourse with four logical quantifications of "'the phallic function," as can be seen below:

For instance, the place of agency in discourse structure is here associated with the expression "there is one that is not subject to the phallic function" or "there is one that says 'no' to castration." Below it the place of truth is associated with the fact that "all are subject to the law of castration." In the place of production in the bottom-right corner "not all are subject to the law of castration," and above it "there is not one who says 'no' to castration." I won't go into detail on these expressions at this point.

Lacan associates the four positions further with the four traditional modal categories of the necessary, the possible, the impossible and the contingent. These are carved out through the function of "the written" (l'ecrit): the necessary marks that which "doesn't stop writing itself," the impossible that which "doesn't stop not writing itself," the contingent that which "stops not writing itself," and the possible that which "stops writing itself." The specific modalities linked to each of the four corners can be seen in Lacan's schema below:

Readers of Lacan will be most familiar with the category of the impossible as applied to the real: "the real is the impossible." This expression must be taken in a technical sense, as in for example the logical conjunction of a term with its denial. That is only one corner, however. I won't elaborate, as for now I am just laying groundwork. I only wish to note at this point that the superimposition of these four modal categories with the permutations of discourse will yield some very interesting results.

Lacan's Four-place Structures

Lacan's mathemes circulate through structures of discourse. Usually referred to as 'the four discourses,' although Lacan has also written a fifth, these structures are based on a fundamental framework. There are four corners to each structure, which I will sometimes refer to here as the places of discourse:

The analyst's discourse is centred in the middle here, but it is only one of the possible discourse-structures. Of importance here are the four places of semblance (semblant), truth (verité), jouissance, and surplus-jouissance (plus-en-jouir). These are by no means the only associations that Lacan makes with each position.

The top-left corner of semblance is dominant in each structure: every discourse is based a on semblance. This position is associated with agency, desire, commandment, as well as other things.

The bottom-left corner is the truth of the structure is question, 'propping-up' the discourse and the semblance it is based upon. Lacan's general comments on truth apply here: for one thing, it can only be half-said, and thus this position can be associated with a kind of split. Lacan's aphorism that "truth has the structure of fiction" also sheds light on the relationship between the place of truth and the place of semblance insofar as the former subtends the latter.

In the top-right corner we find the place of jouissance, sometimes translated in English as 'enjoyment.' It is also the place of the Other, and we can see from the left-to-right arrow how all discourse aims at an Other (as well as at jouissance). When Lacan applies his discourses to the political/economic sphere, he refers to this position as the 'means of production' that the agency of the discourse commands; or, more generally, as work. There is also a sense in which this position is that of the real, which I intend to explore in later posts.

The bottom-right corner of the plus-en-jouir, finally, is the position of surplus, remainder, or production of jouissance in some form or other. In a sense, every discourse-structure can be seen as a mode of production.

Generally speaking, each of these positions links in some way to every other, except for the bottom two. The separation between the bottom-right and bottom-left corner constitutes a fundamental gap in the structure of discourse.

What comes to fill these four positions? Four little letters, in various permutations: $, a, S1, S2. Their turning from one place to another consitutes a shift of discourse. The specific discourses that Lacan writes can be seen below:

I think that this initial primer will be sufficient for now. This will be a fundamental starting-point.