Neill, C. (2009) ‘Who Wants to be in Rational Love?’, Annual Review of Critical Psychology, 7, pp. 140-150.
We can understand that part of what Lacan is pointing to here in his invocation of the phallus as something which cannot be reduced to a mere physical appendage is that sexual difference is never simply a matter of the difference between two complimentary entities (in the sense of ying-yang).
There is always a necessary third party; the phallus. We are sexed in terms of our relation with or to this third position and, therefore, the difference between the sexes is always more than a simple difference. Rather the differences themselves are different. The phallus as a moment of the Other comes radically between the male and female subject. There is no direct relation between them but only distinct relations to a third. […]
In saying that there is no ratio between the sexes, then, we could understand Lacan to be saying that while there clearly is a relating of some sorts between the sexes, there is a conjunction, there is no stability and there is no way of notating this; “the sexual relation cannot be written” (Lacan 1998: 35), which would be to say that it is beyond comprehension
An important question we might raise here is, if there is no saying it all, no unproblematic communication between the sexes, then does this imply that there might be such an unproblematic communication between subjects of the same sex?
Clearly, the answer would be no. Language is necessarily a medium and thus mediator. So why emphasise that there is no rapport between the sexes when there is no rapport between subjects? […]
while perhaps obvious, needs to be stated simply because it is here, in the sexual relation that we hope to find the communicative success which eludes us in other areas of life. Even here, there is no rapport. The Other is always the third party. We might hope to, in our ideal of sex, engage in a true coming together, a communication without or outwith language but such an idea is never anything more than a fantasy;
The four logical statements presented at the top of the diagram can be read as follows:
1. 
there exists at least one of those in category x who is not subject to the phallic function
2. 
all of those in the category of x are subject to the phallic function
3. 
there is not one of those in category x who is not subject to the phallic function
4. 
not all of those in category x are subject to the phallic function
*********
What this produces, then, are two seemingly contradictory or logically impossible statements on each side of the graph. The left side is the side of man, while the right side is the side of woman. Together they describe possible positions available to speaking beings, which is to say “Every speaking being situates itself on one side or the other” (Lacan, 1998: 79).
The logical statements on the left side can be understood to tell the story, or the logic, of the myth of the primal horde (Freud, 1950: 141-143). The one who would exist who is not subject to the phallic function, who has not undergone castration, would be the primal father.
Category x in this instance would then refer to the male position and all those in this position are subject to the phallic function, that is, they have undergone castration. There is, then, one man, the primal father, who is not subject to the function of castration which is the condition of possibility for all those in the male position. The contradiction here can be understood in the sense of an exception to a rule, in that it is the exception which is the condition of possibility for the rule to be a rule.
The statements on the right side can be understood to describe something of the tension between universals and particulars. The two statements might appear to present a blunt contradiction. If none of those in the category is not subject to the phallic function, then this would seem to suggest that all those in the category are subject to the phallic function.
But this is precisely what the second statement refuses. Taken separately, however, we can perhaps begin to make some sense of this. If the function of castration is the condition of possibility of entry into the symbolic order, then all speaking beings in order to be speaking beings would have to be subject to this function.
We can understand this first statement, then, as referring to each member on a one-by-one basis. Each woman – for this is the side of woman – in order to be a speaking being, must be subject to the phallic function. The second statement – the universal statement – should then be understood to refer to the group. The group as a whole, as a category, is not subject to the phallic function. What would this mean?
That, as a universal category, The Woman cannot be located within the symbolic order; La femme n’existe pas.
If one side of the supposed relation between the sexes can be said not to exist, if one side cannot be collapsed into a signified totality, while the other side can only assume a signified position as incomplete, then clearly the model of equal partners balanced in a neutral or exteriorly moderated system of exchange becomes manifestly inappropriate.
Lacan’s claim that there is no rapport between the sexes, that they cannot be composed into a ratio, that they have no relation, furnishes us with a step beyond the superficial and reductive assumptions which so apparently benignly dominate the social sciences.
In reducing intersubjectivity and sexual relations to modes of economy, one not only assumes an untenable equality of status between the supposed operators, but one also misses the crucial point that the pleasure, the jouissance,which might be the currency of such an exchange is never itself so easily quantifiable.
Just as actual economic exchange is problematised with the inescapable notion of surplus value, so intersubjective relations are properly rendered more complex with a notion of surplus jouissance. This surplus of jouissance, the fact that relations can never be collapsed into a whole, a oneness, or even into a two, insofar as there is always, necessarily, the insistence of objet petit a, means that the accounting we would impose on relations always already fails.
Moreover, this failure is inscribed already in our attempts to know – to corral in knowledge – how the relation works, what the ratio is, what mediates the rapport.
It is in stepping beyond this limit that the social sciences might begin to explore, without seeking to end in a finite knowledge, what goes on between the sexes.
