Thanks to Zizek’s 10 minute video on Aristotle’s Square of Opposition and Lacan’s formulae of sexuation, I made a small discovery. Here it is in raw form.

Aristotle’s square of opposition concerns the following:

Universal Affirmative (UA)

Universal Negative (UN)

Particular Affirmative (PA)

Particular Negative (PN)

The contradiction goes diagonal, from UA–>PN and from UN–>PA.

According to Zizek, there is a problem concerning the Particular Affirmation (“There exists an x …”). A literal reading of the particular affirmation could imply that one of two things necessarily follow:

Min. Position: “There exists an x…” but “there exists some x which are not…”)

Max. Position: “There exists an x…” but “maybe all x are…”)

He provided a nice joke to demonstrate the Max. position: “some men are beautiful” but “all men are pigs!”

Lacan takes the maximum position and his contradiction is vertical:

Masc.

E(x)~Phi(x)

A(x)Phi(x)

Fem.

~E(x)~Phi(x)

~A(x)Phi(x)

Now, if we think from Aristotle to Lacan we can produce the following pairs to correspondent with the chart of sexuation above:

Masc.

PN

UA

Fem.

PNN (Double Negative)

UN

Zizek stops here. But there is more worth pointing out. It is much more complicated than even he has demonstrated.

Phi is itself already a negation, of sorts. Phi is the function (or presence) of castration. I have written an entire dissertation on Phi, on the Phallic Function – so I would be open to writing more about why this is the case if I am provoked.

So now we have a real mess to sort out. This means the following:

AxPhi(x) means that “every x is both (1) not whole and (2) castrated.”

~AxPhi(x) means that “not every x is both (1) not whole and (2) castrated.”

Ex~Phi(x) means that “there exists an x which is both (1) not not whole and (2) not castrated.

~Ex~Phi(x) means that “there does not exist an x which is (1) not not whole and (2) not castrated.

You can see the problem.

The function of castration introduces a primordial negation which must be lived with, and the only way we can live with it is to reduce it to some semblance of positivity by naming it “castration” and removing the “negation” from the predicate logic. When a negation is added above the phallic function it refers to a double negation. Thus, ~Phix implies “not not whole.”

The phallic function is always responsible for the subject’s birth into a chain of signifiers (e.g., “a signifier is what represents a subject for another signifier”) at the hands of a dead master signifier (S1). At the other end of this function we get the little object of desire, splitting the chain of signifiers: S2/a.

To be submitted to the phallic function means that one is precisely produced as a subject. A foreclosure of the phallic function implies psychosis and the absence of a subject (strictly speaking).

So here, finally, is our problem.

When we claim that woman is the great figure of liberation within Lacanian psychoanalysis because she is “not all” or because she is not entirely castrated, then we must stop for a moment and rethink the logic with castration removed of its imaginary distortions in the symbolic form. There does not exist one who is not not whole is not the same thing as there does not exist one who is not castrated. Not all women are not whole.

Perhaps the price that woman pays for her liberation is that she is finally produced as a premature subject.

Recall that once Zizek claimed that women are all the more implicated in the symbolic order precisely because of the logic of their sexuation. In a sense, perhaps he was correctly reading Lacan’s logic.

How do you overcome this problem?