Lacan’s formulae of sexuation are well-known to Žižekians. Žižek frequently refers to the exception that grounds the universal and the logic of non-All where this does not work. But I think the formulae still remain quite enigmatic. Let me resolve this enigma through computer science.

A signifier represents the subject to another signifier. In fact, the subject is represented by a unique signifier (called Master-Signifier or S_{1}) to the rest of the signifiers (called S_{2}). This representation by the S_{1} happens at a concluding moment that retroactively determines the preceding chain of signifiers.

Let’s describe the process: At first, there is a need to represent the subject for a signifier S_{a}, then this need to represent is displaced to S_{b}, then it’s displaced to S_{c}, then to S_{d}… etc. At some point, the subject is actually represented by S_{1} for the preceding chain of signifiers (S_{a}, S_{b}, … etc.), and at that moment, we call the preceding chain of signifiers S_{2}. Thus, there are two logical times in the process: (1) The time when a signifier **needs to** represent the subject to another signifier. This signifier is repeatedly displaced, until finally it’s (2) the time when the representing signifier S_{1} is found, and it represents the subject to S_{2}. Therefore, S_{1} stops the continuous displacement of signifiers.

This process resembles what we call a recursive function in computer science. A recursive function has two parts: (1) If the termination condition is not yet met, the function calls itself. (2) If the termination condition is met, the function returns without calling itself further. An example is factorial(x). In the first part, factorial(x) is defined as x*factorial(x-1) for a positive integer x. In the second part, for the condition that x becomes zero, it’s defined as factorial(0) = 1. Here’s how its code looks like:

factorial(x) { if(x>0) return x*factorial(x-1); else return 1; }

If we express signification as a recursive function, what would the termination condition be? Imagine that we have a function called “represent” and that we call “represent(x)” for an x to be represented. When should the function call itself, and when shouldn’t it?

If x is inside language, represent(x) should call itself: in language, all representations refer to one another. If x is outside language, represent(x) shouldn’t call itself: x here becomes the exception to the language. Therefore the termination condition of representation is that x gets out of the field of language, that is, it becomes an exception.

As we know, to be inside language is expressed by the phallic function Φ(x) in Lacan’s formulae of sexuation. We also know that when represent(x) terminates, it should return S_{1}. We can write the function represent(x) based on these ideas.

signifier represent(x) { if(Φ(x)) return represent(displace(x)); else return S1; }

As you can see in the code, represent(x) calls itself when Φ(x) is true, and returns S_{1} when Φ(x) is false. Each time it calls itself, it displaces x, until x gets out of language and Φ(x) becomes false, when it begins returning S_{1}.

Now we can clearly formulate Lacan’s formulae of sexuation in terms of this function.

In the masculine side, “Some x are not Φ(x)” means that the representation function actually terminates because x gets out of language after its displacements. “All x are Φ(x)” means that all of the x before the exception that terminates the function were Φ(x).

In the feminine side, “There’s no x that’s not Φ(x)” means that x never gets out of language in its displacements, and that the representation function never terminates. “Non-all x are Φ(x)” means that x continues to get displaced and it can never be totalized, because the termination condition is never met. The displacements go on and on, and we call it the ex-sistence of the woman.

Işık Barış Fidaner is a computer scientist with a PhD. Admin of Yersiz Şeyler (Placeless Things) blog, Admin/Editor/Curator of Žižekian Analysis, and one of the admins of “Žižek and the Slovenian School” group on Facebook. Twitter: @BarisFidaner

Do you have to accept Saussurian linguistics for this to work? If so, can you please recommend some literature that defends it? I haven’t read Zupancic, but suspect this might be the way. I have Lemaire’s book on Lacan; however, this is quite old now. Thanks in advance!

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Saussurean and Lacanian approaches are different. For Saussure, signified is primary whereas for Lacan, signifier is primary.

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