A psychoanalyst walks into a bar with a book on logic and set theory. He orders a whisky. And another. Twelve hours and a lock-in later, all he has to show for the evening is a throbbing headache and some indecipherable nonsense scribbled on a napkin.

That’s the only conceivable explanation for these diagrams from *The Subversion of the Subject and the Dialectic of Desire in the Freudian Unconscious*, by Jacques Lacan (published in the *Écrits* collection):

But, I hear you ask, surely this notation means something? After all, Lacan is famous and studied across the world, and *f*(*x*) is well-recognised as a function, *f*, applied to argument *x*. So the I(A) and s(A) must mean something?

Here is a brief interlude on functions. The Fibonacci sequence, which pops up in all kinds of interesting places in nature, can be defined as following:

*f*(0) = 0,

*f*(1) = 1,

*f*(*n*) = *f*(*n*-1) + *f*(*n*-2), for *n* > 1.

In English, this says that the first two numbers in the sequence are 0 and 1. The numbers following are obtained by summing the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

If you tell it a number (e.g., 0, 1, 2, …) then it replies with the respective number in the sequence (first, second, third, …). It might look a bit scary if you haven’t seen the notation before, but check out these examples demonstrating how the arithmetic is carried out:

*f*(0) =**0***f*(1) =**1***f*(2) =*f*(1) +*f*(0) = 1 + 0 =**1***f*(3) =*f*(2) +*f*(1) = 1 + 1 =**2***f*(4) =*f*(3) +*f*(2) = 2 + 1 =**3***f*(5) =*f*(4) +*f*(3) = 3 + 5 =**5***f*(6) =*f*(5) +*f*(4) = 5 + 3 =**8**- …

The point here is that the function notation “does something”. It provides a way of defining and referring to (here, mathematical) objects.

Less well-known, but appearing in university philosophy courses, is the lozenge symbol, ◊, which means “possible” in a particular kind of logic called modal logic. It seems plausible that there is something meaningful here in Lacan’s use of the symbol too.

Here is Lacan, “explaining” his notation for non-mathematicians:

Huh?

Lacan doesn’t try to explain what the notion means; he doesn’t seem to want readers to understand. Maybe he is just too clever and if only we persevered we would get what he means. However, elsewhere in the same text Lacan uses arithmetic to argue that “the erectile organ can be equated with √(-1)”. Personally, I am unconvinced.

Alan Sokal and Jean Bricmont have written a book-length critique of Lacan’s maths and others’ similar use of natural science concepts. Having read lots of mathematical texts and seen how authors make an effort to introduce their notation, I think it’s entirely possible Lacan is a fraud. That might sound harsh, but just look at how he writes. I reckon anyone can see for themselves that Lacan is writing nonsense if they take a look and forget for a moment how famous he is.

*Lightly edited 18 Sept 2018, hopefully making clearer!*