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 bollocks scrawled 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, surely this notation means something? After all, Lacan is famous and academics across the world sweat whisky to try to understand his genius.

Also the notion *f*(*x*) is a function, *f*, applied to argument *x* — that’s recognisable from maths. So the I(A) and s(A) must mean something…?

Here is a brief interlude on functions to show how they can be introduced and used. The Fibonacci sequence, which pops up in all kinds of interesting places in nature, is defined as follows:

*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 have a look at these examples showing how the sums are done. You start with 0 and 1 and then to get the numbers for larger values, check back at your previous scribbles and fill in accordingly:

*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**- …

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

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)”. I’m told this is a joke because √(-1) is an imaginary number. Maybe trainee psychoanalysts learn about complex numbers? Maybe all Lacanian discourse is dadaist performance.

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 forget how famous he is and just look at how he writes.