Number and Symptom
Fall Seminar 2023
Number and Symptom: An Introduction to the Analytic Clinic
Seminar of PLACE
First meeting: 10:00am-12:00pm PST – Saturday, Sept.30th (meets every other week)
Open to the general public; participation by Zoom only
Any questions, contact the secretary
In a readily available YouTube video https://www.youtube.com/embed/7qM9nil7xjo of a recent House Committee Hearing an assistant Yale professor of psychology, McNamara, claims to be an expert in gender-affirming medicine whose practice and 'standards of care' back up the supposed effectiveness of gender transition treatment for young children. Yet her arguments are easily taken apart by Congressman Krenshaw as 'only words' with no real systematic study or clinical research to support her position. Left at this level of public debate, any discourse on sex – not to mention war, poverty, mental illness, etc. – devolves into a cultural war and a political opposition between democrats and republicans, liberals and conservatives. Meanwhile, the psychoanalysts are left tongue-tied, since in the lack of a proper methodology, they themselves are only able to produce more words without any effective entry into the debate. We reference this discursive symptom as the reason for our seminar, as it gives a first response to the question: Why topology and psychoanalysis? Or more generally, what is the correlation between mathematics, science, and psychoanalysis? Or more specifically, if the politicians today are only listening to science and statistical studies, is it a participation in ignorance, if not a certain madness, when the majority of analysts today have no entry either into science, mathematics, or logic? Our seminar wants to respond to these questions.
A Clinical Introduction
To get into the wind, we start by addressing not what people understand or should know, but what they do not. In so doing, we show how an analytic clinic is made room for beyond the prophylactic hospital, professional, and asylum versions.
Five major incomprehensions structure contemporary analysis:
1/ What is Freudian analysis?
2/ What is Lacanian analysis?
3/ What is Mathematics-Logic?
4/ What is Science?
5/ A more general ignorance – or Sinthome – can be readily isolated in trying to show the relevance of these fields to each other. This more general ignorance situates but does not exhaust, the clinic of analysis. Rather we ask if the confusion and ignorance, if not anxiety, produced around questions of number are one of the clearest points of entry to the analytic symptom. Our seminar wants to show why this is the case while making our results accessible to anyone, whether savant or debutante.
The Problem of Number
Heidegger describes Number as being the most important of mathemata in the Greek tradition. The problem is how to construct a number that does not trivialize out to a theory of numeration (polynomials), ordinals (set theory), or ciphers (algebra). A similar mathemata problem emerges in asking what a topology is if it is irreducible to a geometry ('normed' topology), algebraic topology (Poncaire/Klein), or a topological algebra (Tarski/Stone/topoi theory). Further still, at the level of applied technology and science, both topology and number become nothing more than numerical calculations in the fields of computer science, biology, and physics, while their dependence on writing and reading is viewed as a mere means of communication[1]. Although category theory has invented a theory of 'forgetful functors' to capture what is lost in going from an indiscreet category such as topology to that of a discrete category of numeration, algebra, and set, the problem is not sufficiently discussed or written about with regards to number. The problem is most often left at the level of a discussion over the problem of diagonalization and the non-correspondence between the real and rational numbers. Our seminar wants to introduce the necessary language, logic, and constructions to reason with the mathemata, while showing how if left at the level of the current educational, scientific, and technical applications, the question of number becomes nothing more than a symptom.
A non-technical introduction to number can be found in Tobias Dantzig's Number (1930); while a more rigorous account can be referred to in Saunders MaClane's Form and Function (1986). These books will not be referenced directly in the seminar but can be used as something of an encyclopedic reference for those who have never tried to construct a number problem seriously or who have forgotten. A reading of M. Heidegger's essay on the mathemata in “Modern Science, Metaphysics and Mathematics” (1962; from Basic Writings, ed. David Farrell Krell [San Francisco: Harper Collins, 1977] 247–82, an excerpt from “What is a Thing?” [1967; Chicago: Regnery, 1969] 66-108) will provide a background to the philosophical argument.
The Problem of the Family Symptom
In order to get into a non-technical introduction to mathematics, we begin by showing how the number problem has the structural characteristics of what Lacan, in Les complexes familiaux (1938), first posed as a 'family symptom'. In making this correspondence, we are already making a bridge between questions 1-4 above. Opposing individual neurosis to family neurosis, Lacan shows how the latter includes the former as an impossibility of treatment most commonly referred to in the epoch as the non-treatment of psychosis (or what Freud first called narcissistic neurosis). Later called a 'discursive neurosis' the family symptom is what is caught not simply by a social or genetic link, but a discourse: what is discovered around a question of the individual and technique, but irreducible to it, through the family. The notion of a symptom here is not that of referring to an illness or pathology, but a question of a complex: an over-marked style around a failure to read, speak, or write. Just as such symptoms, if left unattended to, can be transmitted for generations through the family, a mathematical text can itself be presented symptomatically for generations (one example among many, irrational numbers, first recognized by Pythagoras, were not rigorously written until the 19th century by Cauchy and Dedekind). A participant of the seminar should begin reading through Les complexes familiaux.
The Clinical Problem
As a way to get out from underneath a too-technical presentation of number or a family symptom, we introduce a key text by M. Mauss, Les Techniques du corps (1950). What is important to note for our purposes is that such a text can be used as a negative didactic into the problem of number, the family symptom, and the analytic clinic. Firstly, the analytic clinic does not engage any technique of the body: there is no laying on of hands, experiments, technological hardware, or what M. Foucault called 'techniques of the self'. The body of analysis is the spoken and read body, not simply the corporal, but the incorporeal body. And beyond what Mauss himself enumerates around every domestic situation in the house and family that involves a technique – a way of making supper, going to bed, cleaning, putting on clothes, etc. – there is something like a family symptom. Later Lacan would introduce at this place a way to isolate what he called Names-of-the-Father: seemingly ordinary habits of the individual structured around techniques that nevertheless gum over something extraordinary – a style that marks not only a conjunction but rupture with the family, society, and discourse. What will be important to isolate is how the Name-of-the-Father situates an equivocation in the mathematical text that is productive of a construction irreducible to a technical or scientific application. A reading of Mauss Les Techniques du corps will facilitate this reading.
The Scientific Problem (to follow)"Psychoanalysis is essentially what brings the Name-of-the-Father back into a scientific examination [...]" J. Lacan, Science and Truth
Avoiding an analysis of the function of the letter and signifier in mathematics, Heidegger tends to view mathematics as belonging to the problem of technique and the research program of modern science. Our position will be that writing and the signifier, introduce another clinical dimension of mathematics and logic irreducible to the question of technique or science, but productive of both.