The Real Jouissance of Uncountable Numbers: The Philosophy of Science within Lacanian Psychoanalysis

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Lacan critiqued imaginary intuition for confusing direct perception with unconscious pre-conceptions about people and the world. The emphasis on description goes hand in hand with a rejection of theory and the science of the unconscious and a belief in the naive self-transparency of the world. At the same time, knowing in and of the Real requires a place beyond thinking, multi-valued forms of logic, mathematical equations, and different conceptions of causality, acausality, and chance. This book explores some of the mathematical problems raised by Lacan's use of numbers and the interconnection between mathematics and psychoanalytic ideas. Within any system, mathematical or otherwise, there are holes, or acausal cores and remainders of indecidability. It is this senseless point of non-knowledge that makes change, and the emergence of the new, possible within a system. This book differentiates between two types of void, and aligns them with the Lacanian concepts of a true and a false hole and the psychoanalytic theory of primary repression. Finally, through jouissance, the language of desire is re-joined to the formal marks of the object and the language of science. This explains the connection in Lacanian theory among logic, the Real, mathematics, and jouissance.

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Chapter One - Phenomenology, Empiricism, Hermeneutics, and Lacanian Psychoanalysis

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The philosophy of science

We would like to start the discussion on the various trends within contemporary epistemology by describing some important viewpoints that have been present in the philosophy of science.

When we began with this project we believed that juxtaposing the different trends of knowledge within the social sciences would obviously meet with the approval of most social scientists. This assumption quickly proved to be wrong and in some ways provides evidence for our upcoming thesis regarding the fact that denotation cannot be dissociated from connotation. After all, as Kety used to say, “Many disciplines contribute to understanding human behaviour, each with peculiar virtues and limitations” (Kety, 1960, pp. 1861–1870).

Adherents to the various tendencies have various reactions when their beliefs are considered in the light of other forms of knowledge. This state of affairs also demonstrates Lacan's conviction in his Seminar RSI (Real, Symbolic, Imaginary) that neurotics (most “normal” people are neurotics) develop symptoms in relationship to their beliefs.

 

Chapter Two - Frege and Lacan and the Triadic/Quaternary Theory of the Signifier

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In Frege's work (1892) sense and denotation refer to propositions/descriptions regarding names, naming, and nomination. In connotation and denotation the relationship between language and things, between culture and environment, is reduplicated within language itself, between S1–S2/Name-Proposition and/or Subject-Predicate. Denotation gives the appearance of representing the world directly rather than representing the signifying structure (connotation). Denotation is on the side of (objective) reference and literal meaning (Name), while connotation is on the side of the concept, sense, and the signifier.

However, as mentioned in previous chapter, some names have both denotation and connotation. In certain languages some names have acquired connotation/meaning or sense over time (e.g., Hebrew, Hindi, and Chinese). In addition, denotation can represent the illusion that language is simply a finger or a sign pointing at the reality of things and, therefore, what matters is the object world rather than language.

 

Chapter Three - The Object, the Number, and the Signifier/Name/Statement

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In his paper on the mathematics, logic, and theory of language of Charles Sanders Peirce, Louis Kauffman (2001) revisited some of the questions posed by the relations between Sign and Object and placed them in the context of Godel's principle of incompleteness. Kauffman investigates these questions in relationship to Peirce's rather than Frege's work. Kauffman (2001) begins by quoting Peirce (1933):

According to this, every Sign has a Precept of explanation according to which it is understood to be a sort of emanation, so to speak, of its Object. If the Sign be an Icon, a scholastic might say that the “species” of the Object emanating from it found its matter in the Icon. If the Sign be an Index, we may think of it as a fragment torn away from the Object, the two in their Existence being one whole or a part of such a whole. If the Sign is a Symbol, we may think of it as embodying the ‘ratio’ or reason, of the Object that has emanated from it. These of course are mere figures of speech; but that does not render them useless. (p. 107 in Kauffman, and p. 2.230 in Peirce)

 

Chapter Four - The Singular of the Singular: Singular Propositions and the Not-All

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According to Miller (1965), Grigg (2005), Le Gaufey (2006, 2009), and Fierens (2008), Lacan's logic of the not-all constitutes possible interpretations of the particular in the square of opposition of Aristotelian logic. We will argue that just like Frege's functional analysis of predication freed him from the limitations of Aristotelian logic, and allowed him to extend the use of the particular, Lacan's logic of the not-all extends Frege's use of the particular in the direction of what we will call the singular of the singular or the singular within the single case. In other words the idea is to distinguish between a simple and a complex singularity or a partial and a total singularity.

Lacan used the logic of the not-all in his formulas for sexuation or sexual difference. A woman as a constituent element is not-all under/or in the set of the phallic function of castration: (singular). As per Moncayo (2008):

For Lacan, castration is on the masculine side, it is normal and normalising as a masculine norm. Women instead have more degrees of freedom in their relationship to castration. In Seminar XX Lacan argues that a woman is “not-all” under the phallic function or the law of castration. A woman is “not-all” in the phallic function but, on the other hand, woman as the “not-all” does not constitute a negation of castration either. […] In addition, in my opinion, only a negative dialectic of emptiness can account for a not having which is also having and for a having that does not produce a fixed positive or affirmative synthetic idea/ideal/signifier for femininity. On the feminine side of sexuation, women in general do not have the phallus but a particular woman is something more than simply the absence of the imaginary phallus. However, language does not have a single or fixed signifier for what a woman has of the phallus. Women do not have it but a woman does not not have it either. This, I argue, is the negative dialectic of the not-all. (pp. 50–51)

 

Chapter Five - On Probability, Causality, and Chance

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In God we trust, all others bring data.” Edwards Deming, American statistician and professor, is well known for this statement that has now become a motto for many scientists (Hastie et al., 2009, p. 4). And so we would also like to make an attempt to bring “data” into this chapter and talk about probability, causality, and chance. Before we do that there are two more quotes from Deming that we would like to share, “The most important things cannot be measured” (1991, p. 27). He thought that we couldn't measure in advance things that are important, because sometimes at the time of measuring, we don't understand that they are important. “The most important things are unknown or unknowable” (Deming, 1982, p. 121).

Like an earthquake can be surprising and have a huge impact on the functioning and future of a particular place, can cause a drastic change in technology, or change the trajectory of a company. The two latter rules probably sound quite familiar, not only to statisticians or people who deal with quality improvement but also to psychoanalysts. How come then there is such a pressure to “bring data?” It seems that even in psychology that is considered a soft science people don't want to rely on opinions and hunches, and so they have to get the numbers. Unfortunately, even the proverbial numbers when speaking about human behaviours may not be “free” of opinions. In 1963 the American Psychological Association (APA) published a study of the scientific standing of psychology. It was entitled “Psychology: A study of a science” and led by Sigmund Koch. Here is his final conclusion,

 

Chapter Six - The Third of the Real and the Two Voids

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The differentiation between lawful regularity (in nature and culture) and causality turns causality into its opposite and away from being identical to the concept of natural law. Tyché as causality in the form of a gap, acausality, and the unconditioned, as a new and surprising enigmatic knowledge emerging in the Real of here and now experience, is intrinsically tied to the notion of the unconscious as a larger and different form of mind than ordinary ego-consciousness and intentionality. However, as we have noted, the unconscious as such encompasses automaton and tyché, the symbolic unconscious and the unconscious of the Real or the Real unconscious.

This distinction also applies to the theory of primary repression. There are two types of primary repression corresponding to the two types of chance: tyché and automaton. Lacanian authors sometimes collapse the distinction between the two, although it is clear that the later Lacan distinguishes between the unconscious in its Real and Symbolic acceptations.

 

Chapter Seven - Logical and Mathematical Foundations

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The unary numeral system is the simplest numeral system to represent natural numbers. In order to represent the concept of number, an arbitrary notch, stroke, trait, trace, vertical bar, or a tally mark written “|” or “/” is repeated N times. For example, using the tally mark “|”, the number 4 is represented as “| | | |”.

The terms stroke, trait, vertical bar, or mark are all equivalent terms or words to describe the same concept in different disciplines and areas of knowledge including but not limited to logic, mathematics, linguistics and semiotics, anthropology, history, philosophy, religion, and psychoanalysis. Lacan borrowed the term unary trait from mathematics and applied it to the study of character and identification, following Freud's use of the word trait to describe a third type of identification.

This section will be focused mostly on logic, mathematics, and anthropology to a limited extent. For the time being we will assume familiarity with the use of the term mark by Spencer-Brown's laws of form and calculus of indications and will use the term “mark” interchangeable with the term “trait” or “stroke”. In the appendix we will take up the concept of mark in Spencer-Brown's (1969) work in a more direct and explicit fashion.

 

Chapter Eight - Phi, Phi, and I

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I am speaking about logic—by attributing the function of truth to a signifying grouping. That is why this logical use of the truth is only encountered in mathematics, where as Bertrand Russell says, one never knows in any case what one is talking about. And if one thinks one knows, one is quickly disabused. You have to tidy things up quickly and get rid of intuition.

—Lacan, Seminar XIV, lesson of Wednesday 21st June, 1967, p. I 40)

The previous chapter allowed us to enter the world of Lacanian algebra. Here we would like to explain more in depth some of the mathematical problems raised by Lacan's use of numbers and focus in particular on the Golden number. We are mainly interested in the interconnection between mathematics and psychoanalytic ideas. While we want to stay true to both of the disciplines we are aware of the limitations of such approach. We are familiar with criticisms both from the side of mathematicians who accused Lacan of overusing their theories in order to make analysis more scientific, and psychoanalysts who felt that any attempt at formalising psychoanalysis was risky and by doing that one could lose a singular and personal approach to a subject. Lacan himself in his usual way did not engage in such dialogue. However in Seminar XX: Encore he clearly stated, “mathematical formalisation is our goal, our ideal” (1972–1973, p. 119). In the seminar on Logic he even jokingly suggested that a mathematical exam would be a good passage procedure for analytical candidates.

 

Chapter Nine - Prime Numbers Theorem and the Zeta Function in Psychoanalysis

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And this Real I am talking about is absolutely unapproachable, except along a mathematical path.

—Lacan, 1971–1972, p. 10

In Seminar XIV Lacan (1966–1967) said, “What is at stake is nothing other that the economy of the unconscious, or indeed what is commonly called primary process” (lesson of Wednesday, April 26th, 1967, p. I 96). It is an interesting idea that the economy of the unconscious is a primary process. A little bit earlier in the same seminar we hear, “Jouissance-value, I said, is at the source of the economy of the unconscious” (p. I 90). So we have two things jouissance and primary process, also from the previous chapter we know that the unconscious is structured and is logical. The primary process is an inconvenient form of jouissance (jouissance of the Other) characterised by the tendency for hallucinatory wish fulfilment as Freud defined it. According to Freud, unconscious thinking follows the primary process. Collete Soler (2006) dwells a lot on Lacan's statement that “thought is jouissance”, hence associated with the primary process. However, there are different forms of thinking and different forms of jouissance and of course the logical structure of the unconscious cannot be a primary process since the logical models that Lacan uses are all associated with binary thinking and the secondary process.

 

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