In his book The Unconscious as Infinite Sets: An Essay in Bi-logic the Chilean psychoanalyst Ignacio Matte Blanco presents a framework for understanding the unconscious with the tools of mathematical logic. It is a fascinating attempt to make the unconscious understandable.
To understand better the context Matte Blanco was working in, I want to begin with explaining a fundamental concept of psychoanalysis: the phenomenon of transference. To put it simply, transference is our tendency to bring our childhood experiences into our adult relationships. Exploring the transference and working it through is an important part of psychoanalysis. Therapists are attractive objects for transference, since we come to them to talk about our problems and to seek help, not unlike a child that approaches its parents for help. Therefore, we tend to encounter the same problems that shaped us when we were children. The point is that in the transference, we do not see the therapist the way he/she is – we project our childhood experience onto him/her, and struggle with the same problems we struggled with as children. In contrast to the predicament we encountered as a child, in the safe environment provided by the therapist we can explore our feelings and work them through, and we can find a satisfactory solution, which ultimately frees us from our affliction.
To give an example, imagine someone who grew up with unreliable, abusive parents. As a child, she internalizes deeply that everyone will eventually abandon her and hurt her. It is not hard to imagine how this will cause problems in her adult relationships. In the therapeutic relationship with a therapist, she will be subconsciously believe that the therapist is also unreliable and abusive, and she will have difficulties with being open and with trusting the therapist. If the therapist is trustworthy and capable, the patient will explore her lack of trust and her inability to be open in therapy. This will allow her to work through her trauma, eventually she will be able to trust her therapist, and this will convince her that some people can be trusted and will not hurt and abandon her. She will clearly see her neurosis and overcome it.
Matte Blanco noted the difference between symmetrical logic and asymmetrical logic, and used it to better understand psychological phenomena, like transference. An asymmetrical relation is a relation that cannot be inverted. As an example, the statement “I am taller than my sister” becomes wrong if I invert it: “My sister is taller than me”. Asymmetrical logic helps to understand the relations between two objects by finding differences. It is the logic of our conscious, the logic of everyday problem-solving, the logic of science. Symmetrical logic, on the other hand, is the logic of the unconscious, it tends to erase differences and emphasize similarities. A symmetrical relation can be inverted, and remains true. For example, the statement “I am John’s cousin” remains true when I invert it: “John is my cousin”. If I am John’s cousin, he is also my cousin. Matte Blanco noted that the unconscious tends to treat asymmetrical relations as though they were symmetrical. This leads to interesting consequences; for instance, the unconscious treats a part of the whole as equivalent to the whole. An example would be: “The arm is a part of the body”. Understood with symmetrical logic, this is equivalent to “The body is a part of the arm”. This means that for the unconscious, the difference between the part and the whole vanishes. Similarly, temporal concepts like “before” and “after” have no meaning – to the unconscious, things happen in an eternal now, there is no past, present, and future.
Matte Blanco also noted that the unconscious treats people and objects as belonging to different classes (a class being a collection of things that share a characteristic). As an example, take two people, person A and person B. A is a woman, B is a man. A is small, B is tall. We can say that A belongs to the class of humans who are female. She also belongs to the class of humans who are of small stature. That distinguishes her from B, who belongs to the class of humans who are male, and the class of humans who are tall. Matte Blanco realized that the unconscious sees all members of a class as identical, even if they differ in characteristics other than the characteristic that defines the class they share. As an example: the unconscious may treat all women as identical, despite the fact that among women there is great diversity. Consciously, someone may be aware of the differences between women, but the unconscious perceives them all as the same. Our thinking is always partially symmetrical and partially asymmetrical. The deeper into the unconscious we go, the more symmetrical our thinking becomes – this is why in dreams, the women the person of the above example encounters may all be very similar, since the differences we process with asymmetrical thinking are not present. But also in our everyday lives symmetric logic is present and underlies our thinking.
How is this related to practical problems like the transference described above?
Let’s look at the patient described above. Her parents belong to the following classes: “people who are supposed to take care of her”, “people who are not trustworthy”, “abusive people”, “unreliable people”, and many more. Her therapist, if he is a good therapist, may belong to these classes: “people who are supposed to take care of her”, “trustworthy people”, “reliable people”, “caring people”. Now, from the point of view of asymmetrical logic, her parents and the therapist are completely different people – the only aspect they share is the parental role with respect to the patient. But the symmetrical logic that is active in the patient’s unconscious leads her to believe that, because the therapist shares one characteristic with her parents, he also shares all other characteristics, i.e. that her therapist and her parents are identical.
What this means is that whenever we perceive things and think about them, the infinite multitude of our past experience is always present in the symmetrical unconscious. When I interact with a man, I do not only interact with this person, I interact with all the men and ideas of maleness I have so far encountered in my life. To the symmetrical unconscious this man is identical to all the men I have met so far, and how I perceive him will depend on the experiences I have made with men. The same is true for all women; for all parental figures: parents, teachers, therapists, priests. If I take a decision, all the decisions I have taken so far are present in my mind. If I try to do something new, all my past experiences with newness will color the experience. And so on and so forth.