Understanding the contradictions of the human unconscious, and of reality at large

Reading | Psychology

Nikolaus Lehner, PhD | 2025-08-01

The finite is indeed the negation of infinite, and not the other way around [1]

Even if we are not aware of it, we are in touch with the infinite. Oneness and infinity are not something we need to reach out for, as these concepts likely reflect what the unconscious is at its core.  This is the territory explored by psychoanalyst Ignacio Matte Blanco, who, by synthesizing psychoanalysis and mathematical logic, offered a bold and rigorous hypothesis: that the unconscious mind operates according to a symmetrical logic grounded in the mathematics of infinite sets [2].

Conscious awareness is, in essence, the act of dissecting an inexhaustible continuum into discrete objects and relations. Each logical step, each rational deduction is refracting this boundless continuum into manageable fragments—thoughts, perceptions, mental or physical objects. Conscious experience operates with distinct and finite sets of experiences. The logician George Spencer-Brown articulated this elegantly: “Draw a distinction!”—and a world comes into being [3]. But to make distinctions, we need space and time. To think logically is to think spatially. Logic depends on space, as you need space to establish relations and distinctions between these relations.

Yet, beyond logical reasoning and relating lies another mode of existence, in which boundaries dissolve. The Chilean psychoanalyst Ignacio Matte Blanco termed this mode “symmetrical,” a counterpoint to our dominant “asymmetrical” mode.

In our everyday lives, we often rely on causal relationships to navigate the world. We think in terms of cause-and-effect: “I need to leave at 14:00h to meet my appointment at 15:00.” This asymmetrical mode of thinking is essential for making sense of reality and taking deliberate action. Also, we tend to form hierarchical classes, as in the sentence: “The tree is part of the forest” [4].

In the symmetrical mode such relations can easily be reversed: you leave at 15:00h for your appointment at 14:00h, the forest is part of the tree. The stuff dreams are made of has its roots in this mode of existence.

The asymmetrical mode is directional and functions as a scalpel-like tool to dissect reality: A is part of B, but B is not part of A.  The symmetrical mode, by contrast, erases this directionality: A is part of B, and B is equally part of A. The relationship is mutual, not subordinated. Temporal sequence does not matter anymore, and spatial separation seems to collapse. We live in these two modes of existence simultaneously, although the conscious mind may favor asymmetrical thinking, as it is the domain of reasoning, rationality, and logic.

In the unconscious, however, you typically will find thought processes that correspond to symmetrical thinking: consider a man who is afraid of authority. This man might equate all authority figures with his choleric father, even though on a conscious level he is perfectly aware that they are not his father. In his job, he may live in constant fear of his boss, even though his colleagues would describe him as warm and approachable. For the man, unconsciously, all authority figures belong to the same class. According to Matte Blanco’s theory, this is possible because, in symmetrical logic, all members of a given set are treated as identical and at the same time become the category they belong to [5]. This is what gives life to emotional depth and intensity: when you fall in love with someone, this person seems to become love itself, and all the persons you ever loved. At the same time, you may feel one with the beloved and the world. And when you grieve, you may feel cut off from your aliveness, as the entire world may feel deadened, lost, bereft of meaning. As the poet Walt Whitman writes in Leaves of Grass [6]:

The song is to the singer, and comes back most to him,
The teaching is to the teacher, and comes back most to him,
The murder is to the murderer, and comes back most to him,
The theft is to the thief, and comes back most to him,
The love is to the lover, and comes back most to him,
The gift is to the giver, and comes back most to him — it cannot fail.

There is no strict polarity between the symmetrical and asymmetrical mode of being, although one or the other might be more dominant. Symmetrical thinking is not simply the opposite of rational or logical thinking. It may even be useful to turn to symmetrical thinking for rational reasons. For example, symmetrical thinking allows for generalization, which is what happens when you equate two different apples in order to count and categorize them. Without symmetrical thinking, we likely wouldn’t have metaphor, poetry, or science—yet, the very same capacity makes us prone to stereotyping, as a stereotype is established by equating distinct entities.

In daily life, we engage with unconscious manifestations through our emotions, feelings, dreams, imagination, and symptoms. The deeper you reach into the unconscious, the more of your thinking processes will turn out to be symmetrical and, thus, the stranger the results of these thinking processes will appear when evaluated from the perspective of the asymmetrical mode. We witness this strangeness in our dreams or in states of reverie. When you dive into the deepest layers of  the unconscious, you reach a stratum of experience Matte Blanco calls indivisible unity, in which there is only a purely symmetrical manifestation left. This is the state of consciousness that is typically described as mystical oneness [7].

Matte Blanco’s notion of a unity that is both indivisible and infinite initially may seem to be paradoxical as, since Aristotle, we think of the infinite as something necessarily incomplete [8]. By definition, something that is complete must be finite. However, for Matte Blanco, the mathematical infinite is merely a means of the asymmetrical mode to model the symmetrical mode and its underlying oneness. It was Matte Blanco’s scientific achievement to formulate the symmetrical mode of being within the terms and conditions of the asymmetrical mode. In general, the symmetrical, unconscious mode translates itself into the asymmetrical mode all of the time, even though these translations necessarily remain incomplete and insufficient. As Matte Blanco observes, the unconscious calmly behaves like a geometrician who is forced to represent an n-dimensional space in n-1 or n-2 dimensions: it represents these dimensions by using the dimensions at hand [9]. The unconscious does what it can to express itself, although many aspects of it may be distorted or lost in translation.

While, in his publications, Matte Blanco allowed himself to hint at wider implications of his theory for physics, he was cautious not to step too deep into its possible ontological consequences. Yet, possible implications of his theory might be found in the work of Italian mathematician Giulia Battilotti and colleagues, who translated Matte Blanco’s symmetrical and asymmetrical thinking into a quantum spin model by modeling these states as infinite sets [10]. To do so, Battilotti introduces the term “infinite singleton” in a specific sense that differs from classical set theory. In standard set theory, a singleton is a set with exactly one explicitly identifiable element. Inspired by Matte-Blanco, Battilotti’s “infinite singleton” refers to a set that is formally treated like a singleton—that is, like a set that contains a single entity—but its elements cannot be individually specified or distinguished. Battilotti tells us that this can already happen with sets that contain only one element: if we do not know and cannot characterize this single element, we cannot count it and thus cannot tell if the set is finite or infinite [11]. An “infinite singleton” is a set known to contain only one entity, but this entity cannot be named, distinguished, or characterized by finite means; it is a set for which it makes no difference to say “there is an element with this property” or “all elements have this property.” Concurrently, the set and the elements of the set “merge” into each other. This construction is used to describe states or objects that are indistinguishable and symmetric in Matte Blanco’s sense. Battilotti suggests a formal resemblance between the mathematical structure of the quantum spin and Matte Blanco’s model of the unconscious. Both operate with infinite, symmetrical sets in which classical logic based on negation and consequence does not take hold anymore, whereas a symmetrical logic occurs that mirrors how psychoanalysis conceives the unconscious. Of course, this might be purely coincidental; however, such symmetry between the unconscious and the physical world seems to strangely fit models of consciousness that recur in quantum physical phenomena.

As a psychotherapist, I am inclined to think about Matte Blanco’s theory in terms of its meaning for relationships to oneself and the other. How unlikely it is to find an other in this vastness that is the inside-outside! And yet, it happens naturally, smoothly, every day of your life.

I am writing this brief text under the expectation of my daughter’s imminent birth. I imagine her slowly carving herself out of the infinite, turning into a finite and distinct existence by negating infinity; negating it with her first sensory impressions, her first thoughts, her first breaths and screams, alienating herself from infinity, and yet always remaining entangled with it, in touch with it, living through the infinite, breathing herself out into this.

 

References

[1] Giulia Battilotti, Miloš Borozan and Rosapia Lauro Grotto (2023) ‘The Modal Components of Judgements in a Quantum Model of Psychoanalytic Theory’, Entropy, 25, 1057. Available at: https://doi.org/10.3390/e25071057

[2] See: Ignacio Matte Blanco (1998 [1975]) The Unconscious as Infinite Sets: An Essay in Bi-Logic, London: Karnac Books.

[3] George Spencer-Brown (1997) Laws of Form / Gesetze der Form, Hamburg: Bohmeier Verlag.

[4] Cf. Phil Mollon (2002) ‘The Unconscious’, in: Ivan Ward (ed.) On a Darkling Plain: Journeys into the Unconscious, Duxford, Cambridge: Icon Books Ltd.

[5] Matte Blanco (1998 [1975]), The Unconscious as Infinite Sets.

[6] Walt Whitman (2009 [1860]) Leaves of Grass, Iowa City: University of Iowa Press.

[7] Ignacio Matte-Blanco (1988) Thinking, Feeling, and Being: Clinical Reflections on Fundamental Antinomy of Human Beings in the World, London and New York: Routledge.

[8] See: Paolo Zellini (2004) A Brief History of Infinity, London: Allen Lane, Penguin Books.

[9] Matte Blanco (1998 [1975]), The Unconscious as Infinite Sets.

[10] Battilotti, Borozan and Lauro Grotto (2023), Entropy, 25, 1057.

[11] Giulia Battilotti, Miloš Borozan and Rosapia Lauro Grotto (2021) ‘Infinite Singletons and the Logic of Freudian Theory’, Language and Psychoanalysis, 10(2), pp. 46–62.