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Unconscious as Infinite Sets: An Essay in Bi-Logic, The


In The Unconscious as Infinite Sets: An Essay in Bi-Logic, a major work published in 1975, Ignacio Matte-Blanco introduced an important modification of Freud's notion of the unconscious. His purpose was to save the notion from being progressively forgotten in contemporary psychoanalytic developments. The author refused to consider the unconscious as chaotic (Freud, 1933a [1932]). If a characteristic form of functioning, like the primary process (the processes of the id), may be described as belonging to the unconscious system, then, he thought, one can discover a different organization for it than the one ruling the conscious system. Grounded in this idea, Matte-Blanco studied the logical principles that would allow systematic unconscious violations of classical, asymmetric logic, the basis of consciousness.

Unconscious logic rises from two principles: the principle of generalization and the principle of symmetry. The principle of generalization, also present in classical logic, postulates that in the unconscious each entity is treated as part of a set with other elements, this set being treated in turn as a subset of a greater set, and so forth. Entities are distinguished one from the other and grouped together again through abstraction of their similarities. The second principle is that in the unconscious, asymmetrical relations are selectively treated as if they were symmetrical (Rayner, 1995), with the result that relations of succession and contiguity, like time and three-dimensional space, disappear. A part can equal the whole, and similarities can be transformed into identities.

The unconscious is conceptualized as an aggregate of infinite sets. According to the definition of the mathematician Richard Dedekind (1831-1916), infinite sets are those in which a specific subset, for example, the even numbers, can be placed in a one-to-one correspondence with the whole setfor example, the set of natural numbers. The part is equal to the whole.

Symmetrical logic is the expression of a symmetrical system, according to which reality is a homogenous and indivisible whole. Asymmetrical logic is the manifestation of an asymmetrical system, where reality divides into parts. In states of intense emotion, the experience and logic of the symmetrical system are dominant, so for the mind, the emotional object is infinite and is also part of an infinite set.

Matte-Blanco succeeded in formalizing (or mathematizing) the study of the unconscious. He discovered a startling isomorphism among the emotional, the unconscious, and infinite logic (Bria and Durst, 1992).

Juan Francisco Jordan Moore

See also: Id; Logic(s); Matte-Blanco, Ignacio.

Source Citation

Matte-Blanco, Ignacio. (1975). The unconscious as infinite sets: An essay in bi-logic. London: Duckworth.


Bria, Pietro, and Durst, Margarete. (1992). Ignacio Matte Blanco (Portrait). In A. Negri (Ed.), Novecento filosofico e scientifico. Protagonisti (Vol. 3, pp. 409-443). Marzorati: Milano.

Freud, Sigmund. (1933a [1932]). New introductory lectures on psycho-analysis. SE, 22: 1-182.

Rayner, Eric. (1995). Unconscious logic: An introduction to Matte Blanco's bi-logic and its uses. London: Routledge.

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