# Algebra

Algebra (Fr. algèbre) is a branch of mathematics -- or logic -- concerned with the properties and relationships of abstract entities represented in symbolic form.

## Jacques Lacan

### Formalization of Psychoanalysis

Three main reasons lie behind this attempt at formalization.

1. Formalization is necessary for psychoanalysis to acquire scientific status.
Just as Claude Lévi-Strauss uses quasi-mathematical formulae in an attempt to set anthropology on a more scientific footing, Lacan attempts to do the same for psychoanalysis
Lacan used quasi-mathematical formulae in an attempt to set psychoanalysis on a more scientific footing.
2. Formalization can provide a core of psychoanalytic theory which can be transmitted integrally even to those who have never experienced psychoanalytic treatment.
The formulae thus become an essential aspect of the training of psychoanalysis which take their place alongside training analysis as a medium for the transmission of psychoanalytic knowledge.
3. Formalization of psychoanalytic theory in terms of algebraic symbols is a means of preventing intuitive understanding, which Lacan regards as an imaginary lure which hinders access to the symbolic.
Rather than being understood in an intuitive way, the algebraic symbols are to be used, manipulated and read in various different ways.[1]

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The algebraic symbols used by Lacan, which appear principally in the mathemes, schema l and the graph of desire, are listed below, together with their most common meaning.

However, it is important to remember that the symbols do not always refer to the same concept throughout Lacan's work, but are used in different ways as his work develops.

Even other symbols which are relatively stable in meaning are occasionally used in very different ways.

Therefore some caution should be exercised when referring to the following list of equivalences.

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The typographic details and diacritics are extremely important in Lacanian algebra.

The difference between upper- and lower-case symbols, the difference between italicised and non-italicised symbols, the use of the apostrophe, the minus sign, and subscripts; all these details play their part in the algebraic system.

For example the upper-case letters usually refer to the symbolic order, whereas the lower-case letters usually refer to the imaginary.

The use of the bar is also important.

1. Lacan, Jacques. Écrits: A Selection. Trans. Alan Sheridan. London: Tavistock Publications, 1977. p.313