# Algebra

Algebra is a branch of mathematics

• which reduces the solution of problems to manipulations of symbolic expressions, and
• concerned with the properties and relationships of abstract entities represented in symbolic form.

In 1955, Lacan begins to use algebraic symbols -- in an attempt to formalize psychoanalysis.

## List of Algebraic Symbols

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.

ALGEBRAIC SYMBOL COMMON MEANING
A the big Other
A the barred Other
a (see objet petit a
a' (see objet petit a
1. (before 1957) the subject
2.(from 1957 on) the signifier
3. (in the schemas of Sade) the raw subject of pleasure
the barred subject
the master signifier
the signifying chain/knowledge
s the signified (in the Saussurean algorithm
the signifier of a lack in the Other
the signification of the Other (the message/symptom)
D Demand
d Desire
m the ego (moi)
i the specular image (schema R)
i(a) 1. the specular image (graph of desire)
2. the ideal ego (optical model)
I the ego-ideal (schema R)
I(A) the ego-ideal (graph of desire)
Π the real phallus
Φ the symbolic phallus [upper-case phi]
(-φ) the imaginary phallus [lower-case phi]
S the symbolic order (schema R)
R the field of reality (schema R)
I the imaginary order (schema R)
P the symbolic father / Name-of-the-Father
p the imaginary father
M the symbolic mother
J Jouissance
phallic jouissance
JA the jouissance of the Other
E the statement
e the enunciation
V the will-to-enjoy (volonté de jouissance)

## Development of the Symbols

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.

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

## Typographic Details

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.